A method and apparatus for selecting transverse shear interference shear rate

Abstract

This invention discloses a method and apparatus for selecting the shear rate in transverse shearing interferometry, relating to the field of optical measurement technology. It addresses the problem of unresolved fringes and limited detection accuracy caused by random or theoretically unreferenced shear rate selection in the generalized detection of various types of aspherical surfaces using transverse shearing interferometry. The method includes: iterating over the radius range of an initial reference surface; within each first iteration step, sequentially determining the transverse shearing interferogram fringe density corresponding to the initial shear rate at a second iteration step, based on the iteration range of the initial shear rate; when a maximum transverse shearing interferogram fringe density among the multiple fringe densities is less than the maximum resolvable threshold of the actual interference fringes, obtaining the coarse-optimized shear rate, the first range of the coarse-optimized shear rate, and the radius of the optimal reference surface; and at each third iteration step, when the average fringe density of the transverse shearing interferogram is determined to be less than a judgment condition, obtaining the fine-optimized shear rate and the first range of the fine-optimized shear rate.

Description

Technical Field

[0001] This invention relates to the field of optical measurement technology, and more specifically to a method and apparatus for selecting transverse shear interference shear rate. Background Technology

[0002] Transverse shearing interferometry offers advantages in aspherical surface shape measurement, including resistance to environmental interference, elimination of reference mirror errors, and improvement of fringe densification issues caused by asphericity. However, due to the rich variations in aspherical wavefronts, using a single shear rate to measure multiple types of aspherical surfaces may result in either excessively dense fringes that cannot be resolved or insufficient phase sensitivity due to excessively sparse fringes. Therefore, appropriate shear rates should be matched to the wavefront variations of multiple aspherical surfaces to ensure better measurement accuracy.

[0003] In existing technologies for detecting various types of aspheric surfaces, only the calibration of shear rate and shear quantity in transverse shearing interferometry is considered, without considering adaptive selection methods for the shear rate. In contrast, the adaptive wavefront sensor mentioned by Jason H. Karp et al. in their 2008 paper "Integrated diffractive shearing interferometry for adaptive wavefront sensing" only preliminarily mentions the influence of signal-to-noise ratio and wavefront slope on shear rate selection, without providing specific theoretical models and data support. Similarly, the transverse shearing aspheric surface measurement method mentioned by Jean-Pierre Betend-Bon et al. in their 1991 paper "Double grating phase stepping interferometry for testing aspherics" only provides the transverse shearing aspheric surface measurement device and does not describe the influence of wavefront changes on shear rate selection.

[0004] None of the aforementioned techniques propose a method for adaptively optimizing the shear rate selection for the wavefront of the aspheric surface under test. This is because, prior to the emergence of novel shearing methods, traditional transverse shear interferometry methods could not achieve precise and controllable adjustment of the shear rate. Therefore, research and techniques related to adaptively selecting the shear rate based on aspheric wavefront parameters were not mentioned. In recent years, with the emergence of methods for achieving precise and controllable shear rates, adaptive adjustment of the shear rate for various types of aspheric wavefronts has become possible. Therefore, there is an urgent need to conduct research on adaptive optimal shear rate selection techniques for aspheric wavefronts to promote the rapid development of transverse shear interferometry aspheric surface measurement technology. Summary of the Invention

[0005] This invention provides a method and apparatus for selecting the shear rate in transverse shearing interferometry, which solves the problem of unresolved fringes and limited detection accuracy caused by random or theoretically unreferenced shear rate selection when performing generalized detection of various types of aspherical surfaces using transverse shearing interferometry.

[0006] This invention provides a method for selecting the transverse shear interference shear rate, comprising:

[0007] The radius of curvature at the vertex of the aspherical surface to be measured is determined as the radius of the initial reference surface based on the aperture of the aspherical surface to be measured, the radius of curvature at the vertex of the aspherical surface to be measured, the conic coefficient of the quadratic surface, and the wavefront function of the aspherical surface.

[0008] Based on the radius iteration range of the initial reference surface, a first iteration step size for the radius of the initial reference surface is determined. Within each first iteration step size, based on the iteration range of the initial shear rate and the second iteration step size of the initial shear rate, the transverse shear interference pattern fringe density corresponding to the initial shear rate is sequentially confirmed at the second iteration step size. When there is a maximum transverse shear interference pattern fringe density among the multiple transverse shear interference pattern fringe densities that is less than the maximum analytical threshold of the actual interference fringes, a coarse-optimized shear rate and a first range of coarse-optimized shear rates that match the radius iteration range are obtained. Based on the maximum coarse-optimized shear rate included in the first range of coarse-optimized shear rates, the radius of the optimal reference surface is obtained.

[0009] Based on the first range of the coarse-optimized shear rate and the third iteration step size of the coarse-optimized shear rate, at each third iteration step size, the average fringe density of the transverse shear interferogram is determined sequentially based on the first range of the coarse-optimized shear rate and the radius of the optimal reference surface. When it is determined that the average fringe density of the transverse shear interferogram is less than the judgment condition, the fine-optimized shear rate and the first range of the fine-optimized shear rate that matches the first range of the coarse-optimized shear rate are obtained based on the average fringe density of the transverse shear interferogram.

[0010] Preferably, when there exists a maximum transverse shear interference pattern fringe density less than the maximum analytical threshold of the actual interference fringes, the coarse-optimized shear rate is obtained using the following formula:

[0011]

[0012] Where Max[Density] represents the maximum transverse shear interference pattern fringe density among the plurality of transverse shear interference pattern fringe densities, Density max Ratio1 represents the maximum resolvable threshold of the actual interference fringes, and D represents the coarse-optimized shear rate. aspheric Let y represent the aperture of the aspherical surface to be measured, q represent the pixel size of the detector target surface, and y represent the aperture of the aspherical surface to be measured. diThis represents the ordinate of a point D on the aspherical surface to be measured. The initial shear rate represents the iteration range, and λ represents the wavelength.

[0013] Preferably, the coarse-optimized shear rate and the first range of coarse-optimized shear rates matching the radius iteration range are obtained through the following formula:

[0014]

[0015] Among them, Ratio max This represents the first range of coarse-optimized shear rates that matches the radius iteration range. Max(ratio) represents the iteration range of the radius of the initial reference surface. max ) represents the maximum coarse-optimized shear rate within the first range of coarse-optimized shear rates, and r1 represents the radius of the optimal reference surface.

