WO2024181887A1 - Method and system for non-contact rangefinding and profilometry - Google Patents

Abstract

The invention relates to the field of measuring equipment, and to profilometers and rangefinders. A system for implementing a rangefinding and profilometry method includes at least one image recording device, a computing device, and a projection device containing a spatially extended source of incoherent light and first and second planar periodic gratings arranged in parallel planes on one side of the light source and illuminated by said light source, the second grating being hit by light passing through the first grating, wherein the system makes use of at least one device for moving the highest contrast contour line of a projection of a localized moire structure formed by the projection device along a surface of at least one object. The technical result is that of simplifying the rangefinding and profilometry system.

Description

NAME OF INVENTION

Method and system of non-contact ranging and profilometry

AREA OF TECHNOLOGY

The invention relates to the field of measuring technology and can be used for contactless measurement of distances to objects, coordinates of points on their surface, and also determining the shape of objects.

PRIOR ART

Determining the distance to the points of an object (ranging), measuring their coordinates, as well as the shape of the object's surface (profilometry) is necessary for solving many applied and scientific-technical problems. Contactless methods of ranging and profilometry are used in engineering, design, and reverse engineering. They are also used in computer vision systems, virtual and augmented reality, for controlling vehicles and robotic devices, in medicine, etc. There are many known methods of contactless active optical measurements of the distance to objects, the coordinates of their surface points and its shape (see, for example, [1 - 5]). A significant part of these methods is based on the use of laser devices. In particular, these include time-of-flight methods of ranging and profilometry, using, for example, lidars [1 - 6], as well as methods based on the use of laser triangulation, laser structured illumination, etc. (see, for example, [1 - 5, 7]). The disadvantages of these methods are the complexity and high cost of laser devices, the complexity of the methods for processing the obtained data, the negative impact on the results of measurements of the speckle structure of laser radiation, re-reflection and scattering of laser beams, the danger of laser radiation for the eyes and optical devices, etc.

There are known methods of active optical ranging and profilometry that do not use laser light sources. There is a known method of determining the shape of an object based on measuring the sharpness of focusing on the surface of the object of the image of flat periodic transparencies that are installed in an optical projector and illuminated by incoherent light [8 - 13]. Periodic stripes of light are focused on the surface of the object using a lens installed at the output of the optical projection device. The contrast of the projection of the light stripes on the surface is determined by a computing device based on the image of the object recorded by an image recording device, such as a television camera. Optical axes of the projector and the recording device images usually coincide. The maximum contrast of the fringe image is achieved in the areas of the object surface that coincide with the plane of focus of the projection device lens. The distance to this plane is measured in advance during calibration of the device or calculated. The position of the plane where the contrast of the light fringes is maximum relative to the object is changed by moving the projector or the object along the optical axis of the projector, or by changing the focal length of the projector lens. By moving the focal plane of the projector relative to the object, the surface of the object is scanned with it, the images of the projection of the light fringes onto the surface are recorded, then, by processing the obtained images, the distance to various points of the object surface, as well as its shape, are determined. A measurement method and device similar to those described above are also used to perform profilometry of micro-objects using a wide-field microscope [14, 15]. The disadvantages of this method of optical ranging, profilometry and microscopy are the need to use a complex optical projection device, which includes a high-quality lens, the influence of the imperfection of the lens of the projection device on the accuracy and reliability of measurements, and the limited field illuminated by the projection device.

Optical phase and triangulation methods for measuring the 3D shape of an object are known, which are based on projecting a periodic structured illumination, for example, periodic stripes of light, onto the surface of the object and recording the image of this surface (see, for example, [2, 16 - 20]). Periodic illumination of the surface of an object in space is created using a projector in which an incoherent beam of light emitted by a light source is spatially modulated when passing through a transparency, the transmittance of which periodically depends on the coordinate transverse to the optical axis of the projector. Using a lens, which is installed at the output of this projector, the object is illuminated with a diverging spatially modulated beam of light. The use of computer-controlled optical projectors, for example, with liquid crystal transparencies or other spatial light modulators, makes it possible to dynamically control the period and phase of the spatial modulation of the intensity of light illuminating the object. The projection of periodic stripes of light onto the surface of the object is recorded by an image recording device, for example, a television or photo camera. The angle between the optical The projector axis and the optical axis of the image recording device are usually quite large. The projection pattern of periodic light stripes onto an object is affected by the shape of its surface, in particular, the variation in the projection phase of the periodic light stripes and the shift of a given stripe depend on it. When using the triangulation method, the shape of the object and the distance to its points are determined by the angles at which the stripes of the periodic light structure are projected onto the surface of the object and observed [1]. The disadvantage of the triangulation method is the low accuracy of determining these angles and the complexity of determining the numbers of the stripes of the projected periodic light structure. When using the phase measurement method, the projection phase of the periodic light stripes is determined by finding, for example, the spatial Fourier spectrum of the image of the object's surface or by the method of step-by-step phase shift of these light stripes [2, 19]. The shape of the object is determined by the measured dependence of the projection phase variation on the coordinates on the image of the object. The disadvantage of phase methods is the ambiguity of calculating the phase from the image of the projection of periodically structured light onto the surface of the object. Various methods have been proposed to eliminate the ambiguity of calculating the phase of the image of periodic structured illumination projected onto the surface of an object using an optical projector with a lens (see, for example, patents [21 - 24]). Using such methods, it is possible to measure the absolute values of the coordinates of points on the surface of an object, but this requires a more complex projection system, as well as a method for processing the measurement results. In addition to the above-mentioned specific disadvantages of phase and triangulation methods for measuring the 3D shape of objects using periodic structured illumination, their common disadvantages are:

• Complexity and high cost of an optical projector with a lens,

• Limited transverse size of the surface area illuminated by one projector,

• Difficulty in measuring the shape of uneven surfaces, surfaces with discontinuities or height jumps,

• The need to calibrate the measuring system as a whole.

Methods for forming periodic structured beams of incoherent light without using complex and expensive projection devices with a lens are known [25 - 33]. To form periodically structured beams incoherent light in these methods use a two-grating device, which includes a light source and two flat one-dimensional periodic gratings with the same direction of stripes, which are located on one side of the light source in parallel planes distant from each other. The method of forming periodically structured light beams with such a two-grating device is based on the generalized effect of forming a pseudo-image of the grating. This effect consists in the fact that when incoherent light, emitted by the source, sequentially passes through two flat periodic gratings, light moiré structures appear behind the grating farthest from the light source, which have a periodic spatial modulation of the light intensity. Such a moiré structure is called a generalized pseudo-image of the grating [28, 32, 33]. A special case of the generalized effect of forming a pseudo-image of the grating is the Lau effect [27, 28, 31, 34-36]. In this particular case, a contrast pseudo-image of the grating appears at an infinite distance from the two-grating device, and a lens located behind the grating farthest from the light source is used to form a periodic modulation of light at a finite distance. The publication [37] discusses a method for determining the distance between two parallel gratings with different spatial periods based on measuring the characteristics of the light moiré structure that appears after incoherent light passes through these gratings. An optical two-grating device is also known, designed to measure the magnitude of the displacement of one of the gratings, as well as the magnitude of the displacement of an object attached to it in the plane of this grating in the direction perpendicular to the direction of its stripes, the operation of which is based on the generalized effect of forming a pseudo-image of the grating (see, for example, [29, 38]). Such a device for measuring the magnitude of the displacement of an object is one of the variants of a linear optical encoder. A dual-grating linear encoder is not applicable for measuring the magnitude of displacement in the direction that is perpendicular to the planes of the gratings, and it cannot be used for contactless measurement of the distance to objects, the coordinates of their points and the shape of the surface. Non-contact methods for measuring the shape of objects are known that use the generalized effect of forming a pseudo-image of a grating [39 - 42] or the Lau effect [43]. In these methods, the shape of an object is determined by the magnitude of the spatial variation of the phase of the projection on the surface of the object of a periodic moire structure, which is formed using a two-grating projection device. The image of the surface of the object illuminated by the said projection device is recorded by the image recording device and processed by the computing device using, for example, the Fourier transform or the step phase shift method [40 - 43]. The triangulation measurement method can be used to determine the distance to the points of the object [39]. The system for implementing the profile metry method using the generalized effect of forming a pseudo image of a grating [39] is a prototype of the system proposed in the present invention. The prototype system consists of a lensless projection device, as well as an image recording device and a computing device [39 - 41]. The projection device includes a source of incoherent light, two periodic gratings located in parallel planes distant from each other. The moire structure (pseudo image of the grating), formed by the prototype projection device, is weakly localized in the direction of the optical axis of the projector, which is perpendicular to the planes of the gratings. The advantage of the two-grating projection device proposed in the patent [39] is that it is simpler and cheaper than structured light projectors with a lens. The profilometry method described in the patent [39] is the closest to the proposed method in terms of its technical essence and set of elements for its implementation. This method is a prototype of the proposed method. The known measurement method [39 - 41] has the disadvantages of phase and triangulation methods of profilometry and rangefinding, in particular, the problematic nature of using the method to measure the shape of unsmooth surfaces, the limited width of the surface area illuminated by the projection device, and the need to calibrate the measuring system as a whole. In addition, the disadvantage of the triangulation method is its low accuracy and the complexity of determining the band numbers of the periodic light structure projected onto the object. The use of the phase measurement method is complicated by the ambiguity of calculating the phase of the moire structure projection onto the object and the inability to determine the distance to the object points. In particular, to determine the distance from the projection device at which the object needs to be positioned, the patent [39] suggests using an additional rangefinder, for example, a laser one. DISCLOSURE OF INVENTION

Taking into account the disadvantages of the rangefinding and profilometry methods and systems described in the Prior Art section, the invention is based on the task of proposing a method and a system that will eliminate at least some of these disadvantages. In particular, the task of this invention is to propose a method and a system that allow wide-field measurements of the absolute value of the distance to the surface points of objects, their coordinates, as well as the shape of objects, including objects with a rough surface, using periodically structured light emitted by a lensless projection device. The task of this invention is also to propose a method for measuring the distance to the points of objects and their shape, the implementation of which does not cause the problem of unambiguously determining the phase value and the numbers of the bands of the projection of periodically structured light onto the object.

The essence of the proposed method, as well as the method that is the prototype, consists in projecting a light periodic moire structure onto the surface of an object, formed using a two-grating projection device, which will also be called a two-grating projector, registering an image of the surface area of the object onto which this moire structure is projected using at least one recording device, mathematically processing the obtained images using a computing device, and determining the shape of the surface of the object based on the results of this processing. What is new in the proposed method is that at least one moire structure (a pseudo-image of a grating) is used for rangefinding and profilometry, which is sufficiently strongly localized in the longitudinal direction, which is perpendicular to the planes of the gratings installed in the projection device. Such a localized moire (LM) structure is formed, for example, using the two-grating projection device described in the invention. The projection of the said localized moire structure is moved along the surface of the object, the plane of greatest contrast of the moire structure is aligned with the point on the surface of the object whose coordinates need to be measured. Using the known value of the distance to this plane from the plane of the output grating of the projection device, the distance to the specified points of the object and its longitudinal coordinate. Using these data, as well as the image of the object and the results of calibration of the image recording device, the transverse coordinates of a given point of the object are determined. By scanning the surface of the object with the projection of the said localized moire structure, recording and mathematically processing the images of the object obtained at different positions of the projection of the LM structure, the shape of the object is found. In the proposed method, in contrast to the prototype method, when determining the shape of the object and the distance to its points, it is not necessary to determine the strip number or the phase value of the projection of the moire structure and there is no need to eliminate the ambiguity of the value of this phase. Another new feature of the proposed method is that, unlike the closest analogue, it can be used not only to determine the shape of the object, but also to measure the absolute value of the distance to its points and their coordinates. To implement the proposed method, one or more localized moire structures formed by at least one projection device can be used. The difference between the proposed method and the prototype method is also that it can be implemented with a parallel arrangement of the longitudinal axis of the projection device and the optical axis of the image recording device.

