WO2015130268A1

WO2015130268A1 - Methods of tolerancing an optical surface using a local pupil region

Info

Publication number: WO2015130268A1
Application number: PCT/US2014/018509
Authority: WO
Inventors: Simon Lee; Mark Christian SANSON; Clair Theodore Tienvieri
Original assignee: Corning Incorporated
Priority date: 2014-02-26
Filing date: 2014-02-26
Publication date: 2015-09-03
Also published as: JP2017513043A; DE112014006410T5

Abstract

A method of tolerancing an optical surface of a lens element of an optical system based on an interferogram of the optical surface is disclosed. The method includes defining for the optical surface a local pupil region having a corresponding field point in the image plane; defining a tolerance T on a feature of the optical surface within the local pupil region based on a performance metric of the optical system for the field point; fitting a polynomial to surface topography of the interferogram over the local pupil region to obtain a coefficient C that relates the optical surface feature to the performance metric; and comparing the tolerance T to the coefficient C to establish whether C < T for the field point. The process can be repeated for different local pupil region locations relative to the interferogram to tolerance the entire optical surface.

Description

METHODS OF TOLERANCING AN OPTICAL

SURFACE USING A LOCAL PUPIL REGION

FIELD

[0001] The present disclosure relates to tolera ncing optical surfaces, and in particular relates to methods of tolerancing an optica l surface of an optical system by using a local pupil region.

[0002] The entire disclosure of any publication or patent document mentioned herein is incorporated by reference.

BACKGROUND

[0003] All optica l systems are constituted by one or more optical elements in the form of refractive lenses, mirrors, beam splitters, etc. All methods of manufacturing optical elements produce some type of surface figure errors that reduce optical performance relative to the ideal performance if the optical elements could be made perfectly.

Consequently, optical systems generally require that the optical surfaces of the optical elements of the system be made to within select tolerances. These tolerances can be applied to a number of surface parameters, such as the optical power, surface irregularity, root-mean-square (RMS) variation from the idea l surface, surface slope, and power spectral density, as measured over the clear aperture of the optical element.

[0004] Modern optical design software allows for the modeling of the optical

performance of an optical system based on surface errors for each optical surface in the system. Surface errors can be localized and have a relatively low frequency, such as localized slope errors. Such surface errors can adversely impact imaging performance in small parts of the image field of the optical system. Yet, such localized surface errors can be underemphasized when performing tolerancing on the above-mentioned surface parameters when analyzed over the entire clear aperture. Further, it is preferred to relate a given tolerance to a performance metric of the optical system in which the optical elements resides. Two example performance metrics are field curvature (field flatness) and distortion. SUMMARY

[0005] An aspect of the disclosure is a method of tolerancing an optical surface of a field- lens element of an optica l system which has a pupil and an image plane, wherein the optical surface has a clear aperture a nd a total area AS. The method includes: a) measuring an interferogram of the optical surface, wherein the interferogram measures a surface topography of the optical surface over the entire clear aperture of the optical surface;

b) defining a local pupil region of the optical surface, the local pupil region having an area AR and a location, wherein the local pupil region has a corresponding field point in the image plane;

c) defining a tolerance T on at least one feature of the optical surface within the local pupil region based on at least one performa nce metric of the optical system for the field point;

d) fitting a polynomial to the surface topography of the interferogram over the local pupil region, wherein the polynomial includes at least one coefficient C that relates the at least one feature of the optical surface to the at least one performance metric; and

e) comparing the tolerance T to the at least one coefficient C to establish whether C < T for the field point.

[0006] Another aspect of the disclosure is a method of tolerancing an optical surface of a lens element of an optica l system which has a pupil and an image plane, based on an interferogram of the optical surface. The method includes: a) defining for the optica l surface a local pupil region that has a corresponding field point in the image plane;

b) defining a tolerance T on at least one feature of the optical surface within the local pupil region based on at least one performa nce metric of the optical system for the field point;

c) fitting a polynomial to the surface topography of the interferogram over the local pupil region, wherein the polynomial includes at least one coefficient C that relates at least one feature of the optical surface to the at least one performance metric; and d) comparing the tolerance T to the at least one coefficient C to establish whether C < T for the field point.