[0016] Preferably, the judgment condition is that the average fringe density of the transverse shearing interferogram is less than 50 pixels / fringe;

[0017] When it is determined that the average fringe density of the transverse shearing interferogram is less than the judgment condition, the fine-optimized shear rate and the first range of fine-optimized shear rates that match the first range of coarse-optimized shear rates are obtained by the following formula:

[0018]

[0019] Density average This represents the average fringe density of the transverse shear interference pattern. M represents the number of bright fringes in the transverse shearing interferogram, Ratio2 represents the fine-optimized shear ratio, and ratio1 represents the coarse-optimized shear ratio. This indicates the range of values ​​for the first range of the coarse-optimized shear rate.

[0020] Preferably, the step of sequentially confirming the transverse shear interference pattern fringe density corresponding to the initial shear rate at the second iteration step size specifically includes:

[0021] The shear rate is determined using the following formula based on the diameter of the aspherical surface to be tested and the initial shear rate:

[0022] S = ratio0 * D aspheric

[0023] The center point of the transverse shear interference bright fringes is determined using the following formula based on the aspheric surface to be measured, the initial reference surface, the vertex radius of curvature R0 of the aspheric surface to be measured, and the shearing amount:

[0024]

[0025] The density of the transverse shear interference pattern matching the initial reference surface is determined by the following formula based on the center point positions of two adjacent transverse shear interference bright fringes:

[0026]

[0027] Where S represents the shear rate, Ratio0 represents the initial shear rate, and D... aspheric T represents the aperture of the aspherical surface to be measured. i The x represents the center point of the transverse shear interference bright fringes, r0 represents the radius of the initial reference surface, and x represents the x-axis. di Let x represent the x-coordinate of a point D on the aspherical surface to be measured. ci Let y represent the x-coordinate of a point C on the initial reference surface. di Let y represent the ordinate of a point D on the aspherical surface to be measured. ci Let R0 represent the ordinate of a point C on the initial reference surface, R0 represent the radius of curvature of the vertex of the aspherical surface to be measured, k represent the conic coefficient of the quadratic surface, λ represent the wavelength, and Density represent the fringe density of the transverse shear interference pattern.

[0028] Preferably, after determining the vertex radius of curvature of the aspherical surface to be measured as the radius of the initial reference surface, the method further includes:

[0029] The aspherical surface to be measured is placed in a rectangular coordinate system, and the path difference between the initial reference surface and the aspherical surface to be measured is determined as follows:

[0030]

[0031] Where, x di Let x represent the x-coordinate of a point D on the aspherical surface to be measured. ci Let y represent the x-coordinate of a point C on the initial reference surface. di Let y be the ordinate of a point D on the aspherical surface to be measured. ci Let r0 represent the ordinate of a point C on the initial reference surface, and r0 represent the radius of the initial reference surface. This represents the tangent distance between points C and D.

[0032] This invention provides a transverse shear interference shear rate selection device, comprising:

[0033] The determining unit is used to determine the vertex radius of curvature of the aspherical surface to be measured as the radius of the initial reference surface based on the aperture of the aspherical surface to be measured, the vertex radius of curvature of the aspherical surface to be measured, the conic coefficient of the quadratic surface, and the aspherical wavefront function.

[0034] The first obtaining unit is used to determine the first iteration step size of the radius of the initial reference surface based on the radius iteration range of the initial reference surface. Within each first iteration step size, based on the iteration range of the initial shear rate and the second iteration step size of the initial shear rate, the transverse shear interference pattern fringe density corresponding to the initial shear rate is sequentially confirmed at the second iteration step size. When there is a maximum transverse shear interference pattern fringe density among the multiple transverse shear interference pattern fringe densities that is less than the maximum analytical threshold of the actual interference fringes, a coarse-optimized shear rate and a first range of coarse-optimized shear rates that match the radius iteration range are obtained. The radius of the optimal reference surface is obtained based on the maximum coarse-optimized shear rate included in the first range of coarse-optimized shear rates.

[0035] The second obtaining unit is used to determine the average fringe density of the transverse shearing interferogram according to the first range of the coarse-optimized shearing rate and the third iteration step size of the coarse-optimized shearing rate at each third iteration step size, based on the first range of the coarse-optimized shearing rate and the radius of the optimal reference surface. When it is determined that the average fringe density of the transverse shearing interferogram is less than the judgment condition, the fine-optimized shearing rate and the first range of the fine-optimized shearing rate that matches the first range of the coarse-optimized shearing rate are obtained based on the average fringe density of the transverse shearing interferogram.

[0036] Preferably, the first obtaining unit is specifically used to: obtain the coarse-optimized shear rate using the following formula:

[0037]

[0038] The coarse-optimized shear rate and the first range of coarse-optimized shear rates matching the radius iteration range are obtained through the following formulas:

[0039]

[0040] Where Max[Density] represents the maximum transverse shear interference pattern fringe density among the plurality of transverse shear interference pattern fringe densities, Density max The ratio represents the maximum resolvable threshold of the actual interference fringes, and ratio1 represents the coarse-optimized shear rate. aspheric Let y represent the aperture of the aspherical surface to be measured, q represent the pixel size of the detector target surface, and y represent the aperture of the aspherical surface to be measured. di This represents the ordinate of a point D on the aspherical surface to be measured. The initial shear rate represents the iteration range, λ represents the wavelength, and ratio represents the ratio. max This represents the first range of coarse-optimized shear rates that matches the radius iteration range. Max(ratio) represents the iteration range of the radius of the initial reference surface. max) represents the maximum coarse-optimized shear rate within the first range of coarse-optimized shear rates, and r1 represents the radius of the optimal reference surface.

[0041] This invention provides a computer device, which includes a memory and a processor. The memory stores a computer program, and when the computer program is executed by the processor, the processor performs any of the above-described transverse shear interference shear rate selection methods.

[0042] This invention provides a computer-readable storage medium storing a computer program, which, when executed by a processor, causes the processor to perform any of the above-described transverse shear interference shear rate selection methods.

