RU2496098C2 - Device to define angular deviation of laser beam axis from nominal position - Google Patents

Abstract

FIELD: measurement equipment.

SUBSTANCE: device comprises a prism system consisting of the first pair of pentaprisms including the first and the second pentaprisms principal cross-sections of which are located in one plane P, an optical wedge glued to the first reflecting face of the first pentaprism and made so that its output face is parallel to the input face of the first pentaprism and the glued area surface is fitted with beam-splitting coating, the second pair of pentaprisms including the third and the fourth pentaprisms principal cross-sections of which are located in one plane P'. The input face of the third pentaprism is located beyond the output face of the optical wedge and is parallel to it. The planes P and P' are placed at the angle 2φ to each other. The second and the fourth pentaprisms are optically connected to the objective lens in the focal plane of which a coordinate-sensitive detector is installed with its output being connected to a microprocessor input.

EFFECT: determination of angular deviation of a laser beam using a high-energy laser along with the simultaneous decrease of its beam cross-section screening in the conditions of external mechanical impacts which lead to angular shifts of the prisms of the prism system.

2 cl, 6 dwg

Description

The invention relates to the field of optical instrumentation, more specifically to optical prism systems designed to determine the angular deviation of the axis of the laser beam from the nominal position.

The optical axis of the receiving and transmitting channels of the laser systems must be set with the necessary accuracy. In some cases, this can be achieved at the stage of factory adjustment. Such systems include small-sized optical rangefinders, laser vision systems. They are distinguished by relatively low requirements for alignment of the channel axes - exhibition errors can reach several angular minutes.

For a number of modern location systems, very high demands are placed on the accuracy of alignment of the transceiver channels - the errors of their mutual exhibition should not exceed a few angular seconds. As a rule, such systems have significant dimensions, weight, they can be exposed to external mechanical vibrations and thermal withdrawal of structural elements. Requirements for the accuracy of the alignment of the channels of such systems can be fulfilled only with the use of auto-alignment systems (SAU).

The principle of organizing a similar SAY is as follows. A part of the radiation beam of the working laser of the transmitting channel at the output of the formation system with the help of a prism system (PS) is brought into the receiving channel, changing the direction of propagation exactly the opposite. The diverted beam in the receiving channel is a reference point for the spatial position of the axis of the radiation pattern of the working laser formed in the transmitting channel. In the receiving channel, its angular mismatch with the axis of the receiving channel is measured, which is processed in real time by the correcting elements of the optical system.

In most cases, it is advisable to divert the radiation beam not from the working laser, but from an additional marker radiation source, which has much lower power and transverse dimensions. Previously, its axis is set at the input of the optical system of the transmitting channel relative to the axis of the working laser radiation beam with high accuracy.

As can be seen, the errors in determining the angular mismatch are determined by the error in the beam transfer; therefore, the PS in such an SAU plays a key role. The schemes of their construction should be justified taking into account the operating conditions, and the accuracy characteristics of each scheme should be carefully investigated.

It is known that a corner reflector with dihedral angles between the reflecting faces equal to 90 ° is an ideal retroreflector [Baryshnikov N.V., Karasik V.E., Stepanov PO Study of the reflective characteristics of tetrahedral retroreflectors in the infrared range. Bulletin of MSTU. N.E.Bauman. Ser. "Instrument Engineering", 2010. No. 1, S.3-16]. It reflects the radiation incident on it in exactly the opposite direction (see figa). The matrix M _{UO of} its action has the following form:

$$M_{\mathrm{At}\mathrm{ABOUT}}=\left(\begin{array}{ccc}-\mathrm{one}& 0& 0\\ 0& -\mathrm{one}& 0\\ 0& 0& -\mathrm{one}\end{array}\right)\left(\mathrm{one}\right)$$

Theoretically, this is an ideal PS option. However, the transfer distance a of the axis of the radiation beam is minimal and it is limited by the design parameters of the corner reflector and the technological capabilities of its manufacture.

Modification of the design of the corner reflector - UO with spaced entrance and exit pupils (see fig.1b) provides somewhat larger values of the transfer distance a - up to 100 ... 200 mm. On this, the capabilities of the corner reflector are limited.

A device for determining the angular deviation of the axis of the laser beam from the nominal position (see figure 2), which is the closest analogue and includes a prism system containing optically coupled rhombus prism 1, corner reflector and rhombus prism 2 (N.V. Baryshnikov, V.V. Karachunsky, V.I. Kozintsev A.S. Rumyantsev, D.V. Khudyakov, Using semi-natural modeling methods to study the characteristics of the auto-alignment system Abstracts of the IV NTK “Radio-optical technologies in instrument engineering”, Sochi, 2006, p. .105-108). This system provides large transport distances a .

