A wavefront measurement method and device based on a dual-frequency grating

Abstract

The application discloses a wave front measurement method and device based on a double-frequency grating, and belongs to the technical field of optical detection and precision measurement. The method integrates two improved Hartmann mask plates with different periods on the same substrate to construct a double-frequency grating. When measuring the same to-be-measured wave front, the large dynamic range characteristic of the low-frequency grating is utilized to realize non-ambiguity unwrapping of high-frequency phase information, so that the dynamic range of the system is significantly improved on the premise of completely reserving the original spatial resolution of the high-frequency grating. The core advantage of the application is that the large gradient measurement capability and high spatial resolution accuracy can be achieved through single acquisition, and the problem that the dynamic range and resolution are restricted by each other in the traditional four-wave lateral shearing interferometer is effectively solved, so that an innovative and efficient solution is provided for high-precision complex surface shape detection.

Description

Technical Field

[0001] This invention belongs to the field of optical detection and precision measurement technology, specifically relating to a wavefront measurement method and device based on a dual-frequency grating, which is used to achieve large dynamic range and high resolution measurement of complex wavefronts (such as wavefronts containing large gradients and high-frequency details). Background Technology

[0002] The four-wave transverse shearing interferometer is a high-precision wavefront measurement tool widely used in optical component inspection, adaptive optics, beam quality analysis, and other fields. Its core component is the Modified Hartmann Mask (MHM), a two-dimensional orthogonal complex amplitude grating. When the wavefront to be measured passes through the MHM grating, it generates four diffracted beams. These beams interfere with each other to form an interferogram containing wavefront information. By analyzing and processing the interferogram, the phase distribution of the wavefront can be reconstructed.

[0003] In four-wave transverse shearing interferometers, dynamic range and spatial resolution are inherently contradictory. Dynamic range refers to the maximum wavefront gradient or phase change that the system can unambiguously measure, and it mainly depends on the period of the MHM grating. Wavelength of light and the distance between the grating and the detector target surface Among them, wavelength Determined by the light source being measured, it is usually unchangeable; while distance Fixed by the camera's mechanical structure, this parameter is determined once the camera is selected. Therefore, adjusting the grating period... This has become the main way to extend the dynamic range of the system.

[0004] When using a large-period MHM grating (i.e., a low-frequency grating), the corresponding equivalent wavelength is larger, which can encompass steeper wavefront gradients (such as those of strongly aspherical elements or stepped surfaces), thus enabling large dynamic range measurements. However, the spatial sampling density of a large-period grating is low, resulting in insufficient spatial resolution for reconstructing the wavefront and making it difficult to accurately reproduce the fine structure of the wavefront. Conversely, using a small-period MHM grating (i.e., a high-frequency grating) can achieve a higher spatial sampling density, thereby accurately capturing high-frequency details of the wavefront and achieving high spatial resolution measurements. However, the equivalent wavelength corresponding to a small-period grating is shorter, and when the wavefront gradient change exceeds one equivalent wavelength, the phase will be truncated. Within the principal value range, phase wrapping occurs. A complex phase unwrapping algorithm is then needed to recover the continuous phase. The unwrapping process is not only computationally time-consuming but also extremely sensitive to noise, discontinuities, or excessively large gradients. Traditional spatial phase unwrapping algorithms are prone to failure under such conditions, severely limiting the dynamic range of the system.

[0005] To overcome the aforementioned contradictions, existing technologies have proposed a dual-frequency measurement scheme, which employs two gratings with different periods for two independent measurements: first, a coarse measurement is performed using a large-period grating to obtain an unambiguous phase distribution, and then a fine measurement is performed using a small-period grating to obtain high-resolution information. However, such methods typically require two independent sets of grating elements and complex switching mechanisms, or employ time-division acquisition to obtain multiple images. This not only increases the structural complexity and manufacturing cost of the system but also imposes stringent requirements on the stability of the measurement environment, making it difficult to meet the application needs of real-time, dynamic measurements.