[0043] In summary, this invention provides a method and apparatus for selecting the transverse shear interference shear rate. The method includes: determining the vertex radius of curvature of the aspherical surface to be measured as the radius of an initial reference surface based on the aperture of the aspherical surface to be measured, the vertex radius of curvature of the aspherical surface to be measured, the conic coefficient of the quadratic surface, and the aspherical wavefront function; determining a first iteration step size for the radius of the initial reference surface based on an iteration range of the initial reference surface radius; within each first iteration step size, sequentially confirming the transverse shear interference pattern fringe density corresponding to the initial shear rate at a second iteration step size based on the iteration range of the initial shear rate and a second iteration step size of the initial shear rate; and determining a maximum transverse shear interference pattern fringe density among multiple transverse shear interference pattern fringe densities. When the value is less than the maximum analytical threshold of the actual interference fringes, a coarse-optimized shear rate and a first range of coarse-optimized shear rates matching the radius iteration range are obtained. Based on the maximum coarse-optimized shear rate included in the first range of coarse-optimized shear rates, the radius of the optimal reference surface is obtained. Based on the first range of coarse-optimized shear rates and the third iteration step size of the coarse-optimized shear rate, at each third iteration step size, the average fringe density of the transverse sheared interferogram is determined sequentially based on the first range of coarse-optimized shear rates and the radius of the optimal reference surface. When the average fringe density of the transverse sheared interferogram is determined to be less than the judgment condition, a fine-optimized shear rate and a first range of fine-optimized shear rates matching the first range of coarse-optimized shear rates are obtained based on the average fringe density of the transverse sheared interferogram. This method comprehensively considers the influence of factors such as the surface shape parameters of the aspheric surface under test, the fringe density of the transverse shear interferogram, the radius of the optimal reference surface, and the actual interferogram quality on fringe resolution. It establishes a theoretical model for selecting the fine-optimized shear rate through coarse-optimized and fine-optimized shear rate selection. The coarse-optimized shear rate selection model uses the fringe density of the transverse shear interferogram and the radius of the initial reference surface as optimization targets to determine the first range of the coarse-optimized shear rate, i.e., the selectable range of the coarse-optimized shear rate. Furthermore, the fine-optimized shear rate selection model uses the surface shape reconstruction accuracy as the optimization target, and further selects the fine-optimized shear rate within the first range of the coarse-optimized shear rate. The method provided by this invention can solve the problem of unresolved fringes and limited detection accuracy caused by random or theoretically unreferenced shear rate selection when using transverse shear interferometry for general detection of multiple types of aspheric surfaces. Attached Figure Description

[0044] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0045] Figure 1 This is a schematic flowchart of a method for selecting the transverse shear interference shear rate according to an embodiment of the present invention;

[0046] Figure 2 A schematic diagram illustrating the parameters of an aspherical surface and an optimal reference spherical surface provided in an embodiment of the present invention;

[0047] Figure 3 A schematic diagram of the average stripe density provided for an embodiment of the present invention;

[0048] Figure 4 This is a schematic diagram of the overall process of the adaptive shear rate selection method for secondary iterative optimization provided in an embodiment of the present invention;

[0049] Figure 5 This is a schematic diagram of a transverse shear interference shear rate selection device provided in an embodiment of the present invention. Detailed Implementation

[0050] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0051] Figure 1 This is a schematic flowchart of a transverse shear interference shear rate selection method provided by an embodiment of the present invention; the following is in conjunction with... Figure 1 Taking an example, this invention provides a detailed explanation of the method for selecting the transverse shear interference shear rate according to its embodiments. For instance... Figure 1 As shown, the method includes the following steps:

[0052] Step 101: Determine the radius of curvature of the vertex of the aspherical surface to be measured as the radius of the initial reference surface based on the aperture of the aspherical surface to be measured, the vertex radius of curvature of the aspherical surface to be measured, the conic coefficient of the quadratic surface, and the aspherical wavefront function.

[0053] Step 102: Based on the radius iteration range of the initial reference surface, determine the first iteration step size of the radius of the initial reference surface. Within each first iteration step size, based on the iteration range of the initial shear rate and the second iteration step size of the initial shear rate, sequentially confirm the transverse shear interference pattern fringe density corresponding to the initial shear rate under the second iteration step size. When there is a maximum transverse shear interference pattern fringe density among the multiple transverse shear interference pattern fringe densities that is less than the maximum analytical threshold of the actual interference fringes, obtain the coarse-optimized shear rate and a first range of coarse-optimized shear rates that matches the radius iteration range. Based on the maximum coarse-optimized shear rate included in the first range of coarse-optimized shear rates, obtain the radius of the optimal reference surface.

[0054] Step 103: Based on the first range of the coarse-optimized shear rate and the third iteration step size of the coarse-optimized shear rate, at each third iteration step size, the average fringe density of the transverse shear interferogram is determined sequentially based on the first range of the coarse-optimized shear rate and the radius of the optimal reference surface. When it is determined that the average fringe density of the transverse shear interferogram is less than the judgment condition, the fine-optimized shear rate and the first range of the fine-optimized shear rate that matches the first range of the coarse-optimized shear rate are obtained based on the average fringe density of the transverse shear interferogram.

[0055] Before implementing the transverse shear interference shear rate selection method in this embodiment of the invention, it is necessary to first establish a coarse optimization shear rate selection theoretical model, an optimal reference surface radius theoretical model, and a fine optimization shear rate selection theoretical model.

[0056] Specifically, the coarse optimization rate shearing selection theoretical model is obtained through the following method:

[0057] In practical applications, the positions of interference fringes and the maximum fringe density can be determined by calculating the path differences between a series of spherical and aspherical waves. The aspherical wave front function is the surface shape function of the aspherical surface to be measured, which can be expressed by formula (1):

[0058]

[0059] Where z represents the axis of rotational symmetry, k represents the conic coefficient of the quadratic surface, R0 represents the vertex radius of curvature of the aspherical surface to be measured, and A4, A6, ..., A 2n denoted by , x represents the coefficients of the higher-order aspherical polynomial, x represents the function representation of the aspherical wavefront to be measured, and y and z represent the coordinate positions corresponding to the two-dimensional surface of the wavefront.

[0060] Furthermore, considering the rotational symmetry of the aspherical surface, the intersection of the z=0 plane and the aspherical surface is chosen to describe the aspherical surface shape function to be measured. Therefore, formula (1) can be rewritten as:

[0061]

[0062] Furthermore, the aspherical surface to be measured is placed in a rectangular coordinate system, from... Figure 2 The spherical wave emitted from the wave source at point P returns to the aspherical surface being measured, carrying the wavefront difference between the two waves, denoted as δ. i For the i-th point on the initial reference sphere, the path difference between its normal direction and the aspherical surface to be measured can be expressed by the following formula:

[0063]

[0064] Where, x di Let x represent the x-coordinate of a point D on the aspherical surface to be measured. ci Let y represent the x-coordinate of a point C on the initial reference surface. di Let y be the ordinate of a point D on the aspherical surface to be measured. ci Let r0 represent the ordinate of a point C on the initial reference surface, and r0 represent the radius of the initial reference surface. This represents the tangent distance between points C and D.

