Method and apparatus for double surface profilometry of a transparent optical element

Abstract

This application relates to a method and apparatus for measuring the dual-surface profile of a transparent optical element. The method includes: acquiring a first diffraction pattern of the element under test (DUT); the DUT being a transparent optical element with a dual-surface profile to be measured; performing phase recovery on the first diffraction pattern based on coherent modulation imaging to obtain a reconstructed wavefront of the DUT's reflected surface; establishing a dual-surface profile coupling model of the DUT's reflected surface based on the reconstructed wavefront; the dual-surface profile coupling model containing only the composite information of the dual surfaces of the DUT; and decoupling the dual-surface profile coupling model in reverse to separate the front and rear surface profile information of the DUT from the composite information. The solution provided in this application addresses the problems of related technologies, such as unsuitability for dynamic measurement, sensitivity to noise, unsuitability for measuring large-aperture devices, and high implementation costs.

Description

Technical Field

[0001] This application relates to the field of optical processing technology, and in particular to a method and apparatus for measuring the dual-surface profile of transparent optical elements. Background Technology

[0002] Transparent optical components are currently undergoing a comprehensive revolution, from materials to applications. Through the integration of multiple disciplines, transparent optical components are playing an increasingly important role in fields such as intelligent sensing, quantum computing, and biomedicine. In the precision manufacturing of transparent optical components, the geometric profile of the optical surface provides great flexibility in controlling the propagation of light. Therefore, high-precision measurement of the optical surface profile of transparent optical components is of great significance.

[0003] Measurement techniques in related fields include 3D profilometers, coordinate measuring machines (CMMs), fringe reflection phase deflectometers, and various interferometers. Among these, interferometers are currently the primary equipment for measuring the surface profiles of transparent optical components. However, interferometers are extremely sensitive to noise during measurement, thus requiring strict environmental conditions, such as the absence of vibration. Furthermore, for large-aperture devices, the extremely long optical path limits the effectiveness of physical vibration isolation, making interferometers unsuitable for measuring large-aperture devices. Additionally, all of the aforementioned measurement techniques suppress one surface while measuring another, thus sharing a common limitation: they cannot be applied to dual-surface profile measurements under single-exposure conditions in dynamic scenarios and are prohibitively expensive. Summary of the Invention

[0004] To address or partially address the problems existing in related technologies, this application provides a method and apparatus for measuring the dual-surface profile of transparent optical elements, which can solve the problems of unsuitability for dynamic measurement, sensitivity to noise, unsuitability for measuring large-diameter devices, and high implementation cost in related technologies.

[0005] The first aspect of this application provides a method for measuring the dual-surface profile of a transparent optical element, comprising:

[0006] Obtain the first diffraction pattern of the element under test; the element under test is a transparent optical element with a double-surface profile to be measured;

[0007] Phase recovery is performed on the first diffraction pattern based on coherent modulation imaging to obtain the reconstructed wavefront of the reflected wavefront of the device under test;

[0008] Based on the reconstruction results of the reflected wavefront of the device under test, a dual-surface profile coupling model of the reflected wavefront of the device under test is established; the dual-surface profile coupling model only contains the dual-surface composite information of the device under test.

[0009] The dual-surface contour coupling model is decoupled in reverse so as to separate the front surface contour information and the rear surface contour information of the element under test from the dual-surface composite information.

[0010] In one embodiment, the reconstruction result is an initial coupling model; the phase recovery of the first diffraction pattern based on coherent modulation imaging to obtain the reconstruction result of the reflected wavefront of the device under test includes:

[0011] Phase recovery is performed on the first diffraction pattern based on coherent modulation imaging to reconstruct an initial coupling model of the reflected wavefront of the device under test; the initial coupling model includes the dual-surface synthesis information of the device under test and the illumination light information of the measurement system used to measure the device under test.

[0012] In one embodiment, establishing a dual-surface profile coupling model of the reflected wavefront of the device under test based on the reconstruction results of the reflected wavefront includes:

[0013] The illumination light information is removed from the initial coupling model in order to establish a dual-surface profile coupling model of the reflected wavefront of the element under test.

[0014] In one embodiment, removing the illumination light information from the initial coupling model to establish a bi-surface profile coupling model of the reflected wavefront of the element under test includes:

[0015] Obtain the second diffraction pattern of the standard element; the standard element is a transparent optical element with known single-surface profile information and high flatness;

[0016] Phase recovery is performed on the second diffraction pattern based on the coherent modulation imaging to obtain the reconstruction result of the reflected wavefront of the standard element; the reconstruction result of the reflected wavefront of the standard element includes the known single-surface profile information and the illumination light information;

[0017] The reconstruction result of the reflected wavefront of the standard element is used as the pre-calibration information of the measurement system;

[0018] The pre-calibration information is removed from the initial coupling model in order to establish a dual-surface profile coupling model of the reflected wavefront of the element under test.

[0019] In one embodiment, the reverse decoupling of the dual-surface profile coupling model to separate the front and rear surface profile information of the element under test from the dual-surface composite information includes:

[0020] Determine a first transfer function of the front surface of the component under test, and determine a second transfer function of the rear surface of the component under test;

[0021] Based on the first transfer function and the second transfer function, the target decoupling parameters of the dual-surface profile coupling model are determined; the target decoupling parameters include a first decoupling parameter and a second decoupling parameter, wherein the first decoupling parameter is used to separate the front surface profile information of the component under test, and the second decoupling parameter is used to separate the rear surface profile information of the component under test;

[0022] Using the phase information of the first decoupling parameter, the front surface contour information is solved in reverse from the dual-surface contour coupling model; and using the phase information of the second decoupling parameter, the rear surface contour information is solved in reverse from the dual-surface contour coupling model.

[0023] In one embodiment, the reflected wavefront of the device under test is generated based on coherent light sources of different wavelengths; determining the target decoupling parameters of the dual-surface profile coupling model according to the first transfer function and the second transfer function includes:

[0024] The quasi-Newton iteration method is used to calculate two sets of solutions for the second transfer function at each wavelength; the two sets of solutions include the true solution and the twin solution;

[0025] The true solution of the second transfer function at each wavelength is selected from the two sets of solutions of the second transfer function at each wavelength.

[0026] Using the dual-surface profile coupling model and the true solution of the second transfer function at each wavelength, the true solution of the first transfer function at each wavelength is calculated respectively;

[0027] The true solution of the first transfer function at the target wavelength is used as the first decoupling parameter, and the true solution of the second transfer function at the target wavelength is used as the second decoupling parameter; wherein the target wavelength is any of the wavelengths mentioned above.

[0028] In one embodiment, the step of selecting the true solution of the second transfer function at each wavelength from the two sets of solutions for each wavelength includes:

[0029] Calculate the standard deviation between each set of solutions of the second transfer function at different wavelengths to obtain multiple standard deviation values;

[0030] Determine the smallest standard deviation from the plurality of standard deviations;

[0031] Each solution corresponding to the minimum standard deviation is selected as the true solution of the second transfer function at each wavelength.

[0032] A second aspect of this application provides a dual-surface profile measurement device for a transparent optical element, comprising:

[0033] The first acquisition module is used to acquire the first diffraction pattern of the element under test; the element under test is a transparent optical element with a double-surface profile to be measured.

[0034] The first reconstruction module is used to perform phase recovery on the first diffraction pattern based on coherent modulation imaging to obtain the reconstruction result of the reflected wavefront of the element under test;

[0035] The modeling module is used to establish a dual-surface profile coupling model of the reflected wavefront of the device under test based on the reconstruction results of the reflected wavefront of the device under test; the dual-surface profile coupling model only contains the dual-surface composite information of the device under test.

[0036] The decoupling module is used to decouple the dual-surface contour coupling model in reverse so as to separate the front surface contour information and the rear surface contour information of the element under test from the dual-surface composite information.

[0037] A third aspect of this application provides an electronic device, comprising:

[0038] Processor; and

[0039] A memory that stores executable code, which, when executed by the processor, causes the processor to perform the method described above.

[0040] A fourth aspect of this application provides a computer-readable storage medium having executable code stored thereon, which, when executed by a processor of an electronic device, causes the processor to perform the method described above.

[0041] The fifth aspect of this application provides a computer program product comprising computer instructions that, when executed by a processor, implement the method described above.

