An active compensation method for system errors of an interferometer wavefront

Abstract

The application discloses an active compensation method for wavefront system error of an interferometer, and provides active compensation for wavefront error introduced by a second collimating lens in a large-aperture interferometer. Firstly, an interferometric reference light path system model is established in optical design software Zemax; a polynomial is used to represent wavefront introduced by the second collimating lens; a self-defined surface type in Zemax is used to realize modeling of surface shape error, material uniformity error, residual stress, clamping deformation, gravity deformation and other system errors of the second collimating lens, and to simulate and analyze the influence of the system errors on the reference wavefront. On the basis of accurate modeling of the interferometric system, system errors caused by the above error sources in the reference wavefront of the large-aperture interferometer are compensated by controlling the surface shape parameters of a deformable mirror. The application accurately models the system errors introduced by the second collimating lens in the reference wavefront, and compensates the wavefront error by controlling the surface sag of the deformable mirror, so that the precision is high and the practicability is good.

Description

Technical Field

[0001] This invention relates to the field of optical design for precision optical instruments, specifically to an active compensation method for wavefront system errors in interferometers, which is particularly suitable for large-aperture planar interferometers. Background Technology

[0002] An interferometer is an instrument that uses optical interferometry to perform non-contact measurements on the order of wavelength, making it one of the most effective and accurate methods for inspecting optical components and systems. With the development of science and technology, large optical components are increasingly being used in cutting-edge scientific fields such as astronomy, aerospace, and energy, leading to a growing demand for the inspection of large-aperture planar optical components. Large-aperture interferometers can directly measure the surface shape of large-aperture optical components, and this method offers high accuracy and measurement efficiency.

[0003] The wavefront error introduced by the large-aperture collimating lens in a large-aperture interferometer is a systematic error caused by factors such as the machining error of the collimating objective lens surface, material inhomogeneity, residual stress, clamping error of the support structure, and gravitational deformation of the large-aperture element. Among these, surface machining error refers to the difference between the machined surface and the theoretical surface shape, which affects the quality of the emitted wavefront; material inhomogeneity is due to the uneven distribution of the refractive index of the optical material, resulting in different optical path differences after light passes through a certain thickness of optical material; residual stress can destroy the isotropic property that the optical glass should possess, and the uneven distribution of residual stress leads to inconsistent refractive index distribution, causing wavefront deformation after passing through the optical glass and deteriorating image quality; gravitational deformation refers to the surface shape change caused by the gravity of the large-aperture element; in addition, there is mirror surface deformation caused by support and clamping. Support deformation is mainly divided into rigid displacement components such as mirror rotation, translation, and tilt, as well as mirror surface distortion components. Clamping deformation changes with different clamping methods.

[0004] If the wavefront deformation caused by the aforementioned errors is within the system's aberration tolerance range, it will not affect the measurement results. However, in large-aperture interferometer systems, due to the large aperture of the optical elements and the corresponding material thickness reaching over 100 millimeters, the wavefront error PV value can reach over 1λ, causing non-negligible aberrations to the collimated wavefront, which in turn leads to wavefront transmission deformation, affecting the accuracy of interferometric measurements. Therefore, it is necessary to consider and compensate for the wavefront error introduced by the large-aperture collimating lens.

[0005] Currently, there are various detection methods for factors such as surface processing errors, material inhomogeneity, residual stress, clamping errors of support structures, and gravitational deformation of large-diameter components. For example, the surface error of large-diameter planar components can be detected using a rotation-translation method absolute inspection device, but large-diameter planar optics are bulky, and repeated installation and rotation of the flat crystal are not practical. Regarding the inhomogeneity of optical materials, Liu Yangzhou of Zhejiang University, in "The Influence of Material Inhomogeneity on Imaging Quality in High-Accuracy Optical Systems" (Chinese Journal of Photonics, 2013, 42(004):451-455), used the Runge-Kutta method to achieve ray tracing and analyzed the influence of the uneven refractive index distribution at different positions of the blank glass on the system aberrations. The detection of residual stress in materials still requires the use of a zero-order waveplate of the same diameter, which is a difficult drawback to overcome for the detection of stress in large-diameter components. It can be seen that as the diameter of the measured sample increases, the measurement difficulty increases, and there is no unified compensation method for the various factors that cause systematic errors. Summary of the Invention