[0007] Another aspect of the disclosure is a method of tolerancing a field surface of an optical element of an optical system based on an interferogram representative of surface topography of the field surface. The method includes: a) defining for the field surface a local pupil region that has a corresponding field point FP in an image plane of the optica l system;

b) defining a tolerance T on at least one feature of the field surface within the local pupil region based on at least one performance metric of the optical system for the field point;

c) fitting a polynomial to the surface topography of the interferogram over the local pupil region to obtain at least one polynomial coefficient C that relates at least one feature of the field surface to the at least one performance metric; and d) comparing the tolerance T to the at least one coefficient C to establish whether C < T for the field point.

[0008] In examples, the tolerancing is performed for different locations of the local pupil region relative to the interferogram, wherein the different local pupil region locations have different corresponding field points in the image plane. The movement of the location of the local pupil region relative to the interferogram is referred to herein as "scanning" the local pupil region.

[0009] Also in examples, the optica l system includes multiple field surfaces and the tolerancing methods are applied to more than one of the field surfaces, e.g., all of the field surfaces.

[0010] Additional features and advantages are set forth in the Detailed Description that follows, and in part will be readily apparent to those skilled in the art from the description or recognized by practicing the embodiments as described in the written description and claims hereof, as well as the appended drawings. It is to be understood that both the foregoing general description and the following Detailed Description are merely exemplary, and are intended to provide an overview or framework to understand the nature and character of the claims. BRIEF DESCRIPTION OF THE DRAWINGS

[0011] The accom panying drawings are included to provide a further understanding, and are incorporated in and constitute a pa rt of this specification. The drawings illustrate one or more embodiment(s), and together with the Detailed Description serve to explain principles and operation of the various embodiments. As such, the disclosure will become more fully understood from the following Detailed Description, taken in conjunction with the accompanying Figures, in which:

[0012] FIG. 1A is a schematic diagram of a generalized optical system that includes at least one field-lens group that has one or more field-lens elements, and a pupil group that includes a pupil and optionally one or more pupil-lens elements;

[0013] FIG. IB is an optical diagram of an example of the generalized optical system of FIG. 1A as disclosed in USP 2,696,758, entitled "Wide-angle photographic objective," that illustrates how the pupil of the optical system defines a localized pupil regions on the surfaces of the elements of the optica l system;

[0014] FIG. 2 is a close-up view of a portion of a lens surface of a field-lens element showing the ray bundle that defines the local pupil region on the lens surface;

[0015] FIG. 3 is a front-on view of an example circularly symmetric field-lens element showing an example location and size of a local pupil region of the lens surface;

[0016] FIG. 4 shows an example interferogram for an example field-lens surface, and also showing an example local pupil region being moved (scanned) relative to the interferogram;

[0017] FIGS. 5A and 5B are schematic diagrams that show the movement (scanning) of an example local pupil region shown as progressing over the interferogram from the solid-line to the dashed-line to the dotted-line circle, for two different example stepping distances;

[0018] FIG. 6 is an optical diagram of an example optical system wherein the surface of the front field-lens element has an on-axis surface error that affects the focus position of an on-axis ray bundle;

[0019] FIG. 7 is a plot of the image plane location I P (μιη) versus the focus position fp (in waves, λ) across the field (image plane) for an nominal optical system (triangles) and for the same optical system that has a field-lens element with a non-ideal surface (squares); and [0020] FIG. 8 is a vector representation of distortion that shows the effect of a central artifact on a field-lens element similar to the surface error shown in FIG. 6, wherein the base of each vector V is the ideal placement of each ray bundle.

DETAILED DESCRIPTION

[0021] Reference is now made in detail to various embodiments of the disclosure, examples of which are illustrated in the accompanying drawings. Whenever possible, the same or like reference num bers and symbols are used throughout the drawings to refer to the same or like parts. The drawings are not necessarily to scale, and one skilled in the art will recognize where the drawings have been simplified to illustrate the key aspects of the disclosure.

[0022] The claims as set forth below a re incorporated into and constitute part of this Detailed Description.

[0023] Cartesian coordinates are shown in some of the Figures for the sake of reference and are not intended to be limiting as to direction or orientation.