The proposed system, as well as the system which is its prototype, contains a two-grating projection device, an image recording device and a computing device. The projection device contains a source of incoherent light, first and second flat periodic gratings which are located one after the other in non-coinciding parallel planes on one side of the light source and which are illuminated by the said light source, wherein the light which has passed through the first grating falls on the second grating. What is new is that the width of the light source, the first and second gratings which are installed in the projection device, as well as the width of the angular spectrum of light emitted by the light source, are such that at least one localized moire structure is formed. Increasing the width of the working aperture of the light source and the gratings installed in the projection device allows increasing the width of the continuous region within which it is possible to carry out measurements with the least error. The difference from the prototype also consists in the fact that the proposed system uses a device for scanning the surface of an object by the projection of the LM structure. Unlike the prototype system, where in the projection In the device, the distance between the gratings and their periods are fixed, in the proposed system, the distance between the gratings and their periods can be controlled and thus, in particular, the surface of the object can be scanned by the projection of the LM structure. In the proposed system, a device for changing the mutual orientation of the stripes of the localized moire structure and the object can also be additionally used.

The technical result is a simplification of the rangefinding and profilometry system, including from the standpoint of manufacturing and control, a simplification of the measurement data processing method, the absence of the problem of phase ambiguity, an increase in the width of the area available for taking measurements using a single projection device, the ability to determine the shape of unsmooth surfaces, surfaces with discontinuities and height jumps.

The essence of the invention is explained by the following figures.

Fig. 1 schematically shows a system of optical rangefinding and profilometry, as well as an object onto which a light localized moire structure is projected.

Fig. 2 shows a diagram of a projection device that forms a light moire structure.

Fig. 3 schematically shows the projection onto the plane y = 0 of the elements of the projection device, the image recording device, and also the localized moire structure with the display of the positional and angular relationships between the elements of the devices, the light beams, and the spatial regions of the LM structure.

In Fig. 4 (a, b) a projection onto the plane y = 0 of the elements of the projection device and the localized moire structure is schematically shown with the display of the positional and angular relationships between the elements of the device, the light beams and the spatial regions of the LM structure for 0 sx > 0 _sx (Fig. 4(a)) and for 0 _xm ^< sx ( ^Fig . 4(b)), where 6 _sx is the angular size of half the working aperture of the illuminator, 0 _xm is the half-width of the angular spectrum of light emitted by the illuminator.

Fig. 5 shows images of two types of flat one-dimensional amplitude gratings: a grating with a sinusoidal dependence of the amplitude transmittance on the coordinate (Fig. 5(a)) and a periodic binary raster (Fig. 5(6)). Fig. 6 schematically shows a system of optical rangefinding and profilometry, in which several projection devices and several image recording devices are used.

IMPLEMENTATION OF THE INVENTION

The method of contactless rangefinding and profilometry and the system for implementing it will be discussed with reference to the above-mentioned figures, in which the same reference numerals designate the same elements. The method can be implemented using a system, a schematic representation of which is shown in Fig. 1 (clause 16 of the claims). The system includes a lensless projection device 1, at least one image recording device 2, a computing device 3, and also at least one device for moving the projection of a localized moire structure 4 formed by the projection device 1, along the surface of the controlled object 5. The diagram of the projection device 1 is shown in Fig. 2 (clause 17 of the claims). The projection device 1 according to clause 17 of the invention formula includes a spatially extended source of incoherent light 6, which will also be called an illuminator, and two parallel flat one-dimensional (1D) periodic gratings 7 and 8. The first grating 7, closest to the illuminator 6, and the second, output grating 8 are located on one side of the light source 6. The stripes of these gratings have the same direction. It is preferable that the gratings 7 and 8 have a rectangular shape. The luminous surface of the light source 6 faces the gratings 7 and 8. In a particular case, according to and. 18 of the invention formula, the spatially extended light source 6 installed in the projection device 1 is a source of diffuse light. Such a source of diffuse light, for example, can be the surface of a heated body, a fluorescent lamp, a fluorescent screen, a screen of a telephone, TV, tablet or computer monitor, the surface of an organic and inorganic light-emitting diode. The source of diffuse light may also be a section of the daytime sky, the surface of a random phase transparency, for example, frosted glass, a sheet of tracing paper or tissue paper illuminated from the side opposite the gratings, etc. The projection device 1 forms at least one light LM structure. The localized moire structure may be formed in the geometric optics (GO) zone (clause 2 of the invention formula) or in the Fresnel diffraction zone of the projection device 1 (clause 3 of the invention formula). The conventional the image of the light intensity distribution at the LM structure in a plane parallel to the planes of the gratings (see Fig. 2) or in a plane perpendicular to the direction of their grooves (see Figs. 3 and 4 (a, b)), is designated in the figures by the number 9. Figs. 1 and 2 show the right orthogonal coordinate system with axes x, y and z, which is connected with the projection device 1. The coordinate axis z is directed perpendicular to the planes of gratings 7 and 8, in the direction from the light source 6 to the gratings. If the second grating 8 has a rectangular shape, then the z axis passes through its center, and is called hereinafter the optical axis of the projection device 1. The y axis is directed along the direction of the stripes of gratings 7 and 8 (see Fig. 2). The transmission coefficients of gratings 7 and 8 depend periodically on the x coordinate. The direction of the z-axis will be referred to in the text as longitudinal, and the directions perpendicular to the z-axis will be referred to as transverse. We will refer to the dimensions of the object 5, the working apertures of the light source 6, and the gratings 7 and 8 in the direction of the x-axis as their width, in the direction of the y-axis as their height, and in the direction of the z-axis as their length or thickness. The plane = 0 coincides with the plane of the first grating 7. The second, output grating 8 is located in the plane =, i.e., the planes of the first and second gratings are separated from each other by a distance L, 0 . The distance in the longitudinal direction from the second grating 8 at z > will also be referred to as the distance from the projection device 1. In the particular case where the working surface of the illuminator 6 is flat and is located parallel to the planes of the gratings, the distance between the working surface of the illuminator 6 and the plane of the first grating 7 will be denoted by L _o . It can be equal to zero. The coordinate of the center of the working surface of the illuminator along the y-axis is equal to y = y _s . In Fig. 1 also shows a global fixed coordinate system with axes x', y' and z • In a particular case (clause 19 of the invention formula), a device for determining the coordinates and orientation of the projection device 1 in the global coordinate system can be additionally used in the system.

The range-finding and profilometry system includes at least one device intended for the movement and/or change of orientation of the LM of the structure and object 5 relative to each other. In Fig. 1 and Fig. 2, thick arrows show the directions of possible translational movements and rotations of the elements of the range-finding and profilometry system and object 5 in different particular cases of implementing the method and system. In the particular case (and. 20 of formula (a) a device may be used which changes the distance between the projection device 1 and the object 5 by means of translational movement of the projection device 1 and/or the object 5. In particular, the projection device 1 and the object 5 may be brought closer or further apart at a given speed. In a particular case (clause 21 of the claims), devices for rotating the projection device 1 and/or the object 5 may be used to change the relative position of the LM of the structure and the object 5. As an example, Fig. 1 schematically shows a device 10 intended for moving and/or changing the orientation in space of the projection device 1. In a particular case of implementing the system (clause 22 of the claims), a device may be used in the projection device 1 which controllably changes the distance between the gratings 7 and 8 in the longitudinal direction or brings the gratings 7 and 8 closer or further apart in this direction at a given speed. Additionally, there may be a device for translational movement of at least one of the gratings 7 and 8 in its plane in the direction of the x coordinate, which leads to a change in the phase of the quasi-periodic moire structure formed by the projection device 1 (Article 23 of the invention formula). The devices that in different particular cases of the implementation of the system can implement the movement and rotation of the object 5, the movement of the gratings 7 and 8, are not shown in the figures. The devices with the help of which the change in the relative position and orientation of the projection device 1 and the object 5 is carried out, as well as the change in the position of individual elements of the projection device 1 are well known and commercially available [44 - 47]. The rangefinding and profilometry system also contains at least one device intended for measuring the amount of change in the position and/or orientation of at least one item from the set including the object 5, the projection device 1, the gratings 7 and 8. Such devices are well known and commercially available [44 - 46, 48]. In a particular case, the device for moving and/or changing the orientation of elements of a system or object 5 and the device for measuring the values of their movement, as well as the angles of their rotation, can be combined in one device or be one device.

The image recording device 2 is intended for recording an image of at least one object 5 (see Fig. 1). The image recording device 2 may be, for example, a television camera or a photo camera. The image sensor 11 in the image recording device 2 is, for example, a CCD (charge-coupled device) or CMOS (complementary metal-oxide-semiconductor) matrix. Objective 12 projects light incident on it onto image sensor 11 of image recording device 2 (see Figs. 1 and 3). Preferably, image recording device 2 is pre-calibrated using known methods, for example, using a checkerboard-shaped template [19, 49]. Image recording device 2 can be stationary or it can move translationally and rotate. Well-known devices (not shown in the figures) are used to move and rotate image recording device 2, as well as to determine its position and orientation. In a particular case, at least one image recording device 2 can be rigidly connected to projection device 1, then it moves and rotates together with it. In a particular case (clause 24 of the invention formula), the optical axis of image recording device 2 is parallel to the longitudinal axis of projection device 1.

The computing device 3 is intended for calculating the distance to the points of the surface of the object 5 and their coordinates, as well as the shape of the surface of the object 5 based on the images obtained by the image recording device 2. The computing device 3 is, for example, a computer or a mobile computing device. The computing device 3, in addition to storing and processing the information received from the image recording device 2, processes and stores the data received from other devices of the system, as well as controls the devices of the system and their elements. In particular, it can process and store data on the displacement values, movement speeds and rotation angles of the projection device 1, the image recording device 2, the object 5, the gratings 7 and 8, which are received from the devices recording these values.

The amplitude transmittances of the gratings 7 and 8, which are installed in the projection device 1, can generally be complex. In a particular case of the implementation of the system (clause 25 of the invention formula), at least one grating is installed in the projection device 1, which has a real positive amplitude transmittance, which is called an amplitude grating. In a particular case (clause 26 of the invention formula), at least one grating installed in the projection device 1 is a 1D amplitude grating with a sinusoidal dependence of the magnitude of the change in the amplitude coefficient transmission from the x-coordinate (see Fig. 5(a)) [37, 50, 51]. Such a grating will be called an amplitude grating with sinusoidal transmission. In another particular case (clause 27 of the formula of the invention), at least one grating can be a 1D amplitude grating, which has a binary dependence of the transmission coefficient on the transverse coordinate, for example, it is periodically alternating transparent and opaque parallel rectangular stripes along the x-coordinate, which have sharp boundaries (see Fig. 5(6)) [31, 32, 41, 42, 44, 52, 53]. Such gratings are also called periodic binary rasters. The advantage of using periodic binary rasters in a projection device is the simplicity and low cost of manufacturing these gratings, their commercial availability [44, 48, 53]. In another particular case (clause 28 of the formula of the invention), at least one phase grating may be used in the projection device 1, i.e. a grating with a periodic dependence of the phase of the amplitude transmittance coefficient on the transverse coordinate and a constant modulus of this coefficient [52, 54]. As yet another alternative, at least one grating may be used in the projection device, which combines an amplitude and a phase grating [52, 55, 56]. Amplitude, phase and amplitude-phase gratings are produced by known photographic, holographic, lithographic, printing and other methods. Gratings of some of the mentioned types are commercially available [44, 48, 54]. In a particular case (clause 29 of the formula of the invention), at least one grating, the characteristics of which can be changed, may be used in the projection device 1. For example, at least one of the gratings installed in the optical projection device 1 may be an amplitude binary raster, the fill factor of which and/or period can be changed. In a particular case (clause 30 of the invention formula), a spatial light modulator may be used to form at least one of the gratings installed in the projection device 1 [57 - 59].

