Anti-vibration method and device based on least squares iteration model of multi-surface topography measurement

Abstract

This application discloses a vibration-resistant method and apparatus based on a least-squares iterative model for multi-surface topography measurement, relating to the field of optical interferometry technology. The method involves acquiring an aliased interferogram group, using Fast Fourier Transform to separate the signal contained in each pixel of the aliased interferogram group, and analyzing it to obtain the initial phase of different surfaces. A change compensation factor is calculated based on the initial phase and initial phase shift. Unknown parameters in the interference fringe intensity formula are calculated using the least-squares fitting method and the change compensation factor. The phase shift is calculated using the least-squares fitting method and the unknown parameters. The phase shift is used to determine whether the iteration accuracy has been reached; if it has, the phase value is output; otherwise, the iteration continues. This application solves the problems of low detection accuracy and poor interference image quality in existing technologies using wavelength phase-shifting techniques to measure the multi-surface topography of transparent elements, thus improving the measurement accuracy of the multi-surface topography of transparent elements.

Description

Technical Field

[0001] The present application relates to the technical field of optical interferometry, and in particular to a least squares iterative model anti-vibration method and device based on multi-surface topography measurement. Background Art

[0002] Phase Shifting Interferometry (PSI) is a precise optical measurement method that is widely used in surface topography measurement, optical component inspection, and wavefront analysis. It adjusts the phase in the interference pattern to obtain a high-resolution interference fringe pattern and analyze the surface shape or wavefront information of the object being measured.

[0003] Phase-shift interferometry has gradually replaced traditional wavefront measurement technology due to its advantages of high resolution and high calculation accuracy. Although PSI has high measurement accuracy, when applied in real-world environments, errors will be introduced due to changes in mechanical stress that will inevitably occur during the hardware phase shift process, the quality of the interferometer optical components, and vibrations in the environment. At the same time, when measuring multi-surface components such as parallel transmission thin plates and semiconductor substrate coatings, a set of self-interference fringes will be formed on the front and rear surfaces, and will interfere with the reference mirror respectively, generating two sets of fringes. These two sets of interference fringes eventually form superimposed cross-interference fringes, which will produce large errors when calculating multi-surface interference fringes using traditional phase-shift methods.

[0004] In summary, when the existing technology uses phase-shifting interferometry to measure transparent components, large errors will occur when calculating multi-surface interference fringes due to environmental vibrations, superposition interference of multi-surface fringes, and inconsistent brightness between interference images, resulting in poor quality of the final surface morphology image. Summary of the invention

[0005] To this end, the present application provides a least squares iterative model anti-vibration method and device based on multi-surface morphology measurement to solve the problems of low detection accuracy and poor interference image quality when measuring multi-surface morphology of transparent elements using wavelength phase shifting technology in the prior art.

[0006] In order to achieve the above objectives, this application provides the following technical solutions:

[0007] In a first aspect, a least squares iterative model anti-vibration method based on multi-surface topography measurement comprises:

[0008] Step 1: Obtain an aliased interference pattern group after multiple wavelength phase shifts;

[0009] Step 2: Separate the signal contained in each pixel in the aliased interference pattern group by fast Fourier transform, and analyze to obtain the initial phase of different surfaces;

[0010] Step 3: Calculate the change compensation factor according to the initial phase and the initial phase shift amount;

[0011] Step 4: Calculate the unknown parameters in the interference fringe intensity formula according to the least squares fitting method and the variation compensation factor;

[0012] Step 5: Calculate the phase shift amount according to the least squares fitting method and the unknown parameters;

[0013] Step 6: Determine whether the iteration accuracy is reached according to the phase shift amount. If the iteration accuracy is reached, output the phase value; if the iteration accuracy is not reached, continue to iterate.

[0014] Preferably, in step 3, the calculation formula of the change compensation factor is:

[0015] ,

[0016] in, l k , m k and n k Respectively represent the front surface and the reference surface, the rear surface and the reference surface, the front surface and the rear surface k The compensation factor for the change of the secondary image compared to the first image, The interference fringes between the front surface and the reference surface are shown in k The phase shift of the interference pattern, The interference fringes between the back surface and the reference surface are shown in k The phase shift of the interference pattern, The interference fringes between the front and rear surfaces are shown in k The phase shift of the interference pattern, represents the initial phase generated by the optical path difference between the front surface and the reference mirror, represents the initial phase generated by the optical path difference between the rear surface and the reference mirror, Represents the initial phase caused by the optical path difference between the front and rear surfaces.