[0024] FIG. 1A is a schematic diagram of a generalized optical system 10. Optica l system 10 includes an object plane OP, an optical axis Al and an image plane IP, which can actually be a non-planar image surface. Optical system 10 includes at least one lens element L and has at least one field-lens group GF having one or more field-lens elements LF and a pupil group GP that includes at least a lens pupil P (or aperture stop APS) and that can include one or more pupil-lens elements LP. Generally speaking, pupil-lens elements LP reside relatively close to pupil P, or to a conjugate of P, while field-lens elements LF reside relatively far away from pupil P or from a conjugate of P. The tolerancing methods disclosed herein apply mainly to field-lens elements LF. How pupil-lens elements LP and field-lens elements LF ca n be distinguished in the context of the tolerancing methods set forth herein is discussed in greater detail below. Optical system 10 is not limited to any particular type of optical system. Thus, in various non-limiting examples, optical system can be afocal, focal

(sometimes called "non-afocal"), asymmetric, etc.

[0025] FIG. IB is an optical diagram of an example of the generalized optical system of FIG. 1A as disclosed in USP 2,696,758, entitled "Wide-angle photographic objective" (hereafter, the '758 patent). Optical system 10 includes lens elements L, namely field-lens elements LF1, LF2 in field-lens group GF and pupil-lens elements LP1 - LP4 in pupil group GP. Optical system 10 of FIG. IB includes an object plane OP that is relatively far off to the left and so is not shown. Optical system 10 has twelve lens surface S, denoted SI through S12.

[0026] Also shown FIG. IB are three ray bundles RB, denoted RBI, RB2 and RB3. Ray bundles RBI through RB3 each pass from the object plane OP to image plane IP through field-lens elements LF, pupil P and pupil-lens elements LP. The ray bundles RBI through RB3 are each focused at respective field points FP1, FP2 and FP3 at the image plane IP. Image plane IP is shown in the ideal case as being flat for ease of illustration. Each lens surface SI through S12, as well as pupil P, has an associated clear aperture CA, i.e., a diameter (see FIG. 3, introduced and discussed below). Thus, the clear apertures CA for the two surfaces S of a given lens element L can be different, such as for example the clear apertures of lens surfaces S3 and S4 of lens element L2.

[0027] The example optica l system 10 of FIG. IB is a wide-angle photographic objective that was designed for use with film. As such, it has imaging performance requirements defined by the standards for film-based photographic imaging as known in the art at the time the objective was designed. The imaging performance requirements are characterized by one or more performance metrics. Example performance metrics are field dependent (i.e., they depend on the position at image plane IP) and include: field curvature, distortion, Strehl ratio, depth of focus, wavefront error at the image plane, and the modulation transfer function (MTF).

[0028] Performance metrics are advantageous because they represent a cha racterization of image quality, as compared to say measuring Seidel aberrations, which need to be further processed to understand their actua l impact on image quality.

[0029] Each of the optical surfaces SI through S12 has an optical tolerance that is based on the required or desired imaging performance of optical system 10. The optical tolerance can apply to one or more features of a given optical surface S. The prior-art approach to tolerancing of optical surfaces emphasizes taking an interfero metric measurement

("interferogram") of each optical surface (SI through S12 in our example optical system 10 of FIG. IB) and then evaluating the interferograms over the entire clear aperture of each surface. Interferograms can be measured using known techniques in the art, such as by phase-measurement interferometry, as described in the article by Bruning et al., "Digital wavefront measuring interferometer for testing optical surfaces and lenses," Applied Optics, Vol. 13, No. 11, November 1974, pp. 2693-2703. Interferometers that can measure interferograms for carrying out the tolerancing methods disclosed herein are commercially available from a number of companies, such as Zygo, Inc., of Middlefield, Connecticut, and Veeco Instruments Inc., of Plainview, New York.

[0030] The methods of tolerancing disclosed herein include measuring or otherwise obtaining an interferogram for a given surface S of a given field-lens element LF and then examining regions of the interferogram based on the pupil size as projected onto the surface. With continuing reference to FIG. IB and also to the close-up views of FIG. 2 and FIG. 3, it is observed that each ray bundle RB passes through a corresponding region PR of a given surface S. An example region PR is shown in black bold highlight in FIG. 2, and is shown in FIG. 3 as a smaller circular region within the clear aperture CA of lens L. Each region PR has an area AR defined by the intersection of the ray bundle RB at the surface S. Region PR has a radius r _R.