[0006] In summary, how to effectively extend the dynamic range of a four-wave transverse shearing interferometer without sacrificing spatial resolution, and to simplify the system structure and improve measurement efficiency, has become a technical challenge that urgently needs to be solved by those skilled in the art. Summary of the Invention

[0007] The purpose of this invention is to overcome the shortcomings of existing four-wave transverse shearing interferometers in simultaneously achieving high spatial resolution and large dynamic range, and to provide a wavefront measurement method and device based on a dual-frequency grating, aiming to achieve high-resolution and large dynamic range wavefront measurement through a single grating element and a single acquisition.

[0008] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0009] A wavefront measurement method based on a dual-frequency grating includes the following steps:

[0010] Step 1: Based on the transmittance function of the dual-frequency grating Fabrication of a dual-frequency grating, in which and These are the complex amplitude transmittance functions of the high-frequency MHM grating and the low-frequency MHM grating, respectively.

[0011] Step 2: Place the object to be measured at the measurement position and acquire a dual-frequency interferogram using a single exposure. Frequency domain filtering was used to separate the wrapping phase of the high-frequency grating from the dual-frequency interferogram. and the wrapping phase of the low-frequency grating ;

[0012] Step 3: Calculate the ratio of the high-frequency and low-frequency grating periods using the spectral position coordinates of the high-frequency and low-frequency fringes. ;

[0013] Step 4: Wrap the low-frequency phase Phase unwrapping is performed to obtain continuous low-frequency phase. ;

[0014] Step 5, according to the formula The integer fringe order of the high-frequency grating was calculated. ;

[0015] Step Six: According to the formula Obtaining high-frequency continuous phase ;

[0016] Step 7: Based on the obtained high-frequency continuous phase The wavefront under test is restored by wavefront restoration algorithm.

[0017] A wavefront measurement device based on a dual-frequency grating includes:

[0018] Dual-frequency grating fabrication module: Based on the dual-frequency grating transmittance function Fabrication of a dual-frequency grating, in which and These are the complex amplitude transmittance functions of the high-frequency MHM grating and the low-frequency MHM grating, respectively.

[0019] Phase separation module: Places the object under test at the measurement position and acquires a dual-frequency interferogram in a single exposure. Frequency domain filtering was used to separate the wrapping phase of the high-frequency grating from the dual-frequency interferogram. and the wrapping phase of the low-frequency grating ;

[0020] Period calculation module: Calculates the ratio of the high-frequency and low-frequency grating periods using the spectral position coordinates of the high-frequency and low-frequency fringes. ;

[0021] Low-frequency phase acquisition module: performs low-frequency phase acquisition. Phase unwrapping is performed to obtain continuous low-frequency phase. ;

[0022] Stripe level calculation module: based on formula The integer fringe order of the high-frequency grating was calculated. ;

[0023] Continuous phase acquisition module: based on formula Obtaining high-frequency continuous phase ;

[0024] Restoration module: Based on the obtained high-frequency continuous phase The wavefront under test is restored by wavefront restoration algorithm.

[0025] An electronic device includes: one or more processors; and a memory for storing one or more programs, wherein when the one or more programs are executed by the one or more processors, the one or more processors cause the one or more processors to implement the method.

[0026] A computer-readable storage medium having executable instructions stored thereon, which, when executed by a processor, cause the processor to implement the method described thereon.

[0027] Compared with the prior art, the present invention has the following beneficial effects:

[0028] 1. Achieving both high resolution and large dynamic range: By linearly integrating high-frequency MHM gratings and low-frequency MHM gratings onto a single substrate, the high-frequency grating ensures the system's measurement resolution of the fine wavefront structure, while the low-frequency grating provides unambiguous guidance for the correct unwrapping of the high-frequency phase, thus achieving both high resolution and large dynamic range in the same system.