где R_NM = Mp. Np₂ > 1 , р₁ и p₂ - пространственные периоды первой и второй решетки соответственно [27, 31, 33, 64, 65]. Координата плоскости, где контраст муаровой структуры (N,M) имеет наибольшую величину, равна z = z_NM (см. фиг. 1, фиг. 3 и фиг. The projection device 1 in the particular case of its implementation (clause 31 of the invention formula), when the first grating 7 and the second grating 8 are 1D amplitude gratings, operates as follows. The light emitted by the illuminator 6 passes first through the first grating 7, then through the second grating 8. When the light passes through the amplitude grating, its intensity is spatially modulated, therefore, periodic bands are observed behind each of the gratings 7 and 8 light and shadow. When the grating is illuminated by incoherent light from an extended source or by diffuse light, the contrast of the light and shadow bands decreases with distance from the grating in the longitudinal direction. This occurs because, with a wide angular spectrum of light falling on the grating, the light and shadow bands that arise after plane light waves propagating at different angles to its surface pass through it “mix” at some distance behind the grating. At a sufficiently large distance from the grating, the light intensity becomes almost constant in space. However, there are planes parallel to the planes of gratings 7 and 8 and located from them in the longitudinal direction at known distances, in the vicinity of which projection device 1 can form light moire structures that are periodic in space regions of light and shadow [25–28, 31–33, 60–63]. The projection of these light moire structures onto a plane parallel to the planes of the gratings has the form of periodic light and dark stripes that are directed along the y axis (see Fig. 2). The formation of a localized moire structure can be interpreted, in particular, as a shadow echo effect [60, 62, 63], which is a special case of a modulation echo [61]. The moire structures formed by a two-grating projection device with 1D gratings are designated by two indices (N, M) (see paragraph 4 of the formula of the invention), where N and M are natural numbers. The distance from the plane of the output grating 8 of the projection device 1 to the plane where the contrast of the moire structure (N, M) is maximum is calculated using the formula

where R _NM = Mp. Np ₂ > 1 , p ₁ and p ₂ are the spatial periods of the first and second gratings, respectively [27, 31, 33, 64, 65]. The coordinate of the plane where the contrast of the moire structure (N, M) has the greatest value is z = z _NM (see Fig. 1, Fig. 3 and Fig.

• Зависимость интенсивности света от координаты х 1 ^— NM вблизи плоскости наибольшего контраста муаровой структуры (N,M) z = z_NM описывается периодической функцией, пространственный период P_NM которой вычисляют по формуле [27, 31, 33, 64, 65]

Контраст муаровой структуры (N,M) вычисляют по формуле

где и I . - максимальное и минимальное значение интенсивности света в плоскости z = const [64, 66]. Расстояние в направлении оси х между точками, в которых определяются величины /_тах и Z_min , равно где п - натуральное число,

включая ноль. Пространственное распределение интенсивности света в плоскости у = О недалеко от линии z = z_NM условно изображено на фиг. 3 и 4 и обозначено цифрой 9. Глубину резкости муаровой структуры (N,M) будем обозначать L_NM . Глубина резкости AL_VW равна удвоенному значению длины, при удалении на которую в продольном направлении от плоскости z = z_NM контраст муаровой структуры (N,M) уменьшается в два раза по сравнению со значением ее контраста в плоскости z = z_NM . Проекционное устройство 1 в варианте его реализации, предлагаемом в изобретении, формирует световые муаровые структуры, которые достаточно сильно локализованы в продольном направлении. Локальность муаровой структуры (N,M~) означает, что ее глубина резкости A6_W значительно меньше расстояния от проекционного устройства 1 до плоскости, на которой контраст этой муаровой структуры имеет наибольшее значение AL_NM « L_NM . Конкретно будем полагать, что у локализованной муаровой структуры (N,M) относительная глубина резкости ЛМ ^^NM должна быть по крайней мере меньше 0,25. 4 (a, b)), where z _NU = Ц +L _NM = —

• The dependence of the light intensity on the coordinate x 1 ^— NM near the plane of greatest contrast of the moire structure (N,M) z = z _NM is described by a periodic function, the spatial period P _NM of which is calculated using the formula [27, 31, 33, 64, 65]

The contrast of the moire structure (N,M) is calculated using the formula

where I and I are the maximum and minimum values of light intensity in the plane z = const [64, 66]. The distance in the direction of the x-axis between the points at which the quantities I _max and Z _min are determined is where n is a natural number,

including zero. The spatial distribution of the light intensity in the plane y = 0 near the line z = z _NM is conventionally depicted in Figs. 3 and 4 and designated by the number 9. The depth of field of the moire structure (N, M) will be designated by L _NM . The depth of field AL _VW is equal to the doubled value of the length at which, when removed in the longitudinal direction from the plane z = z _{NM ,} the contrast of the moire structure (N, M) decreases by half compared to the value of its contrast in the plane z = z _NM . The projection device 1 in the embodiment of its implementation proposed in the invention forms light moire structures that are sufficiently strongly localized in the longitudinal direction. The locality of the moire structure (N, M~) means that its depth of field A6 _W is significantly less than the distance from the projection device 1 to the plane on which the contrast of this moire structure has the greatest value AL _NM « L _NM . Specifically, we will assume that for a localized moire structure (N,M) the relative depth of field LM ^ ^NM should be at least less than 0.25.

^NM

An analysis of the characteristics of moire structures formed by a projection device in various particular cases of the implementation of this device, consideration of the conditions under which localized moire structures can be formed, an assessment of the accuracy of the proposed method of rangefinding and profilometry, as well as a number of its other characteristics will be carried out after a description of particular cases of the implementation of the method.

, то проекция 4 ЛМ ^NM структуры на поверхность объекта 5 имеет вид области или нескольких областей, в пределах которых наблюдаются квазипериодические по координате х светлые и темные полосы (см. фиг. 1). Форма области на поверхности объекта 5, где проекция 4 ЛМ структуры имеет относительно высокий контраст, зависит от формы поверхности объекта 5 и глубины резкости муаровой структуры (N,M). Плоскость z = z_NM , где контраст муаровой структуры (N,M) является наибольшим, пересекается с поверхностью объекта 5 по плоской линии, которую будем называть изолинией наибольшего контраста ЛМ структуры. Например, с плоскими поверхностями плоскость z = z_NM пересекается по отрезкам прямых линий (они показаны штрих-пунктирными линиями 14 на фиг. 1), со сферическими поверхностями - по кругу или по дуге окружности. Изображение поверхности объекта 5, освещаемой проекционным устройством 1, регистрируют устройством регистрации изображений 2. Используя вычислительное устройство 3, определяют зависимость контраста квазипериодического в направлении оси х изменения яркости изображения объекта 5 от 2D координат на изображении. Для вычисления контраста используют известные математические методы обработки изображений. В частности, может быть использован Фурье или вейвлет анализ изображений, интерполяция пространственного распределения изменения яркости изображения периодической или квазипериодической функцией, например, синусоидой или вейвлетом. Также может быть применен известный метод пошагового сдвига фазы полос периодической световой структуры, которая освещает эту поверхность [2, 19]. Сдвиг фазы муаровой структуры, которую проецируют на поверхность объекта 5, осуществляют, например, путем поперечного смещения в направлении оси х проекционного устройства 1 или по и. 23 формулы изобретения путем смещения в направлении оси х одной из установленных в нем решеток. Используя результаты вычисления распределения величины контраста изображения поверхности объекта 5, на который спроецирована ЛМ структура (N,M), находят положение изолинии наибольшего контраста этой ЛМ структуры. Для определения координат заданной точки 13 поверхности объекта 5, изолинию наибольшего контраста проекции 4 ЛМ структуры совмещают с этой точкой. Это осуществляют, в частности, следующими способами: The method, in a particular case of its implementation, for measuring the distance to at least one given point 13 of the surface of object 5 (see Fig. 1) and the coordinates of this point is carried out as follows. The surface of object 5 is illuminated with light emitted by projection device 1. In projection device 1, elements are used, in particular, gratings 7 and 8, with such parameters that a at least one localized moire structure. In particular, according to claim 5 of the formula of the invention, at least one of the LM structures can be used to implement the method: (1,3), (1,2), (1,1), (2,1) and (3,1). It is preferable to use structures with a sufficiently high contrast for the LM measurements, for example, according to claim 6 of the formula of the invention, the highest contrast value of the LM structure exceeds 0.2. According to claim 7 of the formula of the invention, several LM structures can be simultaneously formed by one projection device. To simplify the further description of the rangefinding and profilometry method, we will assume that, unless otherwise stated, one LM structure, the index (N,M) of which is known, is projected onto the surface of the object 5. Usually, at least one image recording device 2 is focused approximately on the plane of the greatest contrast of this LM structure. It is preferable, firstly, that the depth of field of the objective 12 of the image recording device 2 be at least twice as large as the depth of field of the moire structure (7V, A7); secondly, that the width of the LM structure (N, M) used for measurements, D^ _M (see Fig. 4 (a, b) exceeds the period of the moire structure P _NM by at least twice. If the width of the projection onto the plane = const of the controlled part of the surface of the object 5 is significantly greater than the period P _NM of the LM structure used, and also the tangent of the angle between the surface of the object and the plane z = z _NM in the areas of their intersection is less than

, then the projection of the 4 LM ^ NM structure onto the surface of the object 5 has the form of a region or several regions within which light and dark stripes that are quasi-periodic in the x coordinate are observed (see Fig. 1). The shape of the region on the surface of the object 5, where the projection of the 4 LM structure has a relatively high contrast, depends on the shape of the surface of the object 5 and the depth of field of the moire structure (N, M). The plane z = z _NM , where the contrast of the moire structure (N, M) is the greatest, intersects the surface of the object 5 along a flat line, which we will call the isoline of the greatest contrast of the LM structure. For example, the plane z = z _NM intersects flat surfaces along segments of straight lines (they are shown by dashed-dotted lines 14 in Fig. 1), and with spherical surfaces - along a circle or an arc of a circle. The image of the surface of object 5, illuminated by projection device 1, is recorded by image recording device 2. Using computing device 3, the dependence of the contrast of the quasi-periodic change in the brightness of the image of object 5 in the direction of the x-axis on the 2D coordinates in the image is determined. Known mathematical methods for image processing are used to calculate the contrast. In particular, Fourier or wavelet analysis of images, interpolation of the spatial distribution of the change in the brightness of the image by a periodic or quasi-periodic function, for example, a sinusoid or a wavelet, can be used. A known method of step-by-step shifting of the phase of the bands of a periodic light structure that illuminates this surface can also be applied [2, 19]. The phase shift of the moire structure that is projected onto the surface of object 5 is carried out, for example, by transverse shifting in the direction of the x-axis of the projection device 1 or, according to clause 23 of the claims, by shifting in the direction of the x-axis one of the gratings installed in it. Using the results of calculating the distribution of the contrast value of the image of the surface of object 5 onto which the LM structure (N, M) is projected, the position of the isoline of the greatest contrast of this LM structure is found. To determine the coordinates of a given point 13 of the surface of object 5, the isoline of the greatest contrast of the projection 4 of the LM structure is combined with this point. This is done, in particular, in the following ways:

1. By changing the distance between the projection device 1 and the object 5, for example, by progressively moving the projection device 1 in the longitudinal direction (Article 8 of the invention formula).

2. By rotating the projection device 1 and/or object 5 (item 9 of the invention formula).

3. By changing the distance L _NM from the projection device 1 to the plane of greatest contrast of the moire structure (clause 10 of the invention formula), for example, by changing the distance between gratings 7 and 8 (see clause 11 of the invention formula) or the spatial period of at least one of them (see clause 12 of the invention formula).