[0031] The area AR of region PR is defined by projecting pupil P through optical system 10 to surface S along the path of ray bundle RB. The location of region PR on a given surface S depends on the direction of ray bundle RB. The area AR is referred to hereinafter as the "local pupil area" and region PR is referred to hereinafter as the "local pupil region." The local pupil region PR corresponds to a single field point FP (see FIG. IB) in the image plane IP. Naturally, imaging of an object by optical system 10 over the entire field of view requires that light rays from the object plane OP travel through the entire surface S of each lens element L to image plane I P. But, the imaging performance at each field point FP is defined by the light rays that pass through the corresponding local pupil region PR at each surface S of each lens element L

[0032] Lens surface S has a total area AS (referred to herein as the "lens surface area") as defined by clear aperture CA of the surface and the surface curvature. The ratio of the local pupil area AR of local pupil region PR to the total area AS of lens surface S over clear aperture CA is defined as η = AR/AS and is referred to hereinafter as the "pupil area ratio." Field-lens elements LF have local pupil regions PR with a smaller pupil area ratio η than pupil lenses LP. In one example, a field-lens element LF is defined as a lens element L where at least one of its lens surfaces S have a pupil area ratio η < 0.75, while a pupil lens LP is defined as a lens element where both of its lens surfaces have a pupil area ratio of η > 0.75. In another example, a field-lens element LF is defined as a lens element L where at least one of its lens surfaces S have a pupil area ratio η < 0.65, while a pupil lens LP is defined as a lens element where both of its lens surfaces have a pupil area ratio of η > 0.65.

[0033] In an example, a given lens element L can technically fall between being a field-lens element and a pupil-lens element, i.e., the surface S farthest from pupil P can be a "field surface" while the opposite surface that is closest to the pupil can be a "pupil surface." Thus, in an example, rather than distinguishing between lens elements L as being either field-lens elements LF or pupil-lens elements LP, the lens surfaces S are distinguished as being either field-lens surfaces or pupil-lens surfaces.

[0034] FIG. 4 is a contour plot of an example interferogram 50 of an example surface S of an example field-lens element LF. Interferogram 50 is shown as having contours 51 representative of a surface topography of surface S. The contour spacing is 0.3λ, and the min/max is -0.18λ to 0.2λ, where λ is the wavelength of the measurement light of the interferometer used to obtain the interferogram. Other representations of the surface topography can be used, e.g., false color, etc. The local pupil region PR is shown as a black circle, and the a rrow 52 attached to the local pupil region indicates movement (scanning) of the local pupil region.

[0035] As noted above, the local pupil area AR of local pupil region PR is defined by the size of pupil P at the surface S of the lens element L for a given field point FP at image plane IP. Often, the local pupil area AR is substantially constant over the entire surface S of field- lens element LF. Tolerancing of surface S of field-lens element LF is accomplished by fitting the surface error of interferogram 50 within local pupil region PR to a polynomial, such as a Zernike polynomial as discussed below. One or more of the coefficients of the polynominal can then be related to one or more performance metrics of the optical system, e.g., distortion, field flatness, tilt, defocus, etc. One or more of the polynomial coefficients can then be compared directly to a tolerance T defined by the performance metric to control the imaging performance of the optical system. The local pupil region PR is moved

(scanned) over the entire interferogram to cover the entire lens surface S, and the tolerancing is performed for each local pupil region. [0036] In example illustrated in FIG. 5A, the local pupil region PR is shown as progressing (scanning) over interferogram 50 from the solid-line to the dashed-line to the dotted-line circle. The progression of FIG. 5A involves stepping the local pupil region PR by a stepping distance d equal to its radius r. In another example illustrated in FIG. 5B, the scanning of local pupil region PR involves stepping the local pupil region by a distance equal to half its radius r _R. In general, any reasonable stepping distance d can be used that adequately samples interferogram 50. The practical limit on the smallness of the scanning distance d is based upon the spatial sampling of the interferogram 50 and the order of the polynomial fit.

[0037] It was noted above that the pupil area ratio η is smaller for field-lens elements LF than for pupil-lens elements LP. The tolerancing method disclosed herein works best for field-lens elements (or more accurately, field-lens surfaces) since the local pupil area AR is relatively small as compared to the surface area AS. When the pupil area ratio η becomes too large, the localized surface effects change very little across the clear aperture. For example, tilt and power as measured over an entire interferogram 50 are usually measured as zero because these two measurement parameters are zeroed out in the interferometer. Yet, the power and tilt can vary over the local pupil region PR when the local pupil area AR is sufficiently small.