[0042] The technical solution provided in this application may include the following beneficial results:

[0043] The technical solution of this application involves acquiring a first diffraction pattern of a device under test (DUT); the DUT is a transparent optical element with a double-surface profile to be measured; phase recovery is performed on the first diffraction pattern based on coherent modulation imaging to obtain a reconstruction result of the reflected wavefront of the DUT; based on the reconstruction result of the reflected wavefront of the DUT, a double-surface profile coupling model of the reflected wavefront of the DUT is established; the double-surface profile coupling model only contains the double-surface composite information of the DUT; the double-surface profile coupling model is decoupled in reverse to separate the front surface profile information and the back surface profile information of the DUT from the double-surface composite information. This application, based on coherent modulation imaging, can achieve rapid reconstruction of the reflected wavefront of the DUT under single-exposure conditions. Then, based on the reconstruction result, a double-surface profile coupling model of the reflected wavefront of the DUT is established, so that the double-surface profile information of the DUT can be obtained by decoupling the double-surface profile coupling model. Therefore, it can be applied to double-surface profile measurement under single-exposure conditions in dynamic scenes, reducing implementation costs. In addition, since coherent modulation imaging has high robustness, it can reduce the requirements for the measurement environment and is suitable for cross-scale measurement.

[0044] It should be understood that the above general description and the following detailed description are exemplary and explanatory only, and do not limit this application. Attached Figure Description

[0045] The above and other objects, features and advantages of this application will become more apparent from the more detailed description of exemplary embodiments thereof in conjunction with the accompanying drawings, wherein the same reference numerals generally represent the same components in the exemplary embodiments thereof.

[0046] Figure 1 This is a schematic flowchart illustrating the dual-surface profile measurement method for a transparent optical element according to an embodiment of this application;

[0047] Figure 2 This is a schematic diagram of the structure of a single-shot dual-surface profile measurement system based on coherent modulation imaging, as shown in an embodiment of this application.

[0048] Figure 3 This is another schematic flowchart illustrating the dual-surface profile measurement method for transparent optical elements shown in the embodiments of this application;

[0049] Figure 4 This is the result of dual-surface reconstruction of the spherical lens in the simulation shown in the embodiments of this application;

[0050] Figure 5 This is the result of dual-surface reconstruction of a freeform lens in the simulation shown in the embodiments of this application;

[0051] Figure 6This is a schematic diagram illustrating the calibration of the modulator's amplitude and phase on an optical experimental platform, as shown in an embodiment of this application.

[0052] Figure 7 This is a schematic diagram showing a comparison between the measurement results obtained in the simulation of this application embodiment and the measurement results obtained using an interferometer in related technologies;

[0053] Figure 8 This is a schematic diagram of the structure of the dual-surface profile measurement device for transparent optical elements shown in the embodiments of this application;

[0054] Figure 9 This is a schematic diagram of the structure of an electronic device shown in an embodiment of this application. Detailed Implementation

[0055] Embodiments of this application will now be described in more detail with reference to the accompanying drawings. While embodiments of this application are shown in the drawings, it should be understood that this application may be implemented in various forms and should not be limited to the embodiments set forth herein. Rather, these embodiments are provided to make this application more thorough and complete, and to fully convey the scope of this application to those skilled in the art.

[0056] The terminology used in this application is for the purpose of describing particular embodiments only and is not intended to be limiting of the application. The singular forms “a,” “the,” and “the” used in this application and the appended claims are also intended to include the plural forms unless the context clearly indicates otherwise. It should also be understood that the term “and / or” as used herein refers to and includes any or all possible combinations of one or more of the associated listed items.

[0057] It should be understood that although the terms "first," "second," "third," etc., may be used in this application to describe various information, this information should not be limited to these terms. These terms are only used to distinguish information of the same type from one another. For example, without departing from the scope of this application, first information may also be referred to as second information, and similarly, second information may also be referred to as first information. Thus, a feature defined as "first" or "second" may explicitly or implicitly include one or more of that feature. In the description of this application, "multiple" means two or more, unless otherwise explicitly specified.

[0058] Measurement techniques in related technologies include 3D profilometers, coordinate measuring machines (CMMs), fringe reflection phase deflectors, and various interferometers. Among these, interferometers are currently the primary equipment for measuring the surface profiles of transparent optical elements. However, interferometers are extremely sensitive to noise during measurement, thus requiring strict environmental conditions, such as the absence of vibration. Furthermore, for large-aperture devices, the extremely long optical path limits the effectiveness of physical vibration isolation, making interferometers unsuitable for measuring large-aperture devices. Moreover, all the aforementioned measurement techniques measure each surface individually. Taking interferometers as an example, when measuring the surface profile of a transparent optical element, the interference between the two surfaces generates parasitic fringes. These parasitic fringes cause phase calculation errors and blurry images acquired by the detector. Therefore, while measuring one surface, the interferometer suppresses the other. For instance, while using reflected light from the front surface to measure the front surface profile, the interferometer suppresses reflected light from the rear surface. Therefore, interferometers cannot be used for measuring the profiles of two surfaces under single-exposure conditions in dynamic scenes and are very expensive (the same applies to other measurement techniques in related technologies).

[0059] To address the aforementioned issues, this application provides a method for measuring the dual-surface profile of a transparent optical element. Based on coherent modulation imaging, it enables rapid reconstruction of the reflected wavefront of the element under test under single-exposure conditions. Then, based on the reconstruction results, a dual-surface profile coupling model of the reflected wavefront of the element under test is established. By decoupling the dual-surface profile coupling model, the dual-surface profile information of the element under test can be obtained. Therefore, it can be applied to dual-surface profile measurement under single-exposure conditions in dynamic scenes, reducing implementation costs. Furthermore, since coherent modulation imaging has high robustness, it can reduce the requirements for the measurement environment and is suitable for cross-scale measurement.

[0060] The technical solutions of the embodiments of this application are described in detail below with reference to the accompanying drawings.

[0061] Figure 1 This is a schematic flowchart illustrating the dual-surface profile measurement method for a transparent optical element as shown in an embodiment of this application.

[0062] See Figure 1 The method for measuring the dual-surface profile of a transparent optical element according to this application may include:

[0063] S110, acquire the first diffraction pattern of the element under test; the element under test is a transparent optical element with a double-surface profile to be measured.

[0064] In the embodiments of this application, it can be applied to a computing device. The computing device is communicatively connected to a single-shot dual-surface profile measurement system based on coherent modulation imaging (hereinafter referred to as the "measurement system"). The computing device can obtain the first diffraction pattern of the element under test from the measurement system. The element under test refers to a transparent optical element with a dual-surface profile to be measured.

[0065] like Figure 2 As shown, the measurement system includes a wavefront sensor, an illumination device, a beam splitter, and a collimating lens. The wavefront sensor can be used to measure the reflected wavefront distribution of the device under test (such as the device under test / standard device) at two wavelengths. The dashed box in the upper right corner is a schematic diagram of the formation of the reflected wavefront of the device under test. The wavefront sensor includes a CMOS (Complementary Metal-Oxide-Semiconductor) image detector, a modulator, and a virtual aperture.

[0066] In practical implementation, the component under test is placed on the component being tested (i.e., Figure 2 The position of the sample under test (SUT) is determined, i.e., the current element under test is the SUT. The computing device can send a first control command to the measurement system. In response to the first control command, the measurement system controls the illumination device to output a dual-wavelength light source. The dual-wavelength light source passes through a beam splitter and a collimating lens in sequence and is then incident vertically on the SUT, so that the SUT generates a reflected wavefront. Since the beam splitter is placed at an angle, it can propagate the reflected wavefront of the SUT to the support domain plane of the virtual aperture. The virtual aperture can converge the reflected wavefront at the support domain plane. The converged reflected wavefront is propagated to the modulator plane. The modulator can modulate the converged reflected wavefront at the modulator plane. When the modulated reflected wavefront is propagated to the detector plane, it will generate a diffraction pattern. For easy distinction, the diffraction pattern of the SUT is defined as the first diffraction pattern. At this time, the measurement system can control the CMOS image detector to acquire the first diffraction pattern at the detector plane. The computing device obtains the first diffraction pattern from the measurement system.

[0067] It should be noted that the reflected wavefront refers to the phase surface of the light wave that leaves after reflection from the surface of a transparent optical element. Since the device under test (DUT) has two surfaces (i.e., front surface + back surface), the DUT exhibits different phases at each wavelength λ. i The reflected wavefronts are all composed of the front and rear surfaces of the device under test based on the corresponding wavelength λ. i coherent light source P i The two sub-wavefronts generated separately form, such as Figure 2 As shown in the dashed box in the upper right corner, the device under test is at wavelength λ1 (i.e., Figure 2The reflected wavefront at wavelength 1 shown is composed of a sub-wavefront generated by a coherent light source P1 based on wavelength λ1 on the front surface of the device under test and a sub-wavefront generated by a coherent light source P1 based on wavelength λ1 on the rear surface of the device under test. The reflected wavefront at wavelength λ2 (i.e., Figure 2 The reflected wavefront at wavelength 2 shown is composed of a sub-wavefront generated by a coherent light source P2 based on wavelength λ2 on the front surface of the device under test and a sub-wavefront generated by a coherent light source P2 based on wavelength λ2 on the rear surface of the device under test.