где F - фокальное расстояние объектива 12 устройства регистрации изображений 2, х_с и у_с - координаты изображений этих точек на поверхности датчика изображений 11 , L_CNM - расстояние от объектива 12 устройства регистрации изображений 2 до плоскости z = z_NM , которое равно L_CNM - L_NM + 1^ -1^ (см. фиг. 3). Координаты заданной точки 13 на поверхности объекта 5 в глобальной системе координат х' , у' , z определяют, с помощью вычислительного устройства 3, на основании полученные данных об ее координатах в системе координат х, у и z, связанной с проекционным устройством 1 , а также данных о положении и ориентации проекционного устройства 1 в глобальной системе координат. It is possible to use a combination of two or three of the above-mentioned methods for moving the projection 4 of the LM structure and the isoline of its greatest contrast along the object 5. The movement is carried out until the isoline of greatest contrast passes through a given point 13 of the surface of the object 5. The distance in the longitudinal direction L _NM from the plane of the second grating 8 of the projection device 1 to the isoline of greatest contrast of the LM structure (N,M) is calculated using formula (1). The longitudinal coordinate of the given point 13 in the coordinate system associated with the projection device 1 is equal to - + L _NM . In this position, the isoline of the greatest contrast of the LM structure determines the transverse coordinates of the point 13 using the measured values of the coordinates of this point on the image of the surface of the object 5 and the results of calibration of the image recording device 2 [19, 49]. In a convenient and easy-to-process particular case, when, firstly, according to clause 24 of the formula of the invention, the optical axis of the image recording device 2 is parallel to the optical axis of the projection device 1 and, secondly, the coordinates of the lens 12 of the image recording device 2 in the coordinate system associated with the projection device 1 are fixed and equal to = 0 , y = Y , z = L _c (see Fig. 1 and Fig. 3), then the coordinates x and y of the points on the surface of the object 5, belonging to the plane z = z _NM , are calculated using the formulas

where F is the focal length of the objective 12 of the image recording device 2, _xc and _yc are the coordinates of the images of these points on the surface of the image sensor 11, _LCNM is the distance from the objective 12 of the image recording device 2 to the plane z = _zNM , which is equal to _LCNM - _LNM + 1^ -1^ (see Fig. 3). The coordinates of a given point 13 on the surface of the object 5 in the global coordinate system x', y', z are determined, using the computing device 3, on the basis of the obtained data on its coordinates in the coordinate system x, y and z associated with the projection device 1, as well as data on the position and orientation of the projection device 1 in the global coordinate system.

The peculiarity of the proposed method in the particular case of its implementation for measuring the shape of an object is that the isoline of the greatest contrast of the projection 4 of at least one LM structure is moved along the entire controlled or measurable part of the surface of the object 5. At each position of the projection 4 of the LM structure, the image of the surface of the object 5 is recorded by the image recording device 2. The processing of the obtained images and control of the movement of the projection 4 of the LM structure along the surface of the object 5 are carried out using a computing device 3. The computing device 3, by processing the images of the surface of the object 5 obtained by the recording device 2 at different positions of the projection 4 of the LM structure, determines the longitudinal and transverse coordinates of the plurality of points of the controlled part of the surface of the object 5. The determination of the coordinates of each of the plurality of points of the surface of the object 5 is carried out in the same way as in the above-described particular case of implementing the method for measuring the coordinates of one specified point 13 of the object. In order to reduce the measurement time, as well as the time and labor intensity of processing their results according to clause 13 of the formula of the invention, it is preferable that at each position of the projection 4 of the LM structure on the surface of the object 5, the coordinates of the plurality of points of the surface of the object 5 located on the isoline of the greatest contrast of this LM structure are determined and stored by the computing device. The proposed method makes it possible to measure the shape of unsmooth surfaces, surfaces with discontinuities and sharp changes in height, the shape and distances to several objects that do not shade each other from the light of the projection device.

Let us consider the application of the method for measuring the shape of a part of the surface of object 5 using an example where the scanning of projection 4 of the LM structure over the surface of object 5 is carried out by progressively moving projection device 1 in the longitudinal direction towards object 5. It is preferable to first align the isoline of the greatest contrast of the LM structure with the region of object 5 that is closest in the longitudinal direction to projection device 1. Projection device 1 is brought step by step in the longitudinal direction to object 5 using movement device 10. At each step, the distance in the longitudinal direction between projection device 1 and object 5 is reduced by a fixed value Δ/ , the value of which is less than AL _WM , for example, Δ/ = 0.1 - AL _W . In this case, the isoline of the greatest contrast of projection 4 of the moire structure also moves over the surface of the object. The distance Az from the area of object 5 closest to the projector to the plane of greatest contrast of the moire structure when moving by t steps will be equal to Az = t • A/ . The approach of the projection device 1 and object 5 can also be continuous at a constant speed V , while the time of recording one image should be much less than the value of AL _W /V . In this case, Az is calculated using the formula Az = V - (tt ₀ ), where t is the time, t ₀ is the moment in time when the isoline of greatest contrast coincided with the area closest to the projector object. The image of the surface of object 5 at each step or at successive moments of time t is recorded by image recording device 2. By processing the image obtained by recording device 2 at step t or at moment of time t by computing device 3, the transverse coordinates x and y of the points of the surface of object 5 located on the isoline of the greatest contrast of the projection of the LM structure at this value of Az are determined. By processing the images of the surface of object 5, which were recorded at different distances in the longitudinal direction from projection device 1 to object 5, the isolines (x, Az) are calculated for different values of Az, and on the basis of this data the shape of the surface of the object Az(x, y) is calculated.

The use of several LM structures with different indices (N, M), formed according to clause 7 of the invention formula by one projection device, makes it possible to expand the range of distance and coordinate measurements, and to reduce the time required to measure the shape of the object surface. The implementation of the method using several moire structures will be similar to the implementation of the method described above in the case of one LM structure. In the case of using several LM structures, it is preferable to use several image recording devices, each of which is focused on the plane of greatest contrast of one of the LM structures. In the case when several LM structures or one LM structure, the index of which (N, M) is not known in advance, are projected onto the surface of the object, it is necessary to distinguish between the images of the projections of the moire structures with different indices (N, M) or to determine the values of the indices (N, M) from the image that is recorded by the image recording device. The images of the projections of the moire structures with different indices (N, M) can be distinguished, for example, by their periods, by the value of their contrast, by the order of their arrangement in the longitudinal direction.

The size of the surface area of object 5, within which its shape is measured, can be increased if, after scanning the part of the surface accessible for measurements, object 5 is rotated by a known angle, for example, around an axis perpendicular to the z axis. This will allow the projection device 1 to illuminate a previously inaccessible section of the surface of object 5 and then scan it with at least one LM structure 4. It is also possible to increase the size of the surface area of object 5, within which its shape is measured, if, after measuring the profile of one part of the object, move the projector 1 and, if necessary, the image recording devices around the object, and then scan another part of the object surface with at least one LM structure. The size of the area of the object surface available for measuring its profile, as well as the speed of such measurements, can be increased by using several projection devices and several image recording devices (see Fig. 6). Scanning the surface of the object with the LM structures formed by each of the projection devices is carried out, for example, by progressively moving the projection devices in their longitudinal direction, or by changing the distance between the gratings in the projection devices and/or by rotating the object with the help of the turntable 15. It is preferable that the areas of the object surface available for observation by the image recording devices overlap. Using the computing device 3, the profiles of different sections of the object surface are calculated, as described above, and then they can be combined by known methods into a single panoramic 3D picture of the surface profile of the object.

Below is given the rationale for the fact that with the help of a projection device, particular cases of implementation of which are proposed in the invention, moire structures localized in the longitudinal direction can be formed, the influence of the parameters of the projection device on the number and characteristics of the moire structures formed by it is considered, and an assessment of the accuracy of the proposed method of rangefinding and profilometry is given.

Let us denote by f (0 _x ,0 _y the function that describes the angular distribution of the intensity of light emitted by small elements of the working surface of the illuminator 6, i.e. describes their directional pattern, where 0 _X is the angle between the direction in which the light wave propagates and the plane x = const, 0,. is the angle between the direction of the light wave and the plane y = const .

For simplicity or certainty, we will assume that

• the working surface of the illuminator 6 is spatially homogeneous, i.e. its luminosity, as well as the angular and frequency spectrum of the light emitted by its elements, are constant within the working aperture of the illuminator surface;

котором распространяется свет, и продольным направлением (см. фиг. 3 и 4). Такое угловое распределение интенсивности диффузного света можно сформировать, например, если рабочая поверхность осветителя 6 является одномерным случайный фазовым транспарантом, на который с противоположной от решеток стороны падает плоская волна некогерентного света, причем 1D полосы, вдоль которых оптическая длина пути света через транспарант постоянна, направлены параллельно оси у. Полуширину в плоскости у = const углового спектра света, излучаемого рабочей поверхностью осветителя 6, по уровню г ² от максимальной величины функции (6» ,О) обозначим 6Ц, ; по п. 31 формулы изобретения в проекционном устройстве 1 установлены амплитудные решетки 7 и 8; по п. 32 формулы изобретения решетки 7 и 8 являются тонкими, т.е. при их прохождении светом, излучаемым осветителем 6, не происходит значительного сужения его углового спектра, например, уменьшение ширины углового спектра света не превышает 20%; по п. 33 формулы изобретения рабочая поверхность осветителя 6 имеет форму прямоугольника, плоскость которого параллельна плоскостям решеток 7 и 8, а его стороны параллельны осям х и у (фиг. 2). Ширина рабочей апертуры осветителя 6 равна Н_х (см. фиг. 3 и фиг. 4 (а, б)), ее высота равна Н (см. фиг. 2); решетки 7 и 8 имеют форму прямоугольников, стороны которых параллельны осям х и у. Ширины рабочей апертуры решеток 7 и 8 равны _lx и D_2x соответственно (см. фиг. 3 и фиг. 4 (а, б)), а высоты равна D_ly и D_2y соответственно (см. фиг. 2). Центры рабочей поверхности осветителя 6, а также первой решетки 7 и второй решетки 8 расположены на оптической оси проекционного устройства, т.е. центры этих элементов проекционного устройства 1 имеют поперечные координаты х = 0, у = y_s = ⁰ ; поперечные размеры рабочей апертуры осветителя 6 и решеток 7 и 8 большие настолько, что в области, где формируется ЛМ структура (N,M), влиянием дифракции света на апертурах этих элементов можно пренебречь, что выполняется при условиях Н »

где H - меньшая из - меньшая из величин D_ix и D , ₂ - меньшая из величин — LQ + L + L_NM например, Н > 10^ L_(W Л , D > 10^ z_NM ,

• the width of the angular distribution of the intensity of light emitted by the elements of the working surface of the illuminator 6 in the plane x = const is much smaller than the width angular distribution of light in the plane y = const , and, therefore, f . In this case, the angle in _x is the angle between the direction in

in which the light propagates, and in the longitudinal direction (see Figs. 3 and 4). Such an angular distribution of the diffuse light intensity can be formed, for example, if the working surface of the illuminator 6 is a one-dimensional random phase transparency onto which a plane wave of incoherent light falls from the side opposite the gratings, and the 1D bands along which the optical length of the light path through the transparency is constant are directed parallel to the y axis. The half-width in the y = const plane of the angular spectrum of the light emitted by the working surface of the illuminator 6, at a level of r ² from the maximum value of the function (6», , 0) will be designated as 6C, ; according to clause 31 of the formula of the invention, amplitude gratings 7 and 8 are installed in the projection device 1; according to clause 32 of the formula of the invention, gratings 7 and 8 are thin, i.e. when the light emitted by illuminator 6 passes through them, its angular spectrum does not significantly narrow, for example, the decrease in the width of the angular spectrum of light does not exceed 20%; according to claim 33 of the claims, the working surface of illuminator 6 has the shape of a rectangle, the plane of which is parallel to the planes of gratings 7 and 8, and its sides are parallel to the x and y axes (Fig. 2). The width of the working aperture of illuminator 6 is equal to H _x (see Fig. 3 and Fig. 4 (a, b)), its height is equal to H (see Fig. 2); gratings 7 and 8 have the shape of rectangles, the sides of which are parallel to the x and y axes. The widths of the working aperture of gratings 7 and 8 are equal to _lx and D _2x , respectively (see Fig. 3 and Fig. 4 (a, b)), and the heights are equal to D _ly and D _2y , respectively (see Fig. 2). The centers of the working surface of the illuminator 6, as well as the first grating 7 and the second grating 8 are located on the optical axis of the projection device, i.e. the centers of these elements of the projection device 1 have transverse coordinates x = 0, y = y _s = ⁰ ; the transverse dimensions of the working aperture of the illuminator 6 and gratings 7 and 8 are so large that in the region where the LM structure (N, M) is formed, the influence of light diffraction on the apertures of these elements can be neglected, which is fulfilled under conditions H »

where H is the smaller of the quantities D _ix and D , ₂ is the smaller of the quantities — LQ + L + L _{NM ,} for example, H > 10^ L _(W Л , D > 10^ z _NM ,

• the width of gratings 7 and 8 significantly exceeds their periods D _lx » p _} , D _lx » p ; for example D _lx > 10 p _} , D _t > 10 ₂ .

