WO2008110782A1 - Lens characterisation process - Google Patents

Abstract

An assessment of the quality criteria of a lens is assessed in an apparatus (2) that simultaneously makes use of upper (4) and lower (6) autocollimators and edge and cap measurement probes. Beams of light are reflected or transmitted through the lens (8) and focused on an image detector that permits a processor to calculate an optical axis error and centre based on a concentric error orbit projected by the beams, with this orbit appearing when the lens is rotated. By operating to mathematically zero the optical axis and in taking N measurement samples around N points around the circumference of the lens, the processor is able to calculate quickly (by inference) the run-out (TIR) error value for the edge and, optionally, cap features of the lens in relation to the actual optical axis of the lens.

Description

LENS CHARACTERISATION PROCESS

Background to the Invention

This invention is concerned, in general, with an improved lens characterisation process, in particular a process and apparatus for determining the specific physical characteristics of a lens in a rapid, precise and repeatable manner.

Summary of the Prior Art

Lens characterisation is the process of defining lens characteristics, in particular the relationship between the mechanical (i.e. mass, inertial, geometric) and optical axes, as accurately as possible. It is also important to characterise lenses by the degree to which their surfaces are eccentric, i.e. offset from the mechanical and optical axes, and furthermore provide some indication as tp the discrepancies in the lens surfaces as compared to equivalent geometric or perfectly ellipsoid, spherical, conical or cylindrical surfaces having a certain desired radius of curvature. In a perfectly centred lens, both the mechanical axis and optical axis coincide and are thus perfectly centred, but manufacturing techniques seldom produce perfect lenses (without great and/or prohibitive expense). Consequently, in the assembly of optical instruments with imperfect lens, undesirable beam-steering effects need to be addressed through appropriate orientation and alignment strategies that compensate for the determined offset between the optical and mechanical axes.

It will be immediately appreciated from the above that the characterisation procedure is a complex one, but very important. This can be understood more readily when lenses for certain applications, which must be within certain tolerances set by manufacturers of high precision optical equipment, can often cost in the order of hundreds, if not thousands of pounds each

Accordingly, lens characterisation allows optical equipment manufacturers to set thresholds or tolerances to be met by lens manufacturers, and furthermore lens manufacturers can quickly grade their lenses for different optical equipment manufacturers and for different applications. As such, lens characterisation allows for improved quality control. Very high reliability and accuracy in the assessment and grading of lens is required for mission critical applications, such as weapons, avionics and medical applications. Where complex systems are constructed from multiple lenses it is also highly desirable to be aware of the lens centration characteristics to ensure that overall, the resulting optical instrument is as precise as it can be.

Currently, the lens characterisation process is capable of achieving an accuracy of +/- 10μm on a radius of curvature of 30mm and a lateral lens radius of 30mm.

Currently, the lens characterisation process is usually conducted using one or both of an optical reflection technique and an optical transmission technique. Firstly, the lens is manually mounted in an air chuck which is then rotated while shining light continuously onto the surface of the lens. A single autocollimator, i.e. a telescope, is arranged to monitor the light projection from the lens to effect monitoring of the optical axis in that lens. Manual manipulation (performed on an iterative basis) of the position of the lens in the air chuck results permits the true optical axis for the lens to be identified, since attainment and observance of a minimised orbit for the light projection corresponds to the optical axis for the lens. At this point, a measurement probe is introduced into the system, which probe contacts the edge of the lens. During one subsequent rotation of the lens, the probe is able to determine the "edge run-out", i.e. the eccentricity of the circumference of the lens, relative to the lens' optical axis. In this way, the edge run-out (e.g. the total indicated run-out or TIR of the edge to the upper face of the lens) is approximated to the optical run-out. From a practical perspective, the light which is shone onto the lens is manually inspected through a reticule or such like, whereafter the operator makes an estimation of lens quality using the scalar gauge in the reticule/veiwfinder as a guide. The operator then makes a simple but subjective "yes/no" assessment/determination as to whether the quality of the particular lens under test is sufficient, or otherwise grades the quality of the lens based on an assessed degree of deviation between the optical and mechanical axes. The procedure involves an often crudely executed manual adjustment of the position of the lens(usually by way of a delicate prodding of the lens in the amount) to achieve minimal error orbits on both surfaces or one surface and an edge or cap simultaneously

The setup of the apparatus is lengthy - typically 20 minutes - and requires a cycle time of approximately 4 to 8 minutes per lens. Typically, one cycle will result in the measurement of one scalar magnitude value defining the error associated with that particular lens. It has already been proposed to upgrade the solely manual measurement system by using 2D image arrays and using a PC connected to digital image capture devices. In the upgraded system, the PC performs a series of calculations and/or analyses according to algorithms on the captured images to provide a metrology data set describing each lens inspected by the apparatus. This data is then stored as a record of the lens physical topology and relative optical parameters.

The above system only provides a lens characterisation to within a repeatability of typically +/- 1.5μm. This is largely dependent on the image array resolution, the image capture frequency and the number of data points captured.

Summary of the Invention

According to the present invention there is provided a method of lens characterisation of a lens having at least two surfaces and an edge, the method comprising: using a light source to cause the lens to generate a focused error pattern onto an image detector; from measurement of the focused error pattern on the image detector, calculating an effective zero for one of an optical axis or a mechanical axis of the lens; and calculating an axis error in a complementary one of the mechanical axis and the optical axis, the axis error resulting from, respectively, the mathematical zeroing of the optical axis and the mechanical axis.

In a preferred embodiment, the method further comprises: rotating the lens to permit measurement of N sampling points about a circumference of the lens; measuring imaging data at each of the N sampling point, the imaging data relating the focused error pattern for each of the least two surfaces to varying position measurement data for both the edge and the cap; and calculating optical and mechanical axis errors based on the imaging data at the N sampling points.

