Method and device for evaluating surface shape of optical element

Abstract

To provide a method that evaluates a surface shape of an optical surface of an optical element.SOLUTION: An optical element as a test object is completely arranged within a measuring range of an interferometric test device. Between individual measurements, the test object is rotated around a test object rotation axis. At least two measurement series are recorded that have a rotation position with M or N pieces of equidistances, where the numbers M and N are mutually prime natural numbers. First and second measurement values of the different measurement series are jointly evaluated. An evaluation operation involves using an iterative evaluation method, that is, a process of repeating identical or same evaluation steps a plurality of times in order to approach a sought end result step by step.SELECTED DRAWING: None

Description

[Technical Field]

[0001] The present invention relates to a method and apparatus for evaluating the surface shape of optical elements, particularly mirrors or lens elements in a microlithography projection exposure apparatus. [Background technology]

[0002] Photolithography and projection exposure systems are currently mainly used in the manufacture of semiconductor components and other microstructure components, such as masks for microlithography. In this process, a structural pattern fabricated for the mask (also called a reticle) is illuminated with illumination light shaped by an illumination system and projected onto a functional layer on a substrate using a projection lens, which is then covered with a photosensitive layer. After development of the photosensitive layer, the structure corresponding to the structural pattern is transferred to the functional layer by etching.

[0003] To enable the miniaturization of fabricated structures, over the past few decades, in addition to refractive and reflective optical systems that operate with light from the deep ultraviolet (DUV) region and have high image-side numerical apertures (NA) close to or greater than 1, with or without immersion, optical systems have also been developed that operate with smaller numerical apertures and achieve high resolution using electromagnetic radiation from the extremely ultraviolet (EUV) region, particularly in the 5nm to 30nm range, for example, with an operating wavelength of about 13.5nm. Since radiation from the extremely ultraviolet region (EUV radiation) is absorbed by transparent optical materials at higher wavelengths, mirror systems are used in EUV lithography.

[0004] Increasing the image-side numerical aperture tends to necessitate an increase in the required mirror area for mirrors used in projection exposure systems. As a result, in addition to manufacturing requirements, the technical demands for testing the surface shape of the mirrors are also becoming more stringent.

[0005] In the method described herein, the surface shape of an optical surface is tested using interferometry. In interferometry, the measurement wave reflected by the surface under test is generally superimposed on a reference wave, and the resulting interference pattern is captured. As a result, the actual shape of the surface accessible by measurement is compared to a desired target shape for testing using interferometry. The deviation is quantified based on the interferogram to determine whether it meets or exceeds manufacturing tolerances.

[0006] For historical reasons, the shape deviation of the optical surface of an object from its target shape is also called the shape error or "figure error amount (Figure)." Therefore, the terms "figure error amount measurement" or "figure error amount test" are often used to refer to such methods. The purpose of figure error amount measurement is to evaluate the figure error amount, i.e., the error of the object being measured, as accurately as possible.

[0007] One problem that arises with such measurement methods is that the interferometer setup is not actually ideal, and deviates from an ideal setup, for example, because the optical components located in the interferometer have deviations from a perfect surface shape and / or are not perfectly aligned. As a result, the reference wave may have errors, for example, because the wavefront of the reference wave does not correspond sufficiently accurately to the predetermined target wavefront. Such errors affect the measurement results as test setup errors, and the evaluation of the surface shape of the measured optical surface may become inaccurate.

[0008] Therefore, the central goal when seeking test results with sufficiently small errors is to reliably separate the error of the object being tested from the error of the test setup.

[0009] In some cases, rotational averaging is applied during shape error measurement to separate the error of the object being inspected from the error of the test setup. The optical element under inspection (hereinafter also referred to as the "object") is rotated by an equal distance around the axis of rotation between each measurement, and interferograms are acquired and evaluated at multiple different rotation positions. Rotational averaging can assign an "adjoint rotation" signature to the object, while "non-adjoint rotation" errors are attributed to the test setup. This provides a very good estimate of the absolute error. However, it cannot capture rotational symmetry and symmetry in the number of rotation positions, so-called undulations. For example, in a measurement method that uses 12 rotation positions for rotational average shape error measurement, it is impossible to distinguish between the 12-fold symmetry of the object error and the 12-fold symmetry of the test setup error.