[0065] In practical applications, when δ i When the optical path difference between the surface wave of the aspherical surface under test and the initial reference spherical wave is ±jλ (j = 1, 2, 3...), the interference fringes produced by this optical path difference are bright fringes. The distance between the centers of adjacent bright fringes is the fringe width, and its reciprocal is the interference fringe density. Based on this theoretical model, the density expression for transverse shear interference fringes can be derived, where the position of the center point of the bright fringe can be determined by the following formula:

[0066]

[0067] Among them, T i The x represents the center point of the i-th transverse shear interference bright fringe, r0 represents the radius of the initial reference surface, and x represents the center point of the i-th transverse shear interference bright fringe. di Let x represent the x-coordinate of a point D on the aspherical surface to be measured. ci Let y represent the x-coordinate of a point C on the initial reference surface. di Let y represent the ordinate of a point D on the aspherical surface to be measured. ci Let R0 represent the ordinate of a point C on the initial reference surface, R0 represent the radius of curvature of the vertex of the aspherical surface to be measured, k represent the conic coefficient of the quadratic surface, λ represent the wavelength, and S represent the shear amount.

[0068] In the above formula, S represents the shear rate, where the value of S is relative to the aspherical aperture. If an initial shear rate is defined, the shear rate can be determined using the following formula:

[0069] S = ratio0 * D aspheric (5)

[0070] Where Ratio0 represents the initial shear rate, D aspheric This indicates the diameter of the aspherical surface to be measured.

[0071] In this embodiment of the invention, since the reciprocal of the position of the center point of the bright fringe is the interference fringe density, the interference fringe density can be expressed by the following formula:

[0072]

[0073] Where Density represents the fringe density of the transverse shear interference pattern, T i T represents the center point position of the i-th transverse shear interference bright fringe. i-1 This indicates the position of the center point of the (i-1)th transverse shear interference bright fringe.

[0074] In practical applications, since aspherical surface shape measurements are typically performed using reflective interferometry systems, the optical path difference returning to the wavefront consists of two parts: the optical path difference transmitted from the reference sphere to the surface under test and the optical path difference reflected from the surface under test to the reference sphere, and these two parts are equal in magnitude. Therefore, the actual optical path difference returning to the wavefront should be twice the calculated optical path difference.

[0075] In a dual-grating transverse shearing interferometer with adjustable shear rate, the shear rate is generally controlled by the diffraction angle of the gratings and the axial distance between the two gratings. The specific calculation formula is as follows:

[0076]

[0077] Where d represents the axial distance between the grating and the mirror, ± represents the diffraction direction, λ represents the wavelength of light, Λ represents the period of the diffraction polarization grating, and D pupil This indicates the diameter of the entrance pupil spot.

[0078] In this embodiment of the invention, based on the Nyquist fringe analysis principle and the influence of actual interferogram errors, a coarse optimization theoretical model for the shear rate can be jointly established, namely, a coarse optimization theoretical model for selecting the shear rate, as shown below:

[0079]

[0080] In the formula, D i (x di y di ) represents the equation of the aspherical wave to be measured, C i (x ci y ci ) represents the initial reference spherical wave equation, RATIO represents the optimized shear rate, and D aspheric The aspherical aperture to be measured is represented by q, the number of available pixels for the detector is , Ratio0 represents the initial shear ratio, and Ratio1 represents the coarse-optimized shear ratio. Iteration range of initial shear rate, Density max The maximum resolvable threshold of the actual interference fringes is represented by max[Density], which represents the maximum transverse shear interference fringe density among the multiple transverse shear interference fringe densities. This threshold is obtained based on the relationship curve between the interference pattern quality and the maximum resolvable threshold established by simulation.

[0081] Specifically, the radius theoretical model of the optimal reference surface is obtained through the following method:

[0082] In this embodiment of the invention, a reverse optimization approach is used to determine the radius of the optimal reference surface. The principle can be summarized as follows: when the position corresponding to the radius of the initial reference surface is optimal, the mean return optical path difference of the aspheric surface under test is minimized, and the measurable range of aspheric surfaces under the same shear rate is maximized. If the maximum selectable shear rate range is satisfied, then the position of the radius of the corresponding optimal reference surface is the optimal value.

[0083] To reduce the iteration optimization time and space of selecting the radius of the optimal reference surface, the position of the vertex curvature radius of the aspheric surface to be tested is selected as the initial value of the iteration, and the intersection point R of the aperture edge normal of the aspheric surface to be tested and the x-axis is selected. n Location is used as the maximum optimization range, specifically as follows: Figure 2 As shown. The theoretical model for determining the radius of the optimal reference surface through inverse optimization can be expressed as follows:

[0084]

[0085] Among them, Ratio max This represents the first range of coarse-optimized shear rates that matches the radius iteration range. Max(Ratio) represents the iteration range of the radius of the initial reference surface. max ) represents the maximum coarse-optimized shear rate within the first range of coarse-optimized shear rates, and r1 represents the radius of the optimal reference surface.

[0086] Specifically, the theoretical model for optimizing the shear rate is obtained through the following method:

[0087] In this embodiment of the invention, the iterative process of finely optimizing the shear rate mainly considers the influence of average fringe density and interferogram quality on the surface reconstruction accuracy. The average fringe density is specifically defined as the number of pixels on the target surface occupied by each fringe, which can be determined by the following formula:

[0088]

[0089] Density averageT represents the average fringe density of the transverse shearing interferogram, M represents the number of bright fringes in the transverse shearing interferogram, and T represents the average fringe density. i This indicates the location of the center point of the transverse shear interference bright fringes.

[0090] Specifically, Figure 3 The image shows the fringe patterns and one-dimensional grayscale distribution along the shear direction at different shear rates, based on... Figure 3 It can be concluded that maintaining an average fringe density below 50 pixels per fringe can ensure good accuracy in shear differential wavefront reconstruction.

[0091] Based on this, an optimization theoretical model based on average fringe density is established, which can be specifically expressed as the following formula:

[0092]

[0093] Density average This represents the average fringe density of the transverse shear interference pattern. M represents the number of bright fringes in the transverse shearing interferogram, Ratio2 represents the fine-optimized shear rate, and Ratio1 represents the coarse-optimized shear rate. This indicates the range of values ​​for the first range of the coarse-optimized shear rate.