[0029] 2. Simplified system structure and improved measurement efficiency: Only a single grating element and a single image acquisition are required, eliminating the need for complex grating switching mechanisms or time-division acquisition processes. This greatly simplifies the system structure, reduces costs, and significantly improves the real-time performance and environmental adaptability of measurements.

[0030] 3. Highly reliable phase unwrapping: By using low-frequency phase to guide high-frequency phase unwrapping, the traditional spatial neighborhood unwrapping problem is transformed into independent calculation of single pixels. This fundamentally avoids unwrapping path errors caused by noise, shadows, or surface discontinuities, and greatly improves the robustness of phase reconstruction.

[0031] 4. Clear physical basis and mathematical expression: Starting from the ideal spectral distribution, the transmittance expression of the dual-frequency grating is rigorously derived through the linear property of the Fourier transform. This provides a clear theoretical basis for dual-frequency measurement.

[0032] 5. Easy to implement and integrate: The linear superposition of the two MHM structures only needs to be completed in the grating design stage. The subsequent micro-nano fabrication process is basically the same as that of a single MHM grating, which has good manufacturability and prospects for widespread application. Attached Figure Description

[0033] Figure 1 The diffraction grating spectrum of an ideal four-wave transverse shearing interferometer;

[0034] Figure 2 The transmittance spectrum amplitude distribution of the dual-frequency grating;

[0035] Figure 3 This is a schematic diagram of the spectral distribution of the interference fringes of a dual-frequency grating.

[0036] Figure 4 Example of a dual-frequency interferogram;

[0037] Figure 5 The wrapping phase of the high-frequency grating and the low-frequency grating in the X and Y directions;

[0038] Figure 6 This is a high-frequency continuous phase diagram after unpacking;

[0039] Figure 7 for Distribution diagrams of the original wavefront, restored wavefront, and restoration error of the dual-frequency grating;

[0040] Figure 8 for Dual-frequency grating;

[0041] Figure 9 A schematic diagram showing the high-frequency wrapped phase, the low-frequency wrapped phase, and the high-frequency unwrapped phase calculated from the low-frequency wrapped phase;

[0042] Figure 10 for Distribution diagram of the original wavefront, restored wavefront, and restoration error of the dual-frequency grating. Detailed Implementation

[0043] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other. To achieve the above objectives, this invention adopts the following technical solution.

[0044] This invention first starts with the transmittance spectrum characteristics of a dual-frequency grating, determines the transmittance function expression of the dual-frequency grating through reverse design, and then derives the interference fringe distribution generated by it in a four-wave transverse shearing interferometer.

[0045] An ideal four-wave transverse shearing interferometer grating has only direction and direction The spatial frequency distribution of the diffracted light is as follows: Figure 1 As shown, this is the sum of four Dirac functions. Let the grating period be... The frequency domain expression for the transmittance of the grating is:

[0046] (1)

[0047] in, Here is the frequency domain expression for the grating transmittance. For impulse functions, and These are the frequency domain coordinates in the horizontal and vertical directions, respectively, and the coefficients. This is for the convenience of subsequent normalization, to ensure that the transmittance amplitude after the inverse Fourier transform does not exceed 1.

[0048] Analysis of the above spectrum shows that the grating period The smaller the grating size, the higher the spatial resolution and the greater the spectral spacing between each order of diffraction; grating period The larger the frequency, the lower the spatial resolution of the grating, and the closer the spectral spacing of each first-order diffraction beam. To achieve the complementary advantages of both, this invention designs a novel dual-frequency grating whose spectral function should simultaneously contain both frequency components mentioned above, i.e., as shown in the figure. Figure 2 As shown, the expression for the grating spectrum is:

[0049] (2)

[0050] Among them, the dual-frequency grating spectrum High-frequency grating spectrum and low-frequency grating spectrum They respectively have the form of equation (1), and their periods are respectively and And satisfy , It is an integer greater than or equal to 3.