An ideally made rhombus-prism transversely displaces the axis of the incident beam without changing its direction. The matrix of its action M _RP has the following form:

$$M_{RP}=\left(\begin{array}{ccc}\mathrm{one}& 0& 0\\ 0& \mathrm{one}& 0\\ 0& 0& \mathrm{one}\end{array}\right)$$

The action of the considered PS can be described by the matrix M:

$$M=M_{RP2}\cdot M_{\mathrm{At}\mathrm{ABOUT}}\cdot M_{RP\mathrm{one}}=\left(\begin{array}{ccc}-\mathrm{one}& 0& 0\\ 0& -\mathrm{one}& 0\\ 0& 0& -\mathrm{one}\end{array}\right)=\text{A.}{M}_{\mathrm{At}\mathrm{ABOUT}}$$

It is easy to see that the matrix M corresponds to the matrix of the angular reflector (1).

At low intrinsic angular displacements, each of the three optical parts of the circuit ideally transfers the beam axis; therefore, such a system is invariant to mechanical vibrations and thermal displacements of mechanical frames. The transfer quality can be affected only by the own temperature deformations of the corner reflector and rhombus prisms, as well as the errors of their manufacture.

To increase the transfer distance a, additional rhombic prisms can be included in the PS scheme. Their maximum number is determined only by the light transmission of the prism system, as well as weight and size restrictions.

However, there is a fundamental drawback of the above schemes. It is due to the fact that the structural elements of the PS can be located at the output of the forming optical system of the transmitting channel, in the cross section of the beam of a high-energy working laser. This circumstance causes numerous problems associated with protecting the design of the PS itself from radiation from the working laser, as well as with violations of the spatial structure of the generated beam of the working laser caused by its shielding.

The technical result achieved by the implementation of the present invention consists in providing the possibility of determining the angular deviation of the axis of the laser beam from the nominal position when using a high-energy laser and at the same time reducing the shielding of the beam cross section under external mechanical stresses leading to angular withdrawals of the prism prism system.

The specified technical result is achieved due to the fact that in the device for determining the angular deviation of the axis of the laser beam from the nominal position containing the prism system, said prism system includes a first pair of pentaprisms containing the first and second pentaprisms, the main sections of which are located in the same plane P, optical a wedge glued to the first reflecting face of the first pentaprism and made so that its output face is parallel to the input face of the first pentaprism, and the gluing surface there is a beam splitting coating, a second pair of pentaprisms containing the third and fourth pentaprisms, the main sections of which are located in the same plane P ', while the input face of the third pentaprism is located behind the output face of the optical wedge and parallel to it, the plane P and P' are at an angle 2φ each to a friend, and the second and fourth pentaprisms are optically connected to the lens, in the focal plane of which is a coordinate-sensitive photodetector, the output of which is connected to the input of the microprocessor.

In this case, the microprocessor can be configured to calculate the angular deviation θ _Z , θ _{Y of the} axis of the controlled beam from the nominal position at the input of the first pentaprism according to the formulas:

θ _z = (- θ _y1 sinφ + θ _z1 cosφ + θ _y2 sinφ + θ _z2 cosφ) / 2cosφ,

θ _y = (θ _y2 sinφ + θ _z2 cosφ + θ _y1 sinφ-θ _z1 cosφ) / 2sinφ,

where θ _y1 ; θ _z1 is the angular deviation from the nominal position of the axis of the laser beam that has passed the first and second pentaprisms;

θ _y2 ; θ _z2 is the angular deviation from the nominal position of the axis of the laser beam that has passed the first, third, and fourth pentaprisms.

In the proposed device due to the fact that instead of a prism system in the form of a monoblock, as in the closest analogue, separate pentaprisms are used, a reduction in the screening of the cross section of its beam is provided. At the same time, the optical properties of the pentaprism make it possible to create a prism system that ensures the determination of the angular deviation of the axis of the laser beam from the nominal position under external mechanical influences, which lead to angular withdrawals of the prism of the prism system.

The invention is described in more detail using the drawings.

On figa, 1b shows a prism system based on an angular reflector.

Figure 2 shows the prism system of the closest analogue based on a corner reflector and two diamond prisms.