[0010] Experiments show that higher-order errors tend to be smaller than lower-order errors. Therefore, they contribute less to the error in the final product. Thus, it is considered valuable to make the swell error as high-order as possible (e.g., 100th-order swell). However, this requires measuring more than 100 rotational positions, which necessitates very long measurement and machine times, thus contributing to the high cost of the final product.

[0011] Patent Document 1 describes a method for interferometrically measuring non-rotationally symmetric wavefront aberration in an object that can be progressively moved to multiple rotational positions by rotation around its rotation axis. At least one measurement result is confirmed at each rotational position. The measurement is performed in at least two measurement sequences (M,N), and the measurement results (M1…Mm, N1…Nm) of each measurement sequence (M,N) are confirmed at rotational positions of the object that are equidistant from each other. Each measurement sequence (M,N) includes measurements of specific numbers n and m, where m and n are natural numbers and relatively prime. Finally, all measurement results are mathematically evaluated. This measurement method can generate "N×M" symmetric swell errors very efficiently from "N+M" rotational positions. This method is based on the fact that it is possible to distinguish between object errors and setup errors related to M- and N-order swells by forming a difference between the N-shape error amount and the M-shape error amount. For this purpose, the N-rotational position measurement or the M-rotational position measurement is corrected by the formed NM-shape error. For the same number of measurement points, this method yields higher absolute accuracy than the rotational position test described above. In other words, this method can achieve accuracy comparable to that of a rotational position test with a significantly reduced number of measurement points.

[0012] Patent Document 2 describes another method for characterizing the surface shape of an optical element. In this method, numerous interference measurements are performed on the object under test, i.e., the optical element, with each measurement accompanied by the recording of an interferogram between a test wave and a reference wave emanating from each part of the optical element. Between these measurements, the position of the optical element relative to the test wave is changed stepwise by rotation around the rotation axis of the object under test. The amount of shape error of the optical element is calculated based on these measurements. The calculation is performed iteratively in multiple iterative steps, in which the amount of shape error of the optical element is confirmed in each case by performing a forward calculation, and each of these iterative steps is in each case based on a reference wave fitted based on the previous iterative step. This method is suitable for testing relatively large mirrors and the like, because it works even when it is not possible to capture the entire surface area of ​​the object under test in a single measurement, but only to record a sub-aperture that does not cover the entire area of ​​the object under test.

[0013] With the further development of optical systems for lithography, the number of optical elements with complex shapes has increased, and testing them using conventional techniques is either impossible or not possible in an economically viable way. The optical system includes, for example, a mirror having a non-rotationally symmetric shape and / or having a notch or hole that is not symmetrically located with respect to the center of symmetry of the optical element.

Prior Art Documents

Patent Documents

[0014]

Patent Document 1

Patent Document 2

Summary of the Invention

Problems to be Solved by the Invention

[0015] The problem addressed by the present invention is to provide a general method (using rotation of the test object) for evaluating the surface shape of the optical surface of an optical element, which enables reliable testing to be carried out within a relatively short total measurement time even when the test surface is not globally rotationally symmetric with respect to the axis used as the test object rotation axis during the test.

Means for Solving the Problems

[0016] To solve this problem, the present invention provides a method having the features of claim 1 and an apparatus having the features of claim 5. Preferred developments are specified in the dependent claims. The language of all claims is incorporated by reference into the content of this specification.

[0017] This method helps to evaluate the surface shape of the optical surface of an optical element. Therefore, it enables a shape error amount test. The optical element can be, for example, a mirror or a lens element that is part of the optical system of a microlithography projection exposure apparatus, such as a projection lens, in a usable mounted state. The optical element is incorporated into the test apparatus as a test object so that the test surface is completely disposed within the measurement region of the interference test apparatus. The term "test object" here refers to an optical element whose optical surface is tested regarding its shape or shape deviation, that is, it refers to the "tested element".