[0006] The purpose of this invention is to provide an error compensation method for wavefront systematic errors caused by factors such as surface shape error of large-aperture collimating lens, material inhomogeneity, residual stress, gravitational deformation, support and clamping errors in large-aperture interferometers. By introducing a deformable mirror into the interference optical path, the wavefront systematic errors can be compensated by controlling the change of the surface sag of the deformable mirror, without having to calibrate each of the above error sources or design suppression schemes.

[0007] The technical solution to achieve the objective of this invention is: an active compensation method for interferometer wavefront system errors, comprising the following steps:

[0008] Step 1: Add a deformable mirror to the optical path of the large-aperture interferometer, as follows:

[0009] The optical path of the large-aperture interferometer includes a laser, a first collimating lens, a beam splitter, a beam splitter plate, a first plane mirror, a second collimating lens, a reference flat crystal, and a second plane mirror. The laser emits a collimated wavefront W, which is transmitted through the first collimating lens and then enters the beam splitter. After being transmitted through the beam splitter, it enters the deformable mirror, is reflected by the deformable mirror, and is then reflected by the beam splitter into the beam splitter plate. The beam splitter then reflects into the first plane mirror, and is reflected by the first plane mirror to the second collimating lens. After passing through the second collimating lens, the beam is expanded, its aperture becomes larger, and it is emitted as collimated light. This collimated light is then reflected back to the second collimating lens by the standard flat crystal, then reflected by the first plane mirror, transmitted through the beam splitter plate, and then reflected by the second plane mirror to form a reference wavefront, proceeding to step 2.

[0010] Step 2: Use the ray transformation matrix to calibrate the systematic error introduced by the second collimating lens. The ray transformation matrices of the rays transmitted through the second collimating lens from the two directions are T. c1and T c2 That is, the transformation matrix of the rays emitted after entering the second collimating lens from the first plane mirror is T. c1 The transformation matrix of the rays emitted after entering the second collimating lens from the reference optical plane is T. c2 Proceed to step 3.

[0011] Step 3: Perform target sampling on the collimated wavefront W emitted by the laser. The collimated wavefront W consists of N light vectors, W = [r1 … r2]. j … r N ], j = 1, 2, ..., N, where the j-th ray vector r j From the ray coordinates (x j ,y j ) and gradient (G) xj G yj ) constitutes, i.e., r j =[G xj G yj x j y j ] T Proceed to step 4.

[0012] Step 4: Determine the matrix transformation relationship between the reference wavefront W' and the collimated wavefront W based on the actual optical path layout:

[0013] W'=T9T d7 T6T d5 T c2 T d6 T8T d6 T c1 T d5 T6T d4 T5T d3 T3T d2 T D T d1 T2W

[0014] Where T2, T3, T5, T6, T8, and T9 correspond to the ray transformation matrices on the surfaces of the first collimating lens, beam splitter, beam splitter plate, first plane mirror, reference flat crystal, and second plane mirror, respectively, and the ray transformation matrix T D Characterizing the effect of deformable mirrors on light, T d1 Let T be the transformation matrix for light propagation in free space between the first collimating lens and the deformable mirror. d2 Let T be the transformation matrix for light propagation in the free space between the deformable mirror and the beam splitter. d3 Let T be the transformation matrix for light propagation in the free space between the beam splitter and the beam splitter plate. d4 Let T be the transformation matrix for light propagation in the free space between the beam splitter and the first plane mirror.d5 Let T be the transformation matrix for the propagation of light in free space between the first plane mirror and the second collimating lens. d6 Let T be the transformation matrix for light propagation in free space between the second collimating lens and the reference flat. d7 Given the transformation matrix for the propagation of light in the free space between the first and second plane mirrors, proceed to step 5.

[0015] Step 5: Assuming the reference wavefront W' is an ideal spherical wave, solve for the gradient matrix G of the corresponding surface of the deformable mirror. D :

[0016] G D =[N1 … N j … N N ]

[0017] Where, N j This represents the local normal direction vector of the deformable mirror surface.