[0017] Preferably, the initial phase shift amount , and The calculation formula is:

[0018] ,

[0019] in, h 1 represents the optical path difference from the reference surface to the front surface, h 2 is the optical path difference from the reference surface to the back surface, h 3 is the optical path difference from the front surface to the back surface, H represents the distance from the reference surface to the front surface,T Indicates the thickness of the component to be measured, n 0 represents the refractive index of the component to be measured, represents the initial wavelength of the laser, Indicates the wavelength tuning value each time.

[0020] Preferably, in step 4, the interference fringe intensity formula is:

[0021] ,

[0022] in, A (x, y), B (x, y), C (x, y), D (x, y), E (x, y), F (x, y) are unknown parameters.

[0023] Preferably, in step 4, the calculation formula of the unknown parameter is:

[0024]

[0025] in,

[0026] .

[0027] Preferably, in step 5, the calculation formula of the phase shift amount is:

[0028]

[0029] in, , , , , and The calculation formula is:

[0030]

[0031] in,

[0032]

[0033] In a second aspect, a least squares iterative model anti-vibration device based on multi-surface topography measurement comprises:

[0034] An aliasing interference pattern acquisition module is used to obtain an aliasing interference pattern group after multiple wavelength phase shifts;

[0035] An initial phase analysis module, used to separate the signal contained in each pixel in the aliased interference pattern group by fast Fourier transform, and analyze it to obtain the initial phase of different surfaces;

[0036] A variation compensation factor calculation module, used to calculate the variation compensation factor according to the initial phase and the initial phase shift amount;

[0037] An unknown parameter calculation module, used to calculate the unknown parameters in the interference fringe intensity formula according to the least squares fitting method and the variation compensation factor;

[0038] A phase shift calculation module, used to calculate the phase shift according to the least squares fitting method and the unknown parameters;

[0039] The judgment module is used to judge whether the iteration accuracy is reached according to the phase shift amount, and if the iteration accuracy is reached, the phase value is output; if the iteration accuracy is not reached, the iteration is continued.

[0040] In a third aspect, a computer device includes a memory and a processor, wherein the memory stores a computer program, and the processor implements the steps of a least squares iterative model anti-vibration method based on multi-surface topography measurement when executing the computer program.

[0041] In a fourth aspect, a computer-readable storage medium stores a computer program, which, when executed by a processor, implements the steps of a least squares iterative model anti-vibration method based on multi-surface topography measurement.

[0042] In a fifth aspect, a computer program product includes a computer program or instructions, which, when executed by a processor, implement the steps of a least squares iterative model anti-vibration method based on multi-surface topography measurement.

[0043] Compared with the prior art, this application has at least the following beneficial effects:

[0044] The present application provides a least squares iterative model anti-vibration method and device based on multi-surface morphology measurement, by obtaining an aliased interference pattern group after multiple wavelength phase shifts, using fast Fourier transform to separate the signal contained in each pixel in the aliased interference pattern group, and analyzing to obtain the initial phase of different surfaces; calculating the change compensation factor according to the initial phase and the initial phase shift amount; calculating the unknown parameters in the interference fringe intensity formula according to the least squares fitting method and the change compensation factor; calculating the phase shift amount according to the least squares fitting method and the unknown parameters; judging whether the iteration accuracy is reached according to the phase shift amount, if the iteration accuracy is reached, outputting the phase value; if the iteration accuracy is not reached, continuing to iterate. The present application solves the problem that the phase shift amount is inaccurate due to the superposition of multi-surface interference fringes, environmental vibration, inconsistent brightness and darkness between interference images, and hardware phase shift in the prior art process of measuring the multi-surface morphology of transparent elements, resulting in low detection accuracy and poor quality of interference images, thereby improving the measurement accuracy of multi-surface morphology of transparent elements. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] In order to more intuitively illustrate the prior art and the present application, exemplary drawings are given below. It should be understood that the specific shapes and structures shown in the drawings should not generally be regarded as limiting conditions for implementing the present application; for example, those skilled in the art are capable of easily making conventional adjustments or further optimizations to the addition / reduction / attribution division, specific shapes, positional relationships, connection methods, dimensional ratios, etc. of certain units (components) based on the technical concepts and exemplary drawings disclosed in the present application.