[0018] To test whether the shape of the surface sufficiently and accurately corresponds to the specification, multiple interference measurements are performed on the test object. In an interference measurement, a test wave emerging from the surface and a reference wave are superimposed or interfered, thereby generating an interferogram containing information about the surface shape. From the intensity distribution of the interferogram, measurement values can be confirmed, for example, in the form of wavefront or phase information, and subsequent evaluation is then performed based on it.

[0019] This method performs rotation of the test object. That is, between individual measurements, the rotational position of the test object with respect to the test apparatus is changed by a restricted rotation of the test object around the rotation axis of the test object. As a result, the test object is measured at a plurality of different rotational positions. In the evaluation operation, the measurement values obtained from the interferogram are evaluated together to confirm the shape information for evaluating the surface shape of the optical surface.

[0020] Similar to the method known from Patent Document 1, this method is assumed to perform at least two measurement series using different numbers of rotational positions. The first measurement series includes M first measurement values confirmed by the first measurement. The measurement values are related to M different equidistant rotational positions with a rotational angle difference of 360° / M between each other. The second measurement values are obtained in a similar manner and form a second measurement series including measurement values regarding N rotational positions. There is a rotational angle difference of 360° / N between the rotational positions at which the second measurement values are obtained. The numbers M and N are relatively prime natural numbers.

[0021] This conventional method yields good results when the target shape of the surface is rotationally symmetric with respect to an axis of symmetry, where the axis of symmetry is used as the axis of rotation of the object under test, and the surface under test is fully realized as long as it has a substantially circular outer contour around the axis of rotation and does not have gaps, notches, or holes that are not rotationally symmetric with respect to the axis of rotation. Such a surface under test is said to be rotationally symmetric in this context. When these conditions are met, the terminology used includes the "axial opening" test.

[0022] Furthermore, the present invention enables reliable testing of "off-axis openings," that is, objects whose test surface is not rotationally symmetrical across its entire surface. The steps proposed for this purpose are described below.

[0023] The essential difference between the method according to the claimed invention and the prior art described above lies in the evaluation of the measurement results. The evaluation process involves the use of an iterative evaluation method, that is, a process in which the same or similar evaluation steps are repeated multiple times to gradually approach the desired final result.

[0024] In step (A), a first shape error is calculated based on the first measurement. The first shape error is a common associated rotational shape error for the first measurement sequence. The first shape error contains shape information that is substantially equal in the first measurement for all M rotational positions. This is based on the consideration that the error actually caused by the shape deviation in the object appears the same at all rotational positions, but at different rotational positions with respect to the object's rotation axis. Therefore, the signature of this error in the interferogram rotates with the object. However, this method step does not allow obtaining the rotational symmetry error portion and the error portion related to the symmetry of the number of rotational positions. As a result, the result of method step (A) still includes the object error related to the Mth undulation and the contribution due to the test setup, i.e., the test setup error.

[0025] In the subsequent step (B), the aforementioned first shape error is subtracted from the first measurement (i.e., from the raw data of the first measurement) to determine the first test setup error. The first test setup error includes non-adjacent rotation errors of the first measurement sequence. These mainly include errors resulting from the improper alignment of the measurement setup, such as fluctuation errors during the rotation of the object under test. Furthermore, these include errors resulting from the deviation of the reference wave actually used from the ideally provided reference wave.

[0026] In the subsequent step (C), the first test setup error thus confirmed is used to calculate the corrected first shape error. The latter is obtained by subtracting the first test setup error from the first measurement, i.e., the raw data of the first measurement.

[0027] In this application, the above series of method steps is also referred to as the first cycle or M cycle. Since the underlying raw data (first measurement) exists at M rotational positions, the M cycle alone cannot distinguish between the error of the object being tested with respect to the Mth swell and the error of the test setup with respect to the Mth swell.