In another aspect of the present invention there is provided Apparatus for assessing lens quality criteria, the apparatus comprising: a knife-edged chuck for mounting, in use, a lens to be tested, the lens having first and second surfaces and an edge; upper and lower autocollimators respectively positioned above and below the knife-edged chuck and having optical axes substantially parallel to the edge of the lens; an edge probe for engaging, in use, against the edge of the lens under test; and an image detector; a light source arranged, in use, to cause the lens to generate a focused error pattern onto the image detector; and a processor, responsive to measurements from the edge probe and further arranged to: i) calculate an effective zero for one of an optical axis or a mechanical axis of the lens based on from measurements of the focused error pattern on the image detector; and ii) calculate an axis error in a complementary one of the mechanical axis and the optical axis, the axis error resulting from, respectively, the mathematical zeroing of the optical axis and the mechanical axis.

In the event that the lens includes a cap, a preferred embodiment further comprising: a cap probe for engaging, in use, against the cap region of the lens under test, the cap probe orientated substantially perpendicular to the edge probe; and wherein the processor is further responsive to measurements from the cap probe (preferably measured contemporaneously with the edge measurements). The processor is then further arranged to calculate optical and mechanical axis errors based on the cap data.

In a further aspect of the present invention there is provided a computer program product containing code that, in use, is arranged to cause a processor to implement procedure to assess an optical quality of a lens having at least two surfaces and an edge and, preferably, also a cap, the code arranged to: i) calculate an effective zero for one of an optical axis or a mechanical axis of the lens, the calculation based on measurements of a focused error pattern projected onto an image detector by the lens under test conditions; and ii) calculate an axis error in a complementary one of the mechanical axis and the optical axis, the axis error resulting from, respectively, the mathematical zeroing of the optical axis and the mechanical axis.

In a preferred embodiment, the code is particularly arranged to: i) measure imaging data at each of N sampling point around a circumference of the lens, the imaging data relating the focused error pattern for each of the least two surfaces to varying position measurement data for at least the edge and preferably, if appropriate, a cap; and ii) calculate optical and mechanical axis errors based on the imaging data at the N sampling points.

Preferably, the lens illumination (from the light source) is one of strobed or continuous, depending on the image array capabilities, the lens material and/or the illumination source wavelength. Preferably, digitally captured images are processed in a PC under the control of a computer program in which are embodied algorithms which simultaneously derive, from the captured digital image information, the direction and magnitude of each deviated optical path from top and bottom optical surfaces based on the captured.

It is worth mentioning that the frequency of lens rotation depends on the image array capabilities and the number of data points required to achieve desired resolution, but typically frequencies of 20 revolutions per minutes (rpm) to 2 rpm are suitable.

Preferably, a control program orchestrates and processes the data collection and calculation procedure in two or more steps relating edge data, cap data, angular position of the lens and error orbit imaging for top and bottom surfaces of the lens.

Generally, the process is carried out iteratively n times, where n is typically between 20 and 2000. In the first step, error orbit imaging permits the control program to derive

Cartesian coordinates of the centre of an optical target (known as tracking). In a subsequent step, the centre and radii of the image data sets are calculated and transposed to be centred on a (0,0) circle centre according to the Cartesian coordinates above to yield adjusted sets of circle data. In another step, the control program and apparatus cooperate to compile the relative data into a 2D data structure referenced to the angular position size of, preferably, (n, 5).

Yet further preferably, the target tracking procedure is conducted using shape recognition procedures with predictive search regions within the field of view.

This particular procedure facilitates rapid and hence real time implementation and is a feature which optimises memory and computational capacity.

Yet further preferably, in the orbit characterising procedure, a circle-fit method is employed using optimised data set from the above procedure.

Yet further preferably, the method embodies software procedures which further process the data set into the desired decentration units. Further detailed description of the de- centration procedures are provided in the specific description hereof.

Most preferably, the computer program outputs a data set including at least the following characterising parameters: 1 Concentricity of the edge diameter to the optical axis as a TIR measurement in millimetres.

2a Perpendicularity of a cap to the optical axis (TIR mm). 2b Perpendicularity of a cap to the optical axis as an arc measurement in degrees, minutes and seconds (d/m/s).

3a Tilt of cap with respect to its surface and the outside edge (TIR in mm). 3b Tilt of a cap with respect to its surface and the outside edge (d/m/s.) 3c Tilt of a cap with respect to the opposite surface and the outside edge (TIR mm) 3d Tilt of a cap face with respect to the opposite surface and the outside edge

(d/m/s). 4a Tilt of a surface with respect to the opposite surface and the outside edge

(d/m/s).

4d Tilt of a surface with respect to the opposite surface and the outside edge (TIR mm).

4b Tilt of a surface with respect to its cap face and the opposite surface (d/m/s). 4e Tilt of a surface with respect to its cap face and the opposite surface (TIR mm). 4c Tilt of a surface with respect to the opposite surface and its cap face (d/m/s). 4f Tilt of a surface with respect to the opposite surface and its cap face (TIR mm).

Ideally, the data set is arranged according to the above identification of parameters.

Preferably, the computer program is also capable of outputting an encrypted/flattened data set, said encryption/flattening including a conversion to a flattened binary stream to act as a traceable descriptor source for that particular lens which can be used to review and recalculate decentration output units subsequently.

Further preferably, the computer program further processes the data set to facilitate the marking of a indicator(s) on a surface(s) to show major orientations of the decentration characteristics by indicating when the angular position of the lens correlates with the desired decentration descriptor.

The invention thus provides a means of reducing cycle time to <6 sec or less as well as increasing objectivity, repeatability and accuracy of the lens characterisation procedure in general. Beneficially, the present invention provides an ability to indicate for marking purposes, major axis of interest on the lens. Additionally, the present invention provides an audit data set to accompany the lens though its subsequent integration cycle.

As will be appreciated from the foregoing description, and from the following specific embodiment, the invention may also be used to provide lens marking with respect to decentration indicators and optical measurements of the mechanical surfaces.

It will be appreciated that the particular light used in the apparatus may emanate from LEDs or lasers, or other suitable light source, and furthermore, the invention might also be extended to cover analogue and digital 2D image arrays.

The invention described above can have application not only in the field of lens characterisation, but also in the field of lens potting, lens potting with access to characterisation data, lens potting with restricted access to surfaces and lens potting using all or part of the characterisation procedures as part of the potting procedures.