Figure 3 shows the location of the prism system of the device for determining the angular deviation of the axis of the laser beam from the nominal position in the location station.

Figure 4 shows a diagram illustrating the determination of the angular deviation from the nominal position of the axis of the laser beam using a coordinate-sensitive photodetector in the absence of angular withdrawals of the prism of the prism system.

Figure 5 shows the prism system of the proposed device based on two pairs of pentaprism.

по отношению к входной грани пентапризмы.Figure 6 shows the location of the XYZ coordinate system and the associated normal $$\overline{N}$$

in relation to the input face of the pentaprism.

Figure 4 shows a diagram illustrating the determination of the angular deviation from the nominal position of the axis of the laser beam using a coordinate-sensitive photodetector in the absence of angular withdrawals of the prism of the prism system.

The XYZ coordinate system is connected with the optical axis of the system formed by the lens and coordinate-sensitive, for example, an array photodetector located in its focal plane. The coordinate center O coincides with the zero sensitive element of the matrix photodetector. In this case, the element located in the center of the matrix of sensitive elements is usually used as the zero element. The OX axis of the selected XYZ coordinate system coincides with the optical axis of the system formed by the lens and the matrix photodetector located in its focal plane and passes through the cardinal points of the lens and the zero element of the matrix photodetector.

Thus, in order to determine the angular deviation of the beam axis in two coordinates, it is necessary to measure the linear coordinates Z1 and Y1 recorded on the matrix photodetector located in the focal plane of the lens, the distribution spot from the controlled laser beam. In this case, the angular deviation θ _Y in the XOY plane can be determined from the mathematical expression

tg (θ _Y ) = Y1 / f ',

where f 'is the focal length of the lens.

Similarly, the angular deviation θ _Z in the XOZ plane (not shown in FIG. 4) can be determined from a mathematical expression

tg (θ _Z ) = Z1 / f '.

Moreover, as a rule, the measured angular deviations are small, they amount to several angular seconds. Therefore, the tangent can be neglected, i.e. use the following expressions:

θ _Y = Y1 / f ', θ _Z = Z1 / f'

Figure 5 shows the prism system of the proposed device based on two pairs of pentaprism.

As you know, pentaprism changes in space the direction vector of the incident beam by 90 degrees along one axis, and this angle is invariant to the small angular withdrawal of the pentaprism itself. Using a pair of pentaprisms, it is possible to provide a back reflection of the laser radiation and measure the angular deviation in the receiving channel, but only along one axis.

To measure the angular deviations along two axes under external mechanical stresses leading to angular withdrawals of the prisms themselves, a device is proposed that includes a prism system including a first pair of pentaprisms containing the first 1 and second 2 pentaprisms. The main sections of these pentaprisms are located in the same plane P. The second pair of pentaprisms contains the third 3 and fourth 4 pentaprisms, the main sections of which are located in the same plane P '. The planes P and P 'are located at an angle of 2φ to each other. Separation of the laser beam between the pairs of prisms is carried out using an optical wedge 5, having the same refractive index as the first 1 pentaprism, and glued to the first reflecting face of the first 1 pentaprism, the gluing surface 6 has a beam-splitting semi-reflective coating, and the output face of the wedge is parallel to the input facets of the first 1 pentaprism. The input face of the third 3 pentaprism is located beyond the output face of the optical wedge 5 and parallel to it. At the output of the second 2 and fourth 4 pentaprism, a lens 7 is located, in the focal plane of which is a coordinate-sensitive photodetector 8, the output of which is connected to the input of the microprocessor 9.

In this case, the microprocessor is configured to calculate the angular deviation θ _Z , θ _{Y of the} axis of the controlled beam from the nominal position at the input of the first 1 pentaprism according to the formulas:

θ _z = (- θ _y1 sinφ + θ _z1 cosφ + θ _y2 sinφ + θ _z2 cosφ) / 2cosφ,

θ _y = (θ _y2 sinφ + θ _z2 cosφ + θ _y1 sinφ-θ _z1 cosφ) / 2sinφ,

where θ _y1 ; θ _z1 is the angular deviation from the nominal position of the axis of the laser beam, passing the first 1 and second 2 pentaprism;

θ _y2 , θ _z2 is the angular deviation from the nominal position of the axis of the laser beam, passing the first 1, third 3 and fourth 4 pentaprism.