[0094] In step 101, the basic parameters of the aspherical surface to be measured are determined as follows: the aperture of the aspherical surface to be measured, the vertex radius of curvature of the aspherical surface to be measured, and the conic coefficient of the quadratic surface. Substituting the above basic parameters of the aspherical surface to be measured into the aspherical wavefront function formula shown in formula (2), in practical applications, since it is a quadratic surface, the higher-order coefficients A4, A6, ..., A in formula (2) are... 2n All are zero. According to formula (2), we can obtain the following: Figure 2 The equation of the aspherical curve in the equation is based on Figure 2 The radius of the initial reference surface can be set to the vertex radius of curvature of the aspherical curve to be measured, and it can also be based on... Figure 2 Set the initial shear rate.

[0095] Furthermore, according to Figure 2 The abscissa and ordinate of a point on the aspheric surface to be measured can be determined, as can the abscissa and ordinate of a point on the initial reference surface. The curve of the aspheric surface to be measured, the initial reference surface and the initial shear rate determined in step 101 are successively substituted into the above formulas (4), (5) and (6) to obtain the shear amount, the position of the center point of the i-th transverse shear interference bright fringe and the fringe density of the transverse shear interference pattern.

[0096] In step 102, the obtained transverse shearing interferogram fringe density, the detector target pixel size used for interferogram acquisition, the maximum resolvable threshold of the actual interferogram fringe, and the initial shear rate are substituted into formula (8). The iteration optimization range of the initial shear rate given in formula (8) is sequentially performed from 0.2 to 0. That is, the iteration is performed according to the iteration range of the initial shear rate and the second iteration step size of the initial shear rate. If there is a maximum transverse shearing interferogram fringe density among the multiple transverse shearing interferogram fringe densities that is less than the maximum resolvable threshold of the actual interferogram fringe, the iteration can be stopped, and the coarse optimization shear rate is output according to the iteration result. If the above conditions are not met, the iteration needs to continue and the iteration is performed according to the second iteration step size.

[0097] Further, the radius iteration range of the initial reference surface is set, and the first iteration step size of the radius of the initial reference surface is determined. In this embodiment of the invention, within each first iteration step size, one round of iteration is performed according to the iteration range of the initial shear rate and the second iteration step size to obtain a coarse optimization shear rate; then, iteration is performed according to the first iteration step size, and the first iteration step size is repeated to obtain a coarse optimization shear rate; after performing multiple rounds of first iteration step sizes, according to formula (9), a maximum coarse optimization shear rate is selected from multiple coarse iteration optimization shear rates, and the radius of the initial reference surface corresponding to the maximum coarse optimization shear rate is determined as the radius of the optimal reference surface. Then, the first range of the coarse optimization shear rate is determined according to multiple coarse iteration optimization shear rates, and the first range of the coarse optimization shear rate matches the radius iteration range of the initial reference surface.

[0098] Once the first range of the coarse optimization shear rate and the radius of the optimal reference surface are determined, the coarse optimization iteration can be considered complete.

[0099] In step 103, the average fringe density of the transverse shearing interferogram can be determined by formula (10) based on the number of bright fringes and the center positions of the bright fringes. Further, the radius of the optimal reference surface determined in the above steps and the first range of the coarse-optimized shear rate are substituted into formula (11), and iteration is performed according to the first range of the coarse-optimized shear rate and the third iteration step size of the coarse-optimized shear rate. At each third iteration step size, if the average fringe density of the transverse shearing interferogram is less than the judgment condition in formula (11), the fine-optimized shear rate is obtained based on the average fringe density of the transverse shearing interferogram. Multiple iterations are performed within the first range of the coarse-optimized shear rate according to the third iteration step size to obtain multiple fine-optimized shear rates. The first range of the fine-optimized shear rate can be obtained based on these multiple fine-optimized shear rates. If the condition is not met within the third iteration step size, further iteration is required. In this embodiment of the invention, the first range of the fine-optimized shear rate matches the first range of the coarse-optimized shear rate, but the first range of the fine-optimized shear rate is smaller than the first range of the coarse-optimized shear rate.

[0100] To more clearly illustrate the transverse shear interference shear rate selection method provided in the embodiments of the present invention, the following is combined with... Figure 4 The method for selecting the transverse shear interference shear rate provided in this invention will be described in detail with specific numerical values.

[0101] like Figure 4 As shown, the method includes the following steps:

[0102] Step 201: Select the basic parameters of the aspheric surface to be measured as follows: vertex radius of curvature r0 = 348 mm, conic coefficient k = -3.5, and diameter D of the aspheric surface to be measured. aspheric =90mm, and the pixel size of the detector target surface used for interferogram acquisition is set to q = 1024*1024 pixels.

[0103] Step 202: Substitute the basic surface parameters of the aspheric surface to be measured from Step 201 into the aspheric wavefront function shown in Formula (2). Since the aspheric surface to be measured is a quadratic surface, the higher-order coefficients A4, A6, ..., A 2n All are zero. According to formula (2), we can obtain the following: Figure 2 The equation of the aspherical curve to be measured is shown. The radius of the initial reference surface is set as the vertex curvature radius of the aspherical surface to be measured, r0 = R0, and the initial shear rate is set as Ratio0 = 0.2.

[0104] Step 203: Substitute the equation of the aspherical curve to be measured, the equation of the initial reference surface curve, and the initial shear rate obtained in step 202 into formulas (4), (5), and (6) to obtain the shear amount, the center point position of the i-th transverse shear interference bright fringe, and the fringe density of the transverse shear interference pattern.

[0105] Step 204: Substitute the fringe density of the transverse shearing interferogram obtained in step 203 and the detector target pixel size q set in step 201 into formula (8), and iterate sequentially from 0.2 to 0 using the initial shear rate iteration optimization range given in formula (8). That is, iterate according to the iteration range of the initial shear rate and the second iteration step size of the initial shear rate.

[0106] Step 205: If the maximum transverse shearing interferogram fringe density among the multiple transverse shearing interferogram fringe densities is less than the maximum analytical threshold of the actual interference fringes, the iteration can be stopped, and the coarse-optimized shear rate can be output based on the iteration results; if the above conditions are not met, the iteration in step 204 needs to be continued, and the iteration should be performed according to the second iteration step size.

[0107] Step 206: Obtain the coarse optimized shear rate by satisfying formula (8).

[0108] Step 207: Execute formula (9) to set the radius iteration range of the initial reference surface to r0∈[R0, R n The first iteration step size for determining the radius of the initial reference surface is then determined, and steps 204, 205, and 206 are repeated. If the condition of step 205 is satisfied within each first iteration step size, the range of coarse optimization shear rates that can be selected for the radii of the corresponding multiple optimal reference surfaces can be obtained.