[0068] S120, Phase recovery is performed on the first diffraction pattern based on coherent modulation imaging to obtain the reconstruction result of the reflected wavefront of the device under test.

[0069] Since the response of the surface profile of the device under test (such as the device under test / standard device) to incident light is mainly focused on phase information, the complex amplitude distribution of the reflected wavefront of the device under test can be completely reconstructed through phase recovery, so as to subsequently invert the surface profile of the device under test.

[0070] In practical applications, after obtaining the first diffraction pattern of the device under test (DUT), the computing device can perform phase recovery on the first diffraction pattern based on coherent modulation imaging (CMI) to obtain the reconstructed wavefront of the DUT. Reconstruction results Characterizes the reflected wavefront distribution of the element under test at the reconstructed support domain plane.

[0071] Where i represents the i-th wavelength (i is a positive integer). In this application embodiment, two wavelengths can be used (i.e., i=2) or more than two wavelengths (i.e., i≥2). Since the twin terms existing in the decoupling process can be filtered out by using two wavelengths to obtain the true solution, more than two wavelengths do not add effective information. Therefore, in this application embodiment, two wavelengths (i.e., i=2) are sufficient.

[0072] The key step in the modulator plane is to apply and remove the modulator's transfer function T(r). m As a priori condition:

[0073] Formula 1

[0074] Formula 2

[0075] Where i represents the i-th wavelength, and k represents the k-th iteration. This represents the original wavefront estimate. This represents the updated wavefront estimate. The front plane of the modulator plane, The back plane of the modulator plane, It is a constant that determines the gradient update rate. It is based on the transfer function of Equation 4 below. The result is obtained by normalization.

[0076] It should be noted that as long as the experimental parameters remain unchanged, the transfer function of the modulator at each wavelength only needs to be calibrated once.

[0077] Specifically, when the light converges, a strong 0-1 constraint is imposed on the reflected wavefront distribution by using a virtual aperture of variable radius at the support domain plane, instead of a true circular aperture. When applying mode constraints at the detector plane, the estimate for each wavelength is updated as follows:

[0078] Formula 3

[0079] Where I represents the intensity of the diffraction pattern acquired by the CMOS image detector (such as the first diffraction pattern of the device under test / the second diffraction pattern of the standard device). This represents the detector plane.

[0080] exist Figure 2 In the measurement system shown, this embodiment of the application uses the Fresnel propagation algorithm to propagate the reflected wavefront between three planes (i.e., the support domain plane, the modulator plane, and the detector plane). By continuously propagating and constraining the reflected wavefront between these three planes for several iterations, when the convergence criterion is met, the estimated reflected wavefront at the support domain plane is the reflected wavefront distribution obtained by phase recovery.

[0081] Therefore, coherent modulation imaging (CMIM) achieves rapid reconstruction of the wavefront distribution under a single exposure by introducing a modulator with a known wavefront distribution. Thus, the embodiments of this application utilize CMIM to achieve rapid reconstruction of the reflected wavefront of the device under test under single exposure conditions. Furthermore, CMIM has a simple lensless system structure, is unaffected by quality issues such as lens aberrations, achieves theoretical spatial resolution at the diffraction limit, and has measurement accuracy on the order of one-hundredth of the wavelength. Therefore, the embodiments of this application utilize CMIM to provide high spatial resolution and high accuracy for the dual-surface profile measurement of transparent optical elements. In addition, the introduction of the modulator helps eliminate twin images and spatially offset ambiguities during the iteration process, achieving robust convergence of a single exposure. This makes CMIM highly robust. Therefore, the embodiments of this application utilize CMIM to reduce the requirements of the measurement environment and are suitable for cross-scale measurements, such as the measurement of large-aperture transparent optical elements.

[0082] S130, Based on the reconstruction results of the reflected wavefront of the device under test, a dual-surface profile coupling model of the reflected wavefront of the device under test is established; the dual-surface profile coupling model only contains the dual-surface composite information of the device under test.

[0083] Due to the reconstruction results of the reflected wavefront of the device under test In addition to the combined information of the two surfaces of the device under test, it also includes the illumination information P of the measurement system. i In order to avoid illumination light information P i This will affect the subsequent decoupling results. In this embodiment, the measurement system can be pre-calibrated to obtain pre-calibration information, which includes illumination light information P. i The embodiments of this application utilize the reconstruction results from the reflected wavefront of the device under test. Removing the pre-calibration information in the middle can remove the illumination light information P. i It can also remove the unavoidable optical path coupling errors introduced by the geometry of the collimating lens, beam splitter and other optical components and measurement system used.

[0084] Reconstruction results from the reflected wavefront of the device under test After removing the pre-calibration information, a dual-surface profile coupled model of the reflected wavefront of the device under test can be established. Dual-surface profile coupling model It only contains the combined information of the two surfaces of the device under test, and does not contain the illumination light information P of the measurement system. i .

[0085] S140, decouple the dual-surface profile coupling model in reverse so as to separate the front and rear surface profile information of the component under test from the dual-surface composite information.

[0086] Dual-surface composite information refers to the information obtained by combining the front surface contour information and the rear surface contour information of the component under test. Therefore, the embodiments of this application can reverse the dual-surface contour coupling model. Decoupling is performed to separate the front surface contour information and the rear surface contour information of the component under test from the dual-surface composite information.

[0087] Because the embodiments of this application can realize the dual-surface shape reconstruction of the device under test under a single exposure (i.e. Therefore, a single exposure means that the continuous change process of the double-surface shape over a certain period of time can be observed through continuous exposure. Compared with interferometric measurement in related technologies, the embodiments of this application have broad application prospects in dynamic measurement. For example, the effectiveness of the embodiments of this application in the field of double-surface profile measurement has been verified in continuous phase plates (CPP) and quartz windows.

[0088] As can be seen from this example, the solution provided in this application obtains a first diffraction pattern of the device under test (DUT); the DUT is a transparent optical element with a double-surface profile to be measured; phase recovery is performed on the first diffraction pattern based on coherent modulation imaging to obtain the reconstruction result of the reflected wavefront of the DUT; based on the reconstruction result of the reflected wavefront of the DUT, a double-surface profile coupling model of the reflected wavefront of the DUT is established; the double-surface profile coupling model only contains the double-surface composite information of the DUT; the double-surface profile coupling model is decoupled in reverse to separate the front surface profile information and the back surface profile information of the DUT from the double-surface composite information. This application can achieve rapid reconstruction of the reflected wavefront of the DUT under single-exposure conditions based on coherent modulation imaging, and then establish a double-surface profile coupling model of the reflected wavefront of the DUT based on the reconstruction result, so that the double-surface profile information of the DUT can be obtained by decoupling the double-surface profile coupling model. Therefore, it can be applied to double-surface profile measurement under single-exposure conditions in dynamic scenes, reducing the implementation cost. In addition, since coherent modulation imaging has high robustness, it can reduce the requirements for the measurement environment and is suitable for cross-scale measurement.

[0089] Figure 3 This is another schematic flowchart of the dual-surface profile measurement method for transparent optical elements shown in this application.

[0090] See Figure 3 The method for measuring the dual-surface profile of a transparent optical element according to this application may include:

[0091] S310, acquire the first diffraction pattern of the element under test; the element under test is a transparent optical element with a double-surface profile to be measured.

[0092] This step can be referred to in the description of step S110 above, and will not be repeated here.

[0093] S320, Phase recovery is performed on the first diffraction pattern based on coherent modulation imaging in order to reconstruct the initial coupling model of the reflected wavefront of the device under test; the initial coupling model contains the dual-surface synthesis information of the device under test and the illumination light information of the measurement system used to measure the device under test.

[0094] This step can be referred to in the description of step S120 above, and will not be repeated here.

[0095] It should be noted that the initial coupling model in this step is the reconstruction result of step S120. Therefore, the initial coupling model Includes bi-surface composite information of the device under test and illumination information of the measurement system P i .

[0096] It should be noted that in actual light propagation, incident light undergoes multiple reflections between the two surfaces of a transparent optical element. Taking quartz glass with a refractive index n≈1.5 as an example, the energy of the second-order reflected light is 1.6% of the energy of the first-order reflected light. To estimate the maximum impact of the second-order reflected light on the complete reflected wavefield, we assume its phase difference relative to other reflected components is... The measurement result corresponds to an error of less than This error magnitude is negligible within the required range. Therefore, to facilitate the initial coupling model... Reconstruction and dual-surface profile coupling model To achieve decoupling, the embodiments of this application approximately assume that the reflected wavefront of the device under test consists only of the first-order reflected wavefronts generated by its front and rear surfaces, respectively.