луча, характеризующего направление пучка лазерного излучения на входе в призменную систему, т.е. на выходе передающего канала локационной системы.Let us trace the transformation by such a prism system of a vector $${\overrightarrow{L}}_0$$

beam characterizing the direction of the laser beam at the entrance to the prism system, i.e. at the output of the transmitting channel of the location system.

We connect the coordinate system X ₀ Y ₀ Z ₀ with the optical axis of the lens of the receiving channel. The axis OX _{0 is} directed along the optical axis of the objective of the receiving channel.

, характеризующего направление пучка излучения лазера на входе объектива приемного канала системы. Вектор $${\overrightarrow{L}}_0$$

в системе координат X₀Y₀Z₀ выражается следующим образом:In the same coordinate system, we will further determine the direction of the vector $${\overrightarrow{L}}_{np}$$

, characterizing the direction of the laser beam at the input of the lens of the receiving channel of the system. Vector $${\overrightarrow{L}}_0$$

in the coordinate system X ₀ Y ₀ Z ₀ is expressed as follows:

$${\overrightarrow{L}}_0=\left(\begin{array}{c}-\mathrm{one}\\ {\theta }_y\\ {\theta }_z\end{array}\right),\left(5\right)$$

where θ _y and θ _z are the angles of deviation of the laser radiation axis from the ideal direction, caused by misalignments of the system. These angles must be measured in the receiving channel.

направления оси излучения лазера парой пентапризм, пространственное положение каждой из которых имеет отступления от идеального.We obtain several general expressions for the pentaprism transformation matrices. These expressions will be used below to describe the transformation of the vector $$\overrightarrow{L}$$

the direction of the laser radiation axis by a pair of pentaprisms, the spatial position of each of which has deviations from the ideal.

к входной грани пентапризмы.Consider the coordinate system XYZ (see Fig.6) and the associated normal $$\overline{N}$$

to the entrance face of the pentaprism.

1. The matrices P 'and P' 'of the action of the ideal pentaprism, respectively, in the forward and reverse directions, recorded in the reduced coordinate system, are determined in a known manner [Computational optics: Reference / MM. Rusinov, A.P. Grammatin, P.D. Ivanov and others. Under the general. ed. M.M. Rusinova. - L .: Mechanical engineering. Leningrad branch, 1984, p.110] as:

$$P\text{'}\text{'}=\left(\begin{array}{ccc}0& 0& -\mathrm{one}\\ 0& \mathrm{one}& 0\\ \mathrm{one}& 0& 0\end{array}\right),P\text{'}\text{'}\text{'}\text{'}\left(\begin{array}{ccc}0& 0& \mathrm{one}\\ 0& \mathrm{one}& 0\\ -\mathrm{one}& 0& 0\end{array}\right)\left(6\right)$$

в рассматриваемой системе координат. Будем считать, что повороты происходят в следующей последовательности:The instability of the spatial position of the pentaprism leads to a rotation of the vector $$\overline{N}$$

in the coordinate system under consideration. We assume that the turns occur in the following sequence:

- around the axis OZ at an angle α;

- around the new axis OY 'at an angle β;

- around the new axis OX '' at an angle γ.

The transformation matrices corresponding to these rotations are as follows [Computational Optics: Reference / MM. Rusinov, A.P. Grammatin, P.D. Ivanov and others. Under the general. ed. M.M. Rusinova. - L .: Mechanical engineering. Leningrad branch, 1984, p.121]:

$$M_z=\left(\begin{array}{ccc}\cos \alpha & -\sin \alpha & 0\\ \sin \alpha & \cos \alpha & 0\\ 0& 0& \mathrm{one}\end{array}\right);M_y=\left(\begin{array}{ccc}\cos \beta & 0& -\sin \beta \\ 0& \mathrm{one}& 0\\ \sin \beta & 0& \cos \beta \end{array}\right);M_x=\left(\begin{array}{ccc}\mathrm{one}& 0& 0\\ 0& \cos \gamma & \sin \gamma \\ 0& -\sin \gamma & \cos \gamma \end{array}\right)(7)$$

описывается матрицей M:The action of all three turns on an arbitrary vector $$\overline{N}$$

is described by the matrix M:

$$M=M_x\cdot M_y\cdot M_z\left(8\right)$$

- вектор падающего на пентапризму луча, записанный в системе координат XYZ. Тогда вектор $$\overrightarrow{L}\text{'}$$