[0046] Figure 1 A basic flow chart of the least squares iterative model anti-vibration method based on multi-surface topography measurement provided in Example 1 of the present application;

[0047] Figure 2 A judgment flow chart of the least squares iterative model anti-vibration method based on multi-surface topography measurement provided in Example 1 of the present application;

[0048] Figure 3 This is a schematic diagram of the structure of the laser interferometer system provided in Example 1 of the present application. DETAILED DESCRIPTION

[0049] The present application is further described below in detail through specific embodiments in conjunction with the accompanying drawings.

[0050] In the description of this application: unless otherwise specified, "plurality" means two or more. The terms "first", "second", "third", etc. in this application are intended to distinguish the objects referred to, and do not have special meanings in terms of technical connotations (for example, they should not be understood as emphasizing the importance or order, etc.). Expressions such as "including", "comprising", "having", etc. also mean "not limited to" (certain units, components, materials, steps, etc.).

[0051] The terms such as "upper", "lower", "left", "right", "middle", etc. cited in this application are usually used to indicate the general relative position relationship for the convenience of intuitive understanding by referring to the drawings, and are not absolute limitations on the position relationship in the actual product. Embodiment 1

[0052] See also Figure 1 and Figure 2 This embodiment provides a least squares iterative model anti-vibration method based on multi-surface topography measurement, including:

[0053] S1: Obtaining a mixed interference pattern group after multiple wavelength phase shifts;

[0054] Specifically, this step uses a laser interferometer system to obtain multiple groups of aliasing interference patterns.

[0055] For more details, see Figure 3 The laser interferometer system includes a Fizeau laser interferometer and a computer. The Fizeau interferometer includes a wavelength-tuned laser and a semi-reflective and semi-transparent mirror, a first imaging mirror, a collimating lens, a reference mirror, a second imaging mirror, a beam expander and a CCD camera arranged in sequence. The wavelength-tuned laser and the CCD camera are connected to the computer. The laser changes the wavelength and the camera acquires an image through the computer control. The optical axes of the semi-reflective and semi-transparent mirror, the first imaging mirror, the collimating lens, the reference mirror, the second imaging mirror, the beam expander and the CCD camera are located in the same straight line and are perpendicular to the optical axis of the optical system.

[0056] The specific steps to obtain the aliasing interference pattern are:

[0057] S101: Correct the field of view to make the optical axes of the half-reflecting half-mirror, the first imaging mirror, the collimating lens, the reference mirror, the second imaging mirror, the beam expander and the CCD coincide with each other;

[0058] S102: Field of view calibration, i.e. determining the correspondence between the pixels of the CCD camera and the actual physical space distance;

[0059] S103: Installing the component to be tested at the component to be tested placement position;

[0060] S104: Start the MST system, collect the reflected superimposed interference fringe pattern using the CCD, and then perform more than 120 wavelength phase shifts to obtain an interference image;

[0061] S105: Store the image obtained by the CCD.

[0062] S2: Separate the signal contained in each pixel in the aliased interference pattern group by fast Fourier transform, and analyze it to obtain the initial phase of different surfaces;

[0063] Specifically, in this step, three signals contained in each pixel in the aliasing interference pattern group are separated by fast Fourier transform, the obtained signals are processed, the signals are parsed into phase diagrams, and the initial phases of the three surfaces are obtained.

[0064] In other words, in this step, the coordinates of all sampling points are fast Fourier transformed, and then the amplitude is taken. In order to highlight the peak, the spectrum is superimposed a hundred times. The horizontal coordinate frequencies of the three peaks are found by screening, and the phase angles of the three frequencies are processed to obtain the initial phases of three different cavity lengths.