[0097] When representing the contour of a single surface, this embodiment takes the lowest point of the surface shape as the zero point of the surface shape height. The relative height of the surface contour with respect to this zero point can then be expressed as h. When illumination light P is incident perpendicularly on a surface, the relationship between the surface transfer function and the surface contour h can be expressed as follows:

[0098] Formula 4

[0099] in, , where j represents the wave number and j represents the imaginary number. .

[0100] Based on Equation 4 above, the contour of the front surface of the component under test can be expressed as h. f This indicates that the profile of the rear surface of the component under test can be obtained using h. r express.

[0101] When the illumination light P (such as Figure 2 When the dual-wavelength light source shown is incident perpendicularly on the device under test (DUT), the front surface of the DUT generates reflected and transmitted light, respectively. The transmitted light from the front surface continues to propagate through the medium (the medium distribution is assumed to be uniform) to the rear surface of the DUT. The reflected light from the rear surface is then transmitted again through the front surface of the DUT. Therefore, the reflected light from the front surface of the DUT... Reflected light from the rear surface of the component under test They can be represented as follows:

[0102] Formula 5

[0103] Formula Six

[0104] in, This represents the refractive index of the medium of the device under test at the i-th wavelength. This represents the reflectivity of the medium of the device under test at the i-th wavelength. This represents the transmittance of the medium of the device under test at the i-th wavelength. This represents a coherent light source with wavelength i.

[0105] Complete reflected wavefront of the device under test (i.e., the initial coupling model in step S320) can be represented as the reflected light from the front surface of the device under test. Reflected light from the rear surface of the component under test Based on the coherent superposition of equations five and six above, we can obtain the following equation seven:

[0106] Formula 7

[0107] S330, remove illumination light information from the initial coupling model in order to establish a dual-surface profile coupling model of the reflected wavefront of the device under test; the dual-surface profile coupling model only contains the dual-surface composite information of the device under test.

[0108] Due to the initial coupling model of the reflected wavefront of the device under test In addition to the combined information of the two surfaces of the device under test, it also includes the illumination information P of the measurement system. i In order to avoid illumination light information P i This will affect the subsequent decoupling results. In this embodiment, the measurement system can be pre-calibrated to obtain pre-calibration information, which includes illumination light information P. i The embodiments of this application utilize the reconstruction results from the reflected wavefront of the device under test. Removing the pre-calibration information in the middle can remove the illumination light information P. i It can also remove the unavoidable optical path coupling errors introduced by the geometry of the collimating lens, beam splitter and other optical components and measurement system used.

[0109] Initial coupling model from the reflected wavefront of the device under test After removing the pre-calibration information, a dual-surface profile coupled model of the reflected wavefront of the device under test can be established. Dual-surface profile coupling model It only contains the combined information of the two surfaces of the device under test, and does not contain the illumination light information P of the measurement system. i .

[0110] In one embodiment, removing illumination information from the initial coupling model to establish a bi-surface profile coupling model of the reflected wavefront of the element under test may include:

[0111] A second diffraction pattern of a standard element is obtained; the standard element is a transparent optical element with known single-surface profile information and high flatness; phase recovery is performed on the second diffraction pattern based on coherent modulation imaging to obtain the reconstruction result of the reflected wavefront of the standard element; the reconstruction result of the reflected wavefront of the standard element includes known single-surface profile information and illumination light information; the reconstruction result of the reflected wavefront of the standard element is used as the pre-calibration information of the measurement system; the pre-calibration information is removed from the initial coupling model in order to establish a double-surface profile coupling model of the reflected wavefront of the element under test.

[0112] In the process of pre-calibrating the measurement system, the embodiments of this application can first select a transparent optical element with a single surface that has been measured and has high flatness as a standard element. That is, the standard element refers to a transparent optical element with known single surface contour information, and the known single surface contour information indicates that the single surface of the standard element has high flatness and small surface undulation, which can be regarded as a pure plane. For example, the known surface undulation of the standard element is close to zero.

[0113] Then, in the embodiments of this application, a standard component can be placed on the component under test (i.e., Figure 2 The position of the sample to be tested (i.e., the current element under test is the standard element) is determined. The computing device can send a second control command to the measurement system. The measurement system responds to the second control command by controlling the illumination device to output a dual-wavelength light source. The dual-wavelength light source passes through a beam splitter and a collimating lens in sequence and is then incident perpendicularly on the standard element, so that the standard element generates a reflected wavefront. Since the beam splitter is placed at an angle, it can propagate the reflected wavefront of the standard element to the support domain plane of the virtual aperture. The virtual aperture can converge the reflected wavefront at the support domain plane. The converged reflected wavefront is propagated to the modulator plane. The modulator can modulate the converged reflected wavefront at the modulator plane. When the modulated reflected wavefront is propagated to the detector plane, it will generate a diffraction pattern. For easy distinction, the diffraction pattern of the standard element is defined as the second diffraction pattern. At this time, the measurement system can control the CMOS image detector to acquire the second diffraction pattern at the detector plane. The computing device obtains the second diffraction pattern from the measurement system.

[0114] After obtaining the second diffraction pattern of the standard element, the computing device can perform phase recovery on the second diffraction pattern based on coherent modulation imaging to obtain the reconstructed wavefront of the standard element. Reconstruction results Characterizing the reflected wavefront distribution of the standard element at the reconstructed support domain plane, and the reconstruction result of the reflected wavefront of the standard element. It can be represented as follows:

[0115] Formula 8

[0116] in, This represents the reflectivity of the standard element medium at the i-th wavelength. Since the reflected light propagates from the optically rarefied medium (air) to the optically dense medium (the component is typically made of quartz), this is introduced. , which represents half-wave loss.

[0117] Similarly, the reconstruction results of the reflected wavefront of the standard element In addition to the known single-surface profile information of the standard components, it also includes the illumination light information P of the measurement system. i Since both the standard element and the element under test are measured in the same measurement environment, the reconstruction result of the reflected wavefront of the standard element is... Includes lighting information P i Initial coupling model with the reflected wavefront of the device under test Includes lighting information P i Similarly, since a single surface of a standard element is a plane, meaning the known surface undulation of a standard element is close to zero, the embodiments of this application can reconstruct the reflected wavefront of the standard element. As pre-calibration information for the measurement system, this is therefore obtained through the initial coupling model derived from the reflected wavefront of the element under test. Remove pre-calibration information from the initial coupling model of the reflected wavefront of the device under test. Reconstruction results of the reflected wavefront after removing standard elements This can be equivalent to the initial coupling model from the reflected wavefront of the device under test. Remove illumination light information P from the measurement system i This enables the dual-surface profile coupling model of the reflected wavefront of the device under test. It only contains the combined information of the two surfaces of the device under test, and does not contain the illumination light information P of the measurement system. i .

[0118] If the illumination light is measured directly, it would be impossible to use the same measurement system because the energy of the illumination light is two orders of magnitude higher than that of the reflected wavefront. Therefore, the embodiments of this application use an initial coupling model from the reflected wavefront of the device under test. Reconstruction results of the reflected wavefront after removing standard elements This allows for the realization of an initial coupling model from the reflected wavefront of the device under test. Remove illumination light information P from the measurement system i.

[0119] Furthermore, the accuracy of interferometry in related technologies largely depends on a high-quality reference plane, which is typically limited to planar or spherical shapes, making it difficult to measure zero values ​​on aspherical surfaces. In contrast to the high-quality reference planes required in related technologies, the plane of the standard element in this application embodiment can have certain undulations. Therefore, this application embodiment can eliminate the need for a high-quality reference plane. Moreover, this application embodiment has no shape restrictions on the surface profile of the element under test; therefore, this application embodiment is applicable regardless of whether the surface profile of the element under test is planar, spherical, or aspherical (such as hyperboloids, freeform surfaces, etc.).

[0120] Furthermore, interferometers in related technologies obtain interferograms by interfering the reflected light from a reference plane with the reflected light from the plane to be measured. Therefore, related technologies require the use of a reference plane for each measurement. Compared to the multiple uses of the reference plane in related technologies, the reconstruction result of the reflected wavefront of the standard element in the embodiments of this application... Since it is not affected by the device under test, the embodiments of this application only need to perform pre-calibration once, thereby greatly reducing the number of pre-calibration times.

[0121] S340 decouples the dual-surface profile coupling model in reverse so as to separate the front and rear surface profile information of the component under test from the dual-surface composite information.

[0122] This step can be referred to in the description of step S140 above, and will not be repeated here.