[0018] Proceed to step 6.

[0019] Step 6: Use a vector-form numerical orthogonal Zernike gradient polynomial as the basis function G to characterize G. D :

[0020] G D =G*α

[0021] Where α is a vector composed of the weights of each numerically quantified orthogonal gradient polynomial.

[0022] Proceed to step 7.

[0023] Step 7: Solve for the distribution matrix of the surface sag z of the deformable mirror:

[0024] z=Zγ

[0025] In the formula, Z is the numerical matrix of the Zernike circular domain polynomial excluding the constant term, and γ is the coefficient matrix corresponding to the surface sag z of the deformable mirror.

[0026] Proceed to step 8.

[0027] Step 8: Adjust the shape of the deformable mirror according to the theoretically calculated surface height distribution matrix z to achieve active compensation for systematic errors in the interferometer wavefront.

[0028] Compared with the prior art, the significant advantages of this invention are:

[0029] (1) The systematic error introduced by the second collimating lens in the interferometer wavefront is directly characterized by the ray transformation matrix. There is no need to calibrate the sources of error such as large-diameter surface processing error, material inhomogeneity, residual stress, gravity deformation, support and clamping, and design error compensation schemes for each.

[0030] (2) The influence of the deformable mirror on the wavefront of the interferometer system is calculated using matrix optics theory, and the wavefront error is then compensated. Therefore, the layout of the deformable mirror is more flexible, no longer limited by the pupil plane, and can be located at any position in the optical path. There are also no strict requirements on the aperture size of the deformable mirror.

[0031] (3) The method of establishing the mathematical relationship between errors originating from systematic errors by using the optical transmission matrix is ​​not limited by the optical path layout, has a wide range of applications, and is highly practical. Attached Figure Description

[0032] Figure 1 This is a schematic diagram of the beam expander of the large-aperture interferometer of the present invention.

[0033] Figure 2 This is a flowchart of the active compensation method for interferometer wavefront system errors described in this invention.

[0034] Figure 3 This is the output wavefront diagram of the beam expander system when the second collimating lens has no error.

[0035] Figure 4 The wavefront diagrams are shown when errors are introduced into the second collimating lens, where (a) to (c) correspond to tilt error, coma, and astigmatism in wave aberrations, respectively.

[0036] Figure 5 In response to Figure 4 The wavefront error of the interferometer and the surface shape distribution of the deformable mirror active compensation are shown in Figures (a) to (c), which correspond to the wavefront error of the interferometer and the surface shape distribution of the deformable mirror active compensation. Figure 4 The active compensation surface shape distribution of deformable mirrors for tilt error, coma and astigmatism present in mid-wave aberrations.

[0037] Figure 6 The images show the outgoing wavefront after active compensation using deformable mirrors, where (a) to (c) correspond to the wavefront images after active compensation using deformable mirrors. Figure 4 The tilt error, coma, and astigmatism present in mid-wave aberrations are actively compensated by adjusting the sagittal height of the deformable mirror, as shown in the outgoing wavefront diagram of the interferometric system's optical path. Detailed Implementation

[0038] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings.

[0039] Combination Figure 1 and Figure 2 An active compensation method for interferometer wavefront systematic errors is proposed, applicable to conventional interferometers and also suitable for large-aperture (1m aperture) interferometers. The specific steps are as follows:

[0040] The optical path of the large-aperture interferometer system includes a laser 1, a first collimating lens 2, a beam splitter 3, a deformable mirror 4, a beam splitter 5, a first plane mirror 6, a second collimating lens 7, a reference flat crystal 8, and a second plane mirror 9. The aperture of the first collimating lens 6 is smaller than that of the second collimating lens 7.