[0051] Performing an inverse Fourier transform on the above spectral expression, and based on the linearity of the Fourier transform, the complex amplitude transmittance function of the dual-frequency grating can be obtained:

[0052] (3)

[0053] in, The complex amplitude transmittance of the dual-frequency grating. and These are the complex amplitude transmittances of high-frequency gratings and low-frequency gratings, respectively. In practical applications, high-frequency gratings... and low-frequency grating All are MHM complex amplitude gratings, and their transmittance can be expressed as the product of the amplitude modulation function and the phase modulation function:

[0054] ;

[0055] in, For high-frequency grating complex amplitude transmittance, For the amplitude modulation function of the high-frequency grating, It is a high-frequency grating phase modulation function. , and These are respectively the low-frequency grating complex amplitude transmittance, amplitude modulation function, and phase modulation function. and A rectangular function with a duty cycle of 2 / 3, and a phase modulation function. and The value is 0 or These correspond to the positive and negative regions of the cosine product, respectively. This design ensures that the even-numbered orders of the MHM grating are completely suppressed, and the energy is concentrated in... class.

[0056] Considering the physical realizability of the grating transmittance function (requiring the amplitude modulation to be non-negative and not exceeding 1), this invention normalizes the above linear superposition result to obtain the final transmittance expression for the dual-frequency grating:

[0057] (4)

[0058] This expression is the core design formula of this invention. In the formula, the coefficients... This ensures that the modulus of the transmittance function is no greater than 1, satisfying the physical constraints of the complex amplitude grating.

[0059] When the wavefront to be measured When incident on the aforementioned dual-frequency grating, the outgoing light field immediately behind the grating is as follows:

[0060] (5)

[0061] Outgoing light field distance After free propagation, the light reaches the detector plane. According to Fresnel diffraction theory, the light field distribution on the detector plane is as follows:

[0062] (6)

[0063] in, Let Fresnel be the pulse response function. The wavelength of light This represents the convolution operation.

[0064] Substituting equation (5) into equation (6), we obtain the complex amplitude distribution on the detector plane as follows:

[0065] (7)

[0066] in, , The intensity distribution of the interferogram on the detector plane is as follows:

[0067] (8)

[0068] Expanding the above equation, we obtain the complete expression for the interference fringes:

[0069] (9)

[0070] In the formula, the first two terms and The four-wave shearing interference fringes are generated independently by the high-frequency and low-frequency gratings, respectively; the third term This represents the cross-interference term between high-frequency and low-frequency components. The spectral distribution of the interference fringes is as follows: Figure 3 As shown.

[0071] Analysis of the above interference fringe expression and its spectral distribution reveals that the dual-frequency grating interferogram fully contains the amplitude and phase information of both the high-frequency and low-frequency gratings, which coexist in the same interferogram in a linear superposition. The cross-interference term between the high-frequency and low-frequency components manifests as sum-frequency and difference-frequency components in the frequency domain. When the low-frequency grating period... and The value is large enough (e.g.) When ), high-frequency components The spectral center is located at Low-frequency components The spectral center is located at The two are completely separated in the frequency domain; cross terms The spectral center is located at It maintains a certain distance from the principal component. Based on the spectral characteristics of the MHM grating (even-order orders completely cancel each other out, energy is concentrated in...),... , , (Level), taking into account both spectral separation and filtering feasibility, the preferred option is... Further optimization This allows for the suppression or elimination of cross terms through frequency domain filtering, enabling the independent extraction of high-frequency and low-frequency phase information.

[0072] The above theoretical analysis proves that by acquiring a dual-frequency interferogram in a single exposure and combining it with an appropriate signal separation algorithm, the wrapping phase information of the high-frequency and low-frequency gratings can be obtained simultaneously, providing a data basis for subsequent phase unwrapping and wavefront reconstruction.