[0123] In one embodiment, decoupling the dual-surface profile coupling model in reverse, so as to separate the front and rear surface profile information of the element under test from the dual-surface composite information, may include:

[0124] A first transfer function for the front surface of the component under test (DUT) and a second transfer function for the rear surface of the DUT are determined. Based on the first and second transfer functions, target decoupling parameters for the dual-surface profile coupling model are determined. The target decoupling parameters include a first decoupling parameter and a second decoupling parameter. The first decoupling parameter is used to separate the front surface profile information of the DUT, and the second decoupling parameter is used to separate the rear surface profile information of the DUT. Using the phase information of the first decoupling parameter, the front surface profile information is solved in reverse from the dual-surface profile coupling model, and using the phase information of the second decoupling parameter, the rear surface profile information is solved in reverse from the dual-surface profile coupling model.

[0125] Based on Equation 4 above and the characteristics of the front surface of the component under test, the first transfer function of the front surface of the component under test can be determined. Based on Equation 4 above and the characteristics of the back surface of the device under test, the second transfer function of the back surface of the device under test can be determined. First transfer function Second transfer function They can be represented as follows:

[0126] Formula Nine

[0127] Formula 10

[0128] According to the first transfer function Second transfer function Determine the dual-surface profile coupling model The target decoupling parameters include a first decoupling parameter and a second decoupling parameter. The first decoupling parameter can be used to separate the front surface contour information of the component under test, and the second decoupling parameter can be used to separate the rear surface contour information of the component under test. Then, the phase information is extracted from the first decoupling parameter. And extracting its phase information from the second decoupling parameter. ,in, and The physical meaning of is the optical path difference introduced by the front and rear surfaces of the device under test. In the embodiments of this application, the phase information of the first decoupling parameter can be used. From the dual-surface profile coupling model The front surface contour information is obtained by reverse engineering. and phase information using the second decoupling parameter. From the dual-surface profile coupling model The back surface profile information is obtained by reverse engineering. .

[0129] In one embodiment, the reflected wavefront of the device under test is generated based on coherent light sources of different wavelengths; the target decoupling parameters of the dual-surface profile coupling model are determined according to a first transfer function and a second transfer function, which may include:

[0130] The quasi-Newton iteration method is used to calculate two sets of solutions for the second transfer function at each wavelength; the two sets of solutions include the true solution and the twin solution; the true solution of the second transfer function at each wavelength is selected from the two sets of solutions for each wavelength; the true solution of the first transfer function at each wavelength is calculated using the dual-surface profile coupling model and the true solution of the second transfer function at each wavelength; the true solution of the first transfer function at the target wavelength is used as the first decoupling parameter, and the true solution of the second transfer function at the target wavelength is used as the second decoupling parameter; wherein, the target wavelength is any wavelength.

[0131] The reflected wavefront of the device under test is generated based on coherent light sources of different wavelengths, such as... Figure 2 As shown, the reflected wavefront of the device under test is generated based on coherent light sources (P1 and P2) with two wavelengths (λ1 and λ2). In this embodiment, the device under test is illuminated by a dual-wavelength light source so that different optical path lengths are introduced at different wavelengths based on the same surface profile of the device under test. The twin solutions (also known as twin terms) existing in the decoupling process are filtered out to obtain the true solution, and the dual surface profile of the device under test is obtained in reverse.

[0132] In practical implementation, based on equations 7, 8, 9, and 10 above, we can obtain equation 11 as follows:

[0133] Formula Eleven

[0134] Ideally, since the surface of the device under test (DUT) is transparent, the first transfer function of the front surface of the DUT is... and the second transfer function of the subsequent surface All of these can be approximated as pure phase modulation, i.e. .

[0135] Based on the above constraints, the decoupling process in this embodiment can be derived as a nonlinear problem, which can be expressed as follows:

[0136] Formula Twelve

[0137] In this embodiment, the quasi-Newton iteration method is used to calculate the second transfer function. Solution at each wavelength Where j=[1,2], it represents two sets of solutions at a certain wavelength, which may include the true solution and the twin solution. Specifically, the initial coupling model of the reflected wavefront of the device under test is obtained through the above phase retrieval. Reconstruction results of reflected wavefronts from standard elements ,Will and Substituting into Equation 11 above, the dual-surface profile coupling model can be obtained. At each wavelength λ i (i=[1,2]) under, will and Substituting into equation 12 above, the second transfer function can be obtained. At the corresponding wavelength λ i The true solution and its twin solution (also known as twin terms) are given, meaning that each wavelength corresponds to two sets of solutions: the true solution and the twin solution.

[0138] To eliminate the influence of twin solutions, the embodiments of this application respectively start from the second transfer function At each wavelength λi Two sets of solutions under (i=[1,2]) In the selection process, the second transfer function is chosen. At each wavelength λ i The true solution for (i=[1,2]): and ,in, It is the second transfer function The true solution at wavelength λ1 It is the second transfer function The true solution at wavelength λ2.

[0139] After selecting the second transfer function At each wavelength λ i The true solution under (i=[1,2]) and After that, the embodiments of this application can couple the dual-surface profile model. The transmittance of the medium of the device under test at the i-th wavelength Second transfer function At each wavelength λ i The true solution below ( and Substituting these values ​​into Equation 11 above, we can solve for the first transfer function. At each wavelength λ i The actual solution below: and ,in, It is the first transfer function The true solution at wavelength λ1 It is the first transfer function The true solution at wavelength λ2. Specifically, at wavelength λ1 (i.e., i=1), the embodiments of this application can... , and Substituting into equation 11 above, the first transfer function can be obtained. The true solution Similarly, at wavelength λ2 (i.e., i=2), the embodiments of this application can... , and Substituting into equation 11 above, the first transfer function can be obtained. The true solution .

[0140] In summary, ( , )and( , This refers to the true solutions obtained at different wavelengths. In this embodiment, any set of true solutions can be selected as the target decoupling parameters. Specifically, this embodiment can use the first transfer function... The true solution at the target wavelength is used as the first decoupling parameter, and the second transfer function is used as the second transfer function. The true solution at the target wavelength is used as the second decoupling parameter, where the target wavelength can be any wavelength. For example, if the target wavelength is wavelength λ1, then the first decoupling parameter is the first transfer function. The true solution The second decoupling parameter is the second transfer function. The true solution Therefore, the target decoupling parameter is ( , If the target wavelength is wavelength λ2, then the first decoupling parameter is the first transfer function. The true solution The second decoupling parameter is the second transfer function. The true solution Therefore, the target decoupling parameter is ( , ).

[0141] In one example, the target decoupling parameter is ( , For example, in this embodiment of the application, the target decoupling parameter can be ( , Information on the front surface contour and back surface contour information Perform the inversion. Specifically, start from the first decoupling parameters. Extract its phase information and from the second decoupling parameter Extract its phase information Based on equations four, five, six, seven, and eleven above, we can start from the first decoupling parameter. Phase information Second decoupling parameter Phase information Inversion yields front surface profile information and back surface contour information Specifically, it can be expressed as follows:

[0142] Formula Thirteen

[0143] Formula Fourteen

[0144] In one embodiment, selecting the true solution of the second transfer function at each wavelength from two sets of solutions for each wavelength may include:

[0145] Calculate the standard deviation between each set of solutions for the second transfer function at different wavelengths to obtain multiple standard deviation values; determine the minimum standard deviation value from the multiple standard deviation values; select each set of solutions corresponding to the minimum standard deviation value as the true solution of the second transfer function at each wavelength.

[0146] Due to the second transfer function The twin solutions are not the same at different wavelengths, therefore, the embodiments of this application can calculate the second transfer function separately. The standard deviation between each set of solutions at different wavelengths yields multiple standard deviation values. Then from these standard deviations Determine the minimum standard deviation The smallest standard deviation Each corresponding solution is the second transfer function. The true solution at each wavelength.

[0147] Specifically, the process of selecting the true solution by calculating the standard deviation can be represented as follows:

[0148] Formula 15

[0149] Formula Sixteen

[0150] Formula 17

[0151] Where N represents The number of samples per side refers to the number of pixels on one side of the first diffraction pattern. m represents the m-th solution selected from wavelength λ1, and n represents the n-th solution selected from wavelength λ2. express The pixel value at coordinates (p, q) in the middle. This represents the difference between measurement results at different wavelengths. This represents the mean.

[0152] At multiple standard deviations Choose one from the options. The set with the smallest value ( , If ), then the corresponding set and These are the second transfer functions. The true solution at each wavelength.

[0153] To verify the effectiveness and accuracy of the method proposed in this application, the following three simulation experiments were conducted:

[0154] Simulation Experiment 1: Figure 4 It is the result of the dual-surface reconstruction of a standard spherical lens in the simulation.