[0028] The method according to the claim makes it possible to separate errors related to M-order swells from errors related to N-order swells. For this purpose, in a somewhat abbreviated expression, the corrected specimen error related to the M-order swell (i.e., the reconstructed first shape error) is fed into or processed in the reconstruction of N rotational position cycles, where the raw data (the second measurement of the second measurement series) carries only the specimen error related to the N-order swell and the test setup error related to the N-order swell. The M-order swell in this cycle is registered only by the correction of the M rotational position cycles and suppressed by the reconstruction at N rotational positions. In other words, this makes it possible to separate the specimen error related to the M-order swell from the test setup error related to the M-order swell.

[0029] Therefore, in a subsequent step, the results of the first measurement series and the results of the second measurement series are "merged" in a specific manner. According to one embodiment of the present invention, this is done in method step (D) by subtracting the corrected first shape error amount confirmed in step (C) from the second measurement value in order to determine the second test setup error. Thus, in this step, information from the M cycle is introduced into the N cycle.

[0030] In step (E), the second test setup error thus confirmed is then used to calculate the corrected second shape error, which is obtained from the raw data of the second measurement sequence, taking the second test setup error into account.

[0031] Subsequently, in step (F), the first test setup error is corrected using the corrected second shape error. This is done by subtracting the corrected second shape error from the first measurement value in order to determine the first test setup error, which at this time includes the non-adjacent rotation error common to the first and second measurement sequences.

[0032] Subsequently, in step (G), the first corrected shape error is calculated again using this corrected first test setup error.

[0033] After the reconstruction of the N rotational position cycle, the reconstruction result is again fed into the reconstruction of the M rotational position cycle as a correction. This leads to correction or further suppression of the object error related to the Nth order swell.

[0034] This series of method steps can be repeated until a sufficiently accurate result is obtained for the surface morphology of the object under test, that is, until a specific convergence criterion is met. Therefore, step (H) includes a comparison with the convergence criterion and repetition of steps (A) to (H) depending on the result of the comparison.

[0035] By repeating these method steps multiple times, i.e., applying them iteratively, the separation of the object error for the Mth swell, the object error for the Nth swell, and the test setup error for the Mth swell and the test setup error for the Nth swell becomes better, so that only the common multiple, i.e., N × M, remains in the final result. Up to this point, this is similar to the method from Patent Document 1 mentioned above.

[0036] However, in contrast, the results of the M-cycle and N-cycle are calculated alternately in an iterative manner, so that corrections for the Nth-order and Mth-order swells are performed over the entire area through which the object passes. This calculation will also be referred to as "stitching" below. As a result, this means that information regarding the test setup error can be obtained for any part of the surface that was located in the measurement area at any stage of the measurement. Even if, in the case of a particular measurement, i.e., a particular rotation position, information is not obtained for a sub-region of the measurement area (leading to a "bad pixel" in this measurement), the test setup error can be reconstructed as long as this region can be measured at any of the rotation positions.

[0037] Thus, "stitching" prevents the duplication of invalid image regions and / or averaged edges. Therefore, this method is also applicable to objects whose region of interest is not rotationally symmetrical with respect to the object's axis of rotation. This could be the case, for example, with a mirror containing an off-axis notch to allow beams to pass through between other mirrors in an optical system in a multiple-fold beam path without vignetting. Another example is the surface of an elliptical mirror, where the outer contour is not circular but centered on the axis of symmetry of a nominally rotationally symmetric surface shape.

[0038] It may be sufficient to perform exactly two measurement series and evaluate their results together. In some embodiments, three or more measurement series, for example, three, four, or five measurement series, are performed and their results are calculated together. This may yield more accurate results, although it may increase the measurement time.