[0041] Step 1: Laser 1 generates a collimated wavefront W. This wavefront is transmitted through the first collimating lens 2 and then enters the beam splitter prism 3. After being transmitted through the beam splitter prism 3, it enters the deformable mirror 4. After being reflected by the deformable mirror 4, it is reflected again by the beam splitter prism 3 into the beam splitter 5. After being reflected by the beam splitter 5, it enters the first plane mirror 6 and is reflected by the first plane mirror 6 to the second collimating lens 7. After passing through the second collimating lens 7, the collimated wavefront W is expanded, the aperture is increased, and collimated light is emitted. This collimated light is then reflected back to the second collimating lens 7 by the standard flat crystal 8, then reflected by the first plane mirror 6, transmitted through the beam splitter 5, and then reflected by the second plane mirror 9 to form a reference wavefront W'. The first collimating lens 2 and the second collimating lens 7 constitute a beam expander group to realize the beam expansion of the collimated wavefront W. The beam splitter prism 3, the beam splitter 5, the first plane mirror 6, and the second plane mirror 7 are used to fold the optical path, making the optical path structure more compact. This optical path layout is not unique.

[0042] Step 2: Use the ray transformation matrix to calibrate the systematic error introduced by the second collimating lens 7. The ray transformation matrices of the rays transmitted through the second collimating lens 7 from two directions are T. c1 and T c2 That is, the transformation matrix of the light rays reflected by the first plane mirror 6 and transmitted through the second collimating lens 7 is T. c1 The transformation matrix of the light rays reflected from the reference flat crystal 8 and transmitted through the second collimating lens 7 is T. c2 .

[0043] Step 3: Sample the collimated wavefront W emitted from laser 1. The collimated wavefront W consists of N rays, W = [r1 … r2]. j … r N ], j = 1, 2, ..., N, where the j-th ray vector r j From the ray coordinates (x j ,y j ) and gradient (G) xj G yj ) constitutes, i.e., r j =[G xj G yjx j y j ] T .

[0044] Step 4: Determine the matrix transformation relationship between the reference wavefront W' and the collimated wavefront W based on the actual optical path layout:

[0045] W'=T9T d7 T6T d5 T c2 T d6 T8T d6 T c1 T d5 T6T d4 T5T d3 T3T d2 T D T d1 T2W

[0046] Where T2, T3, T5, T6, T8, and T9 correspond to the ray transformation matrices on the surfaces of the first collimating lens 2, the beam splitter prism 3, the beam splitter 5, the first plane mirror 6, the reference flat crystal 8, and the second plane mirror 7, respectively, and the ray transformation matrix T D Characterizing the effect of deformable mirror 4 on light, T d1 Let T be the transformation matrix for light propagation in free space between the first collimating lens 2 and the deformable mirror 4. d2 Let T be the transformation matrix for light propagation in the free space between deformable mirror 4 and beam splitter 3. d3 Let T be the transformation matrix for the propagation of light in the free space between beam splitter 3 and beam splitter 5. d4 Let T be the transformation matrix for the propagation of light in the free space between the beam splitter 5 and the first planar mirror 6. d5 Let T be the transformation matrix for the propagation of light in free space between the first plane mirror 6 and the second collimating lens 7. d6 T is the transformation matrix for light propagation in free space between the second collimating lens 7 and the reference flat lens 8. d7 It is the transformation matrix for the transmission of light in the free space between the first plane mirror 6 and the second plane mirror 9.

[0047] Step 5: Based on the ray transformation matrix in Step 4, the ray matrix W that is incident on the surface of the deformable mirror 4 after passing through the first collimating lens 2. in The matrix transformation relationship with the collimated wavefront W is as follows:

[0048] W in =T d1 T2W

[0049] W in Composed of N ray vectors, Win =[r in1 … r inj … r inN ], j = 1, 2, ..., N, where the j-th ray vector r inj From the ray coordinates (x inj ,y inj ) and direction vector (Gx inj ,Gy inj ) constitutes, i.e., r inj =[Gx inj Gy inj x inj y inj ] T .