[0073] Based on the above theoretical analysis, the wavefront measurement method of the dual-frequency grating four-wave transverse shearing interferometer proposed in this invention specifically includes the following steps:

[0074] Step 1: Based on the transmittance function of the dual-frequency grating Fabrication of a dual-frequency grating, in which and These are the complex amplitude transmittance functions of the high-frequency MHM grating and the low-frequency MHM grating, respectively.

[0075] Step 2: Place the object to be measured at the measurement position and acquire a dual-frequency interferogram using a single exposure. By using frequency domain filtering, the wrapping phase of the high-frequency grating is separated from the dual-frequency interferogram. and the wrapping phase of the low-frequency grating ,in .

[0076] Step 3: Calculate the high-frequency grating period using the spectral position coordinates of the high-frequency and low-frequency fringes. and low-frequency grating period proportion .

[0077] Step 4: Wrap the low-frequency phase Phase unwrapping is performed to obtain continuous low-frequency phase. Due to the period of the low-frequency grating The wavelength is relatively large, and its corresponding equivalent wavelength is relatively long, resulting in high reliability of the unwrapping process.

[0078] Step 5: Unwrap the high-frequency wrapped phase using the proportional relationship between the low-frequency and high-frequency phases. As the design principle of a dual-frequency grating shows, under ideal conditions, the high-frequency continuous phase... With low-frequency continuous phase satisfy:

[0079] (10)

[0080] In actual measurements, high-frequency wrapped phase With continuous phase The relationship is:

[0081] (11)

[0082] in, Let be the integer fringe order of the high-frequency grating. Combining equations (10) and (11), we get:

[0083] (12)

[0084] In the formula, This indicates rounding to the nearest integer. Due to low-frequency phase... A continuous distribution has been obtained by unpacking, and Since the integers are known, the integer fringe order of the high-frequency grating can be calculated point by point using equation (12). ,

[0085] Step six, further obtain high-frequency continuous phase, such as Figure 6 As shown in (a) and (b):

[0086] (13)

[0087] Step 7: After obtaining continuous high-resolution wavefront slopes, the measured wavefront can be reconstructed using wavefront reconstruction algorithms (such as the region integration method or the least squares method). ,like Figure 7 As shown.

[0088] Specific Implementation Example: This embodiment provides a wavefront measurement method based on a dual-frequency grating, specifically including the following steps:

[0089] Step 1: Fabrication of the dual-frequency grating. Based on the core design formula of this invention... Two different periods of MHM gratings were fabricated on a single substrate using micro-nano fabrication techniques. The high-frequency grating period... Low-frequency grating period Period ratio ,like Figure 4 As shown.

[0090] Step 2: Place the object to be measured at the measurement position and acquire a dual-frequency interferogram using a single exposure. By using frequency domain filtering, the wrapping phase of the high-frequency grating is separated from the dual-frequency interferogram. and the wrapping phase of the low-frequency grating .

[0091] Step 3: Calculate the ratio of the high-frequency and low-frequency grating periods using the spectral position coordinates of the high-frequency and low-frequency fringes. .

[0092] Step Four: Figure 5 From (a), (b), (c), and (d), we can see the low-frequency phase. No package, low-frequency phase It is continuous.

[0093] Step 5: Calculate the integer fringe order of the high-frequency grating according to equation (12). :

[0094] (14)

[0095] Step 6: Obtain the high-frequency continuous phase according to equation (13) :

[0096] (15)

[0097] Step 7: After obtaining continuous high-resolution wavefront slopes, the measured wavefront is reconstructed using a wavefront reconstruction algorithm (such as the least squares method). .

[0098] Example 2

[0099] This embodiment is basically the same as Embodiment 1, such as... Figures 8-10 As shown, the difference lies in the period ratio. Low-frequency grating period High-frequency grating period Experiments have shown that when the gradient of the wavefront to be measured changes significantly, It can achieve both high dynamic range and high resolution, but the spectral separation is slightly lower than that of the other two versions. In such cases, a narrower frequency domain filter is required.