In summary, the preferred embodiment of the present invention therefore provides an improved lens characterisation system and method and an innovative software- enhanced characterisation procedure.

Brief Description of the Drawings

Exemplary embodiments of the present invention will now be described with reference to the accompanying schematic representations in which:

Figs.1 to 4 show varying schematic views of a knife-edge mounted lens in apparatus suitable for carrying out the method of the invention; each of these drawings identifies a particular variable which appears in the following description of the mathematics used in the invention, and which is ultimately embodied in the computer program which forms part of the present invention.

Detailed Description of a Preferred Embodiment

Referring firstly to Figure 1 , there is shown an apparatus 2 comprising an upper telescope 4 and a lower telescope 6 between which is mounted a lens on respective first and second knife edges 10, 12 which are relatively rigidly mounted within the apparatus (not shown). Ideally, this mounting arrangement will be a vacuum knife edge mounting which can be rotated without the lens being displaced. As is the case with the other Figures 2 to 4, Fig. 1 also identifies a number of linear and angular dimension characteristics which are relevant to the calculations which are carried out according to the invention. Reference should be had to all the Figures in the following mathematical analyses.

It is to be understood that the implementation of the following analyses in software is capable by one suitably skilled in the art.

According to the underlying principle of the various embodiments of the present invention, the apparatus and method operate to effectively zero (through a mathematically process) either the mechanical or optical axis, whereafter quality criteria of the lens under test is assessed based upon calculation of a resultant effect on the other affected variable (i.e. the optical axis if the mechanical axis is zeroed, or the mechanical axis if the optical axis is zeroed). For example, given a mathematical zeroing of the optical axis, a preferred embodiment would operate to calculate the runout (TIR) error value for the edge and/or cap.

To achieve this function and quality assessment, upper and lower autocollimators are brought into position above and below a lens under test; this is unlike the prior art. The lens is held in place by a annular knife-edge air chuck that, in light of the fact that the lens includes at least one convex or concave surface, effectively causes a tilt in the lens¹ orientation; this is in common with the prior art.

The position of the two autocollimators is controlled by motors that select their respective positions based on a combination of a physical parameters of the lens

(stored in a look-up table; see table below titled "LENS CONFIGURATION TABLE") and physical aspects of the knife edge chuck (which are again stored in a table).

Consequently, automatic focus of a reflected or transmitted beam (through both the upper and lower autocollimators) onto a suitable image detector, such as a charge coupled device (ccd) under microprocessor control, takes into account nominal manufacturing parameters and properties of the lens. In this respect, the autocollimators are furthermore arranged to select complementary optical elements that attain focus for both lens surfaces (S1 and S2), with these complementary optics engaged into the light path by their appropriate processor-controlled insertion or removal. Contemporaneously with the positioning of the autocollimators, cap and edge probes are brought into contact with the lens held in the air chuck; this is again different to the systems in the prior art. As will be appreciated, the lens look-up table is built up from accumulated lens configuration data supplied by the lens manufacturer.

Once the autocollimators have been positioned for focus, the system of the preferred embodiment operates to calculate a radius for optical axis errors. As will be understood, reflected (or transmitted, as the case may be) light projects an error pattern, generated by use of an optical mask on the light source for the respective surfaces of the lens (given its current location in the air chuck) onto the image detector, which pattern has a nominal centre. Measurement data from the error pattern (which is substantially circular in nature) is taken from the image detector and used by a processor to determine a calculated optical centre for the lens/projected image. The lens is then rotated through 360 degrees to collect simultaneously at least three sets of imaging data, namely concentric orbit data for both upper and lower autocollimators and also related edge for N radial test points located around the circumference of the lens. Optionally, a cap probe a cap probe is provided to engage, in use, against the cap region of the lens under test, the cap probe orientated substantially perpendicular to the edge probe. In this case, measurements from the cap probe are recorded contemporaneously with the edge probe data and related to the concentric orbit (i.e. error pattern) data. Armed with a set of 3Λ/ (or AN in the case of the optional cap) data points, the processor is then able to calculate the optical and mechanical axis errors for the lens and, since the lens is tilted in the air chuck, it is furthermore now possible to infer the edge run-out (i.e. a linear measure in millimetres of the TIR) and, optionally (if appropriate for the lens under test) the cap run-out (TIR). As will be understood, the data points are preferably and generally provided by a position encoder arranged to describe the angular position of the lens in rotation.

Particularly, in a preferred embodiment where the optical path is mathematically zeroed, a complete data set for a particular lens effectively contains the magnitude and direction measurements of two (deviated) optical paths relative to the mechanical axis, the magnitude and direction measurements of both edge and cap and the angular disposition of the lens relative to the above. Consequently, in an overall cycle that only runs to a small number of seconds, the preferred embodiment of the present invention is able to assess a quality criteria of the lens under test. In accordance with the preferred embodiment of the present invention, the primary characteristics, i.e. those which are physically measured within the apparatus by suitable devices, are the edge concentricity to the optical axis and/or the cap face perpendicularity to the optical axis. From these measurements various other parameters may be calculated.

For the purpose of the initial set up of the machine the first five of the following relationships are calculated:-

1 Concentricity of the edge diameter to the optical axis (TIR in mm).

2a Perpendicularity of a cap face to the optical axis (TIR in mm).

2b Perpendicularity of a cap face to the optical axis (d/m/s)

3a Tilt of a cap face when its surface and the outside edge are data (TIR in mm).

3b Tilt of a cap face when its surface and the outside edge are data (d/m/s). 3c Tilt of a cap face when the opposite surface and the outside edge are data (TIR in mm).

3d Tilt of a cap face when the opposite surface and the outside edge are data, (d/m/s)

4a Tilt of a surface when the opposite surface and the outside edge are data. (d/m/s)

4b Tilt of a surface when its cap face and the opposite surface are data (d/m/s).

4c Tilt of a surface when the opposite surface and its cap face are data (d/m/s).

4d 4a, 4b and 4c may be specified as a TIR (in mm) close to the edge of the clear surface.

These identifications will be used in the following description.

