Undersampling interference fringe wrapped phase demodulation method
By combining gradient Zernike aberration fitting and least squares fitting, the phase demodulation problem of undersampled interferometric fringe patterns was solved. This method enables efficient demodulation of undersampled wrapped phases without changing the hardware structure of the interferometric system, reducing costs and improving demodulation accuracy.
Patent Information
- Application Number
- CN202510893433.2
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-06-30
- Publication Date
- 2025-10-17
AI Technical Summary
In existing technologies, when performing large aberration measurements, the phase demodulation of undersampled interferometric fringe patterns cannot be accurately demodulated, resulting in a limited dynamic range of interferometric measurements. This usually requires changes to the hardware structure to expand the range, which increases costs.
A method combining gradient Zernike aberration fitting and least squares fitting is adopted. By calculating the phase gradient distribution, Zernike polynomial fitting, and least squares fitting, the low-frequency and high-frequency components of the undersampled wrapped phase are separated and demodulated.
It achieves efficient demodulation of undersampled wrapper phase without changing the hardware structure of the interferometric system. The cost is low and the demodulation process is simple, avoiding the cost increase caused by hardware modification.
Smart Images
Figure CN120800443A_ABST
Abstract
Description
TECHNICAL FIELD
[0001] The present application relates to the field of optical detection technology, in particular to a kind of under-sampling interference fringe wrapped phase demodulation method. BACKGROUND
[0002] Interferometry is a non-contact high-precision detection method, which can be widely used in optical element surface detection, material micro-deformation, refractive index uniformity and a series of physical quantity measurement containing optical path difference concept. However, due to the limitation of sampling law, the dynamic range of interferometry is limited by the wavelength of light and the resolution of detector. Therefore, when measuring large aberration, such as optical element polishing early stage and non-spherical surface and free-form surface non-zero position process detection, under-sampling problem of interference fringe pattern will occur. For the phase corresponding to the under-sampling interference fringe, the traditional unwrapping algorithm cannot give accurate demodulation result. This leads to the problem of limited dynamic range of interferometry. Generally, long-wavelength laser light source such as 10.6um infrared light source or larger target surface and higher resolution detector are needed to solve the problem of dynamic range. Both methods need to change the hardware structure of interferometry instrument, which increases the measurement cost. The present application proposes a method combining gradient Zernike aberration fitting and least square fitting to solve the demodulation of under-sampling wrapped phase data, in which: gradient Zernike fitting realizes the separation of low-frequency components of large aberration phase data, and least square fitting realizes the global demodulation of high-frequency components, and finally completes the solution of under-sampling wrapped phase data.
[0003] In view of the above problems, an under-sampling interference fringe wrapped phase demodulation method is proposed. SUMMARY
[0004] The present application aims to at least solve one of the problems in the prior art, and provides an under-sampling interference fringe wrapped phase demodulation method, which can solve the problems in the background art.
[0005] To achieve the above-mentioned purpose, the present application provides the following technical scheme: an under-sampling interference fringe wrapped phase demodulation method, comprising the following steps:
[0006] S1, according to the original wrapped phase to be demodulated Calculate the phase gradient distribution in x, y direction: grad x ,grad y ;
[0007] S2, according to the gradient information of wrapped phase, use Zernike polynomial to fit, get the Zernike coefficient Z of the measured phase, such as 36 terms; here the measured phase can be expressed by Zernike polynomial;
[0008] S3, subtracting the phase information Pl fitted by 36 Zernike polynomials in step 2 from the original wrapped phase WP of the to-be-demodulated package to obtain a wrapped phase WPh of high-frequency residuals;
[0009] S4, globally unwrapping the residual wrapped phase based on least square fitting to obtain a high-frequency residual phase Ph;
[0010] S5, final demodulation phase P of the undersampled fringe wrapped phase P = Ph + Pl.
[0011] Preferably, in S1
[0012] Preferably, the S2 can obtain the coefficients C of the Zernike polynomials by solving the above linear equations, and then recombine to obtain the first 36 low-order aberrations Pl of the to-be-measured phase.
[0013] Compared with the prior art, the present application has the beneficial effects that:
[0014] (1) The undersampled interference fringe wrapped phase demodulation method, compared with the traditional method of expanding the dynamic range by changing the structure of the interferometer, has the advantages that: the present application does not need to make any changes to the interference system, and only needs to post-process the phase data to realize the phase calculation of the undersampled data, has higher universality and lower cost.