First, we will determine the characteristics of the LM structures formed by the projection device 1, in the particular case when its parameters and the parameters of its elements are such that, according to clause 2 of the formula of the invention, the effect of light diffraction on the amplitude gratings 7 and 8 on the characteristics of the LM structures is negligibly small. In this particular case, the geometric optics approximation is applicable to describe the characteristics of the moire structures formed by the two-grating projector 1. In the geometric optics approximation, the characteristics of the moire structures do not depend on the wavelength of light, therefore, a source of both monochromatic and non-monochromatic light, in particular, a source of broadband light, for example, white light, can be used as an illuminator in the projection device. The effect of diffraction on the gratings 7 and 8 on the characteristics of the LM structure (N, M) can be ignored if the first and second gratings are located close to each other, according to clause 34 of the formula of the invention, the distance between their planes must satisfy the condition < 0.2

(see [26, 62, 63]), where the length Lj, (2) is calculated by the formula

величина равна Л_т = 2₀ + ДА , где Я - центральная длина волны света, излучаемого осветителем, АЛ - полуширина спектра света по длине волны по уровню г ² . «>)

the value is equal to L _m = 2 ₀ + ΔA, where L is the central wavelength of light emitted by the illuminator, ΔA is the half-width of the light spectrum by wavelength at level ^r2 .

As a typical example, we will consider the properties and evaluate the characteristics of LM structures formed in the geometric optics zone, in a particular case when, according to clause 35 of the invention formula, 1D amplitude gratings 7 and 8 with sinusoidal transmission are used in the projection device 1. Amplitude the transmission coefficients of the first grating 7 T(x) and the second grating 8 _T2 (x) are given by the formulas respectively

Т^х) = ^-[1 + cos(^ ₁ x + ^// ₁ )] for \ ^X \ < ^D J ² ' ы < ^D ly/ ² '

(7) for \X\ < D ₂ J2 , \y\ < D _2y /2 ,

<//₂ -2l 2l where < 1 , C ₂ < 1 - modulation depth, K ₁ — , L ₂ = — - wave number,

<// ₂ -

а именно (1,2), (1,1), (2,2) и (2,1), возникают, если p_t > 2р₂.A RU is the phase of the amplitude transmittance of the first grating 7 and the second grating 8, respectively. We assume that gratings 7 and 8 are surrounded by opaque frames on the outside along the perimeter (not shown in the figures), so the transmittance of the first grating 7 7 (x, y) is zero at |x| > П _1л /2 or |y| > D _ly /2 , and the transmittance of the second grating 8 T ₂ (x, y) is zero at |x| > D _2x /2 or |y| > D _2y /2. Using a projection device with two 1D amplitude gratings with sinusoidal transmission, it is possible to form no more than four moiré structures (real pseudo-images of the grating) N < 2 , M < 2 [65]. Four moiré structures

namely (1,2), (1,1), (2,2) and (2,1), arise if p _t > 2р ₂ .

They are located in the vicinity of three planes, which are removed from the second lattice 8 by distances L _NM , which are calculated using formula (1). As follows from formula (1),

< L _ll = L ₂₂ < L ₂₁ . Spatial periods of moire structures (1,2), (1,1), (2,2) and

(2.1) are calculated using formula (2). The following relationship exists between the values of the periods of these moire structures: P ₁₂ < P ₂₂ < P _i < P ₂₁ ■ Phases of moire structures (1,2) (1,1)

(2.2) and (2.1) are equal respectively

> р₂ , то проекционным устройством формируются три муаровые структуры, а муаровая структура (2,1) не возникает. При р₂ > р_{ > р₂ /2 возникает только одна муаровая структура (1,2). При р < р₂ /2 муаровых структур не возникает. < 2i = P ~ 2</5 • If

> р ₂ , then the projection device forms three moire structures, and the moire structure (2,1) does not arise. When р ₂ > р _{ > р ₂ /2, only one moire structure (1,2) arises. When р < р ₂ /2, moire structures do not arise.

If the LM structure (N,M) arises far enough from the projection device 1, then near the region of its localization there are no longer any stripes of light and shadow from the gratings 7 and 8. In particular, for L _o = 0 and p ₁ , p ₂ « H _x the stripes of light and shadow from the gratings in the region localizations of the moire structure (N, M) have low contrast, for example, it is less

важном для многих потенциальных приложений способа случае, когда

— — < 0,1 , ^NM муаровые структуры с разными индексами

формируемые проекционным устройством с двумя 1D амплитудными решетками с синусоидальным пропусканием, почти не перекрываются в пространстве. Исключение составляют муаровые структуры (1,1) и (2,2), которые расположены вблизи одной плоскости z = z_n , где z_n = 1^ +1^ . В окрестности этой плоскости z = z_n интенсивность света равна

0.1 if the conditions ^Z NM are met

important for many potential applications of the method in the case where

— — < 0.1 , ^NM moire structures with different indices

formed by a projection device with two 1D amplitude gratings with sinusoidal transmission, almost do not overlap in space. The exception is the moire structures (1,1) and (2,2), which are located near one plane z = z _n , where z _n = 1^ +1^ . In the vicinity of this plane z = z _{n ,} the light intensity is equal to

(see [65]), where 1 ₀ is the intensity of incoherent light incident on the first grating 7. In the vicinity of the planes z = z ₁₂ and z - z ₂₁ , where the moire structure (1,2) and (2,1) are localized, respectively, the light intensity is calculated using the formula

(see [65]), where the subscript NM has the value 12 and 21 for the moire structure (1,2) 2/ and (2,1), respectively, K _NM = - . For all moire structures (N,M), the value

где C_NM (z_NM ) - значение контраста муаровой структуры (N,M) в плоскости z = z_NM ■ Муаровая структура (1,1) является самой контрастной из четырех. В зоне ГО при > р₂ и = С₂ = 1 ее контраст в плоскости z = z_u равен C_n(z_n) = 8/9 [56]. Контраст муаровой структуры (2,2) самый малый, в плоскости z = z_u он равен C₂₂(z₂₂) = 1/18.^NM contrast 0 < C _NM (z) < 1 if R _NM = Mp Np ₂ > 1 , and C _NM (z) = 0 if R _NM < 1 . The contrast of moire structures (N,M) depends on the longitudinal coordinate z, and this dependence is described by the formula

where C _NM (z _NM ) is the contrast value of the moire structure (N,M) in the plane z = z _NM ■ The moire structure (1,1) is the most contrasting of the four. In the GO zone at > p ₂ and = C ₂ = 1, its contrast in the plane z = z _u is equal to C _n (z _n ) = 8/9 [56]. The contrast of the moire structure (2,2) is the smallest; in the plane z = z _u it is equal to C ₂₂ (z ₂₂ ) = 1/18.

The maximum contrast of the moire structures (1,2) and (2,1) in the GO zone at C1 = _C2 = 1 is equal to ^12 (^12 ) ⁼ Gi ( ^z 2i ) ⁼ 2/9 [65]. The functions W _NM (z ~ z _NM ) describe the dependence of the contrast of the moire structure (N,M) on the longitudinal coordinate . Its value at z = z _NM is maximal and equal to 1, i.e. W _NM (0) = 1 . The function W _NM (z - z _NM ) decreases to 0 with distance from the plane z = z _NM both towards the projection device and away from it. The depth of field L _NM of the moire structure (N,M) is equal to the full width at half maximum (FWHM) of the function W _NM ( z _NM ), where Az _NM z Z _NM ■

Let us estimate the depth of field of the moire structure (N,M), which is formed by the projection device 1 in some particular cases of its implementation. We will assume that the frames limiting the first and second lattice do not vignette the illuminator in the direction of the coordinate x when it is observed from the point x = 0, y = 0 and

Z = z _NM (see Figs. 3 and 4). This condition is satisfied, for example, if the width of the working aperture of gratings 7 and 8 is greater than or equal to the width of the working aperture of illuminator 6

D., D, > H. (11)

угловой размер первой и второй решеток в плоскости у = О больше, чем угловой размер осветителя, где упомянутые угловые размеры осветителя и решеток определяются из точки х = 0 , у = 0 и z = z_NM . В частном случае, когда угловой размер осветителя меньше ширины углового спектра излучаемого им света (см. фиг. 4(a)), т.е. 6_хт > 6_SX , а также когда яркость осветителя не зависит от угла в_х при |^_x| < в_хт , функция W_NM ( z_NM ) вблизи ПЛОСКОСТИ X = 0 при равна

где AZ_NM = AZ_NM - - — (CM. [39, 67 - 69]). Из формулы (12) следует, что глубину

резкости муаровой структуры (N,M) вблизи плоскости х = 0 можно вычислить по формуле

Муаровая структура (N,M) при 6_хт > 0_sx является сильно локализованной L_NM « L_NM , если выполняется условие

The angular size of half the working aperture of the light source 6 in the plane y = 0 when observed from a point with coordinates x = 0, y = 0 and z = z _NM is denoted by 0 _sx (see Figs. 3 and 4). It is equal to where L _tNM = 7^ + 7^ + L _NM . From formula (11) it follows that

the angular size of the first and second gratings in the plane y = 0 is greater than the angular size of the illuminator, where the said angular sizes of the illuminator and gratings are determined from the point x = 0, y = 0 and z = z _NM . In the particular case when the angular size of the illuminator is less than the width of the angular spectrum of the light emitted by it (see Fig. 4(a)), i.e. 6 _xm > 6 _SX , and also when the brightness of the illuminator does not depend on the angle in _x for |^ _x | < 6 _xm , the function W _NM ( z _NM ) near the plane X = 0 for is equal to

where AZ _NM = AZ _NM - - — (CM. [39, 67 - 69]). From formula (12) it follows that the depth

the sharpness of the moire structure (N,M) near the plane x = 0 can be calculated using the formula

The moire structure (N,M) for 6 _xm > 0 _sx is strongly localized L _NM « L _NM if the condition is satisfied

From formula (13) it follows that the depth of field of the moire structure (N,M) is less

является локализованной (. L_NM < . ), если Н_х > 5P_NM — — . Например, при L_o = 0 иAnd P quarters of the distance L _NM at — — > 5— At L _o = O moire structure (N,M) pits _NM

is localized (. L _NM < . ), if H _x > 5P _NM — — . For example, when L _o = 0 and

4 Np ₂ d = 2p ₂ the moire structure (1,1) will be localized if the width of the working aperture of the illuminator H _x is greater than 10d.