[0050] If deformable mirror 4 is used to compensate for the systematic error in the reference spherical wave, then it can be assumed that the compensated reference wavefront W' is an ideal spherical wave, and the ray matrix W after reflection by deformable mirror 4 is... out Matrix transformation relationship with reference wavefront W':

[0051] W out =[T9T d7 T6T d5 T c2 T d6 T8T d6 T c1 T d5 T6T d4 T5T d3 T3T d2 ] -1 W′

[0052] W out Composed of N ray vectors, W out =[r out1 … r outj … r outN ], j = 1, 2, ..., N, where the j-th ray vector r outj From the ray coordinates (xo utj yo utj ) and direction vector (Gxo) utj Gyo utj ) constitutes, i.e., r outj =[Gx outj Gy outj x outj y outj ] T .

[0053] Using the incident ray vector (Gx) of the j-th ray on the surface of deformable mirror 4 inj ,Gy inj) and the outgoing ray vector (Gx) on the surface of deformable mirror 4 outj ,Gy outj Solve for the local normal direction vector N of the deformable mirror. j :

[0054]

[0055] Deformable mirror 4 local normal direction vector N j The set of elements constitutes the surface gradient matrix G of deformable mirror 4. D :

[0056] G D =[N1 … N j … N N ]

[0057] Step 6: Use a vector-form numerical orthogonal Zernike gradient polynomial as the basis function G to characterize G. D :

[0058] G D =G*α

[0059] Where α is a vector composed of the weights of each numerically quantified orthogonal gradient polynomial.

[0060] Step 7: Solve for the distribution matrix of the surface elevation z of deformable mirror 4:

[0061] z=Zγ

[0062] In the formula, Z is the numerical matrix of the Zernike circular domain polynomial excluding the constant term, and γ is the coefficient matrix corresponding to the surface elevation z of the deformable mirror 4.

[0063]

[0064] in, Let α be the efficient estimate of α based on the least squares method; M is the transformation matrix that transforms the Zernike circular domain orthogonal polynomial into a numerical orthogonal polynomial; D is the transformation matrix that transforms the Zernike circular domain orthogonal gradient polynomial into a numerical orthogonal gradient polynomial.

[0065] Step 8: Adjust the shape of the deformable mirror according to the surface height distribution matrix z of the deformable mirror 4 obtained by theoretical calculation to achieve active compensation for the systematic error in the wavefront of the interferometer.

[0066] Example 1

[0067] Combination Figures 1 to 6This paper presents a method for compensating for systematic errors in the wavefront of an interferometer, particularly suitable for large-aperture interferometers with a 1-meter aperture and a working wavelength of 633nm. The collimated wavefront W emitted from laser 1 has an aperture of 100mm, the first collimating lens 2 has an aperture of 108mm, and the second collimating lens 7 and the reference flat crystal 8 have apertures of 1080mm, made of BK7 glass. When the second collimating lens 7 does not introduce systematic errors, the interferometer system wavefront W' is as follows: Figure 3 As shown, due to the combined effects of factors such as the machining error of the second collimating lens 7 surface, material inhomogeneity, residual stress, gravitational deformation, support and clamping errors, etc., in practical applications, systematic errors will exist in the wavefront W' of the interferometer system. Figure 4 Figures (a) to (c) correspond to the system output wavefront diagrams when the interferometer reference wavefront W' has tilt error, coma, and astigmatism under the influence of various error factors, with PV values ​​of 4.9910λ, 5.2234λ, and 5.2242λ, respectively. To address this issue, the present invention proposes an active compensation method for interferometer wavefront system errors, the implementation steps of which are as follows:

[0068] Step 1: Add a deformable mirror 4 to the optical path of the large-aperture interferometer. The optical path of the large-aperture interferometer includes a laser 1, a first collimating lens 2, a beam splitter 3, a deformable mirror 4, a beam splitter 5, a first plane mirror 6, a second collimating lens 7, a reference flat crystal 8, and a second plane mirror 9. The laser generates a collimated wavefront W, which is transmitted through the first collimating lens 2 and then enters the beam splitter 3. After being transmitted through the beam splitter 3, it enters the deformable mirror 4, is reflected by the deformable mirror 4, and then reflected again by the beam splitter 3 into the beam splitter 5. The beam splitter 5 reflects the wavefront into the first plane mirror 6, and then reflects it to the second collimating lens 7. Finally, the wavefront is reflected by the second plane mirror 9. The collimating lens 7 expands the collimated wavefront W to a diameter of 1000mm and emits collimated light. This collimated light is then reflected back to the second collimating lens 7 by the standard flat crystal 8, then reflected by the first plane mirror 6, then transmitted through the beam splitter 5, and finally reflected by the second plane mirror 9 to form the reference wavefront W'. The first collimating lens 2 and the second collimating lens 7 constitute a beam expander group, expanding the collimated wavefront W with a diameter of 100mm to 1000mm. The beam splitter prism 3, beam splitter 5, first plane mirror 6 and second plane mirror 7 are used to fold the optical path, making the optical path structure more compact. This optical path layout is not unique.