[0155] In simulation experiment one, this embodiment of the application generates two refractive lenses to verify the proposed method. One is a standard spherical lens, and the other is a freeform lens composed of two randomly generated continuous optical surfaces. In this embodiment of the application, the homogeneity of the element medium is used as a default condition.

[0156] exist Figure 4 In the diagram, (a) is the front surface of the spherical lens under test, (b) is the rear surface of the spherical lens under test, (c)~(f) are two sets of reconstructed surfaces (using illumination light with a wavelength of 1053nm), and (g)~(j) are the residuals between (c)~(f) and their corresponding nominal profiles in (a)~(b), where the profiles (i)~(j) correspond to the dashed lines in (a)~(b) and (e)~(f).

[0157] The front and rear surface contours of the simulated standard spherical lens in this embodiment are as follows: Figure 4 As shown in (a) and (b), the peak and valley values ​​are 372.71 nm and 283.28 nm, respectively. In the simulation, the illumination source wavelengths selected in this embodiment are 633 nm and 1053 nm, respectively, and the reconstructed RMSE (Root Mean Square Error) is less than [value missing]. For ease of demonstration, Figure 4 Only two sets of decoupling results for a wavelength of 633nm are shown. Figure 4 (c)~(f). Among them, Figure 4 (g)~(j) respectively show Figure 4 The residuals between the results of (c)~(f) and their corresponding nominal surface profiles. After filtering σ in equations 15~17 above, Figure 4 The two dashed boxes represent the true solution and its corresponding residuals, with PV (Peak to Valley) values ​​of 0.687 nm and 0.455 nm, respectively. This means that the method proposed in this application can achieve a good match between the generated surface and the reconstructed surface, achieving nanometer-level detection accuracy. Furthermore, in this application embodiment... Figure 4 The (k)~(l) section gives the dashed profile and the nominal surface in the figure. Figure 4 For a direct comparison of the measured surface profiles, enlarged views of (k)~(l) can be found in [reference needed]. Figure 4The lower half of the graph shows the peak and valley values ​​on the horizontal axis and the surface undulation magnitude (i.e., surface profile) on the vertical axis. The dark curve represents the reconstruction result obtained using coherent modulation imaging in this embodiment, while the light curve represents the simulated real result. Figure 4 As shown in (k)~(l), the dark curves completely overlap with the light curves, thus verifying that the reconstruction results obtained by coherent modulation imaging in this application embodiment are completely consistent with the simulated real results.

[0158] The method proposed in this application requires only a single exposure and acquisition, meeting the needs of application scenarios requiring dynamic measurement of certain components. When reconstructing the complex amplitude distribution using coherent modulation imaging (CMI), the number of samples per side is set to 512, and a real binary phase plate is used as the modulator in the wavefront sensor, resulting in fewer than 350 reconstruction iterations. Therefore, on a computing device configured with an Intel Core i7-12700F 2.10 GHz CPU, 32 GB RAM, x64 processor, and NVIDIA GeForce RTX4060 GPU, the total time, including complete phase retrieval and dual-surface profile decoupling, is approximately 44.79 seconds, enabling simultaneous, fast, and stable measurement of both front and rear surface profiles.

[0159] To further verify the universality of the method proposed in this application for the surface profile of transparent optical elements, this application provides simulation experiment two: Figure 5 It is the result of the two-surface reconstruction of the freeform lens in the simulation.

[0160] exist Figure 5 In the diagram, (a) is the front surface of the freeform lens under test, (b) is the rear surface of the freeform lens under test, (c)~(f) are two sets of reconstructed surfaces (using illumination light with a wavelength of 1053nm), and (g)~(j) are the residuals between (c)~(f) and their corresponding nominal profiles in (a)~(b), where the profiles (i)~(j) correspond to the dashed lines in (a)~(b) and (c)~(d).

[0161] This application's embodiments simulate testing a freeform surface refractive index lens. Figure 5 (a)~(b) are random generalized front and back surfaces with PV values ​​of 73.20 nm and 90.97 nm, respectively. Other experimental parameters are the same as those for the standard spherical lens mentioned in Simulation Experiment 1 above. Similarly, the dashed boxes represent the true solution and its corresponding residuals, with PV values ​​of 1.64 nm and 1.66 nm, respectively.

[0162] This application embodiment also provides simulation experiment three to demonstrate the effectiveness and accuracy of the method proposed in this application embodiment. Based on the proposed method, this application embodiment builds a measurement system on an optical experimental platform and calibrates the amplitude and phase of the modulator, such as... Figure 6 As shown, A is the amplitude of the binary random amplitude modulation plate, B is the phase of the binary random amplitude modulation plate, and the binary random amplitude modulation plate is the modulator.

[0163] As a key component of the measurement system, the modulator in the wavefront sensor requires precise knowledge of its transfer function relative to the image detector before performing dual-surface profile measurements. The experiment used a binary random amplitude modulation plate with a linewidth of 15 μm, whose distribution resembled a checkerboard grid, with each grid cell having a transmittance of approximately 0 or 1 for the beam. In this embodiment, the modulator is preloaded onto a bidirectional translation stage, and the ePIE algorithm is used to evaluate the modulator's transfer function (…). ) to be rebuilt.

[0164] Figure 7 This is a schematic diagram comparing the measurement results obtained in the simulation of the embodiments of this application with the measurement results obtained using an interferometer in related technologies. Figure 7 In the diagram, (a) is the front surface profile measured in an embodiment of this application, (b) is the front surface profile measured using an interferometer in related technologies, (c) and (d) correspond to the profile values ​​at the dashed lines in (a) and (b), respectively, where (c) and (d) respectively show the amplitude and phase distribution of the calibrated modulator, (e) is the rear surface profile measured in an embodiment of this application, (f) is the rear surface profile measured using an interferometer in related technologies, and (g) and (h) correspond to the profile values ​​at the dashed lines in (e) and (f), respectively.

[0165] It should be noted that the light sources used in the experiment had wavelengths of 632.8 nm and 405 nm, respectively. After passing through a 2-inch achromatic double collimating lens with a focal length of 300 mm, the combined collimated beam from the dual-wavelength light source was incident perpendicularly on the device under test (DUT). The reflected wavefront from the DUT was then converged again after passing through the collimating lens. The converged beam was deflected at the beam splitter, modulated by the modulator, and finally propagated to the detector plane. The image detector used in the experiment had a maximum resolution of 4104 × 3006, a pixel size of 3.45 micrometers, and 12-bit ADC (Analog-to-Digital Converter) accuracy.

[0166] The device under test (DUT) used is a 2-inch transparent optical window. The effectiveness and accuracy of the method proposed in this embodiment are verified by comparing the measurement results obtained in this application with those obtained using an interferometer in related technologies. Specifically, this embodiment selects a wedge-shaped optical window with a wedge angle of 30' and a center thickness of 10 mm as a standard element for pre-calibrating the measurement system. Since there is a fixed wedge angle between the front and rear surfaces of the standard element, the reflected light from the rear surface is deflected away from the detector plane during pre-calibration. Therefore, the image detector only receives the reflected wavefront information from the front surface of the standard element. The refractive indices of the medium of the DUT at wavelengths of 632.8 nm and 405 nm are 1.457 and 1.470, respectively, and are assumed to be homogeneous. The diameter and average thickness of the DUT are 50.8 mm and 4 mm, respectively.

[0167] exist Figure 7 In this embodiment, the decoupled dual-surface profile at a wavelength of 405 nm is used as an example for verification experiments and compared with the measurement results obtained by interferometer in related technologies. (c), (d), (g), and (h) correspond to the profile lines at the dashed lines in (a), (b), (e), and (f), respectively. Regarding the actual measurement values, the peak-valley values ​​(PV) of the front and rear surfaces measured in this embodiment are 227.5 nm and 240.5 nm, respectively, corresponding to interferometer measurement results of 230.3 nm and 234.8 nm, respectively. The peak-valley value error is less than [value missing]. Therefore, it can be seen that the measurement results obtained by the embodiments of this application are consistent with the measurement results obtained by using an interferometer in related technologies, thereby verifying the effectiveness and accuracy of the method proposed in the embodiments of this application.

[0168] from Figure 4 , Figure 5 and Figure 7 As can be seen, the method proposed in this application embodiment can simultaneously achieve effective and accurate measurement of the dual surface profiles of transparent optical elements.

[0169] Through simulation experiments one, two, and three described above, it can be verified that the method proposed in this application can achieve the measurement of the dual-surface profile of transparent optical elements with a measurement accuracy at the nanometer level. Furthermore, it can also be applied to a certain extent to the detection of discontinuous or non-optical elements. This application provides a new method for in-situ and dynamic measurement of transparent optical elements.