In the opposite case, when, according to clause 36 of the formula of the invention, the angular size of the working aperture of the illuminator 6 in the plane y = 0 when observed from a point with coordinates x = 0, y = 0 and z = z _NM is greater than the width of the angular spectrum of light emitted by the elements of the surface of the illuminator 6, 0 _SX > 0 _xm (see Fig. 4 (b)), the depth

71 sharpness L _NM of the moire structure (N,M) near the plane x = 0 at _xm can be estimated by the formula

The relative depth of field of the moire structure (N,M) at 0 _SX > 0 _хт is calculated using the formula

The moire structure (N,M) for 6 _SX > 6 _хт is localized L _NM « L _NM if the condition is satisfied

L P in particular, L _NM at tgO _xm > 2.5^4- . From inequality (17) and the condition 0 _SX > 0 _xm ,

4 _NM which can be written as H _x > 2L _tNM tgd _xm , again the necessary condition (14) follows 7/ P _NM

проекционным устройством 1, в котором установлены первая и вторая решетки с угловыми размерами в плоскости у = const больше, чем угловой размер рабочей апертуры осветителя, формировалась локализованная муаровая структура NM), в этом проекционном устройстве по и. 37 формулы изобретения нужно использовать осветитель 6, у которого тангенс углового размера в плоскости у = const половины

рабочей апертуры, равный — , а также тангенс полуширины в этой 2(L₀ + ⁺ ^NM ) плоскости углового спектра излучаемого им света более чем в пять раз превышают отношение

- » - , when executing which the moire structure will be localized. In /NM _NM in particular, . Thus, in order to

projection device 1, in which the first and second gratings are installed with angular dimensions in the plane y = const greater than the angular dimension of the working aperture of the illuminator, a localized moire structure NM is formed), in this projection device, according to clause 37 of the formula of the invention, it is necessary to use an illuminator 6, in which the tangent of the angular dimension in the plane y = const is half

working aperture, equal to — , and also the tangent of the half-width in this 2(L ₀ + ⁺ ^NM ) plane of the angular spectrum of the light emitted by it is more than five times greater than the ratio

структуры примерно равна L_NM ~ P_NM . Из этой оценки L_NM , а также формул (1) и (2) следует, что относительная глубина резкости ЛМ структуры (N,M) примерно равна _Pi_ Исходя из такой оценки относительной глубины резкости, находим, что ^NM ^А при p_l = 1 мм у муаровой структуры (1,1) в зоне геометрической оптики, где выполняется условие (5), величины ^А_!_ может быть порядка процента. In the particular case of the implementation of projection device 1, when the half-width of the angular spectrum of light emitted by the elements of the illuminator surface is equal to # « , and the width of the working aperture of the illuminator exceeds the distance from it to the 6 plane of greatest contrast of the moire structure (N, M) by more than two times H _x > L _tNM , i.e. 0 _sx > 0 _хт , it follows from formula (15) that the depth of field of the moire

structure is approximately equal to L _NM ~ P _NM . From this estimate of L _NM , as well as formulas (1) and (2) it follows that the relative depth of field LM of the structure (N,M) is approximately equal to _Pi_ Based on such an estimate of the relative depth of field, we find that ^NM ^A at p _l = 1 mm for the moire structure (1,1) in the zone of geometric optics, where condition (5) is satisfied, the value of ^A_!_ can be of the order of one percent.

Ai

The width of the moire structure (Д/,Л/ in the plane z = z _NM is equal to (see Fig. 4 (a, b))

^D NM ~ ^Н Х ⁺ ^tNM ^xm ■ (18)

The contrast and depth of field of LM structures depend on the transverse coordinate x. The localized moire structure (N,M) has the greatest contrast and the smallest depth of field near the plane x = 0 . In the vicinity of this plane there is a region width D _NM (CM. Fig. 4 (a, b)), within which the contrast and depth of field of the LM structure (N, M) do not change or change little, for example, less than 1.2 times. We will call this region the central region of the moire structure (N, M). The width of the central region D _NM can be estimated by the formula (see Fig. 4 (a, b))

^D NM \H _x ~ ^L _tNM tg0 _xm \ . (19)

To implement the proposed method of ranging and profilometry, it is preferable that D _NM > P _NM .

резкости ЛМ структуры (N,M) в области

можно оценить по формулам (13) или (15), которые можно заменить одной обобщенной формулой

где 0_Ех - наименьшая из величин 0_хт и 0_SX . Thus, according to clause 14 of the invention formula, if the frames limiting the first and second grating do not vignette the illuminator in the direction of the x coordinate when it is observed from the central region of this LM structure, then when _xm <

sharpness of the LM structure (N,M) in the region

can be estimated using formulas (13) or (15), which can be replaced by one generalized formula

where 0 _Ex is the smallest of the values 0 _xm and 0 _SX .

® Д£_ж (0) . Таким образом, предлагаемые в изобретении способ и система позволяют осуществлять широкопольную дальнометрию и профилометр ию. Приведем первый численный пример, в котором определим характеристики муаровых структур, формируемых в зоне геометрической оптики проекционным устройством 1 с тонкими амплитудными решетками 7 и 8. Полагаем, что в проекционном устройстве установлены первая и вторая решетки с синусоидальным пропусканием с периодами р₁ = 2 мм и р₂ = 1 мм соответственно. Глубина модуляции функции пропускания этих решеток равна = С₂ = 1. Расстояние между первой решеткой 7 и второй решеткой 8 равно L, = 20 см. Осветитель 6 расположен вплотную к первой решетке L_o = 0. Источник света 6, первая и вторая решетки имеют равную ширину Н_х = D_lx = D_2X = 100 см. Осветитель 6 излучает диффузный свет в диапазоне = 0,5 + 0,1 мкм. Полуширина углового спектра света, излучаемого малыми некогерентными элементами поверхности осветителя, 0^ равна 30°. Проекционным устройством 1 с такими параметрами формируются две муаровые структуры с контрастом более 0,2: это муаровые структуры (1,1) и (1,2). Муаровая структура (2,1) не возникает, т.к. —

= 2. The absolute error in determining the distance from the projection device to a given point of object 5 is proportional to the depth of field of the moire structure and usually does not exceed the value of L _NM ■ For rangefinding and profilometry, it is preferable to use LM structures with a small depth of field, for example, according to §15 of the formula of the invention, it is proposed to use LM structures in which the relative depth of field in the central region is less than three percent. In order to increase the accuracy and reduce the measurement time, it is advisable to optimize the characteristics of the LM structure projected onto the surface of object 5, in particular, to select the optimal period of the LM structure, its depth of field and the direction of the stripes. In the case of 0 _SX > 0 _хт (see Fig. 4(6)), by increasing the width of the light source, as well as the width of the gratings, as follows from formulas (11) and (19), it is possible to practically unlimitedly increase the width of the central region D _NM , within which the accuracy of measuring the distance to the points of the object and its shape will be approximately the same as in the center of the LM structure

® Д£ _ж (0) . Thus, the method and system proposed in the invention make it possible to carry out wide-field ranging and profilometry. Let us present the first numerical example in which we will determine the characteristics of the moire structures formed in the geometric optics zone by the projection device 1 with thin amplitude gratings 7 and 8. We assume that the first and second gratings with sinusoidal transmission with periods p ₁ = 2 mm and p ₂ = 1 mm, respectively, are installed in the projection device. The modulation depth of the transmission function of these gratings is equal to = C ₂ = 1. The distance between the first grating 7 and the second grating 8 is equal to L, = 20 cm. The illuminator 6 is located close to the first grating L _o = 0. The light source 6, the first and second gratings have equal widths H _x = D _lx = D _2X = 100 cm. The illuminator 6 emits diffuse light in the range = 0.5 + 0.1 μm. The half-width of the angular spectrum of light emitted by small incoherent elements of the illuminator surface, 0^, is equal to 30°. The projection device 1 with such parameters forms two moire structures with a contrast greater than 0.2: these are moire structures (1,1) and (1,2). The moire structure (2,1) does not arise, since —

= 2.

R ₂

равное 33 см, поэтому влиянием дифракции света на характеристики муаровых структур (1,1) и (1,2) можно пренебречь. Пространственный период муаровой структуры (1,1) равен Р = 2 мм. Эта муаровая структура будет иметь наибольший контраст в плоскости, удаленной от второй решетки на расстояние Гц = 20 см. Максимальная величина ее контраста примерно равна C_n (z_n) ~ 0,9. Ширина центральной области ЛМ структуры (1,1) равна П_п ~ 54 см. Глубина резкости муаровой структуры (1,1) в ее центральной области равна М_Л1 « Р_п «2 мм. Муаровая структура (1,2) с пространственным периодом Р₁₂ = 0,67 мм локализована вблизи плоскости, удаленной от второй решетки на расстояние 1^₂ ~ 6,7 см. Ее максимальный контраст равен примерно С₁₂ (z₁₂) = 0,22. Ширина центральной области ЛМ структуры (1,2) равна П₁₂ « 69 см. Глубина резкости этой муаровой структуры AL^ в ее центральной области равна AL^ ® Р₁₂ ® 0,7мм. Относительная глубина резкости муаровых структур (1,1) и (1,2) примерно равна 1%. The distance between the lattices L is less than the distance

equal to 33 cm, therefore the influence of light diffraction on the characteristics of moire structures (1,1) and (1,2) can be neglected. The spatial period of moire structure (1,1) is equal to P = 2 mm. This moire structure will have the greatest contrast in the plane located at a distance of Hz = 20 cm from the second grating. The maximum value of its contrast is approximately equal to C _n (z _n ) ~ 0.9. The width of the central region of LM structure (1,1) is equal to П _n ~ 54 cm. The depth of field of moire structure (1,1) in its central region is equal to М _Л1 « П _n « 2 mm. Moire structure (1,2) with spatial period П ₁₂ = 0.67 mm is localized near the plane located at a distance of 1 ^ ₂ ~ 6.7 cm from the second grating. Its maximum contrast is approximately equal to С ₁₂ (z ₁₂ ) = 0.22. The width of the central region of the LM structure (1,2) is equal to П ₁₂ « 69 cm. The depth of field of this moire structure AL^ in its central region is equal to AL^ ® П ₁₂ ® 0.7 mm. The relative depth of field of the moire structures (1,1) and (1,2) is approximately equal to 1%.

Note that formulas (13), (15), (19) and (20) provide only an approximate estimate of the depth of field of the moire structure (N, M) and the width of its central region. To increase the accuracy of measurements using the proposed method of rangefinding and profilometry, it is preferable to first measure the dependence of the contrast of the moire structure (N, M) on the longitudinal coordinate z and transverse coordinate x, and, based on the data from these experiments, determine the measurement error of the distance and coordinates.

In a number of other particular cases of the implementation of the proposed rangefinding and profilometry system, a projection device 1 is used in it, in which at least one amplitude grating with a periodic non-sinusoidal dependence of the transmittance on the x coordinate is installed. With the help of the projection device 1, in which at least one amplitude grating with non-sinusoidal transmission is installed, it is possible to form moire structures (N, M), in which the maximum values of the integer indices N and M are not limited to the value two [27, 64, 66, 70]. The number of moire structures formed by such a projection device can be greater than in the particular case when two amplitude gratings with sinusoidal transmission are used. The distances from the projection device 1 to the plane where the contrast of these moire structures has the greatest value are calculated using formula (1), their periods are calculated using formula (2). The contrast value of the moire structure (N,M) in the plane Z = Z _NM in the GO zone is determined, in particular, by the dependence of the transmission coefficients of the first and second gratings on the coordinate x. The depth of field of the LM structures can be estimated using formula (20).

A periodic binary raster (see Fig. 5 (b)) can be used as an amplitude grating with non-sinusoidal transmission (Article 27 of the invention formula). The filling factor of the binary raster is equal to ap _i , where p _t is the grating period, a, is the width of its transparent stripes, and index I denotes the grating number in projection device 1. An amplitude binary raster with a _{ / p _{ = 0.5 is also called a Ronchi grating. In the particular case where the first grating 7 and the second grating 8 in projection device 1 are Ronchi gratings, relatively contrasting moire structures (1.1), (1.3), and (3.1) can arise in the field of geometric optics. The condition for their occurrence is Mr > Np ₂ , where N and M are equal to 1 or 3. The greatest contrast of the moire structure (1.1) at p > p ₂ is approximately the same as when using two amplitude gratings with sinusoidal transmission C _n (z _n ) ~ 0.9. The greatest the contrast value of the moire structures (1,3) and (3,1) is approximately 0.3. The remaining moire structures (N,M), formed by the projection device with two Ronchi gratings, have a contrast of less than 0.2 in the geometric optics zone. When using at least one binary raster with a fill factor smaller than that of the Ronchi grating in the projection device, i.e. ap^Q.,5, the number of relatively contrast moire structures can be significantly greater than three. For example, in the particular case when the first grating in the projection device is a binary raster with a p _r = 0.25 , and the second grating is a Ronchi grating or a grating with sinusoidal transmission at p _x > 4 ₂ , contrast moire structures (1,4), (1,3), (1,2), (1,1), (2,1), (3,1) and (4,1) will be formed (with a contrast

The installation in the projection device of at least one amplitude grating with non-sinusoidal transmission, in a number of cases, allows better adaptation of the proposed method to the conditions of a specific rangefinding and profilometry task. In particular, in the case when a large number of relatively contrasting LM structures are formed by the projection device, for example, their number is greater than three, it is possible to expand the range and accuracy, as well as to reduce the time of measuring distances, coordinates and shapes of objects. The advantage of using a projection device in which at least one binary grating is installed is also the ability to control the characteristics of the LM structures, for example, their number and contrast, by changing the period and/or the fill factor of the grating.