луча, преобразованного пентапризмой, пространственное положение которой имеет отступления от номинального, можно определить следующим образом:Let be $$\overrightarrow{L}$$

is the vector of the ray incident on the pentaprism recorded in the XYZ coordinate system. Then the vector $$\overrightarrow{L}\text{'}\text{'}$$

a beam transformed by a pentaprism, the spatial position of which has deviations from the nominal, can be determined as follows:

$$\overrightarrow{L}\text{'}\text{'}=\left(M\cdot P\text{'}\text{'}\cdot M^{-\mathrm{one}}\right)\cdot \overrightarrow{L}=T\cdot \overrightarrow{L},\left(9\right)$$

where: T = M · P '· M ^-1 ;

We assume that the rotation angles α, β, γ in the circuit are small. Then, up to terms of the second order of smallness in rotation angles, taking into account (7) and (8), we can write the expressions for M and M ^-1 :

, $$M=\left(\begin{array}{ccc}\mathrm{one}& -\sin \alpha & -\sin \beta \\ \sin \alpha & \mathrm{one}& \sin \gamma \\ \sin \beta & -\sin \gamma & \mathrm{one}\end{array}\right)=\left(\begin{array}{ccc}\mathrm{one}& -\alpha & -\beta \\ \alpha & \mathrm{one}& \gamma \\ \beta & -\gamma & \mathrm{one}\end{array}\right)$$

,

. $$M^{-\mathrm{one}}=\left(\begin{array}{ccc}\mathrm{one}& \sin \alpha & \sin \beta \\ -\sin \alpha & \mathrm{one}& -\sin \gamma \\ -\sin \beta & \sin \gamma & \mathrm{one}\end{array}\right)=\left(\begin{array}{ccc}\mathrm{one}& \alpha & \beta \\ -\alpha & \mathrm{one}& -\gamma \\ -\beta & \gamma & \mathrm{one}\end{array}\right)$$

.

It follows that

$$T=M\cdot P\text{'}\text{'}\cdot M^{-\mathrm{one}}=\left(\begin{array}{ccc}0& -\alpha -\gamma & -\mathrm{one}\\ -\alpha +\gamma & \mathrm{one}& -\alpha -\gamma \\ \mathrm{one}& \alpha -\gamma & 0\end{array}\right)\left(10\right)$$

будет определяться:Taking into account (9) and (10), at the exit from the pentaprism, the direction of the vector $$\overrightarrow{L}\text{'}\text{'}$$

will be determined:

$$\overrightarrow{L}\text{'}\text{'}=\left(\begin{array}{c}0\\ \alpha -\gamma \\ -\mathrm{one}\end{array}\right)\left(\mathrm{eleven}\right)$$

This vector lies in the XOZ plane (i.e., it is perpendicular to the normal of the beam at the entrance to the pentaprism) and the angle between the OZ axis and this beam is equal to α-γ.

Using the expressions obtained, one can describe the conversion of laser radiation by a pair of pentaprisms, for example, the first 1 and second 2 pentaprisms, each of which has its own random deviations from the nominal position.

(5) записан в системе координат X₀Y₀Z₀. Запишем вектор $${\overrightarrow{L}}_1$$

, соответствующий вектору $${\overrightarrow{L}}_0$$

, но уже в системе координат X₁Y₁Z₁, связанной с первой 1 пентапризмой первой пары пентапризм. Для этого используем известное выражение (7) для матрицы M_φ разворота системы координат вокруг оси OX на угол φ:Vector $${\overrightarrow{L}}_0$$

(5) is written in the coordinate system X ₀ Y ₀ Z ₀ . Write the vector $${\overrightarrow{L}}_{\mathrm{one}}$$

corresponding to the vector $${\overrightarrow{L}}_0$$

, but already in the coordinate system X ₁ Y ₁ Z ₁ associated with the first 1 pentaprism of the first pair of pentaprisms. To do this, we use the well-known expression (7) for the matrix M _{φ of the} rotation of the coordinate system around the axis OX by the angle φ:

$$\begin{array}{l}{\overrightarrow{L}}_{\mathrm{one}}=M_{\phi }\cdot {\overrightarrow{L}}_0=\left(\begin{array}{ccc}\mathrm{one}& 0& 0\\ 0& \cos \phi & \sin \phi \\ 0& -\sin \phi & \cos \phi \end{array}\right)\cdot \left(\begin{array}{c}-\mathrm{one}\\ {\theta }_y\\ {\theta }_z\end{array}\right)=\\ =\left(\begin{array}{c}-\mathrm{one}\\ \cos \phi \cdot {\theta }_y+\sin \phi \cdot {\theta }_z\\ -\sin \phi \cdot {\theta }_y+\cos \phi \cdot {\theta }_z\end{array}\right)=\left(\begin{array}{c}-\mathrm{one}\\ {\theta }_y^{\text{'}\text{'}}\\ {\theta }_z^{\text{'}\text{'}}\end{array}\right)\left(12\right)\end{array}$$