The following tables identify the various preliminary characteristics which are either already known from the lens characteristics and the knife edge mounting prior to characterization, or which can be easily calculated, and in either case are required. LENS CONFIGURATION TABLE

KNIFE EDGE DATA

In general, it generally advisable to place the lens on the knife edge mounting with its steepest curve contacting the knife edges. In the event that only one surface of the lens is specified as a datum, then that surface should contact the knife edge. If a cap face lens is specified as a datum then it must be placed uppermost so that the measurement probe is able to contact the face.

As the lens is placed in the machine by the operator in a particular orientation (i.e. with a particular surface facing upward), it is automatically known which surface (S1 or S2) contacts the knife edge, and this becomes R_L (see Fig. 2). The other surface (the upper one ) is R_u (where R_L and R_u are their radii respectively. )

At this point a suitable knife edge tool is selected or specified.

In the following analyses, if a lens surface is CONVEX then it will be given a POSITIVE radius and if CONCAVE then it will be given a NEGATIVE radius.

Cap heights are considered NEGATIVE if the surfaces they are associated with are CONCAVE, and POSITIVE if the associated surface is CONVEX.

The following mathematical analysis provides the TELESCOPE CALCULATIONS.

For convenience in the calculations for the location etc. of the telescopes, said telescopes and the surfaces being measured are considered independently.

The required supplementary lens, location of the telescope, focus setting and path of the image at the camera are calculated as follows :-

where

U₀ = distance of graticule from objective lens. V₀ = distance of graticule image formed by objective from objective.

U₁ = distance of graticule image formed by (objective) from supp. lens.

V₁ = distance of graticule image formed by supplementary lens from it. a = zero offset to ensure that the supp. lens does not foul the test lens. h = height of supp. lens above O' on telescope slide. f₀ = focal length of telescope OG. fι = focal length of supp. lens s = focus movement of telescope OG. d = separation of OG and supp. lens at s = 0.

R = radius of curvature of lens surface being assessed.

U₀ fo + S

_

V₀ ) _ fa. . Un fn - ( fn + S fo • ( fn + S )

(u o - fo) (fo + S - fo ) S

u1 d - S - vθ = d - S - fn . ( fn + S )

S

V₁ 1

₌ fi . { d - S - [fo - ( fn + S ) ] } \ { d - s - [fo . ( fn + s ) ] fi}

f, . ( S . d - S² - fn . ( fn + S )\ \ S . d - S² - fn . ( fn + S ) - S . f 1

S S

fi . ( S . d - S² - fn . ( fn + S )) s . d - s² - fo . ( fo + s ) - s . fi

H = V₁ - R - a Where H is the distance between the telescope and the lens upper surface.

fi i . i S . d - S² - fn . ( fn + S )) - ( R + a ) s . d - s² - fo . ( fo + s ) - s . fι

The following table is used to identify suitable supplementary lenses and focus settings of telescope for the surface radii to be tested. The table shows a range of surface radii of curvature suitable for measurement with each of the proposed supplementary lenses, the position and focus setting of the telescope and the radius of the path of the image at the camera for a 0.1 mrad. surface tilt. For these calculations, the closest that the telescope could reach the surface was taken to be 20mm. (= a)

[The "Special lens" is an inverted telephoto design. The optimum location for this lens will depend upon the layout of the rest of the supplementary lenses and allowances for clearances around the surface under test. Since this lens will be some 40mm diameter at its widest, it will significantly affect the design of the probe to measure the vertical run-out of the surface under test. In this context, the special lens is realised by a combination of optical elements in an assembly that achieves image focus.] The table above represents an example set of lenses and the calculated, associated variables utilised in an autocollimator configured for measuring the surface ranges of the radius of curvature Rmax-Rmin.

In most instances there will be a range of focus settings and, hence, telescope locations that will be satisfactory for any particular surface radius. For optimum illumination and mechanical conditions it will be convenient to have a clearance of less than 150 mm between the telescope and the lens under test.

The best location of the telescope and its focus setting is determined by means of the following equation, in which H is calculated for the available range of focus settings and use the clearance criteria to decide upon the optimum.

H = fi f s .d - s² - fn ( f_n + s )l - (R + a) s.d-s²-f₀ (fo+s ) - S^₁

It is to be noted that 'a' will be different for the two telescopes and the 'Special Lens'. The particular vertical scale reading will vary with knife edge and lens location details. A more general equation is given later.

The radius of the path of the image at the camera is then calculated from the following equations:-

M = S.d - S² -fn ( fn + S ) - S^f₁ fO . fl

c = 2.R.p.M (= 9.696. 10^"3 .R.p.M , if p is in seconds of arc).

Where M = magnification. c = path radius in mm. p = surface tilt in milliradians. A slight variation is to select the supplementary lens as above and then calculate the focus settings which allow positioning of the telescope within a useable range of Η'. In "Mathcad" the above equations are modified as follows:-

H_n fi r Sn .d - Sn² - fO ( fO + sn )l - R - a , s_n.d - S_n ² - fo ( fo + S_n ) - s_n.fi

M_n = Sn.d - Sn² -fn ( fn + Sn) - Sn.fi

C_n = 2.R.p.M_n

where n = 0,2....48 and S_n = 24 - n.

This process allows ¹H', 'M¹ and 'c' to be calculated for the range of values of 's' from -24 to +24.

(Rules will be needed to select the preferred value of 's' and hence of Η' and 'c'.)

From the above, the radius 'r¹ of the path of the centre of curvature of the surface under test is:

0.5 . c microns,

M where the factor 0.5 allows for the reflection at the lens surface.

The above calculations are carried out for both telescopes.

EQUATIONS for CALCULATIONS of LENS DECENTRE

In the following, 'tθ' is taken as the start position of the upper camera, i.e. when the 'Y' and 'X' coordinates are '0' and 'ru' respectively, and the "lower camera image", the "lens edge probe" and the "cap face probe" are assumed to be out of phase to the upper camera by θ, φ, and β respectively. the measured radius of the path of the upper c of c be: ru, the measured radius of the path of the lower c of c be: rl , the measured radius of the runout of the edge of the lens be: re , the radius of the runout of the edge of the lens, resulting from the angle between the optical and air bearing axes be: reΔ the measured radius of the runout of the cap face of lens be : rf , the radius of the runout of the cap face of the lens, resulting from the angle between the optical and air bearing axes be : rfΔ the radius of the upper surface be: Ru the radius of the lower surface be : RL

the centre thickness of the lens be: Ct the upper cap height be: Cu the lower cap height be: CL the projections of 'r' on to Cartesian co-ordinates be: X and Y.