[0065] S3: Calculate the change compensation factor according to the initial phase and the initial phase shift amount;

[0066] Specifically, the interference fringe intensity formula is generally:

[0067] (1)

[0068] in, represents the background light intensity, The light emphasis system of the interference fringes produced by the front surface and the reference mirror, The light emphasis system of the interference fringes produced by the rear surface and the reference mirror, The light emphasis system showing the interference fringes on the front and rear surfaces, represents the initial phase generated by the optical path difference between the front surface and the reference mirror, represents the initial phase generated by the optical path difference between the rear surface and the reference mirror, It represents the initial phase produced by the optical path difference between the front and rear surfaces. The interference fringes between the front surface and the reference surface are shown in k The phase shift of the interference pattern, The interference fringes between the back surface and the reference surface are shown in k The phase shift of the interference pattern, The interference fringes between the front and rear surfaces are shown in k The phase shift of the interference pattern.

[0069] During the phase shift process, the background light intensity is theoretically It does not change with the change of phase shift. In order to reduce the number of unknowns, a new set of interference fringe intensity formulas are defined as follows:

[0070] (2)

[0071] After simplifying equation (2) using the trigonometric formula, we get:

[0072] (3)

[0073] The unknown parameters are:

[0074] (4)

[0075] This embodiment takes into account that the inconsistency of the brightness and darkness between the interference images during phase-shift interference will lead to weight differences, which will cause too many iterations of the fitting process, thereby increasing the error amount. Therefore, a variable compensation factor based on the contrast of different interference patterns is introduced for the three surfaces to make the method more suitable for different actual environments in practical applications. Therefore, the interference fringe intensity formula after introducing the variable compensation factor is:

[0076] (5)

[0077] in, l k , m k and n k Respectively represent the front surface and the reference surface, the rear surface and the reference surface, the front surface and the rear surface k The compensation factor of the change between the secondary image and the first image. l k , m k and n k Both are set to 1.

[0078] By taking the partial derivative of the unknown quantity in formula (5) and setting the result to zero, the calculation formula of the change compensation factor can be obtained as follows:

[0079] (6)

[0080] According to the interference theory, the phase shift , and It can be expressed by cavity length:

[0081] (7)

[0082] in, h 1 represents the optical path difference from the reference surface to the front surface, h 2 is the optical path difference from the reference surface to the back surface, h 3 is the optical path difference from the front surface to the back surface, Hrepresents the distance from the reference surface to the front surface, T Indicates the thickness of the component to be measured, n 0 represents the refractive index of the component to be measured, represents the initial wavelength of the laser, Indicates the wavelength tuning value each time.

[0083] Because the initial phase is known and the initial phase shift can be expressed by the cavity length, the variation compensation factor can be calculated based on the initial phase and the initial phase shift.

[0084] S4: Calculate the unknown parameters in the interference fringe intensity formula based on the least squares fitting method and the variation compensation factor;

[0085] Specifically, combining the least squares fitting principle to obtain a calculation formula that is more suitable for the actual environment needs to meet the following requirements:

[0086] (8)

[0087] in, K Represents the total number of interference fringes collected, Indicates the interference light intensity value measured by CCD.

[0088] According to formula (8), the unknown parameters A (x, y), B (x, y), C (x, y), D (x, y), E (x, y), F Taking the partial derivative of (x, y) we get:

[0089] (9)

[0090] in,

[0091]

[0092] Calculated:

[0093]

[0094] In this step, the unknown parameters can be calculated by equation (9): A (x, y), B (x, y), C (x, y), D (x, y), E (x, y), F (x, y).

[0095] S5: Calculate the phase shift amount according to the least squares fitting method and unknown parameters;

[0096] Specifically, according to the principle of the least squares fitting method, it is necessary to meet the following requirements:

[0097] (10)

[0098] According to formula (10), , , , , and Taking partial derivatives, we get the formula:

[0099] (11)

[0100] in,

[0101] .

[0102] It can be calculated by formula (11) , , , , and , then according to , , , , and The phase shift can be calculated using the following formula:

[0103] (12)

[0104] S6: judging whether the iteration accuracy is reached according to the phase shift amount, if the iteration accuracy is reached, outputting the phase value; if the iteration accuracy is not reached, continuing the iteration.

[0105] Specifically, at the end of this step, the deviation between the Nth iteration phase shift and the first iteration phase shift is compared with the set accuracy ε. If they are within the range, the iteration process ends and the initial phase is output. , and If it is not within the range, the newly generated initial phase is brought into the anti-vibration method to repeat the iterative calculation, that is, the above steps S3-S6 are repeated.