[0109] Step 208: According to the judgment condition in formula (9), whether the first range of coarse optimization shear rates generated by multiple coarse optimization shear rates includes the maximum coarse optimization shear rate; if the condition is met, step 209 can be executed; if not, step 207 is repeated.

[0110] Step 209: Output the radius of the optimal reference surface as r1 = 357.08 mm, and the first range of the coarse optimization shear rate is Ratio1 ∈ [0 ~ 0.035].

[0111] Step 210: Substitute the radius of the optimal reference surface determined in step 209 and the first range of the coarse optimization shear rate into formula (10) to calculate the average fringe density of the transverse shear interference pattern; further, substitute the radius of the optimal reference surface determined in the above steps and the first range of the coarse optimization shear rate into formula (11), and iterate according to the first range of the coarse optimization shear rate and the third iteration step size of the coarse optimization shear rate, with the first range of the coarse optimization shear rate iterating sequentially from 0.035 to 0.

[0112] Step 211: Within the third iteration step, the fine optimization shear rate is obtained based on the average fringe density of the transverse shearing interferogram. Within the first range of the coarse optimization shear rate, multiple iterations are performed according to the third iteration step. If the average fringe density of the transverse shearing interferogram satisfies the judgment condition in formula (11), multiple fine optimization shear rates can be obtained; if the judgment condition is not satisfied, then step 210 is executed.

[0113] Step 212: Based on multiple fine-optimized shear rates, the first range of the fine-optimized shear rate can be obtained as Ratio∈[0.021~0.035].

[0114] Through the above steps, the basic parameters of the aspherical surface to be measured are obtained: R0 = 348 mm, k = -3.5, D... aspheric The first range of the fine-tuned shear ratio for a hyperbolic aspherical surface with a diameter of 90 mm is Ratio∈[0.021~0.030]. The fine-tuned shear ratio optimization ends and the optimization results are output.

[0115] In summary, this invention provides a method and apparatus for selecting the shear rate in transverse shearing interferometry. This method comprehensively considers the influence of factors such as the surface shape parameters of the aspheric surface under test, the fringe density of the transverse shearing interferogram, the radius of the optimal reference surface, and the actual quality of the interferogram on fringe resolution. It establishes a coarse-optimized shear rate selection theoretical model and a fine-optimized shear rate selection theoretical model to achieve fine-optimized shear rate selection. Specifically, the coarse-optimized shear rate selection theoretical model uses the fringe density of the transverse shearing interferogram and the radius of the initial reference surface as optimization targets to determine a first range of coarse-optimized shear rates, i.e., the selectable range of coarse-optimized shear rates. Further, the fine-optimized shear rate selection theoretical model uses the surface shape reconstruction accuracy as the optimization target, and further selects fine-optimized shear rates within the first range of coarse-optimized shear rates. The method provided by this invention can solve the problem of unresolved fringes and limited detection accuracy caused by random or theoretically unreferenced shear rate selection in the transverse shearing interferometry method for the generalized detection of multiple types of aspheric surfaces.

[0116] Based on the same inventive concept, this invention provides a transverse shear interference shear rate selection device. Since the principle of this device in solving the technical problem is similar to that of a transverse shear interference shear rate selection method, the implementation of this device can refer to the implementation of the method, and the repeated parts will not be described again.

[0117] like Figure 5 As shown, the device includes a first determining unit 301, a first obtaining unit 302, and a second obtaining unit 303.

[0118] The first determining unit 301 determines the vertex radius of curvature of the aspherical surface to be measured as the radius of the initial reference surface based on the aperture of the aspherical surface to be measured, the vertex radius of curvature of the aspherical surface to be measured, the conic coefficient of the quadratic surface, and the aspherical wavefront function.

[0119] The first obtaining unit 302 determines the first iteration step size of the radius of the initial reference surface based on the radius iteration range of the initial reference surface. Within each first iteration step size, based on the iteration range of the initial shear rate and the second iteration step size of the initial shear rate, it sequentially confirms the transverse shear interference pattern fringe density corresponding to the initial shear rate under the second iteration step size. When there is a maximum transverse shear interference pattern fringe density among the multiple transverse shear interference pattern fringe densities that is less than the maximum analytical threshold of the actual interference fringes, it obtains the coarse-optimized shear rate and a first range of coarse-optimized shear rates that matches the radius iteration range. Based on the maximum coarse-optimized shear rate included in the first range of coarse-optimized shear rates, it obtains the radius of the optimal reference surface.

[0120] The second obtaining unit 303, based on the first range of the coarse-optimized shear rate and the third iteration step size of the coarse-optimized shear rate, determines the average fringe density of the transverse shear interferogram sequentially according to the first range of the coarse-optimized shear rate and the radius of the optimal reference surface at each third iteration step size. When it is determined that the average fringe density of the transverse shear interferogram is less than the judgment condition, the fine-optimized shear rate and the first range of the fine-optimized shear rate that matches the first range of the coarse-optimized shear rate are obtained based on the average fringe density of the transverse shear interferogram.

[0121] The first obtaining unit 302 is specifically used to: obtain the coarse-optimized shear rate through the following formula:

[0122]

[0123] The coarse-optimized shear rate and the first range of coarse-optimized shear rates matching the radius iteration range are obtained through the following formulas:

[0124]

[0125] Where Max[Density] represents the maximum transverse shear interference pattern fringe density among the plurality of transverse shear interference pattern fringe densities, Density max Ratio1 represents the maximum resolvable threshold of the actual interference fringes, and D represents the coarse-optimized shear rate. aspheric Let y represent the aperture of the aspherical surface to be measured, q represent the pixel size of the detector target surface, and y represent the aperture of the aspherical surface to be measured. di This represents the ordinate of a point D on the aspherical surface to be measured. The iterative range of the initial shear rate is represented by λ, where λ represents the wavelength, and Ratio is... max This represents the first range of coarse-optimized shear rates that matches the radius iteration range. Max(Ratio) represents the iteration range of the radius of the initial reference surface. max ) represents the maximum coarse-optimized shear rate within the first range of coarse-optimized shear rates, and r1 represents the radius of the optimal reference surface.

[0126] The second obtaining unit 303 is specifically used for:

[0127] The judgment condition is that the average fringe density of the transverse shearing interference pattern is less than 50 pixels per fringe.