[0039] Further advantages and aspects of the present invention will become apparent from the description of exemplary embodiments of the present invention, which will be described below with reference to the claims and drawings. [Brief explanation of the drawing]

[0040] [Figure 1] A schematic diagram of the setup of an interferometry testing apparatus for evaluating the surface shape of the optical surface of an object under test is shown. [Figure 2] This document presents an evaluation algorithm for methods using conventional technology (PA). [Figure 3] This paper illustrates the mediating effect of M-order swells and the problems encountered during testing of off-axis openings using conventional methods. [Figure 4] A schematic outline of the method steps for the evaluation operation in one embodiment of the present invention is shown below. [Modes for carrying out the invention]

[0041] An exemplary embodiment of the method and measuring apparatus according to the present invention will be described below based on the evaluation of the surface shape of the optical surface of the projection lens or illumination system mirror of a microlithography projection exposure apparatus.

[0042] This method can be performed using various interference testing devices. Figure 1 is a very schematic basic diagram showing the setup of a test device 100 for evaluating the surface shape of the optical surface 210 of an object 200 in the form of an optical element. The test device is shown as an optical setup, such as a Michelson interferometer, as an example. It can also operate according to other interferometer principles; for example, the test device may be configured as a Fizeau interferometer. The test is based on the measurement results of the interference measurement, and for this reason, the test device 100 may also be referred to as a measuring device 100.

[0043] Interference testing apparatus 100, in particular, apparatus 150 comprising a light source 110, a reference element 120, a beam splitter 130, and a detector for capturing the resulting interference pattern. The apparatus may, for example, have a camera. Apparatus 150 is coupled to a control unit 160 which houses an evaluation unit 170, in particular a computer-based data processing unit, in which measurement operations are performed to evaluate the measured values ​​obtained from the interferogram. The control unit 160 functions to coordinate and control the operation of the automated testing apparatus.

[0044] The object under test is mounted in an object holder that is rotatably attached so that the surface under test 210 is completely positioned within the measurement area 140 of the test apparatus. The object holder is rotatable by a control unit so that the object under test rotates around the object rotation axis 220 in predetermined angular increments and stops at a specific rotation position.

[0045] The target shape of the surface 210 of the object 200 is rotationally symmetric (spherical or aspherical) with respect to the axis of symmetry of the surface. The object is housed such that the axis of symmetry corresponds as accurately as possible to the axis of rotation of the object.

[0046] Interferometry is performed on the object under test, and the interferogram between the test wave emanating from surface 210 and the reference wave emanating from the reference element is observed for each interferometry measurement. Between measurements, the rotational position of the object relative to the test apparatus is changed by a limited rotation of the object around the object rotation axis 220. In the evaluation operation, the interferogram or the measured values ​​obtained therefrom are also evaluated to confirm shape information for evaluating the surface shape of the optical surface.

[0047] To form the first measurement series, M measurements are performed. In this case, M measurement values are obtained at M rotational positions (M1, M2, etc.) having a rotational angle difference of 360° / M. To form the second measurement series, N measurement values (N1, N2, etc.) are obtained at N rotational positions having a rotational angle difference of 360° / M. In this case, M and N are relatively prime natural numbers. The M measurement values of the first measurement series are also referred to herein as "first measurement values", and the N measurement values of the second measurement series are correspondingly also referred to as "second measurement values". FIG. 1 shows the situation of the rotational positions based on an example of M = 3 and N = 5. In each measurement series, the rotational positions are arranged at equidistant or equally spaced angular positions over the full rotation of the test object 200.

[0048] Regarding these general aspects, the procedure corresponds to the method described in Patent Document 1, but the above method is modified to avoid specific drawbacks.

[0049] To deepen the understanding, first, the method known from Patent Document 1 will be described in more detail, and this method is also referred to herein as the "N + M method". The algorithm underlying this conventional method is schematically shown in FIG. 2. This method includes first recording measurement data or measurement values regarding equidistant rotational positions of 360° / N and 360° / M. These series or cycles of measurement value recordings are represented in FIG. 1 as N-CYC (N cycles) and M-CYC (M cycles), respectively. Each raw data is subsequently reconstructed at each step REC(P N ) and REC(P M ) to form the amount of form error for each cycle. In FIG. 2, P N represents N form error amounts derived from the N cycles, that is, the reconstructions from N rotational positions. The same applies to P M , that is, the form error amount (N form error amounts) from the M cycles. The reconstruction REC(P N ) of the N rotational positions for calculating the form error amount P N ) can be expressed as follows. Figure N =Figure+Errors rot +FigureSet-up N

[0050] The same applies to the M cycle. In this case, the parameter "Errors rot This includes rotationally symmetrical objects and test setup errors, i.e., errors that cannot be determined by rotational averaging. Parameter "FigureSet-up N This indicates the inseparable error of the Nth-order swell in the specimen and test setup. The reconstructed shape error quantities PN and PM each include the specimen and test setup errors related to the Mth-order swell.