[0069] Step 2: Use the ray transformation matrix to calibrate the systematic error introduced by the second collimating lens 7. The ray transformation matrices of the rays transmitted through the second collimating lens 7 from two directions are T. c1 and T c2 That is, the transformation matrix of the light rays reflected by the first plane mirror 6 and transmitted through the second collimating lens 7 is T. c1The transformation matrix of the light rays reflected from the reference flat crystal 8 and transmitted through the second collimating lens 7 is T. c2 .

[0070] Step 3: Sample the collimated wavefront W emitted from laser 1. The collimated wavefront W consists of N rays, W = [r1 … r2]. j … r N ], j = 1, 2, ..., N, where the j-th ray vector r j From the ray coordinates (x j ,y j ) and gradient (G) xj G yj ) constitutes, i.e., r j =[G xj G yj x j y j ] T .

[0071] Step 4, Combining Figure 1 The optical path layout shown determines the matrix transformation relationship between the reference wavefront W' and the collimated wavefront W:

[0072] W'=T9T d7 T6T d5 T c2 T d6 T8T d6 T c1 T d5 T6T d4 T5T d3 T3T d2 T D T d1 T2W

[0073] Where T2, T3, T5, T6, T8, and T9 correspond to the ray transformation matrices on the surfaces of the first collimating lens 2, the beam splitter prism 3, the beam splitter 5, the first plane mirror 6, the reference flat crystal 8, and the second plane mirror 9, respectively, and the ray transformation matrix T D Characterizing the effect of deformable mirror 4 on light, T d1 Let T be the transformation matrix for light propagation in free space between the first collimating lens 2 and the deformable mirror 4. d2 Let T be the transformation matrix for light propagation in the free space between deformable mirror 4 and beam splitter 3. d3 Let T be the transformation matrix for the propagation of light in the free space between beam splitter 3 and beam splitter 5. d4 Let T be the transformation matrix for the propagation of light in the free space between the beam splitter 5 and the first planar mirror 6. d5Let T be the transformation matrix for the propagation of light in free space between the first plane mirror 6 and the second collimating lens 7. d6 T is the transformation matrix for light propagation in free space between the second collimating lens 7 and the reference flat lens 8. d7 It is the transformation matrix for the transmission of light in the free space between the first plane mirror 6 and the second plane mirror 9.

[0074] Step 5: Based on the ray transformation matrix in Step 4, the ray matrix W that is incident on the surface of the deformable mirror 4 after passing through the first collimating lens 2. in The matrix transformation relationship with the collimated wavefront W:

[0075] W in =T d1 T2W

[0076] W in Composed of N ray vectors, W in =[r in1 … r inj … r inN ], j = 1, 2, ..., N, where the j-th ray vector r inj From the ray coordinates (x inj ,y inj ) and direction vector (Gx inj ,Gy inj ) constitutes, i.e., r inj =[Gx inj Gy inj x inj y inj ] T ;

[0077] If deformable mirror 4 is used to compensate for the systematic error in the reference spherical wave, then it can be assumed that the compensated reference wavefront W' is an ideal spherical wave, and the ray matrix W after reflection by deformable mirror 4 is... out Matrix transformation relationship with reference wavefront W':

[0078] W out =[T9T d7 T6T d5 T c2 T d6 T8T d6 T c1 T d5 T6T d4 T5T d3 T3T d2 ] -1 W′