[0106] in, , and The calculation formula is:

[0107] (13)

[0108] The principle of the anti-vibration method of this embodiment is to generate K interference fringe patterns by wavelength phase shifting, and then continuously iterate using the least squares fitting method to improve the three phase shift quantities in the interference fringe intensity formula. , and The accuracy is increased until the required level is reached. Then, the phase image can be unwrapped, Zernike fitted, and other operations can be performed to obtain the desired three-dimensional topography images of the three surfaces.

[0109] The least squares iterative model anti-vibration method based on multi-surface morphology measurement provided in this embodiment uses fast Fourier transform to perform signal processing and analysis on the image pixel by pixel, disassembles the multi-peak signal, and obtains three phase maps of the three peaks. Then, an iterative model is constructed based on the least squares fitting principle, and a compensation factor based on the change of the contrast of different interference patterns is introduced to make the method more suitable for different practical environments. The three phase maps are substituted into the model as the initial phases, and the phase shift amounts of the three aliasing cavities are obtained. The new initial phase is then solved by the phase shift amount, and it is iterated until the accuracy meets the requirements. Subsequently, the phase map is unwrapped, Zernike fitting and other operations are performed to obtain the three-dimensional morphology surface map of the three surfaces.

[0110] The least squares iterative model anti-vibration method based on multi-surface morphology measurement provided in this embodiment can be applied to transparent components. Compensation factors based on the contrast of different interference patterns are introduced for different surfaces to solve the problem of increased error due to too many iterations caused by inconsistent brightness between interference images, reduce the error caused by inaccurate phase shift due to environmental vibration and hardware phase shift during the phase shifting process, improve measurement accuracy and image quality, and can quickly and accurately realize phase correction in a vibration environment, thereby realizing accurate measurement of multi-surface morphologies of components in a dynamic environment. Embodiment 2

[0111] This embodiment provides a least squares iterative model anti-vibration device based on multi-surface topography measurement, comprising:

[0112] An aliasing interference pattern acquisition module is used to obtain an aliasing interference pattern group after multiple wavelength phase shifts;

[0113] An initial phase analysis module, used to separate the signal contained in each pixel in the aliased interference pattern group by fast Fourier transform, and analyze it to obtain the initial phase of different surfaces;

[0114] A variation compensation factor calculation module, used to calculate the variation compensation factor according to the initial phase and the initial phase shift amount;

[0115] An unknown parameter calculation module, used to calculate the unknown parameters in the interference fringe intensity formula according to the least squares fitting method and the variation compensation factor;

[0116] A phase shift calculation module, used to calculate the phase shift according to the least squares fitting method and the unknown parameters;

[0117] The judgment module is used to judge whether the iteration accuracy is reached according to the phase shift amount, and if the iteration accuracy is reached, the phase value is output; if the iteration accuracy is not reached, the iteration is continued.

[0118] For the specific implementation content of each module in the least squares iterative model anti-vibration device based on multi-surface morphology measurement, please refer to the above definition of the least squares iterative model anti-vibration method based on multi-surface morphology measurement, which will not be repeated here. Embodiment 3

[0119] This embodiment provides a computer device, including a memory and a processor, wherein the memory stores a computer program, and when the processor executes the computer program, the steps of the least squares iterative model anti-vibration method based on multi-surface topography measurement are implemented. Embodiment 4

[0120] This embodiment provides a computer-readable storage medium having a computer program stored thereon. When the computer program is executed by a processor, the steps of the least squares iterative model anti-vibration method based on multi-surface topography measurement are implemented. Embodiment 5

[0121] This embodiment provides a computer program product, including a computer program or instructions, which, when executed by a processor, implements the steps of a least squares iterative model anti-vibration method based on multi-surface topography measurement.

[0122] The technical features of the above embodiments may be arbitrarily combined (as long as there is no contradiction in the combination of these technical features). To make the description concise, not all possible combinations of the technical features in the above embodiments are described; these embodiments that are not explicitly written should also be considered to be within the scope of this specification.