[0128] The fine-optimized shear rate and the first range of fine-optimized shear rates that match the first range of coarse-optimized shear rates are obtained using the following formulas:

[0129]

[0130] Density averageThis represents the average fringe density of the transverse shear interference pattern. M represents the number of bright fringes in the transverse shearing interferogram, Ratio2 represents the fine-optimized shear rate, and Ratio1 represents the coarse-optimized shear rate. This indicates the range of values ​​for the first range of the coarse-optimized shear rate.

[0131] Preferably, the first determining unit 302 is specifically used for:

[0132] The shear rate is determined using the following formula based on the diameter of the aspherical surface to be tested and the initial shear rate:

[0133] S = Ratio0 * D aspheric

[0134] The center point of the transverse shear interference bright fringes is determined using the following formula based on the aspheric surface to be measured, the initial reference surface, the vertex radius of curvature R0 of the aspheric surface to be measured, and the shearing amount:

[0135]

[0136] The density of the transverse shear interference pattern matching the initial reference surface is determined by the following formula based on the center point positions of two adjacent transverse shear interference bright fringes:

[0137]

[0138] Where S represents the shear rate, Ratio0 represents the initial shear rate, and D... aspheric T represents the aperture of the aspherical surface to be measured. i The x represents the center point of the transverse shear interference bright fringes, r0 represents the radius of the initial reference surface, and x represents the x-axis. di Let x represent the x-coordinate of a point D on the aspherical surface to be measured. ci Let y represent the x-coordinate of a point C on the initial reference surface. di Let y represent the ordinate of a point D on the aspherical surface to be measured. ci Let R0 represent the ordinate of a point C on the initial reference surface, R0 represent the radius of curvature of the vertex of the aspherical surface to be measured, k represent the conic coefficient of the quadratic surface, λ represent the wavelength, and Density represent the fringe density of the transverse shear interference pattern.

[0139] It should be understood that the units included in the above-described transverse shear interference shear rate selection device are merely a logical division based on the functions implemented by the device. In practical applications, the units can be superimposed or split. Furthermore, the functions implemented by the transverse shear interference shear rate selection device provided in this embodiment correspond one-to-one with the transverse shear interference shear rate selection method provided in the above-described embodiment. The more detailed processing flow implemented by this device has been described in detail in the first embodiment of the method described above, and will not be described in detail here.

[0140] Another embodiment of the present invention provides a computer device, the computer device including: a processor and a memory; the memory is used to store computer program code, the computer program code including computer instructions; when the processor executes the computer instructions, the electronic device performs each step of the transverse shear interference shear rate selection method shown in the above method embodiment.

[0141] Another embodiment of the present invention provides a computer-readable storage medium storing computer instructions that, when executed on a computer device, cause the computer device to perform the various steps of the transverse shear interference shear rate selection method shown in the above-described method embodiment.

[0142] Although preferred embodiments of the invention have been described, those skilled in the art, upon learning the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the appended claims are intended to be interpreted as including both the preferred embodiments and all changes and modifications falling within the scope of the invention.

[0143] Obviously, those skilled in the art can make various modifications and variations to this invention without departing from its spirit and scope. Therefore, if these modifications and variations fall within the scope of the claims of this invention and their equivalents, this invention also intends to include these modifications and variations.

Claims

1. A method for selecting the transverse shear interference shear rate, characterized in that, include: The radius of curvature at the vertex of the aspherical surface to be measured is determined as the radius of the initial reference surface based on the aperture of the aspherical surface to be measured, the radius of curvature at the vertex of the aspherical surface to be measured, the conic coefficient of the quadratic surface, and the wavefront function of the aspherical surface. Based on the radius iteration range of the initial reference surface, a first iteration step size for the radius of the initial reference surface is determined. Within each first iteration step size, based on the iteration range of the initial shear rate and the second iteration step size of the initial shear rate, the transverse shear interference pattern fringe density corresponding to the initial shear rate is sequentially confirmed at the second iteration step size. When there is a maximum transverse shear interference pattern fringe density among the multiple transverse shear interference pattern fringe densities that is less than the maximum analytical threshold of the actual interference fringes, a coarse-optimized shear rate and a first range of coarse-optimized shear rates that match the radius iteration range are obtained. Based on the maximum coarse-optimized shear rate included in the first range of coarse-optimized shear rates, the radius of the optimal reference surface is obtained. Based on the first range of the coarse-optimized shear rate and the third iteration step size of the coarse-optimized shear rate, at each third iteration step size, the average fringe density of the transverse shear interferogram is determined sequentially based on the first range of the coarse-optimized shear rate and the radius of the optimal reference surface. When it is determined that the average fringe density of the transverse shear interferogram is less than the judgment condition, the fine-optimized shear rate and the first range of the fine-optimized shear rate that matches the first range of the coarse-optimized shear rate are obtained based on the average fringe density of the transverse shear interferogram. The step of sequentially confirming the transverse shear interference pattern fringe density corresponding to the initial shear rate at the second iteration step size specifically includes: The shear rate is determined using the following formula based on the diameter of the aspherical surface to be tested and the initial shear rate: S=Ratio0*D aspheric The center point of the transverse shear interference bright fringes is determined using the following formula based on the aspheric surface to be measured, the initial reference surface, the vertex radius of curvature R0 of the aspheric surface to be measured, and the shearing amount: The density of the transverse shear interference pattern matching the initial reference surface is determined by the following formula based on the center point positions of two adjacent transverse shear interference bright fringes: Where S represents the shear rate, Ratio0 represents the initial shear rate, and D... aspheric T represents the aperture of the aspherical surface to be measured. i The x represents the center point of the transverse shear interference bright fringes, r0 represents the radius of the initial reference surface, and x represents the x-axis. di Let x represent the x-coordinate of a point D on the aspherical surface to be measured. ci Let y represent the x-coordinate of a point C on the initial reference surface. di Let y represent the ordinate of a point D on the aspherical surface to be measured. ci Let R0 represent the ordinate of a point C on the initial reference surface, R0 represent the radius of curvature of the vertex of the aspherical surface to be measured, k represent the conic coefficient of the quadratic surface, λ represent the wavelength, and Density represent the fringe density of the transverse shear interference pattern.

2. The method as described in claim 1, characterized in that, When the maximum transverse shear interference pattern fringe density among the plurality of transverse shear interference pattern fringe densities is less than the maximum analytical threshold of the actual interference fringes, the coarse-optimized shear rate is obtained by the following formula: Where Max[Density] represents the maximum transverse shear interference pattern fringe density among the plurality of transverse shear interference pattern fringe densities, Density max Ratio1 represents the maximum resolvable threshold of the actual interference fringes, and D represents the coarse-optimized shear rate. aspheric Let y represent the aperture of the aspherical surface to be measured, q represent the pixel size of the detector target surface, and y represent the aperture of the aspherical surface to be measured. di This represents the ordinate of a point D on the aspherical surface to be measured. The initial shear rate represents the iteration range, and λ represents the wavelength.