[0079] W out Composed of N ray vectors, W out =[rout1 … r outj … r outN ], j = 1, 2, ..., N, where the j-th ray vector r outj From the ray coordinates (x outj ,y outj ) and direction vector (Gx outj ,Gy outj ) constitutes, i.e., r outj =[Gx outj Gy outj x outj y outj ] T ;

[0080] Using the incident ray direction vector (Gx) in front of deformable mirror 4 inj ,Gy inj ) and the direction vector of the outgoing light ray after deformable mirror 4 (Gx outj ,Gy outj Solve for the local normal direction vector N of deformable mirror 4. j :

[0081]

[0082] Deformable mirror 4 local normal direction vector N j The set of elements constitutes the surface gradient matrix G of deformable mirror 4. D :

[0083] G D =[N1 … N j … N N ]

[0084] Step 6: Use a vector-form numerical orthogonal Zernike gradient polynomial as the basis function G to characterize G. D :

[0085] G D =G*α

[0086] Where α is a vector composed of the weights of each numerically quantified orthogonal gradient polynomial.

[0087] Step 7: Solve for the distribution matrix of the surface elevation z of deformable mirror 4:

[0088] z=Zγ

[0089] In the formula, Z is the numerical matrix of the Zernike circular domain polynomial excluding the constant term, and γ is the coefficient matrix corresponding to the surface sag z of the deformable mirror:

[0090]

[0091] in, Let α be the efficient estimate of α based on the least squares method; M is the transformation matrix that transforms the Zernike circular domain orthogonal polynomial into a numerical orthogonal polynomial; D is the transformation matrix that transforms the Zernike circular domain orthogonal gradient polynomial into a numerical orthogonal gradient polynomial.

[0092] Figure 5 Figures (a) to (c) are for... Figure 4 The system errors in Figures (a) to (c) are actively compensated, and the resulting sag distribution of deformable mirror 4 is calculated. The sag PV values ​​are 0.0378 mm, 0.0136 mm, and 0.0014 mm, respectively.

[0093] Step 8: Adjust the elevation distribution of the deformable mirror according to the theoretically calculated surface elevation distribution matrix z of deformable mirror 4, i.e. Figure 5 Figures (a) to (c) show the active compensation performed on various systematic errors present in the emitted wavefront. The reference wavefront W' emitted by the large-aperture interferometric system after compensation is as follows: Figure 6 As shown in Figures (a) to (c), the wavefront PV values ​​are 0.0089λ, 0.0118λ, and 0.0056λ, respectively, which meet the design requirements of the interferometer system for the reference wavefront and realize the active compensation for systematic errors in the interferometer wavefront.

[0094] This example addresses three typical error distribution types introduced by large-aperture collimating objectives. Through a series of measures, it achieves active compensation for wavefront system errors in a large-aperture interferometer. The final result is a reference wavefront that meets design requirements. This example demonstrates that even with complex and diverse error sources and distribution types, this method can effectively achieve active compensation for wavefront errors in large-aperture interferometric optical paths. Furthermore, this method offers high accuracy, practicality, and flexibility.