Sign convention: The surface radii (Ru , RL ) and cap heights (Cu , CL ) are positive when measurements from the pole of the surface to the centre of curvature (c of c) or to the cap face respectively are in a direction away from the measuring telescope. (Note: Ct is always positive).

When the air bearing has rotated through angle 'n.g', then

the (X₁Y) coordinates of the upper image are: Xu = ru cos n.g , (1) Yu = ru sin n.α the (X₁Y) coordinates of the lower image are: XL = rL cos (nα + θ) (2)

YL = rL sin (nα + θ) the (X₁Y) coordinates of the edge probe are: Xe = re cos (nα + φ) (3)

Ye = re sin (nα + φ) the (X₁Y) coordinates of the capface probe are: Xf = re cos (nα + β) (4)

Yf = re sin (nα + β)

The above relationships are those of the measurements which are made. In Fig. 1 , H_u and H_L are the distances between the upper and lower telescopes and the upper and lower surfaces of the lens respectively, h_ud and h_Ld are the distances between the upper and lower telescope and the knife edge interface (the measurement datum) h_u and h_L are the readings on the vertical digital scales for the telescope positions of hud and h_Ld , respectively.

The minimum allowed value of Hu

Hu_mi_n = h_ud - [ h₃ + h! - C_k + C, + a_u ( - C_u when C_u < 0 )] (5)

The minimum allowed value of H_L

H_Lmin = h_Ld - [ h₃ + h, - C_k + a_L ] (6)

Where a_u and a_L are safety clearances to prevent the telescopes fouling the lens or the fixturing.

The relationship of the scale readings h_u and h_L with h_ud and h_Ld respectively will need to be determined experimentally.

1 CONCENTRICITY OF EDGE DIAMETER TO THE OPTICAL AXIS

First correction

In the procedure, the optical axis of the lens is moved laterally to bring centre of curvature of lower surface on to the rotational axis of the air bearing.

Then the new coordinates of the upper image are:

X_ui = ru cos n.α - rl_ cos (nα + θ) (7)

Y_ui = ru sin n.q- rl_ sin (nα + θ)

Then the new coordinates of the lower image are:

Xn = 0, (8)

Yu = 0 Then the new coordinates of the edge probe are:

Xe1 =re cos (nα + φ)- rLcos (nα + θ) (9)

Ye1 =re sin (nα + φ) - rL sin (nα + θ)

Then the new coordinates of the capface probe are:

Xf = rccos(nα + β) (10)

Yf = re sin (nα + β)

(see Fig.2).

From Fig.2, the following are derived:

Ck = R_L ± (R_L ² - (b - s)²)^1/j Where s = b.R_k/(R_L+R_k) and b and R_k are specific to each knife edge.

R_L - (R_L ² - (b - s)² )^1/2 for normal lenses. (11)

C_L = R_L ± (R_L ² - 0² )^/a where 0 is the radius of the outside edge of the lens.

= R_L-(R_L ² - ø²)⁵⁴ for normal lenses. (12)

C_u = Ru ± (Ru² - 0² f'

= Ru-(Ru² - 0²)^% for normal lenses. (13)

C_e = C - C_u - C_L (14)

C_p = C_e /2 +C_L - C_K = (C - C_u + C_L - 2C_K)/2 (15)

h₃ = R_k.(R_L - C_k)/ R_L (16)

h_p = hi + h₃ + Cp and hi is specific to each "knife edge". (17) The optical axis is rotated about the centre of curvature of the lower surface so as to bring the centre of curvature of the upper surface on to the rotational axis of the air bearing. The optical axis will now coincide with the rotational axis. (Hence the residual error on the edge probe is the decentration of the lens).

Allowance is made for the centre thickness (CO of the lens, and the upper and lower cap heights (C_u and C_L). The height (h_p) of the edge probe above the base of the knife edge (datum level) is calculated to allow contact at the middle of the edge of the lens. If there are no cap faces, then the 'cap heights' are to the points of intersection between the lens edge and the optical surfaces.

Then the new coordinates of the upper image are: X_u2 = 0, (18)

Then the new coordinates of the lower image are: X_L2 = 0 , (19)

Y_L2 = 0

Then the new coordinates of the edge probe are:

Xe2 ⁼ XefXeΔ

= Xel - X_u1 . (2R₁ - Ct + C, - C. )

)

Ye2 = YeI- Y_11A

= Y_ei- Ym ■ (2 R, - C, +C. - C. ) (20)

The concentricity (TIR in mm) of the edge diameter to the optical axis is given by:

2 . r_e = 2 . (X₆₂ ² + Y_e2 ² )^% (21) 2a PERPENDICULARITY OF A CAP FACE TO THE OPTICAL AXIS (TIR in mm). 2b PERPENDICULARITY OF A CAP FACE TO THE OPTICAL AXIS (d/m/s).

First Correction: The optical axis of lens is move laterally to bring centre of curvature of the lower surface on to the rotational axis of the air bearing (equations: (1), (2), (3) and (4))

Then the new coordinates of the upper image are: Then the new coordinates of the upper image are: Xui = ru cos n.α - rL cos (nα + θ) (22)

Y_ui = ru sin n.α;- rL sin (nα + θ)

Then the new coordinates of the lower image are :

Xn = 0 (23)

Yu = 0

Then the new coordinates of the capface probe are:

XfI = rL cos (nα + β) (24)

Yf1 = re sin (nα + β)

The cap probe readings are unchanged because the lateral correction to the optical axis is parallel to the cap face.

The edge probe readings are not required in this calculation.

Second correction:

The optical axis is rotated about the centre of curvature of the lower surface so as to bring the centre of curvature of the upper surface on to the rotational axis of the air bearing. The optical axis will now coincide with the rotational axis. (Hence the residual error on the cap face probe is a measure of the decentration of the lens.)