Claims

1. A wavefront measurement method based on a dual-frequency grating, characterized in that, Includes the following steps: Step 1: Based on the transmittance function of the dual-frequency grating Fabricating a dual-frequency grating, in which and These are the complex amplitude transmittance functions of the high-frequency MHM grating and the low-frequency MHM grating, respectively. Step 2: Place the object to be measured at the measurement position and acquire a dual-frequency interferogram using a single exposure. Frequency domain filtering was used to separate the wrapping phase of the high-frequency grating from the dual-frequency interferogram. and the wrapping phase of the low-frequency grating ; Step 3: Calculate the ratio of the high-frequency and low-frequency grating periods using the spectral position coordinates of the high-frequency and low-frequency fringes. ; Step 4: Wrap the low-frequency phase Phase unwrapping is performed to obtain continuous low-frequency phase. ; Step 5, according to the formula The integer fringe order of the high-frequency grating was calculated. ; Step Six: According to the formula Obtaining high-frequency continuous phase ; Step 7: Based on the obtained high-frequency continuous phase The wavefront under test is restored by wavefront restoration algorithm.

2. The method according to claim 1, characterized in that, The high-frequency MHM grating and low-frequency MHM grating Both are complex amplitude gratings, and their transmittance is expressed as the product of the amplitude modulation function and the phase modulation function, respectively: , The amplitude modulation function and A rectangular function with a duty cycle of 2 / 3, and a phase modulation function. and The value is 0 or .

3. The method according to claim 1, characterized in that, The high-frequency grating period With low-frequency grating period satisfy ,in It is an integer greater than or equal to 3.

4. The method according to claim 1, characterized in that, In step two, frequency domain filtering is used to separate the high-frequency wrapped phase from the dual-frequency interferogram. and low-frequency wrap phase At that time, by selecting an appropriate bandpass filter, the signals at spatial frequencies are extracted respectively. and The spectral component centered at the center is then subjected to inverse Fourier transform to obtain the corresponding complex amplitude distribution, and the wrap phase is then calculated.

5. The method according to claim 1, characterized in that, In step four, the low-frequency wrapping phase is... Spatial phase unwrapping algorithms are used for phase unwrapping, including branch cutting, minimum norm, or quality graph-guided phase unwrapping algorithms.

6. The method according to claim 1, characterized in that, The wavefront restoration algorithm in step seven includes either the region integration method or the least squares method.

7. The method according to claim 3, characterized in that, Preferred Further optimization .

8. A wavefront measurement device based on a dual-frequency grating, characterized in that, include: Dual-frequency grating fabrication module: Based on the dual-frequency grating transmittance function Fabricating a dual-frequency grating, in which and These are the complex amplitude transmittance functions of the high-frequency MHM grating and the low-frequency MHM grating, respectively. Phase separation module: Places the object under test at the measurement position and acquires a dual-frequency interferogram in a single exposure. Frequency domain filtering was used to separate the wrapping phase of the high-frequency grating from the dual-frequency interferogram. and the wrapping phase of the low-frequency grating ; Period calculation module: Calculates the ratio of the high-frequency and low-frequency grating periods using the spectral position coordinates of the high-frequency and low-frequency fringes. ; Low-frequency phase acquisition module: performs low-frequency phase acquisition. Phase unwrapping is performed to obtain continuous low-frequency phase. ; Stripe level calculation module: based on formula The integer fringe order of the high-frequency grating was calculated. ; Continuous phase acquisition module: based on formula Obtaining high-frequency continuous phase ; Restoration module: Based on the obtained high-frequency continuous phase The wavefront under test is restored by wavefront restoration algorithm.

9. An electronic device, characterized in that, include: One or more processors; A memory for storing one or more programs, wherein when the one or more programs are executed by the one or more processors, the one or more processors cause the one or more processors to implement the method of any one of claims 1 to 7.

10. A computer-readable storage medium, characterized in that, It stores executable instructions that, when executed by a processor, cause the processor to perform the method described in any one of claims 1 to 7.

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