Claims

1. An active compensation method for interferometer wavefront systematic errors, characterized in that, The steps are as follows: Step 1: Add a deformable mirror (4) to the optical path of the large-aperture interferometer, as follows: The optical path of the large-aperture interferometer includes a laser (1), a first collimating lens (2), a beam splitter (3), a beam splitter (5), a first plane mirror (6), a second collimating lens (7), a reference flat crystal (8), and a second plane mirror (9). The laser (1) emits a collimated wavefront W, which is transmitted through the first collimating lens (2) and then enters the beam splitter (3). After being transmitted through the beam splitter (3), it enters the deformable mirror (4), and after being reflected by the deformable mirror (4), it passes through the beam splitter again. The mirror (3) reflects the beam into the beam splitter (5), and then the beam splitter (5) reflects the beam into the first plane mirror (6). The beam is then reflected by the first plane mirror (6) to the second collimating lens (7). After passing through the second collimating lens (7), the beam is expanded, the aperture becomes larger, and the collimated light is emitted. The collimated light is then reflected back to the second collimating lens (7) by the standard flat crystal (8), and then reflected by the first plane mirror (6). It is then transmitted through the beam splitter (5) and then reflected by the second plane mirror (9) to form a reference wavefront. Step 2: Use the ray transformation matrix to calibrate the systematic error introduced by the second collimating lens (7). The ray transformation matrices of the rays transmitted through the second collimating lens (7) from two directions are respectively and That is, the transformation matrix of the rays emitted after entering the second collimating lens (7) from the first plane mirror (6) is: The transformation matrix of the rays emitted after entering the second collimating lens (7) from the reference flat (8) is: ; Step 3: Perform target sampling on the collimated wavefront W emitted from the laser (1). The collimated wavefront W is composed of N light vectors. , where the j-th ray vector From ray coordinates and gradient Composition, that is ; Step 4: Determine the matrix transformation relationship between the reference wavefront W' and the collimated wavefront W based on the actual optical path layout: ； in, , , , , , These correspond to the ray transformation matrices on the surfaces of the first collimating lens (2), beam splitter (3), beam splitter (5), first plane mirror (6), reference flat crystal (8), and second plane mirror (9), respectively. The ray transformation matrix T D Characterize the effect of the deformable mirror (4) on light. Let be the transformation matrix for the propagation of light in the free space between the first collimating lens (2) and the deformable mirror (4). Let be the transformation matrix for light propagation in the free space between the deformable mirror (4) and the beam splitter (3). Let be the transformation matrix for light propagation in the free space between the beam splitter (3) and the beam splitter (5). Let be the transformation matrix for light propagation in the free space between the beam splitter (5) and the first plane mirror (6). Let be the transformation matrix for light propagation in free space between the first plane mirror (6) and the second collimating lens (7). Let be the transformation matrix for light propagation in free space between the second collimating lens (7) and the reference flat lens (8). The transformation matrix is ​​used to represent the transmission of light in free space between the first plane mirror (6) and the second plane mirror (9); Step 5: Assuming the reference wavefront W' is an ideal spherical wave, solve for the surface gradient matrix corresponding to the deformable mirror (4). : ； Where, N j This represents the local normal direction vector of the deformable mirror surface; Step 6: Use a vector-form numerical orthogonal Zernike gradient polynomial as the basis function G to characterize G. D : G D =G*a Where α is a vector composed of the weights of each numerical orthogonal gradient polynomial; Step 7: Solve for the distribution matrix of the surface elevation z of the deformable mirror (4): ； In the formula, Z is the numerical matrix of the Zernike circular domain polynomial excluding the constant term. The coefficient matrix corresponding to the surface elevation z of the deformable mirror (4); Step 8: Adjust the shape of the deformable mirror (4) according to the theoretically calculated surface vector distribution matrix z to achieve active compensation for the systematic error in the interferometer wavefront.

2. The active compensation method for interferometer wavefront system errors according to claim 1, characterized in that: The beam-splitting plate (5), the first plane mirror (6), and the second plane mirror (9) are all used to fold the optical path, making the optical path structure more compact. The layout of this optical path is not unique.

3. The active compensation method for interferometer wavefront system errors according to claim 1, characterized in that: The aperture of the first collimating lens (2) is smaller than that of the second collimating lens (7).

4. The active compensation method for interferometer wavefront system error according to claim 1, characterized in that: In step 5, the local normal direction vector N of the deformable mirror surface j Specifically as follows: ； In the above formula, Let be the incident ray vector of the j-th ray on the surface of the deformable mirror (4). Let be the vector of the j-th ray emitted from the surface of the deformable mirror (4), where the superscript T indicates transpose.

5. The active compensation method for interferometer wavefront system error according to claim 1, characterized in that: In step 7, The coefficient matrix corresponding to the surface elevation z of the deformable mirror (4) is as follows: ； in, Let α be the efficient estimate of α based on the least squares method; M is the transformation matrix that transforms the Zernike circular domain orthogonal polynomial into a numerical orthogonal polynomial; D is the transformation matrix that transforms the Zernike circular domain orthogonal gradient polynomial into a numerical orthogonal gradient polynomial.

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