The calculation of the effect upon the cap face of the lens is made by means of similar triangles.

Allowance has to be made for the centre thickness (CT) of the lens, and the upper and lower cap heights (Cu and CL). The height (hp + Ce 12) of the cap face probe above the base of the knife edge (datum level) is calculated to allow the probe to contact the cap face of the lens. The distance (Rf) of the cap face probe from the bearing axis must be determined or set manually by the engineer or operator setting up the lens for the test.

W / q = Xu1 / ( RL + Ru - Ct ) (by similar triangles). (25)

Hence W = q. Xu1 / ( RL + Ru - Ct ) (26)

Z / W Rf / q (by similar triangles). (27)

Hence W q . Z / Rf (28)

Hence q . Z / Rf q. Xu1 / ( RL + Ru - Ct ) (29)

Therefore Rf . Xu1 / ( RL + Ru - Ct ) (30)

But XfΔ (31)

Hence XfΔ = Rf . Xu1 / ( RL + Ru - Ct ) (32)

Then the new coordinates of the upper image are: Xu2 = 0 (33)

Yu2 = 0.

Then the new coordinates of the lower image are: XL2 = 0 (34)

YL2 = 0

Then the new coordinates of the cap face probe are:

Xf2 =Xf1- XfA=Xf 1 - Rf . Xu1 (35) ( RL + Ru - Ct )

Yf2 =Yf 1 - YfA= Yf1 - Rf . Xu1 (37)

( RL + Ru - Ct ) 2a PERPENDICULARITY OF A CAP FACE TO THE OPTICAL AXIS ( Tir in mm.) IS GIVEN BY

2b PERPENDICULARITY OF A CAP FACE TO THE OPTICAL AXIS (d/m/s).

The tilt of the cap face ( Tf ) = Tan ¹ (rf / 2 ) / ( 2.Rf )

Tf Tan^"1 (rf / 4.Rf ) (39)

[ An alternative approach which gives much the same answer.

The angle of cap face in the X direction,

Tfx1 = Xf1 / 2.Rf radians.

Angle of cap face after rotation about lower centre, in X direction,

TfX2 = Xf1 / 2.Rf - Xu1 / ( Ru + RL - Ct ) radians. And in Y direction

TfY2 = Yf 1 / 2.Rf - Yu 1 / ( Ru + RL - Ct ) radians.

Hence the resultant angle (T) is given by,

I - ( I fX2 ⁺ I fY2 ) radians.

Hence the resultant TIR

T. 2 . Rf mm.

3a CAP FACE TILT, when ITS SURFACE and the OUTSIDE EDGE ARE DATA. (TIR mm.)

3b CAP FACE TILT, when ITS SURFACE and the OUTSIDE EDGE ARE DATA, (d/m/s).

Reference is had to Figure 3 in this section. The DATUM SURFACE on this lens will be Ru, i.e. the upper surface to allow the measurement probe to have access to the cap face.

First correction:

The optical axis is moved of lens laterally to bring the centre of curvature of the upper surface on to the rotational axis of the air bearing.

Then the new coordinates of the upper image are: Xu1 = 0 (40) Yu1 = 0

Then the new coordinates of the lower image are:

XL1 = rL cos (nα + θ) - ru cos n.α , (41)

YL1 = rL sin (nα + θ) - ru sin n.α

Then the new coordinates of the edge probe are:

Xe1 =rl_ cos (nα + φ) - ru cos n.α (42)

Ye1 =rl_ sin (nα + φ ) - ru sin n.α

Then the new coordinates of the capface probe are:

Xf1 = xf = rL cos (nα + β) (43)

Yf1 = yf = re sin (nα + β)

Second correction

The Optical Axis is rotated about the centre of the upper surface to bring the Edge Probe to zero runout.

In the above figure we have:

the residual error of the edge of the lens (after lateral shift) Xe1 ,

the residual error of the lower centre (after rotation) XL2 = XL1 - XLeI (44)

the residual error of the cap face probe (after lateral shift) Za correction to the cap face probe (after rotation) Zb

the residual error of the cap face probe (after rotation) Xf2 = Z a - Zb (45)

the distance of the cap face probe from the bearing axis Rf, the distance of the cap face probe from the upper centre q .

Then by similar triangles,

xl_e1 = RL + RU - Ct (46) xe1 Ru - Cu - Ce / 2

xLe1 = 2 . Xe1 . ( RL + RU - Ct ) (47) 2 . (Ru - Cu ) - Ce

Also by similar triangles,

3 RL + Ru - Ct so Wb

Wb α . XLeI XLeI (RL + Ru - Ct) (48)

Also by similar triangles,

Wb = 3 so Wb = g . Zb (49)

Zb Rf Rf

So q . Zb _ α . XLeI (50)

Rf (RL + Ru - Ct )

So Zb = XLeI . Rf

(RL + Ru - Ct ) 2.Rf . Xe1 . ( RL + RU - Ct ) [ 2 . (Ru - Cu ) - Ce ] . [RL + Ru - Ct ]

= 2 . Rf . Xe1 . (51)

[2 . (Ru - Cu ) - Ce ]

Now the residual error at the cap face xf2 Za - Zb (52)

Xf1 - 2 . Rf . Xe1 (53)

[2 . (Ru - Cu ) - Ce ]

By similarity yf2 = Yf1 - 2 . Rf . Ye1 (54) [2 . (Ru - Cu ) - Ce ]

So rf (X_f2 ² + Y_f2 ² )⁷² (55)

3a So cap tilt (TIR mm )2 rf = 2 . (X_f2 ² + Y_f2 ² )^Vl (56)

3b The cap tilt (d/m/s) = Tan ¹ ( rf / Rf ) . (57)

3c CAP TILT when OPPOSITE SURFACE and EDGE ARE DATA (TIR in mm) & 3d CAP TILT when OPPOSITE SURFACE and EDGE ARE DATA (d/m/s).

The DATUM SURFACE on this lens will be RL, i.e. the lower surface to allow access of the cap probe to the face to be measured.