[0015] (2) The undersampled interference fringe wrapped phase demodulation method, compared with the sub-Nyquist technology, has the advantages that: the present application has a simpler calculation process and does not have a principle error. BRIEF DESCRIPTION OF DRAWINGS
[0016] The present application will be further described below in combination with the drawings and embodiments:
[0017] Figure 1 It is a schematic diagram of the original undersampled wrapped phase of the present application;
[0018] Figure 2 It is a schematic diagram of the x-direction phase gradient of the to-be-measured phase of the present application;
[0019] Figure 3 It is a schematic diagram of the x-direction phase gradient of the to-be-measured phase of the present application;
[0020] Figure 4 It is a schematic diagram of the 36-order Zernike fitting low-frequency phase of the to-be-measured phase of the present application;
[0021] Figure 5 It is a schematic diagram of the high-frequency residual wrapped phase of the to-be-measured phase of the present application;
[0022] Figure 6 It is a schematic diagram of the high-frequency residual unwrapped phase of the to-be-measured phase of the present application;
[0023] Figure 7 The final unwrapping phase diagram of the phase to be measured in the application;
[0024] Figure 8 The unwrapping flow chart of the application. DETAILED DESCRIPTION
[0025] The technical solutions in the embodiments of the application will be described clearly and completely below with the accompanying drawings in the embodiments of the application. Obviously, the described embodiments are only part of the embodiments of the application, rather than all the embodiments. Based on the embodiments in the application, all the other embodiments obtained by those skilled in the art without creative work belong to the protection scope of the application.
[0026] The application will be described in detail with the accompanying drawings to further understand the application.
[0027] Please refer to Figures 1-8 The application provides a technical solution: an undersampling interference fringe unwrapping phase demodulation method, comprising the following steps: according to the original unwrapping phase to be demodulated Calculate the phase gradient distribution in the x and y directions: grad x ,grad y
[0028]
[0029] At the same time, for the continuous phase There are:
[0030]
[0031] Let S x =grad x ; S y =grad y ; (3)
[0032] According to the gradient information of the unwrapping phase, the Zernike polynomial is used for fitting, and the Zernike coefficient Z of the phase to be measured is obtained, such as 36 terms; here, the phase to be measured can be expressed by the Zernike polynomial, as follows:
[0033]
[0034] Substitute it into the formula Get:
[0035]
[0036] In this way, by solving the above linear equations, the coefficient C of the Zernike polynomial can be obtained, and the first 36 terms of the low-order aberration Pl of the phase to be measured are obtained by recombination.
[0037] The wrapped phase of the high frequency residual WPh is obtained by subtracting the phase information Pl fitted by the 36 Zernike polynomials in the second step from the original wrapped phase to be demodulated WP.
[0038] The global unwrapping of the residual wrapped phase based on the least square fitting is performed to obtain the high frequency residual phase Ph.
[0039] The demodulation phase of the final under-sampling fringe wrapped phase is P = Ph + Pl.
[0040] Finally, it should be noted that the above only for the preferred embodiments of the present application, and is not intended to limit the present application, although the foregoing embodiments of the present application have been described in detail, for those skilled in the art, it still can be recorded in the technical solutions of the foregoing embodiments, or part of the technical features of the equivalent replacement, within the spirit and principles of the present application, any modification, equivalent replacement, improvement, etc., should be included within the scope of the present application.
Claims
1. A method for phase demodulation based on under-sampling interference fringe wrapping, characterized by: The following steps are involved: S1, according to the original demodulated package phase Calculate the phase gradient distribution in the x and y directions: grad x ,grad y ; S2. Using Zernike polynomials to fit the gradient information of the wrapped phase, the Zernike coefficients Z of the phase to be measured are obtained, such as 36 items; here, the phase to be measured can be expressed by Zernike polynomials; S3, using the original parcel phase WP to be demodulated minus the phase information Pl obtained by fitting the 36-term Zernike polynomial in the second step to obtain the parcel phase WPh of the high-frequency residual; S4, performing global unwrapping based on least squares fitting on the residual wrapped phase to obtain a high-frequency residual phase Ph; S5. The demodulated phase P of the final undersampled fringe wrapping phase is P=Ph+Pl.
2. The under-sampling interference fringe wrapping phase demodulation method according to claim 1, characterized in that: The S1 3. The under-sampling interference fringe wrapping phase demodulation method according to claim 2, characterized in that: By solving the above linear equations, S2 can obtain the coefficients C of the Zernike polynomials, and then recombine them to obtain the first 36 low-order aberrations Pl of the phase to be measured.