[0038] FIG. 6 shows another example optical system 10 that includes a biconvex field-lens element LF1 having a front surface S that includes a surface error SE in the form of a small concave indentation. Optical system 10 also includes a second field-lens element LF2 in the form of a plane parallel plate. Eleven ray bundles RBI through RB11 are shown, along with their associated field points FP in image plane (or more accurately, image surface) IP.

[0039] To limit localized focus shifts at image plane IP over the entire image field, the optical power is measured for each local pupil region PR. The surface error SE resides in local pupil region PR6 associated with ray bundle RB6 and on-axis field point FP6. Because surface error SE has a diameter that nearly matches the size of corresponding local pupil region PR6, it will have an effect on the focus of the corresponding center field point FP6, as well as an effect on the distortion around this center field point. The change in focus as a function of field position is represented by the central bump in the image plane (surface) IP. The change in the distortion is not evident in FIG. 6 because the ray bundles RB and corresponding field points represent a relatively sparse sampling for measuring distortion. [0040] FIG. 7 is a plot of the image plane location IP (μιη) as a function of the focus position fp (in waves λ) for an example optical system 10. The curve defined by the small triangles represents the focus position fp for the nominal design of the optical system 10, while the curved defined by the squares represents the focus position fp for the optical system when there is a non-ideal surface for a field-lens element LF in the optical system 10. The non-ideal surface S of the field-lens element LF causes undesirable excursions in the focus position fp. The frequency of the excursions is also increased.

[0041] FIG. 8 is a vector representation of distortion that shows the effect of a central artifact on a field-lens element L similar to the surface error SE shown in FIG. 6. The base of each vector V is the ideal placement of each ray bundle RB, wherein the ray bundles have uniform spacing. The distortion error ca used by a rotationally symmetric artifact at the center of a field-lens element L is not seen on the on-axis field point FP, but is seen on those field points surrounding the on-axis field point. Once the ray bundles RB move off of the central artifact, the distortion of the optical system 10 remains substantially unaffected.

[0042] In an example that illustrates the tolerancing methods disclosed herein, suppose that the imaging requirements of an optical system 10 dictate that no surface S of a field- lens element LF can contribute more than 200 nm of distortion to the overall image at image plane I P. That is, the distortion tolerance is 200 nm. The method includes measuring interferograms 50 for each surface S of each field-lens element LF. The appropriately sized local pupil region PR is scanned over the corresponding interferogram 50 for the given surface S to measure the local tilt for each local pupil region location.

[0043] The amount of local tilt for each R on each surface S can be related to an amount of distortion at the corresponding field point FP at image plane IP. This relation is established using standard optical design software and tolerancing techniques. Thus, a tolerance T on the amount of local tilt is determined based on the distortion tolerance of 200 nm and the optical design of the optical system.

[0044] In an example, the amount of measured tilt for each of the local pupil regions PR is embodied in a coefficient of the polynomial fit to the interferogram data. This allows the tilt tolerance T as calculated from the distortion performance metric to be compared directly to one or more of the polynom ial coefficients of the fitted interferogram over the loca l pupi l region PR.

[0045] An example polynom inal fit ca n be based on the Extended Fringe Zernike

Polynomia l Set, which can be defined as:

Z = {c-r²/[l+B] } +∑C_j+1 ZP_j, where

• z is the sag of the surface S pa ral lel to the optical axis Al

• c is the vertex curvature

• B = [l - (l+k)-cV]^1/2

• k is the conic constant

• r is the radia l distance out to a maxim um radius R

• ZP_j is the j ^h Zernike polynomia l, which can be expressed in polar coordinates (r, Θ).

• Cj₊i is the coefficient for ZP_j

[0046] The second and third Ze rnike polynomials a re ZP₂ = R-cosB and ZP₃ = R-s^'mQ and represent the tilt in the wavefront, so that the corresponding coefficients Ci and C₂ are tolera nced, i.e., are limited to having a maximum value. The value of the tolerance is based upon the tilt required for the given surface S at the given loca l pupil region PR to produce a 200 nm distortion at the corresponding field point FP in image plane I P. As noted above, this is readily determined by ana lyzing the optica l system using conventiona l lens design software, such as CODE V lens design softwa re, available from Synopsys, Pasadena, CA.