[0051] These cannot be separated from each other due to the limited number of rotational positions. One advantage of this "M+M method" is that the reconstructed shape error quantities PN and PM for the Nth and Mth order swells separate the individual object and test setup errors for the Nth and Mth order swells from each other. As a result, only the swell of least common multiple N × M may remain in the final result.

[0052] To achieve this objective, in the subsequent method step DIFF, a difference is first formed between the two reconstructed shape error quantities, which is represented by the symbol "-" in Figure 2. This difference is accompanied by the Nth and Mth order swells of the object under test and the test setup error. The parameter CorrNM is calculated by the difference formation, and the following holds true for this parameter. Corr NM =FigureSet-up M -FigureSet-up N

[0053] In the subsequent step AVE, this difference is rotated over N equidistant 360° / N steps, and the difference from each rotation is averaged. This is described below. Corr NM_N =FigureSet-up N -FigureSet-up N×M

[0054] As a result, the M-th order swell is suppressed by averaging with coefficient N. This provides a good approximation of the N-th order swell of the test setup error using the residual of N × M-th order swells.

[0055] Next, in step CORR, this Nth-order swell can be corrected by subtracting it from the reconstructed N rotational position measurements. Figure M The correction can be described as follows: Figure N×M =Figure M -Corr NM_N =Figure+Errors rot +FigureSet-up N×M

[0056] Only the errors in the test object and test setup related to the N×M order swell remain in the final result, and these errors cannot be separated from each other using this method.

[0057] In the inventors' view, a practical drawback of this method is that applying this N+M rotational averaging method to a specific object can result in large regions where there are gaps in the shape error measurement results. Therefore, this "conventional" N+M rotational averaging method is only effective for openings that are rotationally symmetric throughout. These openings are also referred to herein as "on-axial openings." An on-axial opening exists when the surface under test is rotationally symmetric with respect to the object's axis of rotation and is realized throughout (i.e., without, for example, off-axial gaps or notches).

[0058] However, there are many geometric shapes of objects in which the surface under test is not rotationally symmetrical with respect to the axis of rotation of the object under test. One example is a mirror surface that has an off-axis and / or non-circular notch and / or a non-circular outer circumference. These cases are referred to as "off-axis openings" in this specification.

[0059] In the inventors' view, the main problem with the limited applicability of the N+M rotational position method in the case of off-axis openings is the CORR NM_NThe method for determining the Nth-order undulation involves the use of mediation between the object under test and the test setup error. Because the complete test setup aperture is not measured in the off-axis system, the measurement image consists of invalid pixels, i.e., image elements to which no region elements of the measurement area are assigned, at varying rates (depending on the shape of the object under test).

[0060] The averaging problem that arises in the off-axis N+M method will be explained with reference to Figure 3. Figure 3 schematically shows a plan view of the surface to be measured of the object under test 200, which has a circular outer circumference, and its center is used as the axis of rotation of the object under test 220. In this example, a notch 230, which can also be realized as a hole, is provided in the mirror, eccentric to the center. The small square symbols represent exemplary fourth-order swells from N cycles, and the cross marks represent exemplary third-order swells from M cycles.