First correction: The optical axis of lens is moved laterally to bring centre of curvature of the lower surface on to the rotational axis of the air bearing

Then the new coordinates of the upper image are:

Xu1 = ru cos (nα + θ) - ru cos n.α (58) Yu 1 =ru sin (nα + θ) - ru sin n.α Then the new coordinates of the lower image are: XL1 = 0 _v (59)

YL1 = 0

Then the new coordinates of the edge probe are:

Xe1 =re cos (nα + φ) - rl_ cos (nα + θ) (60)

Ye1 =re sin (nα + φ) - rL sin (nα + θ)

Then the new coordinates of the capface probe are: Xf 1 = rc cos (nα + β) (61)

Yf1 = re sin (nα + β)

The cap probe readings are unchanged because the lateral correction to the optical axis is parallel to the cap face.

Second correction:

The Optical Axis is rotated about the centre of the lower surface to bring the Edge

Probe to zero run-out.

In the above figure we have:

the residual error of the edge of the lens (after lateral shift) Xe1 , the residual error of the upper centre (after rotation) Xu2 = Xu1 - Xue1 (62) the residual error of the cap face probe (after lateral shift) Za correction to the cap face probe (after rotation) Zb the residual error of the cap face probe (after rotation) Xf2 = Z a - Zb , (63) the distance of the cap face probe from the bearing axis Rf the distance of the cap face probe from the lower centre q .

Then by similar triangles,

Xue1 = RL + RU - Ct (64)

Xe1 RL CL - Ce / 2 Xue1 = 2. Xe1. ( RL + RU - Ct ) (65) 2. (RL - CL ) - Ce

Also by similar triangles, g = RL + Ru - Ct so Wb = α .Xue (66) Wb Xue1 (RL + Ru - Ct)

Also by similar triangles,

Wb g. so Wb Zb (67) Zb Rf Rf

So . . Zb q . Xue1 (68) Rf (RL + Ru - Ct)

So Zb Xue1 . Rf (RL + Ru - Ct)

2. Rf . Xe1. ( RL + RU - Ct) [ 2. (RL - CL ) - Ce ] . [RL + Ru - Ct ]

2 . Rf . Xe1. (69) [2.(RL - CL ) - Ce ]

Now the residual error at the cap face xf2 Za - Zb (70)

Xf 1 - 2 . Rf . Xe1 (71)

[2.(RL - CL ) - Ce ]

By similarity Yf2 Yf1 - 2. Rf . Ye1 (72)

[2. (Rl - CL ) - Ce ] So rf (Xf2² + Yf2² )^1/2 (73)

3c So cap tilt (TIR mm ) 2 rf = 2 . (Xf2² + Yf2² )^y' (74)

3d The cap tilt (d/ms) = . Tan ¹ ( rf / Rf ) (75)

4d SURFACE TILT when OPPOSITE SURFACE and EDGE ARE DATA (TIR in mm)

4a SURFACE TILT when OPPOSITE SURFACE and EDGE ARE DATA (d/m/s)

The DATUM SURFACE on this lens will be RL, i.e. the lower surface, (see Fig. 4)

First correction:

The optical axis of lens is moved laterally to bring centre of curvature of the lower surface on to the rotational axis of the air bearing

Then the new coordinates of the upper image are :

Xu1 = cos n.α - rL cos (nα + θ) (76) Yu1 =ru sin n.q- rL sin (nα + θ)

Then the new coordinates of the lower image are: XL1 = 0 , (77)

YL1 = 0

Then the new coordinates of the edge probe are:

Xe1 =re cos(nα + φ) -rLcos (nα+θ) (78)

Ye1 =re sin(nα + φ) - rLsin(nα + θ)

Then the new coordinates of the capface probe are: Xf1 = rc cos (nα ÷ β) (79)

Yf1 = re sin (nα + β)

The cap probe readings are unchanged because the lateral correction to the optical axis is parallel to the cap face. Second correction:

Rotate the Optical Axis about the centre of the lower surface to bring the Edge Probe to zero runout.

In figure 4, the residual error of the edge of the lens (after lateral shift) Xe1 , the residual error of the upper centre (after rotation) Xu2 = Xu1 - Xue1 (80)

Then by similar triangles,

Xue1 = RL + RU - Ct (81)

Xe1 RL - CL - Ce / 2

Xue1 = 2 . Xe1 . ( RL + RU - CH (82) 2 . (RL - CL ) - Ce

The tilt of the upper surface is the resultant of the tilts in the X and Y directions.

The X tilt = tan^"1 [Xu2 / Ru ]

tan^"1 rXu1 - Xue1 1 Ru

tan^"1 [ Xu1 - 2 . Xe1 . ( RL + RU - Ct ) ] (83) [2 . (RL - CL ) - Ce]

By similarity the Y tilt = tan ¹ [Yu2 / Ru ]

tan ¹ fYu1 - Yue1 1 Ru

tan^"1 [ Yu1 - 2 . Ye1 . ( RL + RU - Ct ) ] [2 . (RL - CL ) - Ce] 4a The resultant surface tilt = [ ( X tilt )² + ( Y tilt )² ) f

The surface tilt in TIR (mm) as close to the edge of the surface as reasonable is given by

Tan [ ( X tilt f + ( Y tilt f ) f x the clear diameter.

The clear diameter (2 . Rc) may be calculated if the cap height and the surface radius (Ru ) are known.

2 . Rc = 2 . [ Cu . (2 . Ru - Cu ) ] ^Vl

4d The surface tilt in TIR (mm) = 2 .Rc . Tan [ ( X tilt f + ( Y tilt f ) f

It will of course be appreciated that the above description has been given by way of example only and that modifications in detail may be made within the scope of the present invention. For example, while the preferred embodiment discusses the calculation of errors in the cap and edge given an optical axis, the reverse process could be employed. Existing equipment may therefore be modified to include upper and lower autocollimators and to modify the function of the test equipment to reflect the preferred architecture and operating methodology of the present invention. Consequently, aspect of the present invention may be provided in the form of a computer program embodied on a storage device for loading into a computer.