[0047] Thus, the tolera ncing method includes compa ring the tilt tolerance T to the tilt coefficients Ci and C₂ to establish whether the tilt tolerance has been met, i.e., whether

[0048] In a n example, the tole rance T need not be a single number for all field points FP and ca n va ry with the location of the field points. This situation can arise when the imaging performance in one pa rt of the field needs to be higher than other parts of the field. For example, it may be accepta ble to have a higher amount of distortion at the edges of the image plane I P than at the center. [0049] Thus, an example method of tolerancing an optical surface S of a field-lens element LF of an optical system 10 based on an interferogram 50 of the optical surface includes: a) defining for the optica l surface S a local pupil region PR that has a corresponding field point FP in the image plane IP;

b) defining a tolerance T on at least one feature of the optical surface within the local pupil region PR based on at least one performance metric of the optical system 10 for the field point FP;

c) fitting a polynomial to surface topogra phy of the interferogram 50 over the local pupil region PR, wherein the polynomia l includes at least one coefficient C that relates at least one feature of the optical surface S to the at least one performance metric; and

d) comparing the tolerance T to the at least one coefficient C to establish whether C < T for the field point.

[0050] Another example method of tolerancing an optica l surface of a field-lens element of an optica l system is as follows, wherein the optical system has a pupil P and an image plane I P, and wherein the optica l surface has a clear aperture CA and a total area AS: a) measuring an interferogram 50 of the optical surface S, wherein the

interferogram measures a surface topography of the optical surface over the entire clear aperture CA of the optical surface;

b) defining a local pupil region PR of the optica l surface, the local pupil region

having an area AR, wherein the local pupil region has a location and a corresponding field point FP in the image plane;

c) defining a tolerance T on at least one feature of the optical surface S within the local pupil region PR based on at least one performance metric of the optical system for the field point;

d) fitting a polynomial to the surface topography of the interferogram 50 over the local pupil region PR, wherein the polynomial includes at least one coefficient C that relates the at least one feature of the optical surface S to the at least one performance metric; and

e) comparing the tolerance T to the at least one coefficient C to establish whether C < T for the field point. [0051] Another aspect of the disclosure is a method of tolerancing of field surface S of an optical element LF of an optical system 10 based on an interferogram 50 of the field surface. The method includes: a) defining for the field surface S a local pupil region PR that has a corresponding field point FP in an image plane I P of the optical system 10;

b) defining a tolerance T on at least one feature of the field surface S within the local pupil region PR based on at least one performance metric of the optical systemlO for the field point FP;

c) fitting a polynomial to the surface topography of the interferogram 50 over the local pupil region PR to obtain at least one polynomial coefficient C that relates at least one feature of the field surface S to the at least one performance metric; and

[0052] By way of example, the tolerancing methods disclosed here were applied to the optical system 10 of 758 patent as shown in FIG. 2. An analysis of optical system 10 of the 758 patent showed that the distortion at image plane IP is about 175 μιη. To prevent the field-lens elements LF from creating a n objectionable amount of localized distortion, a limit of 50 μιη of localized distortion is set for each of the first four lens surfaces SI- S4, and the design sensitivity was used to determine what tolerance to place on the local pupil regions R for each lens surface S.

[0053] It was found that a tilt of 10.87 μιη over the local pupil region R of the surfaces SI and S2 for the first field-lens element LF1 resulted in a change of 25 μιη to the image placement at the image plane I P. This translates into 17 fringes of tilt when fitted to the Fringe Zernike Polynomial. As noted above, the 2^nd and 3^rd polynomial terms ZP₂ and ZP₃ represent tilt.

[0054] The tolerance T on the tilt for local pupil region R for surfaces SI and S2 of first field-lens element LF1 was then calculated to be T = [C₂ ²+C₃ ²]^{1 2} < 17 Fringes or 10.87 μιη. Following the same method for the second field lens LF2, the tolerance T = [C₂ ²+C₃ ²]^{1 2} < 18.8 Fringes or 11.7 μιη. Note how for each surface the deduced tolerance T is directly compared to a numerical value calculated from the two tilt polynomial coefficients.

[0055] The size of local pupil region R for each of the surfaces S for field-lens elements LF1 and LF2 can be determined by the marginal ray height of the axial field position. The local pupil regions R for surfaces S1- S4 were found to be 30 mm, 29.26 mm, 29.2 mm, and 28.8 mm, respectively.