3. The method as described in claim 1, characterized in that, The coarse-optimized shear rate and the first range of coarse-optimized shear rates matching the radius iteration range are obtained through the following formulas: Among them, Ratio max This represents the first range of coarse-optimized shear rates that matches the radius iteration range. Max(Ratio) represents the iteration range of the radius of the initial reference surface. max ) represents the maximum coarse-optimized shear rate within the first range of coarse-optimized shear rates, and r1 represents the radius of the optimal reference surface.

4. The method as described in claim 1, characterized in that, The judgment condition is that the average fringe density of the transverse shearing interference pattern is less than 50 pixels per fringe. When it is determined that the average fringe density of the transverse shearing interferogram is less than the judgment condition, the fine-optimized shear rate and the first range of fine-optimized shear rates that match the first range of coarse-optimized shear rates are obtained by the following formula: Density average This represents the average fringe density of the transverse shear interference pattern. M represents the number of bright fringes in the transverse shearing interferogram, Ratio2 represents the fine-optimized shear rate, and Ratio1 represents the coarse-optimized shear rate. This indicates the range of values ​​for the first range of the coarse-optimized shear rate.

5. The method as described in claim 1, characterized in that, After determining the vertex radius of curvature of the aspherical surface to be measured as the radius of the initial reference surface, the method further includes: The aspherical surface to be measured is placed in a rectangular coordinate system, and the path difference between the initial reference surface and the aspherical surface to be measured is determined as follows: Where, x di Let x represent the x-coordinate of a point D on the aspherical surface to be measured. ci Let y represent the x-coordinate of a point C on the initial reference surface. di Let y be the ordinate of a point D on the aspherical surface to be measured. ci Let r0 represent the ordinate of a point C on the initial reference surface, and r0 represent the radius of the initial reference surface. This represents the tangent distance between points C and D.

6. A transverse shear interference shear rate selection device, characterized in that, include: The determining unit is used to determine the vertex radius of curvature of the aspherical surface to be measured as the radius of the initial reference surface based on the aperture of the aspherical surface to be measured, the vertex radius of curvature of the aspherical surface to be measured, the conic coefficient of the quadratic surface, and the aspherical wavefront function. The first obtaining unit is used to determine the first iteration step size of the radius of the initial reference surface based on the radius iteration range of the initial reference surface. Within each first iteration step size, based on the iteration range of the initial shear rate and the second iteration step size of the initial shear rate, the transverse shear interference pattern fringe density corresponding to the initial shear rate is sequentially confirmed at the second iteration step size. When there is a maximum transverse shear interference pattern fringe density among the multiple transverse shear interference pattern fringe densities that is less than the maximum analytical threshold of the actual interference fringes, a coarse-optimized shear rate and a first range of coarse-optimized shear rates that match the radius iteration range are obtained. The radius of the optimal reference surface is obtained based on the maximum coarse-optimized shear rate included in the first range of coarse-optimized shear rates. The second obtaining unit is used to determine the average fringe density of the transverse shearing interferogram according to the first range of the coarse optimization shearing rate and the third iteration step size of the coarse optimization shearing rate at each third iteration step size, based on the first range of the coarse optimization shearing rate and the radius of the optimal reference surface. When it is determined that the average fringe density of the transverse shearing interferogram is less than the judgment condition, the fine optimization shearing rate and the first range of the fine optimization shearing rate that matches the first range of the coarse optimization shearing rate are obtained based on the average fringe density of the transverse shearing interferogram. The first obtaining unit is specifically used for: The shear rate is determined using the following formula based on the diameter of the aspherical surface to be tested and the initial shear rate: S=Ratio0*D aspheric The center point of the transverse shear interference bright fringes is determined using the following formula based on the aspheric surface to be measured, the initial reference surface, the vertex radius of curvature R0 of the aspheric surface to be measured, and the shearing amount: The density of the transverse shear interference pattern matching the initial reference surface is determined by the following formula based on the center point positions of two adjacent transverse shear interference bright fringes: Where S represents the shear rate, Ratio0 represents the initial shear rate, and D... aspheric T represents the aperture of the aspherical surface to be measured. i The x represents the center point of the transverse shear interference bright fringes, r0 represents the radius of the initial reference surface, and x represents the x-axis. di Let x represent the x-coordinate of a point D on the aspherical surface to be measured. ci Let y represent the x-coordinate of a point C on the initial reference surface. di Let y represent the ordinate of a point D on the aspherical surface to be measured. ci Let R0 represent the ordinate of a point C on the initial reference surface, R0 represent the radius of curvature of the vertex of the aspherical surface to be measured, k represent the conic coefficient of the quadratic surface, λ represent the wavelength, and Density represent the fringe density of the transverse shear interference pattern.

7. The apparatus as claimed in claim 6, characterized in that, The first obtaining unit is specifically used to: obtain the coarse-optimized shear rate using the following formula: The coarse-optimized shear rate and the first range of coarse-optimized shear rates matching the radius iteration range are obtained through the following formulas: Where Max[Density] represents the maximum transverse shear interference pattern fringe density among the plurality of transverse shear interference pattern fringe densities, Density max Ratio1 represents the maximum resolvable threshold of the actual interference fringes, and D represents the coarse-optimized shear rate. aspheric Indicates the aperture of the aspherical surface to be measured, (indicates the pixel size of the detector target surface, y) di This represents the ordinate of a point D on the aspherical surface to be measured. The iterative range of the initial shear rate is represented by λ, where λ represents the wavelength, and Ratio is... max This represents the first range of coarse-optimized shear rates that matches the radius iteration range. Max(Ratio) represents the iteration range of the radius of the initial reference surface. max ) represents the maximum coarse-optimized shear rate within the first range of coarse-optimized shear rates, and r1 represents the radius of the optimal reference surface.

8. A computer device, characterized in that, The computer device includes a memory and a processor. The memory stores a computer program, which, when executed by the processor, causes the processor to perform the transverse shear interference shear rate selection method as described in any one of claims 1-5.

9. A computer-readable storage medium, characterized in that, The system contains a computer program that, when executed by a processor, causes the processor to perform the transverse shear interference shear rate selection method as described in any one of claims 1-5.

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