[0061] Figure 3 clearly illustrates the mediating effect of the M-th order swell (when M=3). Subfigures ST1, ST2, ST3, and ST4 show four rotational positions of the object 200 in the form of a mirror with a notch 230 located outside the center (object rotation axis 220), each offset by 90° in the azimuthal direction. Furthermore, subfigure Corr_NM_N reveals the problem when invalid image regions overlap. Even with other averaging methods (e.g., methods where the invalid region value is intentionally set to "0"), edges occur at region boundaries, making the results inaccurate. For these reasons, the conventional N+M method works properly only with full-axis apertures.

[0062] Here, please refer briefly to the method described in Patent Document 2. This method is suitable for correcting overall test setup errors. Since different measurement results are calculated together in an iterative manner, the procedure used in this method is also referred to in this application as "iterative stitching." Here again, the method begins with recording the necessary measurement data. In this case, typically only a single measurement cycle at the corresponding N rotation positions is recorded. The number of individual measurements in this cycle is generally significantly greater than in the aforementioned N+M method. In this method, it is not possible to separate the object error related to the Nth order swell from the test setup error related to the Nth order swell.

[0063] The method according to the claimed invention herein presents an improvement. An exemplary embodiment will be described with reference to the schematic diagram in Figure 4. Figure 4 schematically shows a series of method steps of an evaluation operation used to evaluate measurements taken at different rotational positions. The text field enclosed by a short dashed line (represented as M-CYC on the right) relates to an M cycle, i.e., a series of measurements having M measurements. This series of measurements is also collectively referred to here as a first series of measurements having M first measurements. Correspondingly, the reference code N-CYC indicates an N cycle related to a second series of measurements having N measurements (second measurements). The related text field is enclosed by a long dashed line. The curved arrows connecting the blocks horizontally at the bottom of the figure indicate the repeatability of the evaluation method.

[0064] To enable the application of the conventionally known N+M method to off-axis systems, specific steps are performed during evaluation to separate the object error and test setup error related to the Nth and Mth order swells. In other words, the influence of the test setup error on all relevant measurement points on the surface under test can be reconstructed through an iterative procedure.

[0065] The test method begins with recording measurements, as illustrated in Figure 1, for the conventional N+M method. Therefore, in the first measurement sequence for, for example, M rotational positions, the corresponding interferograms are obtained, and the first measurement values ​​are derived from them. It is sufficient to record N rotational position cycles and M rotational position cycles for rotations at equidistant positions.

[0066] A difference from the known N+M method is that this method also allows for testing of off-axis systems in terms of their surface shape, although this occurs during evaluation.

[0067] The exemplary method in Figure 4 begins with an iteration performed in M ​​cycles, as an example. In this case, first, a first shape error P1 is calculated based on the first measurement (for M rotation positions). As illustrated, the first shape error is a common associated rotation shape error for the first measurement sequence. In this case, the error occurring at the corresponding location of each rotation position is related to the (rotated) object and not to the (fixed) test setup. This first shape error P1 is, so to speak, a first-order approximation of the actual shape error, i.e., the surface of the object.

[0068] The next step involves calculating the first test setup error PA1, which includes the common non-accompanied rotation error of the first measurement sequence. For this purpose, the first shape error P1 obtained above is subtracted from the first measurement value. In other words, the error associated with rotation of the object under test is subtracted from the error not associated with rotation of the object under test and assigned to the object under test and the test setup, respectively.

[0069] In the next method step, the first test setup error PA1 thus obtained is subsequently used to calculate the corrected first shape error P1K. This corrected first shape error is obtained from the first shape error P1 by subtracting the first test setup error PA1. Since there is underlying raw data at M rotational positions, i.e., raw data of the first measurement, this result, i.e., the corrected first shape error P1K, still includes the object error related to the Mth swell and the test setup error related to the Mth swell.

[0070] Next, in order to separate the error related to the M-th order swell from the error related to the N-th order swell, the reconstructed object error including the M-th order swell, i.e., the corrected first shape error P1K, is introduced into the corresponding reconstruction of the N rotation position cycle N-CYC. This change to the other cycle is represented by the diagonal arrow W1. In the image of Figure 4, the corrected first shape error P1K is thus subtracted from the second measurement, i.e., from the raw data of the N cycle. As a result, the second test setup error PA2 is obtained based on the measurement of the N cycle. In a subsequent method step, the corrected second shape error P2K is calculated using the above second test setup error. The corrected second shape error P2K is obtained from the raw data of the second measurement sequence (second measurement) taking the second test setup error into account.