на выходе первой 1 пентапризмы с учетом (10) и (11) находим следующим образом:In the coordinate system X ₁ Y ₁ Z ₁ the beam vector $${\overrightarrow{L}}_{\mathrm{one}}^{\text{'}\text{'}}$$

at the output of the first 1 pentaprism, taking into account (10) and (11), we find as follows:

$${\overrightarrow{L}}_{\mathrm{one}}^{\text{'}\text{'}}=T_{\mathrm{one}}\cdot {\overrightarrow{L}}_{\mathrm{one}}=\left(\begin{array}{ccc}0& -{\alpha }_{\mathrm{one}}-{\gamma }_{\mathrm{one}}& -\mathrm{one}\\ -{\alpha }_{\mathrm{one}}+{\gamma }_{\mathrm{one}}& \mathrm{one}& -{\alpha }_{\mathrm{one}}-{\gamma }_{\mathrm{one}}\\ \mathrm{one}& {\alpha }_{\mathrm{one}}-{\gamma }_{\mathrm{one}}& 0\end{array}\right)\left(\begin{array}{c}-\mathrm{one}\\ {\theta }_y^{\text{'}\text{'}}\\ {\theta }_z^{\text{'}\text{'}}\end{array}\right)=\left(\begin{array}{c}-{\theta }_z^{\text{'}\text{'}}\\ -{\alpha }_{\mathrm{one}}-{\gamma }_{\mathrm{one}}+{\theta }_y^{\text{'}\text{'}}\\ -\mathrm{one}\end{array}\right)$$

where: α ₁ , γ ₁ - the rotation angles of the first prism:

. $$T_{\mathrm{one}}=\left(\begin{array}{ccc}0& -{\alpha }_{\mathrm{one}}-{\gamma }_{\mathrm{one}}& -\mathrm{one}\\ -{\alpha }_{\mathrm{one}}+{\gamma }_{\mathrm{one}}& \mathrm{one}& -{\alpha }_{\mathrm{one}}-{\gamma }_{\mathrm{one}}\\ \mathrm{one}& {\alpha }_{\mathrm{one}}-{\gamma }_{\mathrm{one}}& 0\end{array}\right)$$

.

в вектор $${\overrightarrow{L}}_2$$

, записанный в системе координат X₂Y₂Z₂:We associate with the second 2 pentaprism the coordinate system X ₂ Y ₂ Z ₂ (see Figure 3a), oriented relative to the prism itself in the same way as the coordinate system X ₁ Y ₁ Z _{1 is} oriented relative to the first 1 pentaprism. Transform vector $${\overrightarrow{L}}_{\mathrm{one}}^{\text{'}\text{'}}$$

in vector $${\overrightarrow{L}}_2$$

recorded in the coordinate system X ₂ Y ₂ Z ₂ :

$${\overrightarrow{L}}_2=\left(\begin{array}{c}-\mathrm{one}\\ {\alpha }_{\mathrm{one}}-{\gamma }_{\mathrm{one}}+{\theta }_y^{\text{'}\text{'}}\\ {\theta }_z^{\text{'}\text{'}}\end{array}\right)$$

второй пентапризмой можно записать как:Vector conversion $${\overrightarrow{L}}_2$$

the second pentaprism can be written as:

$$\begin{array}{l}\overrightarrow{L_2^{\text{'}\text{'}}}=T_2\cdot \overrightarrow{L_2}=\left(\begin{array}{ccc}0& -{\alpha }_2-{\gamma }_2& -\mathrm{one}\\ -{\alpha }_2+{\gamma }_2& \mathrm{one}& -{\alpha }_3-{\gamma }_2\\ \mathrm{one}& {\alpha }_2-{\gamma }_2& 0\end{array}\right)\left(\begin{array}{c}-\mathrm{one}\\ {\alpha }_{\mathrm{one}}-{\gamma }_{\mathrm{one}}+{\theta }_y^{\text{'}\text{'}}\\ {\theta }_z^{\text{'}\text{'}}\end{array}\right)=\\ =\left(\begin{array}{c}-{\theta }_z^{\text{'}\text{'}}\\ \left({\alpha }_{\mathrm{one}}-{\gamma }_{\mathrm{one}}\right)+\left({\alpha }_2-{\gamma }_2\right)+{\theta }_y^{\text{'}\text{'}}\\ -\mathrm{one}\end{array}\right)\end{array}$$

where: α ₂ , γ ₂ - the rotation angles of the second prism;