[0056] The tolerancing methods disclosed herein have a number of advantages over prior- art tolerancing methods. One advantage is cost reduction. By having a tolerance tied to a local pupil region PR (or tolerances tied to different local pupil regions), overly tight tolerances on the optical surface or surfaces can be avoided. Further, the costs as well as time associated with using local measurements of the interferogram are significantly less than building a complete optical system then having to test a large number of field points. Further, since the tolera ncing of a local pupil region is applied to the departure from the ideal surface, the tolerances can easily be applied to generally any type of surface shape, e.g., sphere, asphere or free-form. In addition, the methods disclosed herein can be used on optical systems that are non-rotationally symmetric.

[0057] it will be apparent to those skilled in the a rt that various modifications to the preferred embodiments of the disclosure as described herein can be made without departing from the spirit or scope of the disclosure as defined in the appended claims.

Thus, the disclosure covers the modifications and variations provided they come within the scope of the appended claims and the equivalents thereto.

Claims

What is claimed is:

1. A method of tolerancing an optical surface of a field-lens element of an optical system which has a pupil and an image plane, wherein the optical surface has a clear aperture and a total area AS, the method comprising:

a) measuring an interferogram of the optical surface, wherein the interferogram measures a surface topography of the optical surface over the entire clear aperture of the optical surface;

2. The method according to claim 1, further comprising repeating acts d) and e) for different locations of the local pupil region relative to the interferogram, wherein the different local pupil region locations have different corresponding field points in the image plane.

3. The method according to claim 2, wherein said repeating of acts d) and e) is performed by moving the local pupil region relative to the interferogram to cover substantially the entire interferogram.

4. The method according to claim 1, wherein AR/AS < 0.75.

5. The method according to claim 4, wherein AR/AS < 0.65.

6. The method according to claim 1, wherein the at least one performance metric is selected from the group of performance metrics comprising: field curvature, distortion, Strehl ratio, depth of focus, wavefront error at the image plane, and modulation transfer function.

7. The method according to claim 1, wherein the tolerance T varies as a function of position of the field point.

8. The method according to claim 1, wherein the optical surface comprises a spherical surface.

9. The method according to claim 1, wherein the optical system is afocal.

10. A method of tolerancing an optica l surface of a lens element of an optical system which has a pupil and a n image plane, based on an interferogram that includes surface topography of the optica l surface, the method comprising:

a) defining for the optica l surface a local pupil region that has a corresponding field point in the image plane;

c) fitting a polynomial to the surface topography of the interferogram over the local pupil region, wherein the polynomial includes at least one coefficient C that relates at least one feature of the optical surface to the at least one performance metric; and

11. The method according to claim 10, further comprising repeating acts c) and d) for different locations of the local pupil region relative to the interferogram, wherein the different local pupil region locations have different corresponding field points in the image plane.

12. The method according to claim 11, wherein the tolerance T depends on the position of the field point in the image plane.

13. The method according to claim 11, wherein said repeating of acts c) and d) is performed by moving the local pupil region relative to the interferogram to cover substantially the entire interferogram.

14. The method according to claim 10, wherein the local pupil region has an area AR, the optical surface has an area AS, and wherein AR/AS < 0.75.

15. The method according to claim 14, wherein AR/AS < 0.65.

16. The method according to claim 10, wherein the at least one performance metric is selected from the group of performance metrics comprising: field curvature, distortion, Strehl ratio, depth of focus, wavefront error at the image plane, and modulation transfer function.

17. A method of tolerancing of a field surface of an optical element of an optical system based on an interferogram representative of surface topography of the field surface, comprising:

a) defining for the field surface a local pupil region that has a corresponding field point in an image plane of the optical system;

b) defining a tolerance T on at least one feature of the field surface within the local pupil region based on at least one performance metric of the optical system for the field point; c) fitting a polynomial to the surface topography of the interferogram over the local pupil region to obtain at least one polynomial coefficient C that relates at least one feature of the field surface to the at least one performance metric; and

18. The method of claim 17, wherein the optical system includes multiple field surfaces, and further comprising repeating acts a) through d) for each field surface.

19. The method of claim 17, wherein the optical system consists of refractive lens elements wherein in at least one of the refractive lens elements constitutes a field-lens element.

20. The method of claim 17, wherein the local pupil region has an area AR, the field surface has an area AS, and wherein AR/AS < 0.75.