[0170] Therefore, a comparison between the measurement results obtained by coherent modulation imaging in this application embodiment and the measurement results obtained by interferometer in related technologies confirms that the embodiment of this application has high accuracy and stability in simultaneously measuring the dual-surface profile of transparent optical elements.

[0171] As can be seen from this example, the solution provided in this application can achieve rapid reconstruction of the reflected wavefront of the device under test under single exposure conditions based on coherent modulation imaging. Then, based on the reconstruction result, a dual-surface profile coupling model of the reflected wavefront of the device under test is established. By decoupling the dual-surface profile coupling model, the dual-surface profile information of the device under test can be obtained. Therefore, it can be applied to dual-surface profile measurement under single exposure conditions in dynamic scenes, reducing implementation costs. In addition, since coherent modulation imaging has high robustness, it can reduce the requirements for the measurement environment and is suitable for cross-scale measurement.

[0172] Furthermore, the solution provided in this application can eliminate the need for a high-quality reference plane and has no shape restrictions on the surface profile of the component under test. Therefore, the solution provided in this application is applicable to any surface profile of the component under test, whether it is a plane, a sphere, or an aspherical surface (such as a hyperboloid, a freeform surface, etc.).

[0173] Furthermore, the scheme provided in this application reconstructs the reflected wavefront of the standard element. Since it is not affected by the device under test, the solution provided in this application only requires one pre-calibration, thereby greatly reducing the number of pre-calibrations.

[0174] Corresponding to the aforementioned application function implementation method embodiments, this application also provides a dual-surface profile measurement device for transparent optical elements, an electronic device, and corresponding embodiments.

[0175] Figure 8 This is a schematic diagram of the structure of a dual-surface profile measurement device for a transparent optical element shown in an embodiment of this application.

[0176] See Figure 8 The present application provides a dual-surface profile measurement device for transparent optical elements, which may include:

[0177] The first acquisition module 810 is used to acquire the first diffraction pattern of the element under test; the element under test is a transparent optical element with a double-surface profile to be measured.

[0178] The first reconstruction module 820 is used to perform phase recovery on the first diffraction pattern based on coherent modulation imaging to obtain the reconstruction result of the reflected wavefront of the device under test.

[0179] Modeling module 830 is used to establish a dual-surface profile coupling model of the reflected wavefront of the device under test based on the reconstruction results of the reflected wavefront of the device under test; the dual-surface profile coupling model only contains the dual-surface composite information of the device under test.

[0180] The decoupling module 840 is used to decouple the dual-surface profile coupling model in reverse so as to separate the front surface profile information and the rear surface profile information of the component under test from the dual-surface composite information.

[0181] In one embodiment, the reconstruction result is an initial coupled model; the first reconstruction module 820 may include:

[0182] The first reconstruction submodule is used to perform phase recovery on the first diffraction pattern based on coherent modulation imaging, so as to reconstruct an initial coupling model of the reflected wavefront of the device under test; the initial coupling model includes the dual-surface synthesis information of the device under test and the illumination light information of the measurement system used to measure the device under test.

[0183] In one embodiment, the modeling module 830 may include:

[0184] The modeling submodule is used to remove illumination information from the initial coupled model in order to establish a dual-surface profile coupled model of the reflected wavefront of the element under test.

[0185] In one implementation, the modeling submodule may include:

[0186] The second acquisition unit is used to acquire the second diffraction pattern of the standard element; the standard element is a transparent optical element with known single-surface contour information and high flatness.

[0187] The second reconstruction unit is used to perform phase recovery on the second diffraction pattern based on coherent modulation imaging to obtain the reconstruction result of the reflected wavefront of the standard element; the reconstruction result of the reflected wavefront of the standard element includes known single-surface profile information and illumination light information.

[0188] The first definition unit is used to use the reconstruction result of the reflected wavefront of the standard element as the pre-calibration information of the measurement system;

[0189] The modeling unit is used to remove pre-calibration information from the initial coupled model in order to establish a dual-surface profile coupled model of the reflected wavefront of the device under test.

[0190] In one embodiment, the decoupling module 840 may include:

[0191] The transfer function determination submodule is used to determine the first transfer function of the front surface of the component under test and the second transfer function of the rear surface of the component under test.

[0192] The target decoupling parameter determination submodule is used to determine the target decoupling parameters of the dual-surface profile coupling model based on the first transfer function and the second transfer function. The target decoupling parameters include the first decoupling parameter and the second decoupling parameter. The first decoupling parameter is used to separate the front surface profile information of the component under test, and the second decoupling parameter is used to separate the rear surface profile information of the component under test.

[0193] The inversion submodule is used to reverse-solve the front surface contour information from the dual-surface contour coupling model using the phase information of the first decoupling parameter, and to reverse-solve the rear surface contour information from the dual-surface contour coupling model using the phase information of the second decoupling parameter.

[0194] In one embodiment, the reflected wavefront of the device under test is generated based on coherent light sources of different wavelengths; the target decoupling parameter determination submodule may include:

[0195] The first computing unit is used to calculate two sets of solutions for the second transfer function at each wavelength using a quasi-Newton iteration method; the two sets of solutions include the true solution and the twin solution;

[0196] The filtering unit is used to filter out the true solution of the second transfer function at each wavelength from the two sets of solutions of the second transfer function at each wavelength;

[0197] The second computing unit is used to calculate the true solution of the first transfer function at each wavelength by using the dual-surface profile coupling model and the true solution of the second transfer function at each wavelength.

[0198] The second defining unit is used to take the true solution of the first transfer function at the target wavelength as the first decoupling parameter, and the true solution of the second transfer function at the target wavelength as the second decoupling parameter; wherein the target wavelength is any wavelength.

[0199] In one embodiment, the filtering unit may include:

[0200] The third calculation subunit is used to calculate the standard deviation between each set of solutions of the second transfer function at different wavelengths, and obtain multiple standard deviation values.

[0201] Minimum value determination subunit, used to determine the minimum standard deviation from multiple standard deviation values;

[0202] The filtering sub-unit is used to filter each solution corresponding to the smallest standard deviation as the true solution of the second transfer function at each wavelength.

[0203] As can be seen from this example, the solution provided in this application obtains a first diffraction pattern of the device under test (DUT); the DUT is a transparent optical element with a double-surface profile to be measured; phase recovery is performed on the first diffraction pattern based on coherent modulation imaging to obtain the reconstruction result of the reflected wavefront of the DUT; based on the reconstruction result of the reflected wavefront of the DUT, a double-surface profile coupling model of the reflected wavefront of the DUT is established; the double-surface profile coupling model only contains the double-surface composite information of the DUT; the double-surface profile coupling model is decoupled in reverse to separate the front surface profile information and the back surface profile information of the DUT from the double-surface composite information. This application can achieve rapid reconstruction of the reflected wavefront of the DUT under single-exposure conditions based on coherent modulation imaging, and then establish a double-surface profile coupling model of the reflected wavefront of the DUT based on the reconstruction result, so that the double-surface profile information of the DUT can be obtained by decoupling the double-surface profile coupling model. Therefore, it can be applied to double-surface profile measurement under single-exposure conditions in dynamic scenes, reducing the implementation cost. In addition, since coherent modulation imaging has high robustness, it can reduce the requirements for the measurement environment and is suitable for cross-scale measurement.

[0204] Regarding the apparatus in the above embodiments, the specific manner in which each module performs its operation has been described in detail in the embodiments related to the method, and will not be elaborated further here.

[0205] Figure 9 This is a schematic diagram of the structure of an electronic device shown in an embodiment of this application.

[0206] See Figure 9 The electronic device 900 includes a memory 910 and a processor 920.

[0207] The processor 920 can be a Central Processing Unit (CPU), or other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. A general-purpose processor can be a microprocessor or any conventional processor.

[0208] Memory 910 may include various types of storage units, such as system memory, read-only memory (ROM), and permanent storage devices. ROM may store static data or instructions required by the processor 920 or other modules of the computer. Permanent storage devices may be read-write storage devices. Permanent storage devices may be non-volatile storage devices that retain stored instructions and data even when the computer is powered off. In some embodiments, permanent storage devices use mass storage devices (e.g., magnetic or optical disks, flash memory) as permanent storage devices. In other embodiments, permanent storage devices may be removable storage devices (e.g., floppy disks, optical drives). System memory may be a read-write storage device or a volatile read-write storage device, such as dynamic random access memory. System memory may store some or all of the instructions and data required by the processor during operation. Furthermore, memory 910 may include any combination of computer-readable storage media, including various types of semiconductor memory chips (e.g., DRAM, SRAM, SDRAM, flash memory, programmable read-only memory), and disks and / or optical disks may also be used. In some embodiments, the memory 910 may include a removable storage device that is readable and / or writable, such as a laser disc (CD), a read-only digital multifunction optical disc (e.g., DVD-ROM, dual-layer DVD-ROM), a read-only Blu-ray disc, an ultra-high density optical disc, a flash memory card (e.g., SD card, mini SD card, Micro-SD card, etc.), a magnetic floppy disk, etc. Computer-readable storage media do not contain carrier waves or transient electronic signals transmitted wirelessly or via wired connections.