. $$T_2=\left(\begin{array}{ccc}0& -{\alpha }_2-{\gamma }_2& -\mathrm{one}\\ -{\alpha }_2+{\gamma }_2& \mathrm{one}& -{\alpha }_2-{\gamma }_2\\ \mathrm{one}& {\alpha }_2-{\gamma }_2& 0\end{array}\right)$$

.

We write this vector in the coordinate system X ₁ Y ₁ Z ₁ (see Figure 3a):

$${\overrightarrow{L}}_2^{\text{'}\text{'}\ast }=\left(\begin{array}{c}\mathrm{one}\\ \left({\alpha }_{\mathrm{one}}-{\gamma }_{\mathrm{one}}\right)+\left({\alpha }_2-{\gamma }_2\right)+{\theta }_y^{\text{'}\text{'}}\\ -{\theta }_z^{\text{'}\text{'}}\end{array}\right)\left(13\right)$$

луча на входе в приемную систему, записанный в системе координат X₀Y₀Z₀:And finally, we write it in the coordinate system X ₀ Y ₀ Z ₀ using the rotation matrix around the axis OX (7) by the angle -φ. Thus, we obtain the desired vector $${\overrightarrow{L}}_{np}$$

beam at the entrance to the receiving system, recorded in the coordinate system X ₀ Y ₀ Z ₀ :

$$\begin{array}{l}\overrightarrow{L_{np}}=M_{\left(-\varphi \right)}{\overrightarrow{L}}_2^{\text{'}\text{'}\ast }=\left(\begin{array}{ccc}\mathrm{one}& 0& 0\\ 0& \cos \left(-\varphi \right)& \sin \left(-\varphi \right)\\ 0& -\sin \left(-\varphi \right)& \cos \left(-\varphi \right)\end{array}\right)\cdot \left(\begin{array}{c}\mathrm{one}\\ \omega +{\theta }_y^{\text{'}\text{'}}\\ -{\theta }_z^{\text{'}\text{'}}\end{array}\right)=\\ =\left(\begin{array}{c}\mathrm{one}\\ \left(\omega +{\theta }_y^{\text{'}\text{'}}\right)\cos \varphi +{\theta }_z^{\text{'}\text{'}}\cdot \sin \varphi \\ \left(\omega +{\theta }_y^{\text{'}\text{'}}\right)\sin \varphi -{\theta }_z^{\text{'}\text{'}}\cdot \cos \varphi \end{array}\right)=\left(\begin{array}{c}\mathrm{one}\\ {\theta }_{ynp}\\ -{\theta }_{znp}\end{array}\right)\left(\mathrm{fourteen}\right)\end{array}$$

where ω = (α ₁ -γ ₁ ) + (α ₂ -γ ₂ ).

на выходе пары пентапризм не позволяют определить искомые угловые отклонения θ_y и θ_z вектора $${\overrightarrow{L}}_0$$

, т.к. в выражении для θ_ynp и θ_znp присутствуют углы α₁, γ₁, α₂, γ₂ отклонения пентапризм от номинального положения.Analyzing expression (14), we can conclude that direct measurements of the angular deviations θ _ynp and θ _{znp of the} vector $${\overrightarrow{L}}_{np}$$

at the output of the pair of pentaprisms, it is not possible to determine the desired angular deviations θ _y and θ _{z of the} vector $${\overrightarrow{L}}_0$$

because in the expression for θ _ynp and θ _znp there are angles α ₁ , γ ₁ , α ₂ , γ ₂ deviations of the pentaprism from the nominal position.

, на которую не влияют случайные возмущения (см. (12)). Используя это выражение, можно найти искомые значения θ_y и θ для луча на выходе передающего канала по следующей методике:Note that in the expression (13) is present $${\theta }_z^{\text{'}\text{'}}$$

which is not affected by random perturbations (see (12)). Using this expression, we can find the desired values of θ _y and θ for the beam at the output of the transmitting channel using the following procedure:

, характеризующего направление оси пучка излучения лазера на выходе второй пентапризмы 2.2. In the coordinate system X ₀ Y ₀ Z ₀ the angular deviations θ _ynp and θ _{znp of the} vector are _measured $${\overrightarrow{L}}_{np}$$

characterizing the direction of the axis of the laser beam at the output of the second pentaprism 2.