Furthermore, while the preferred embodiment of the present invention has considered the situation where a lens includes both an edge and a cap region, it will be understood that (in lens design) the cap is sometimes optional or not required, since the cap is generally used for mounting purposes. In other words, in certain optical systems, a lens can simply include an edge that is sufficient to permit direct mounting of the lens into the optical path of the apparatus. Moreover, an edge may actually be realised by a knife- edge defined by the meeting of the radii of two lens surfaces. In this case, the lens still has concentricity (and hence experiences optical and mechanical axis alignment/orientation issues) that needs to be assessed through the mathematical zeroing technique of the present invention, although the apparatus is now simplified. Specifically, in the absence of a cap region, there is a no requirement to use the cap probe (which can thus be stored or removed from the test apparatus) and data processing is reduced as a consequence of a reduced data set.

In summary, an assessment of the quality criteria of a lens is assessed in an apparatus that simultaneously makes use of upper and lower autocollimators and at least an edge measurement probe and, as appropriate, also a cap measurement probes. Beams of light are reflected or transmitted through the lens and focused on an image detector that permits a processor to calculate an optical axis error and centre based on a concentric error orbit projected by the beams, with this orbit appearing when the lens is rotated. By operating to mathematically zero the optical axis and in taking N measurement samples around N points around the circumference of the lens, the processor is able to calculate quickly (by inference) the run-out (TIR) error value for the edge and, optionally, cap features of the lens in relation to the actual optical axis of the lens.

Claims

Claims

1. A method of lens characterisation of a lens having at least two surfaces and an edge, the method comprising: using a light source to cause the lens to generate a focused error pattern onto an image detector; from measurement of the focused error pattern on the image detector, calculating an effective zero for one of an optical axis or a mechanical axis of the lens; and calculating an axis error in a complementary one of the mechanical axis and the optical axis, the axis error resulting from, respectively, the mathematical zeroing of the optical axis and the mechanical axis.

2. The method according to claim 1 , further comprising: rotating the lens to permit measurement of N sampling points about a circumference of the lens; measuring imaging data at each of the N sampling point, the imaging data relating the focused error pattern for each of the least two surfaces to varying position measurement data for at least the edge; and calculating optical and mechanical axis errors based on the imaging data at the

N sampling points.

3. The method according to claim 2, further comprising: calculating edge run-out (TIR); and presenting the edge run-out out as a linear measure reflecting an assessed optical quality of the lens under test.

4. The method according to claim 2 or 3, further comprising: relating the focused error pattern and the varying position measurement data for the edge to varying position measurement data for a cap on the lens; and calculating a cap run-out (TIR).

5. The method according to claim 1, 2 or 3, further comprising: automatically focusing upper and lower autocollimators by selecting and de- selecting optical elements in a light path from the light source, the selection based on: i) physical properties of the lens stored in a lens configuration look-up table; and ii) physical attributes of a knife-edge air chuck arranged to hold the lens.

6. Apparatus for assessing lens quality criteria, the apparatus comprising: a knife-edged chuck for mounting, in use, a lens to be tested, the lens having first and second surfaces and an edge; upper and lower autocollimators respectively positioned above and below the knife-edged chuck and having optical axes substantially parallel to the edge of the lens; an edge probe for engaging, in use, against the edge of the lens under test; and an image detector; a light source arranged, in use, to cause the lens to generate a focused error pattern onto the image detector; and a processor, responsive to measurements from the edge probe and further arranged to: i) calculate an effective zero for one of an optical axis or a mechanical axis of the lens based on from measurements of the focused error pattern on the image detector; and ii) calculate an axis error in a complementary one of the mechanical axis and the optical axis, the axis error resulting from, respectively, the mathematical zeroing of the optical axis and the mechanical axis.

7. The apparatus according to claim 6, wherein the processor is further arranged to effect positioning of the upper and lower autocollimators to effect focus of the error pattern.

8. The apparatus according to claim 5 or 6 , further comprising: a motor to cause rotation of the knife-edged chuck such that the processor acquires measured imaging data at each of N sampling points about a circumference of the lens under test, the imaging data relating the focused error pattern for each of the least two surfaces to varying position measurement data for at least the edge; and wherein the processor is arranged calculate optical and mechanical axis errors based on the imaging data at the N sampling points.

9. The apparatus according to claim 6, 7 or 8, further comprising: a cap probe for engaging, in use, against the cap region of the lens under test, the cap probe orientated substantially perpendicular to the edge probe; and wherein the processor is further responsive to measurements from the cap probe and is further arranged to calculate optical and mechanical axis errors based on cap data.

10. The apparatus according to claim 9, wherein the edge probe and cap probe are, in use, engaged simultaneously against the edge and cap region of the lens under test.

11. The apparatus according to claim 9 or 10, further comprising: a display; and wherein the processor is further arranged to: i) calculate edge run-out and cap run-out (TIR) for the lens; and ii) present the edge run-out and cap-run out as a linear measure reflecting an assessed optical quality of the lens under test.

12. The apparatus according to any of claims 6 to 11 , further comprising: a look-up table containing: i) physical properties of at least one lens to be tested; and ii) physical attributes of the knife-edge chuck arranged to hold the lens; and wherein the processor is arranged to cause automatic focusing of the upper and lower autocollimators by effecting the introduction or removal of optical elements into light paths in the respective upper and lower autocollimators based on data within the look-up table.

13. A computer program product containing code that, in use, is arranged to cause a processor to implement procedure to assess an optical quality of a lens having at least two surfaces and an edge and, preferably, also a cap, the code arranged to: calculate an effective zero for one of an optical axis or a mechanical axis of the lens, the calculation based on measurements of a focused error pattern projected onto an image detector by the lens under test conditions; calculate an axis error in a complementary one of the mechanical axis and the optical axis, the axis error resulting from, respectively, the mathematical zeroing of the optical axis and the mechanical axis.

14. The computer program product according to claim 13, further comprising code arranged to: i) measure imaging data at each of Λ/ sampling point around a circumference of the lens, the imaging data relating the focused error pattern for each of the least two surfaces to varying position measurement data for at least the edge and preferably, if appropriate, a cap; and ii) calculate optical and mechanical axis errors based on the imaging data at the N sampling points.