[0209] The memory 910 stores executable code, which, when processed by the processor 920, can cause the processor 920 to execute part or all of the methods described above.

[0210] Furthermore, the method according to this application can also be implemented as a computer program or computer program product, which includes computer program code instructions for performing some or all of the steps in the method described above.

[0211] Alternatively, this application may be implemented as a computer-readable storage medium (or a non-transitory machine-readable storage medium or a machine-readable storage medium) storing executable code (or computer program or computer instruction code) that, when executed by a processor of an electronic device (or server, etc.), causes the processor to perform part or all of the steps of the methods described above according to this application.

[0212] This application also provides a computer program product, which includes computer instructions that, when executed by a processor, implement the method described above.

[0213] The various embodiments of this application have been described above. These descriptions are exemplary and not exhaustive, nor are they limited to the disclosed embodiments. Many modifications and variations will be apparent to those skilled in the art without departing from the scope and spirit of the described embodiments. The terminology used herein is chosen to best explain the principles, practical application, or improvement of the technology in the market, or to enable others skilled in the art to understand the embodiments disclosed herein.

Claims

1. A method for measuring the dual-surface profile of a transparent optical element, characterized in that, include: Obtain the first diffraction pattern of the device under test; The element under test is a transparent optical element with a dual-surface profile to be measured; Phase recovery is performed on the first diffraction pattern based on coherent modulation imaging to obtain the reconstructed wavefront of the reflected wavefront of the device under test; Based on the reconstruction results of the reflected wavefront of the device under test, a dual-surface profile coupling model of the reflected wavefront of the device under test is established; the dual-surface profile coupling model only contains the dual-surface composite information of the device under test. The dual-surface contour coupling model is decoupled in reverse so as to separate the front surface contour information and the rear surface contour information of the element under test from the dual-surface composite information; The reconstruction result is the initial coupling model; The phase recovery of the first diffraction pattern based on coherent modulation imaging to obtain the reconstruction result of the reflected wavefront of the device under test includes: Phase recovery is performed on the first diffraction pattern based on coherent modulation imaging to reconstruct an initial coupling model of the reflected wavefront of the device under test; the initial coupling model includes the dual-surface synthesis information of the device under test and the illumination light information of the measurement system used to measure the device under test; The establishment of a dual-surface profile coupling model of the reflected wavefront of the device under test based on the reconstruction results of the reflected wavefront includes: Remove the illumination light information from the initial coupling model in order to establish a dual-surface profile coupling model of the reflected wavefront of the element under test; The step of removing the illumination light information from the initial coupling model to establish a dual-surface profile coupling model of the reflected wavefront of the device under test includes: Obtain the second diffraction pattern of the standard element; the standard element is a transparent optical element with known single-surface profile information and high flatness; Phase recovery is performed on the second diffraction pattern based on the coherent modulation imaging to obtain the reconstruction result of the reflected wavefront of the standard element; the reconstruction result of the reflected wavefront of the standard element includes the known single-surface profile information and the illumination light information; The reconstruction result of the reflected wavefront of the standard element is used as the pre-calibration information of the measurement system; Remove the pre-calibration information from the initial coupling model in order to establish a dual-surface profile coupling model of the reflected wavefront of the device under test; The reverse decoupling of the dual-surface contour coupling model, in order to separate the front and rear surface contour information of the component under test from the dual-surface composite information, includes: Determine a first transfer function of the front surface of the component under test, and determine a second transfer function of the rear surface of the component under test; Based on the first transfer function and the second transfer function, the target decoupling parameters of the dual-surface profile coupling model are determined; the target decoupling parameters include a first decoupling parameter and a second decoupling parameter, wherein the first decoupling parameter is used to separate the front surface profile information of the component under test, and the second decoupling parameter is used to separate the rear surface profile information of the component under test; Using the phase information of the first decoupling parameter, the front surface contour information is solved in reverse from the dual-surface contour coupling model; and using the phase information of the second decoupling parameter, the rear surface contour information is solved in reverse from the dual-surface contour coupling model.

2. The method according to claim 1, characterized in that, The reflected wavefront of the device under test is generated based on coherent light sources of different wavelengths; determining the target decoupling parameters of the dual-surface profile coupling model according to the first transfer function and the second transfer function includes: The quasi-Newton iteration method is used to calculate two sets of solutions for the second transfer function at each wavelength; the two sets of solutions include the true solution and the twin solution; The true solution of the second transfer function at each wavelength is selected from the two sets of solutions of the second transfer function at each wavelength. Using the dual-surface profile coupling model and the true solution of the second transfer function at each wavelength, the true solution of the first transfer function at each wavelength is calculated respectively; The true solution of the first transfer function at the target wavelength is used as the first decoupling parameter, and the true solution of the second transfer function at the target wavelength is used as the second decoupling parameter; wherein the target wavelength is any of the wavelengths mentioned above.

3. The method according to claim 2, characterized in that, The step of selecting the true solution of the second transfer function at each wavelength from the two sets of solutions for each wavelength includes: Calculate the standard deviation between each set of solutions of the second transfer function at different wavelengths to obtain multiple standard deviation values; Determine the smallest standard deviation from the plurality of standard deviations; Each solution corresponding to the minimum standard deviation is selected as the true solution of the second transfer function at each wavelength.

4. A dual-surface profile measuring device for a transparent optical element, said device being applied to the method as described in any one of claims 1-3, characterized in that, include: The first acquisition module is used to acquire the first diffraction pattern of the component under test; The element under test is a transparent optical element with a dual-surface profile to be measured; The first reconstruction module is used to perform phase recovery on the first diffraction pattern based on coherent modulation imaging to obtain the reconstruction result of the reflected wavefront of the element under test; The modeling module is used to establish a dual-surface profile coupling model of the reflected wavefront of the device under test based on the reconstruction results of the reflected wavefront of the device under test; the dual-surface profile coupling model only contains the dual-surface composite information of the device under test. A decoupling module is used to decouple the dual-surface contour coupling model in reverse so as to separate the front surface contour information and the rear surface contour information of the element under test from the dual-surface composite information. The reconstruction result is the initial coupling model; The first reconstruction module includes: The first reconstruction submodule is used to perform phase recovery on the first diffraction pattern based on coherent modulation imaging, so as to reconstruct an initial coupling model of the reflected wavefront of the device under test; the initial coupling model includes the dual-surface synthesis information of the device under test and the illumination light information of the measurement system used to measure the device under test; The modeling module includes: The modeling submodule is used to remove the illumination light information from the initial coupling model in order to establish a dual-surface profile coupling model of the reflected wavefront of the element under test. The modeling submodule includes: The second acquisition unit is used to acquire the second diffraction pattern of the standard element; the standard element is a transparent optical element with known single-surface contour information and high flatness; The second reconstruction unit is used to perform phase recovery on the second diffraction pattern based on the coherent modulation imaging to obtain the reconstruction result of the reflected wavefront of the standard element; the reconstruction result of the reflected wavefront of the standard element includes the known single-surface profile information and the illumination light information. The first defining unit is used to use the reconstruction result of the reflected wavefront of the standard element as the pre-calibration information of the measurement system; A modeling unit is used to remove the pre-calibration information from the initial coupling model in order to establish a dual-surface profile coupling model of the reflected wavefront of the element under test. The decoupling module includes: The transfer function determination submodule is used to determine the first transfer function of the front surface of the component under test and the second transfer function of the rear surface of the component under test. The target decoupling parameter determination submodule is used to determine the target decoupling parameters of the dual-surface profile coupling model based on the first transfer function and the second transfer function; the target decoupling parameters include a first decoupling parameter and a second decoupling parameter, the first decoupling parameter is used to separate the front surface profile information of the component under test, and the second decoupling parameter is used to separate the rear surface profile information of the component under test; The inversion submodule is used to reverse-solve the front surface contour information from the dual-surface contour coupling model using the phase information of the first decoupling parameter, and to reverse-solve the rear surface contour information from the dual-surface contour coupling model using the phase information of the second decoupling parameter.

5. An electronic device, characterized in that, include: processor; as well as A memory having executable code stored thereon, which, when executed by the processor, causes the processor to perform the method as described in any one of claims 1-3.

6. A computer-readable storage medium, characterized in that, It stores executable code that, when executed by a processor of an electronic device, causes the processor to perform the method as described in any one of claims 1-3.

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