. Как следует из выражений (13) и (12), значение $${\theta }_z^{\text{'}}$$

этого вектора определяется для первой пары пентапризм 1 и 2 следующим образом:3. These values are recalculated into the coordinate system X ₁ X ₁ Z ₁ taking into account the rotation by the angle φ, similar to expression (12). We get a vector $${\overrightarrow{L}}_2^{\text{'}\text{'}}{}^{\ast }$$

. As follows from expressions (13) and (12), the value $${\theta }_z^{\text{'}\text{'}}$$

of this vector is determined for the first pair of pentaprisms 1 and 2 as follows:

$${\theta }_z^{\text{'}\text{'}}=-{\theta }_{y\mathrm{one}}\sin \varphi +{\theta }_{z\mathrm{one}}\cos \varphi ={\theta }_{z\mathrm{one}}^{\text{'}\text{'}}\left(\mathrm{fifteen}\right)$$

:We perform similar transformations for the second pair of pentaprisms, i.e. for the third 3 and fourth 4 pentaprism. We take into account that for this pair the angle φ has a negative value. As a result, we obtain the expression for $${\theta }_{z2}^{\text{'}\text{'}}$$

:

$${\theta }_{z2}^{\text{'}\text{'}}={\theta }_{y2}\sin \varphi +{\theta }_{z2}\cos \varphi \left(16\right)$$

3. Having these two measurements, we determine the desired values of θ _y and θ _z :

$${\theta }_z=\left({\theta }_{z\mathrm{one}}^{\text{'}\text{'}}+{\theta }_{z2}^{\text{'}\text{'}}\right)/2\cos \varphi$$

$${\theta }_y=\left({\theta }_{z2}^{\text{'}\text{'}}-{\theta }_{z\mathrm{one}}^{\text{'}\text{'}}\right)/2\sin \varphi$$

Or, taking into account (15) and (16):

$${\theta }_z=\left(-{\theta }_{y\mathrm{one}}\sin \varphi +{\theta }_{z\mathrm{one}}\cos \varphi +{\theta }_{y2}\sin \varphi +{\theta }_{z2}\cos \varphi \right)/2\cos \varphi (17)$$

θ _y = (θ _y2 sinφ + θ _z2 cosφ + θ _y1 sinφ-θ _z1 cosφ) / 2sinφ

Thus, the obtained expressions (17) show that the proposed device for determining the angular deviation of the laser beam axis from the nominal position, containing a prism system built on the basis of two pairs of pentaprisms, provides the determination of the angular deviation of the laser beam axis from the nominal position under external mechanical stresses leading to angular withdrawals of prisms of the prism system. It is important to note that when using the high-energy working laser in the system, the proposed prism system makes it possible to reduce and even practically eliminate screening of the beam cross section.

Claims (2)

1. A device for determining the angular deviation of the axis of the laser beam from the nominal position, containing a prism system comprising a first pair of pentaprisms containing the first and second pentaprisms, the main sections of which are located in the same plane P, an optical wedge glued to the first reflective face of the first pentaprism and made so that its output face is parallel to the input face of the first pentaprism, and the gluing surface has a beam splitting coating, a second pair of pentaprisms containing a third and fourth pent aprisms, the main sections of which are located in the same plane P ', while the input side of the third pentaprism is parallel to the output face of the optical wedge, the planes P and P' are at an angle of 2φ to each other, and the second and fourth pentaprisms are optically connected to the lens , in the focal plane of which is a coordinate-sensitive photodetector, the output of which is connected to the input of the microprocessor. 2. The device according to claim 1, characterized in that the microprocessor is configured to calculate the angular deviation θ _Z , θ _{Y of the} axis of the controlled beam from the nominal position at the input of the first pentaprism according to the formulas:
θ _z = (- θ _y1 sinφ + θ _z1 cosφ + θ _y2 sinφ + θ _z2 cosφ) / 2cosφ,
θ _y = (θ _y2 sinφ + θ _z2 cosφ + θ _y1 sinφ-θ _z1 cosφ) / 2sinφ,
where θ _y1 ; θ _z1 is the angular deviation from the nominal position of the axis of the laser beam that has passed the first and second pentaprisms;
θ _y2 ; θ _z2 is the angular deviation from the nominal position of the axis of the laser beam that has passed the first, third, and fourth pentaprisms.

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