[0071] After this reconstruction of the N rotational position cycle, the reconstruction result (i.e., the corrected second shape error amount P2K) is reintroduced as a correction to the reconstruction of the N rotational position cycle, represented by the diagonal arrow W2. This method step leads to the suppression or correction of the object error related to the Nth order undulation.

[0072] The corrected second shape error P2K is then used to correct the first test setup error PA1 by subtracting the corrected second shape error P2K from the raw data of N cycles, i.e., from the first measured value. The resulting corrected first test setup error PA1K still contains only the common swell error of both the first and second measurement sequences, i.e., both the M cycle and the N cycle.

[0073] Through the iterative application of this method, the errors in the test object and test setup related to the Mth and Nth order swells are more reliably separated from each other, ideally leaving only the common multiple, i.e., N × M, in the final result, similar to the conventional N+M method. This algorithm gradually approaches the final result. Each obtained result is compared with the convergence criterion, and if the convergence criterion is found to be met, the calculation can be terminated. Otherwise, the iterative loop is performed at least one more time.

[0074] Only the least common multiple, i.e., N × M, remains in the final result RES, which in this respect corresponds to the conventional N + M method. However, in this method, by including the execution of iterative cross-calculation of the results of two cycles relating to different undulations (iterative stitching), correction for Nth and Mth undulations can be performed over the entire area through which the object passes, and therefore no invalid image regions or overlapping averaged edges (as shown in Figure 3) occur.

Claims

1. A method for evaluating the surface shape of an optical surface of an optical element, comprising: the optical element is incorporated into the test apparatus as a test object so that the optical surface is completely positioned within a measurement region of the interference test apparatus; A plurality of interferometric measurements are performed on the test object; and Between the measurements, the rotational position of the specimen relative to the test apparatus is changed by limited rotation of the specimen about a specimen rotation axis; To form a first measurement sequence by the first measurement, M first measurement values ​​are acquired at M rotational positions having a rotational angle difference of 360° / M, and to form a second measurement sequence, N second measurement values ​​are acquired at N rotational positions having a rotational angle difference of 360° / N, where M and N are relatively prime natural numbers; and In an evaluation operation, measurements are also evaluated to ascertain shape information for evaluating the surface shape of the optical surface; The evaluation operation includes the steps of: (A) calculating a first geometric error amount based on the first measurements, the first geometric error amount being a common associated rotational geometric error amount of the first measurement series; (B) subtracting the first geometric error amount from the first measurements to determine a first test setup error including a common non-associative rotation error of the first measurement series; (C) calculating, using the first test setup error, a corrected first shape error amount obtained from the first shape error amount by subtracting the first test setup error; (D) subtracting the corrected first shape error amount from the second measurement to obtain a second test setup error; (E) using the second test setup errors to calculate a corrected second figure error amount resulting from the second measurements taking into account the second test setup errors; (F) correcting the first test setup error by subtracting the corrected second shape error amount from the first measurement values ​​to obtain a corrected first test setup error including a common non-associative rotation error of the first measurement series and the second measurement series; (G) calculating a compensated first shape error amount again using the compensated first test setup error; (H) comparing the result with a convergence criterion and optionally repeating steps (A) through (H) depending on the result of the comparison; How it is performed iteratively.

2. 2. The method of claim 1, wherein a specimen in the form of a mirror (200) is tested, said mirror having a reflective surface (210), the surface area of ​​which is not rotationally symmetric about an axis of symmetry.

3. 3. The method of claim 2, wherein the mirror has an off-center hole (230).

4. 4. The method according to claim 1, wherein three or more measurement series are carried out and the results are calculated relative to one another.

5. An apparatus (100) for evaluating the surface shape of an optical surface of an optical element, characterized in that it is configured to perform the method according to claim 1.

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