Claims

1. A least squares iterative model anti-vibration method based on multi-surface topography measurement, characterized in that: include: Step 1: Obtain an aliased interference pattern group after multiple wavelength phase shifts; Step 2: Separate the signal contained in each pixel in the aliased interference pattern group by fast Fourier transform, and analyze to obtain the initial phase of different surfaces; Step 3: Calculate the change compensation factor according to the initial phase and the initial phase shift amount; Step 4: Calculate the unknown parameters in the interference fringe intensity formula according to the least squares fitting method and the variation compensation factor; Step 5: Calculate the phase shift amount according to the least squares fitting method and the unknown parameters; Step 6: judging whether the iteration accuracy is reached according to the phase shift amount, if the iteration accuracy is reached, outputting the phase value; if the iteration accuracy is not reached, continuing the iteration; In step 3, the calculation formula of the change compensation factor is: ， in, l k , m k and n k Respectively represent the front surface and the reference surface, the rear surface and the reference surface, the front surface and the rear surface k The compensation factor for the change of the secondary image compared to the first image, The interference fringes between the front surface and the reference surface are shown in k The phase shift of the interference pattern, The interference fringes between the back surface and the reference surface are shown in k The phase shift of the interference pattern, The interference fringes between the front and rear surfaces are shown in k The phase shift of the interference pattern, represents the initial phase generated by the optical path difference between the front surface and the reference mirror, represents the initial phase generated by the optical path difference between the rear surface and the reference mirror, Represents the initial phase caused by the optical path difference between the front and rear surfaces.

2. The least squares iterative model anti-vibration method based on multi-surface topography measurement according to claim 1 is characterized in that: The initial phase shift , and The calculation formula is: ， in, h 1 represents the optical path difference from the reference surface to the front surface, h 2 is the optical path difference from the reference surface to the back surface, h 3 is the optical path difference from the front surface to the back surface, H represents the distance from the reference surface to the front surface, T Indicates the thickness of the component to be tested, n 0 represents the refractive index of the component to be measured, represents the initial wavelength of the laser, Indicates the wavelength tuning value each time.

3. The least squares iterative model anti-vibration method based on multi-surface topography measurement according to claim 2 is characterized in that: In step 4, the interference fringe intensity formula is: ， in, A (x, y), B (x, y), C (x, y), D (x, y), E (x, y), F (x, y) are unknown parameters.

4. A least squares iterative model anti-vibration device based on multi-surface topography measurement, characterized in that: include: An aliasing interference pattern acquisition module is used to obtain an aliasing interference pattern group after multiple wavelength phase shifts; An initial phase analysis module, used to separate the signal contained in each pixel in the aliased interference pattern group by fast Fourier transform, and analyze it to obtain the initial phase of different surfaces; A variation compensation factor calculation module is used to calculate the variation compensation factor according to the initial phase and the initial phase shift amount; wherein the calculation formula of the variation compensation factor is: ， in, l k , m k and n k Respectively represent the front surface and the reference surface, the rear surface and the reference surface, the front surface and the rear surface k The compensation factor for the change of the secondary image compared to the first image, The interference fringes between the front surface and the reference surface are shown in k The phase shift of the interference pattern, The interference fringes between the back surface and the reference surface are shown in k The phase shift of the interference pattern, The interference fringes between the front and rear surfaces are shown in k The phase shift of the interference pattern, represents the initial phase generated by the optical path difference between the front surface and the reference mirror, represents the initial phase generated by the optical path difference between the rear surface and the reference mirror, It represents the initial phase produced by the optical path difference between the front and rear surfaces; An unknown parameter calculation module, used to calculate the unknown parameters in the interference fringe intensity formula according to the least squares fitting method and the variation compensation factor; A phase shift calculation module, used to calculate the phase shift according to the least squares fitting method and the unknown parameters; The judgment module is used to judge whether the iteration accuracy is reached according to the phase shift amount, and if the iteration accuracy is reached, the phase value is output; if the iteration accuracy is not reached, the iteration is continued.

5. A computer device comprising a memory and a processor, wherein the memory stores a computer program, wherein: When the processor executes the computer program, the steps of the method according to any one of claims 1 to 3 are implemented.

6. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of the method according to any one of claims 1 to 3 are implemented.

7. A computer program product comprising a computer program or instructions, characterized in that When the computer program or instruction is executed by a processor, the steps of the method according to any one of claims 1 to 3 are implemented.

Images