In a particular case (clause 3 of the invention formula), one or more localized moire structures, the characteristics of which are affected by the light diffraction effect, are used to implement the rangefinding and profilometry method. The diagram of the system for implementing the method according to clause 3 of the invention formula is the same as the diagram of the system for implementing the method according to clause 2 of the invention formula, when the controlled objects are located in the GO zone of the projection device. It is shown in Fig. 1. The difference is that in the particular case of implementing the method according to clause 3 of the invention formula, the parameters of the projection device 1 and its elements, in particular, the types and periods of gratings 7 and 8, the distances between them are such that the LM structures are formed in the Fresnel diffraction zone of the projection device. In In a projection device which is used to implement the method according to claim 3 of the invention, not only amplitude gratings but also phase gratings [69, 71, 72], as well as amplitude-phase gratings [55, 56] can be used as the first and/or second grating. A two-grating device which forms moiré structures (pseudo-images of the grating) in the Fresnel diffraction zone is called a Talbot-Lau interferometer in a number of publications [55, 70, 73]. Some properties of moiré structures formed by a two-grating device (Talbot-Lau interferometer) in the Fresnel diffraction zone are considered in publications [28-30, 39, 64, 65, 69, 74, 75]. The width of the central regions of the LM structures and their depth of field in the central region in the Fresnel diffraction zone can be estimated using formulas (19) and (20). In order to achieve a relatively high contrast of the moire structures formed in the Fresnel diffraction zone, instead of condition (5), which is necessary for the applicability of the GO approximation, other conditions must be met that impose restrictions on the parameters of the projection device. As an example, we will determine the conditions under which contrast LM structures are formed in the Fresnel diffraction zone, in the particular case when two amplitude gratings with sinusoidal transmission are used in the projection device according to clause 35 of the formula of the invention. We will assume that > 2p ₂ . In this case, in the vicinity of three planes with coordinates z = z ₁₂ , Z = Z _n = z ₂₂ and z = Z ₂₁ , moire structures (1,2), (1,1), (2,2) and (2,1) arise, respectively. As shown in publications [27, 30, 32, 64, 65, 75], the dependences of the contrast of the LM structure on the distance between the first and second gratings, on the width of the frequency spectrum of light emitted by the illuminator, are qualitatively different for moire structures (N, M) with an odd and even value of the index M. For this reason, we will first determine the conditions for the formation of contrast moire structures (1,1) and (2,1), for which M = 1, and then separately the conditions for the formation of the contrast moire structure (1,2), for which M = 2. The contrast of the moire structure (2,2) is small, so we will not take it into account.

может быть больше 0,7C_Nl(z_Nl) , где С_м

- контраст муаровой структуры (N,V) в плоскости z = Z_Ni в приближении геометрической оптики, индекс N равен 1 и 2 для муаровых структур (1,1) и (2,1) соответственно. Будем считать, что в проекционном устройстве 1 используется осветитель, который расположен вблизи первой решетки ( L_o « 0 ) и который излучает монохроматический некогерентный свет с длиной волны Л_!) , а также выполняется условие

. В этом случае контрастThe contrast of the moiré structures (1,1) and (2,1) in the Fresnel diffraction region depends, in particular, on the distance between the gratings D and the length Lj. (2) (see [32, 33, 65, 67, 68]). By varying the distance between the gratings, their periods, the wavelength and the width of the light spectrum, it is possible to change the value of the maximum contrast of the moiré structures (1,1) and (2,1) from a small value, which is less than 0.1, to the largest value, which is close to the largest value of their contrast in the geometric optics approximation, in in particular, the value of C _N1

may be greater than 0.7C _Nl (z _Nl ) , where C _m

- the contrast of the moire structure (N,V) in the plane z = Z _Ni in the geometric optics approximation, the index N is equal to 1 and 2 for the moire structures (1,1) and (2,1), respectively. We will assume that the projection device 1 uses an illuminator that is located near the first grating ( L _o « 0 ) and that emits monochromatic incoherent light with a wavelength of L _!) , and the condition is also satisfied

. In this case, the contrast

к единице (см. [65]). Это требование выполняется при условии

где V = 0, 1, 2, 3, ... . Частный случай V = 0 - это случай, когда величина

мала 6 ^xt /t of the moire structure (Y, 1) in the plane z = Z _Ni will have a value that is not much less than the value of its contrast in the GO zone, if the value is close in modulus

to one (see [65]). This requirement is satisfied provided that

where V = 0, 1, 2, 3, ... . The special case V = 0 is the case when the quantity

small

[65]). Контраст муаровых структур (1,1) и (2,1), формируемых проекционным устройством 1 в зоне дифракции Френеля, при освещении решеток 7 и 8 немонохроматическим светом будет меньше, чем их контраст в случае, когда решетки освещаются монохроматическим светом. Уменьшение контраста муаровых структур будет не очень значительным, если излучаемый осветителем свет имеет полуширину спектра по длине волны, ограниченную условием , например, в случае АЛ меньше

1 (e.g. < 0.2 — — (Л —>) ); it corresponds to the approximation of geometric optics for describing the characteristics of LM structures. At r > 1, i.e. in the Fresnel zone of the projection device, the contrast of the moire structures (1,1) and (2,1) in the planes z = Z _Nl will exceed, respectively, 0 C 21 (z 21 ) and 0.7C ₂₁ (z ₂₁ ) , if the distance between the gratings varies within the intervals

[65]). The contrast of the moiré structures (1,1) and (2,1) formed by the projection device 1 in the Fresnel diffraction zone, when gratings 7 and 8 are illuminated with non-monochromatic light, will be less than their contrast in the case when the gratings are illuminated with monochromatic light. The decrease in the contrast of the moiré structures will not be very significant if the light emitted by the illuminator has a spectral half-width in wavelength limited by the condition , for example, in the case of AL less than

1

могут формироваться при освещении решеток немонохроматическим светом с шириной спектра несколько десятых долей Яд . 0, 4Л ₀ ~ 0, Лй^ the decrease in contrast compared to C _Nl (z _Nl ) will be no more than two times [64, 67], here v ₁ = 1, 2, 3, ... . From this estimate it follows that at a distance between gratings 7 and 8 less than 2, 21^. moire structures (1,1) and (2,1) with contrast

can be formed when the gratings are illuminated with non-monochromatic light with a spectrum width of several tenths of a Yad.

полушириной спектра по длине волны ЛЯ меньше, чем О ЯдЦ^¹ . Thus, if the LM structure (1,1) is used for rangefinding and profilometry in the Fresnel diffraction zone of the projection device, then, according to clause 38 of the formula of the invention, it is preferable that the distance between the amplitude gratings with sinusoidal transmission installed in the projection device be within the ranges from (i, - 0, 2) Lj. (YaD) to (ij + 0, 2) 1^ ( _YaO ), and the illuminator installed in the projection device emits light with a spectral half-width by wavelength ΔY less than 0 YaD1^ ^1. When using the LM structure (2,1), according to clause 39 of the formula of the invention, it is preferable that the distance between the first and second amplitude gratings with sinusoidal transmission be within the ranges from (and the illuminator emits light with

the half-width of the spectrum at wavelength LA is less than 0 ЯдЦ^ ¹ .

The greatest value of the contrast of the moire structure (1,2), in contrast to the moire structures (1,1) and (2,1), depends weakly on the distance between gratings 7 and 8 and their periods, as well as the wavelength and the width of the spectrum of light emitted by the illuminator [65]. In the particular case when the half-width of the angular spectrum of light emitted by the illuminator is less than 30° and the light source is located close to the first grating 2/? ^{2 2}

, (for example, L _o < 0.2 — — ) the contrast value of the moire structure (1.2) in the Y Y plane z = z ₁₂ will be from 0.21 to 0.25 for arbitrary values of the width of the frequency spectrum of light emitted by the illuminator, as well as the distance between the gratings and their periods [65].

= 22,5 см . Длина Lj.

равна 25 см. При указанных выше параметрах проекционного устройства 1 ЛМ структуры будут формироваться в зоне дифракции Френеля, так как Д « 0,9Д, (Д) . Для муаровой структуры (1,1) параметр V равен 1. Пространственный период муаровой структуры (1,1) равен

0,5 мм. Эта муаровая структура будет иметь наибольший контраст в плоскости, удаленной от второй решетки на расстояние Д[ = 22,5 см. Величина Cjj

превышает 0,6. Угловой размер половины апертуры осветителя 0_sx равен 48°. Он больше, чем полуширина углового спектра света, излучаемого элементами рабочей поверхности осветителя 6, 0_sx > в_хт . Глубина резкости муаровой структуры (1,1) примерно равна Д « 1,7Д =0,8 мм. Относительная глубина резкости ЛМ структуры (1,1) равна АД^Д! - 0,34 10’². Ширина центральной области ЛМ структуры (1,1) равна примерно D_u « 67 см. Пространственный период муаровой структуры (1,2) равен Р₁₂ = 0,17 мм. Эта муаровая структура имеет наибольший контраст на расстоянии Д₂ = 7,5 см от проекционного устройства. Наибольшее значение контраста муаровой структуры (1,2) примерно равно 0,23. Глубина резкости муаровой структуры (1,2) равна ДД₂ ® 1,7Д₂ = 0,3 мм, ее относительная глубина резкости равна ^² - 0,4 -10~² . ШиринаIn the second numerical example, we will determine the characteristics of the moiré structures formed in the Fresnel diffraction zone by the projection device 1 with two amplitude gratings with sinusoidal transmission. We assume that the period of the first grating 7 is equal to = 0.5 mm, the period of the second grating 8 is equal to p ₂ = 0.25 mm, = C ₂ = 1 . Both gratings are thin. The central wavelength of the light emitted by the illuminator 6 is equal to λd = 0.5 μm, the half-width of the light spectrum λa is equal to 0.1 μm. The half-width of the angular spectrum of light emitted by the elements of the surface of illuminator 6 is 0^ = 20°. Illuminator 6 is located close to the first grating L _o = 0. Light source 6 and gratings 7 and 8 have a working aperture width equal to H _x - D _lx - D _2X = 1 M. The distance between the gratings is

= 22.5 cm. Length Lj.

equals 25 cm. With the above parameters of the projection device, 1 LM structures will be formed in the Fresnel diffraction zone, since D « 0.9D, (D). For the moire structure (1,1), the parameter V is equal to 1. The spatial period of the moire structure (1,1) is equal to

0.5 mm. This moire structure will have the greatest contrast in the plane removed from the second grating at a distance of D[ = 22.5 cm. The value of Cjj

exceeds 0.6. The angular size of half the aperture of the illuminator 0 _sx is equal to 48°. It is greater than the half-width of the angular spectrum of light emitted by the elements of the working surface of the illuminator 6, 0 _sx > 6 _хт . The depth of field of the moire structure (1.1) is approximately equal to D « 1.7D = 0.8 mm. The relative depth of field of the LM of the structure (1.1) is equal to ΔΔ^Δ! - 0.34 10' ² . The width of the central region of the LM of the structure (1.1) is equal to approximately D _u « 67 cm. The spatial period of the moire structure (1.2) is equal to P ₁₂ = 0.17 mm. This moire structure has the greatest contrast at a distance of D ₂ = 7.5 cm from the projection device. The greatest contrast value of the moire structure (1.2) is approximately equal to 0.23. The depth of field of the moire structure (1.2) is equal to DD ₂ ® 1.7D ₂ = 0.3 mm, its relative depth of field is equal to ^ ² - 0.4 -10~ ² . Width

The central region of the LM structure (1,2) is equal to D _n = 78 cm. If, without changing the other parameters of the projection device 1, the distance from the first grating 7 to the second grating 8 is made equal to 45 cm, then the moire structure (1,2) will have a maximum contrast in the plane located at a distance of D ₂ = 15 cm from the projection device. The angular size of half the working aperture of the illuminator 0 _sx in this case is equal to 40°. It is greater than the half-width of the angular spectrum of light emitted by the elements of the illuminator surface, 0 _SX > _π . At D = 45 cm, the width of the central region of the LM structure (1,2) is equal to D ₁₂ = 62 CM, its relative depth of field is equal to

A projection device with parameters at which the LM structure according to claim 3 of the invention formula is formed in its Fresnel diffraction zone is preferably used for rangefinding and profilometry in cases where there is a need to minimize the period and relative depth of field of the LM structure, provided that the plane of greatest contrast of the LM structure is located at a given distance from the projection device. An advantage of implementing the method according to claim 3 of the invention formula may also be that in this case it is possible to form and use for rangefinding and profilometry an LM structure with a given, for example, optimal for measurements, spatial period, which is removed from the projection device at a relatively large distance, which is at least greater than the distance from the projection device to the boundary of its GO zone. Specific features of implementing the method according to claim 3 of the invention formula. 3 formulas of the invention are related, in particular, to restrictions for LM structures (N,M) with an odd value of the index M on the width of the frequency spectrum of light, as well as on the range of variation of the distances between gratings and/or their periods.

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Claims

43 Invention formula 1. A method for contactless ranging and profilometry, which includes projecting onto the surface of an object a periodic moiré light structure formed using a projection device containing a spatially extended light source, which is also called an illuminator, as well as a first, closest to the light source, and a second, output, flat grating with a spatially periodic dependence of the transmittance, recording using an image recording device an image of the surface of the object onto which this periodic moiré structure is projected, calculating by a computing device the dependence of the brightness of the image of the surface of the object on the coordinates in the image, characterized in that at least one moiré structure is formed and projected onto the object, localized in a direction that is perpendicular to the plane of the output grating and which is called longitudinal, where the localization of the moiré structure means that the smallest depth of field of this moiré structure is at least four times less than the distance from the plane of the output grating of the projection device to a plane parallel to it, on which the contrast of this moiré structure has the greatest value, is found by mathematical processing of the image of the surface of the object, the isoline of the greatest contrast of the projection onto the object of the localized moire (LM) structure, moving the projection of the LM structure along the surface of the object, combining the isoline of the greatest contrast of the projection of the LM structure with one or more points on the surface of the object, determining the longitudinal coordinates of these points, using for this the known value of the distance from the plane of the output grating of the projection device to the plane of the greatest contrast of the LM structure, finding the values of the transverse coordinates of the points of the surface of the object and its shape, using for this the found values of their longitudinal coordinates and the image of the object. 2. The method according to claim 1, characterized in that at least one localized moire structure is formed in the area of the geometric optics of the projection device. 3. The method according to claim 1, characterized in that at least one localized moire structure is formed in the Fresnel diffraction region of the projection device. 44 4. The method according to claim 1, characterized in that a localized moire structure designated by indices (N, M), where N and M are natural numbers, is projected onto the surface of the object, which is formed using a projection device that includes a spatially extended light source, as well as a first, closest to the light source, and a second, output, flat one-dimensional gratings that are located in parallel planes on one side of the light source, wherein these gratings have the same direction of stripes along which the transverse y-axis is directed, and a periodic dependence of the amplitude transmittance on the transverse coordinate x, perpendicular to the direction of their stripes, determine the dependence of the contrast of a quasi-periodic change in the brightness of the image of the object's surface in the direction of the x-axis on the coordinates in the image, and take into account that the spatial period of the change in the brightness of the object's surface in the direction of the x-axis is equal to the period P _NM of the moire structure (N, M), which is calculated using the formula

where R _NM = Mp Np ₂ > 1 , and ₂ are the periods of the first and second gratings, respectively, the distance from the plane of the output grating to the plane where the contrast of the moire structure (N, M) is maximum is calculated using the formula

where is the distance between the planes of the first and second lattices; based on these data, the longitudinal coordinates of the points located on the isoline of the greatest contrast of the projection of the moire structure (N, M~) are determined. 5. The method according to item 4, characterized in that at least one of the LM structures is used for its implementation: (1,3), (1,2), (1,1), (2,1) and (3,1). 6. The method according to claim 1, characterized in that for its implementation at least one LM structure is used, the greatest contrast value of which exceeds 0.2. 7. The method according to item 1, characterized in that, using one projection device, several localized moire structures are formed, and their projections are simultaneously or sequentially moved over the surface of one or more objects. 45 8. The method according to paragraph 1, characterized in that the movement of the projection of one or more LM structures along the surface of the object is carried out by means of translational movement of the projection device or object. 9. The method according to item 1, characterized in that the movement of the projection of one or more LM structures along the surface of the object is carried out by rotating the projection device and/or the object. 10. The method according to item 1, characterized in that the movement of the projection of one or more localized moire structures along the surface of the object is carried out by changing the distance from the plane of the output grating of the projection device to the plane of greatest contrast of the LM structure. 11. The method according to item 4, or item 10, characterized in that the change in the distance from the plane of the output grating of the projection device to the plane of greatest contrast of the LM structure is carried out by changing the distance between the first and second gratings installed in the projection device. 12. The method according to item 4, or item 10, characterized in that the change in the distance from the plane of the output grating of the projection device to the plane of greatest contrast of the LM structure is carried out by changing the spatial period of at least one of the gratings installed in the projection device. 13. The method according to item 1, characterized in that the isoline of greatest contrast of the projection of at least one LM structure is moved along the entire controlled part of the surface of the object, and at each position of the isoline of greatest contrast, the coordinates of a set of points of the surface located on this isoline are determined. 14. The method according to item 4, characterized in that a localized moire structure (N, M) is formed using a projection device for this purpose, which includes first and second thin amplitude gratings, as well as an illuminator with a flat homogeneous luminous surface, which is parallel to the planes of the gratings and has the shape of a rectangle with sides parallel to the x and y axes, wherein the half-width in the y plane = y _s of the angular spectrum of the light emitted by the illuminator is 6 _xm 71 less — , and the frames limiting the first and second gratings do not vignette the illuminator in the direction of the x-axis when it is observed from the central region of the LM structures (N, M), estimate the depth of field of this LM structure at |x| < 0.5 D^ _M using the formula

where D _NM is the width of the central region of the moire structure (N, M), which is calculated using the formula

0 _Ex is the smallest of the values 0 _sx and 6 _xt , 0 _sx - angular size in the plane y = y _s of half the aperture of the working surface of the illuminator, equal to

H _x - aperture width of the working surface of the illuminator, L _o is the distance between the plane of the working surface of the light source and the plane of the first grating, y _s is the coordinate of the center of the working surface of the illuminator along the y axis. 15. The method according to item 1, characterized in that for its implementation a localized moire structure is formed, the smallest relative depth of field of which is less than three percent. 16. A rangefinding and profilometry system comprising at least one image recording device, a computing device and a projection device containing a spatially extended source of incoherent light, first and second flat periodic gratings which are located in parallel planes on one side of the light source and which are illuminated by said light source, wherein the light that has passed through the first grating falls on the second grating, characterized in that the system uses at least one device for moving the isoline of the greatest contrast of the projection of the LM structure formed by the projection device along the surface of at least one object. 17. The system according to claim 16, characterized in that it uses a projection device in which one-dimensional periodic gratings are used as the first and second gratings, with their stripes directed parallel. 18. The system according to item 16, characterized in that a diffuse light source is used as an illuminator in the optical projection device. 19. The system according to item 16, characterized in that it additionally uses a device for determining the coordinates and orientation of the projection device in the global coordinate system. 20. The system according to item 16, characterized in that it uses at least one device that carries out the translational movement of the projection device and/or object and determines the magnitude of this movement. 21. The system according to claim 16, characterized in that it uses at least one device that rotates the projection device or object and determines the magnitude of this rotation. 22. The system according to item 16, characterized in that it uses a device that controllably changes the distance between the planes of the first and second gratings installed in the projection device. 23. The system according to claim 17, characterized in that a device is additionally used that controllably moves at least one of the gratings installed in the projection device along the transverse coordinate x, perpendicular to the direction of the grating strips. 24. The system according to claim 16, characterized in that the optical axis of at least one image recording device is parallel to the longitudinal axis of the projection device. 25. The system according to item 16, characterized in that it uses a projection device in which at least one amplitude grating is installed. 26. The system according to claim 17, characterized in that it uses a projection device in which at least one amplitude grating is installed with a sinusoidal dependence of the magnitude of the change in the amplitude transmittance coefficient on the transverse coordinate. 27. The system according to claim 17, characterized in that it uses a projection device in which an amplitude binary raster is used as at least one grating. 28. The system according to claim 16, characterized in that it uses a projection device in which at least one grating is a phase grating. 48 29. The system according to claim 16, characterized in that it uses a projection device in which the characteristics of at least one grating can be changed. 30. The system according to claim 16, characterized in that it uses a projection device in which a spatial light modulator is used to form at least one grating. 31. The system according to item 17, characterized in that it uses a projection device in which the first and second gratings are amplitude gratings. 32. The system according to item 16, characterized in that it uses a projection device in which thin first and second gratings are installed, when passing through which the angular spectrum of light emitted by the illuminator narrows by less than 20%. 33. The system according to item 17, characterized in that the projection device uses an illuminator with a uniform flat luminous surface that is parallel to the planes of the gratings and has the shape of a rectangle with sides parallel to the x and y axes. 34. The system according to item 31, characterized in that for the formation of the LM structure (N, M), a projection device is used in it, in which the first and second gratings are located at a distance from each other L T, less than P1P2 >

I _t = D, + DY, DY is the central wavelength of light emitted by the illuminator, AL is the half-width of its spectrum by wavelength. 35. The system according to item 31, characterized in that it uses a projection device in which the first and second gratings have a sinusoidal dependence of the magnitude of the change in the amplitude transmittance on the x coordinate. 36. The system according to item 33, characterized in that the projection device uses an illuminator, first and second thin amplitude gratings with angular dimensions in the plane y = y _s greater than the width in this plane of the angular spectrum of light emitted by the illuminator, where the said angular dimensions of the illuminator and gratings are determined from the center of the plane in which the contrast of the LM structure used for measurements is maximum. 37. The system according to item 33, characterized in that it uses a projection device in which first and second thin amplitude gratings are installed with an angular size in the plane y = const greater than the angular size of the working aperture. 49 illuminator, and an illuminator is installed, for which the tangent of the angular size in the plane y = const of half of its working aperture and the tangent of the half-width in this plane of the angular spectrum of the light emitted by it exceed the ratio p ¹ NM NM by more than five times 38. The system according to item 35, characterized in that it uses a projection device that uses a light source with a spectrum half-width in wavelength λλ less than 0.4 L _{o 1} ⁴ , a first grating with a spatial period greater than the spatial period of the second grating p _} > p ₂ , and the first and second gratings are located at a distance from each other within the ranges (vj -0,

(vj + 0.2)/^ (2ts) , where Vj = 1, 2, 3, ... . 39. The system according to claim 35, characterized in that it uses a projection device in which a light source with a spectrum half-width in wavelength λλ less than 0.4 _o r ₁ ^-1 , a first grating with a spatial period greater than twice the spatial period of the second grating d >2/> ₂ , and the first and second gratings are located at a distance from each other within the ranges from ( , -0.2)144) _{to (} „ _{] + 0} , 2)1441.