A multi-directional four-wave shearing interferometry measurement method

Abstract

The present invention belongs to the field of optical measurement technology and relates to a multi-directional four-wave shearing interferometry measurement method. The method comprises the following steps: collecting the interference pattern obtained by the interferometer, obtaining the spectrum of the four-wave lateral shearing interferogram by fast Fourier transform; selecting a specific area from the Fourier spectrum and performing inverse Fourier transform to obtain the shear wavefront ΔW x (x,y) and ΔW y (x, y); before and after obtaining the shear waves in two directions, the test wavefront is used to restore the surface shape by differential Zernike polynomial fitting (DZF); after phase data registration processing, the differential Zernike fitting algorithm and the least square method are used to obtain the Zernike coefficients corresponding to the multiple sets of orthogonal differential phases, and the Zernike coefficients of the multiple sets of different orthogonal directions are fused, and the surface shape data of the wavefront to be measured is reconstructed using the fused Zernike coefficients. The advantages of the present invention are: it can realize high-precision measurement of multi-dimensional data of the surface shape, and can realize reconstruction with high spatial resolution, and has strong stability performance for workshop detection in complex environments.

Description

Technical field:

[0001] The invention belongs to the technical field of optical measurement and relates to a multi-directional four-wave shearing interference measurement method. Background technology:

[0002] As one of the effective means of optical detection, lateral shearing interferometry is widely used in wavefront detection and aspheric surface detection. The performance of the optical component surface plays a decisive role in the overall performance of the optical system. Therefore, it is crucial to use lateral shearing interferometry to achieve high-precision optical component surface detection.

[0003] In traditional shearing interferometers, parallel plates are generally used to achieve lateral shearing, which can only generate a set of shear wavefronts in a single direction. The phase deviation in the orthogonal direction is missing in the interference pattern, so it is necessary to rotate the shearing device or use the split-beam method to obtain the phase information in another orthogonal direction. When measuring again, there will be problems such as resetting the shearing device, secondary calibration of the shearing amount, and calculation errors. Traditional shearing interferometers can only obtain two sets of wavefront data in orthogonal directions, and data in other directions cannot be obtained, making it difficult to achieve high-precision measurement of multiple sets of data on the measured surface shape.

[0004] In order to overcome the problems of the aforementioned traditional lateral shearing interferometer, existing research results have proposed a four-wave lateral shearing interferometer, in which a two-dimensional grating is used to diffract the incident wavefront into four tilted and transversely sheared copies. However, the problems in its measurement are: 1. Using the four-wave lateral shearing interferometer method of two-dimensional grating, it is difficult, complicated and expensive to design an ideal sinusoidal transmission structure to produce only 4 ±1 orders of light; 2. It is impossible to avoid the influence of unnecessary parasitic diffraction orders, and all structures that produce four-wave shearing devices are still inseparable from the transmittance limitation of the two-dimensional grating; 3. The complex structural design, the frequency overlap of high and low transmission orders, and the low resolution of lateral sampling also lead to great limitations on image resolution, which easily introduces additional errors and causes damage to measurement accuracy. Summary of the invention:

[0005] The purpose of the present invention is to provide a multi-directional four-wave shearing interferometry measurement method to overcome the problems of expensive equipment and low measurement accuracy in the prior art.

[0006] The present invention can be beneficial to the acquisition of data in any orthogonal shearing direction and multiple sets of directions, fixed shearing amount, high-precision measurement of multiple sampling data, and strong stability in workshop inspection under complex environments. The present invention uses precision rotation to achieve multi-directional shearing to make up for the lack of data in other dimensional directions, and effectively increases the number of data points. For example, any four sets of data in shearing directions can increase the number of sampling points by 1.5 times, and any eight sets of data in shearing directions can increase the number of sampling points by 3 times. Through the registration and fusion processing of phase data in multiple sets of mutually orthogonal directions, the influence of system random errors on the measurement results can be effectively eliminated, and finally high-precision measurement of multi-dimensional data of the surface shape can be achieved.

[0007] To achieve the above object, the technical solution adopted by the present invention is: a multi-directional four-wave shearing interferometry measurement method, characterized in that it includes the following steps:

[0008] Step 1: Collect the interference pattern obtained by the interferometer, and obtain the frequency spectrum of the four-wave lateral shearing interference pattern through fast Fourier transform;

[0009] Step 2: Select from the Fourier spectrum and The shear wavefront ΔW is obtained by performing an inverse Fourier transform (IFFT) on the region of x (x,y) and ΔW y (x,y);

[0010] Step 3: Before and after obtaining the shear waves in two directions, the test wavefront is used to restore the surface shape by differential Zernike polynomial fitting (DZF);

[0011] Step 4: After the phase data is aligned, the Zernike coefficients corresponding to the multiple sets of orthogonal differential phases are obtained by using the differential Zernike fitting algorithm, and the surface shape data of the wavefront to be measured is reconstructed by fusing the multiple sets of Zernike coefficients in different orthogonal directions;

[0012] In the interferometer used in the method, the orthogonal shearing beam splitting component (8) comprises a first birefringent crystal (14) and a second birefringent crystal (15) arranged on the output light path of the polarizer (7), wherein the angle between the light transmission axis direction of the polarizer (7) and the x-axis is 0°, the angle between the optical axis of the first birefringent crystal (14) and the x-axis is 45°, the second birefringent crystal (15) is rotated 45° along the vertical direction relative to the birefringent crystal (14), and the angle between the light transmission axis direction of the analyzer (9) and the x-axis is 45° or 135°.

[0013] Furthermore, in the above step 1, the Fourier spectrum of the four-wave transverse shearing interference pattern is

[0014]

[0015] Among them, δ(u,v) is the central spectrum, F x (u,v),F y (u,v) are translations in the x and y directions respectively, and the carrier frequency is 2f0. x (u,v) and F y (u,v) are the two-dimensional Fourier spectra of the complex amplitude of the shear wavefront in the x and y directions, respectively.

[0016] Furthermore, the matrix formula in step 3 of step 1 above is

[0017] ΔW=ΔZa (11)

[0018] The difference wavefront matrix and the difference Zernike matrix are shown below:

[0019]

[0020] The coefficients of the Zernike polynomials are obtained using the least squares solution of equation (11),

[0021] a=(ΔZ T ΔZ) -1 ΔZ T ΔW (13)

[0022] Substituting the coefficients of the Zernike polynomial into equation (7)

[0023]

[0024] The measured wavefront shape is reconstructed.

[0025] Compared with the prior art, the present invention has the following advantages and effects:

[0026] (1) The present invention makes up for the lack of data in other dimensional directions and effectively increases the number of data points. For example, any four sets of data in the shearing directions can increase the number of sampling points by 1.5 times, and any eight sets of data in the shearing directions can increase the number of sampling points by 3 times. Through the registration and fusion processing of phase data in multiple sets of mutually orthogonal directions, the influence of system random errors on the measurement results can be effectively eliminated, and ultimately high-precision measurement of multi-dimensional data of the surface shape can be achieved.

[0027] (2) The present invention can realize the acquisition of data in any orthogonal shearing direction and multiple sets of directions, and realize the fixation of the shearing amount. It only needs one calibration and no resetting process. The shearing amount does not change when rotating in any direction. It effectively realizes high-precision measurement of multi-sampling data and has strong stability in workshop inspection under complex environments.

[0028] (2) Multi-directional shearing makes up for the missing data in other dimensions and effectively increases the number of data points. By aligning and fusing multiple sets of phase data in mutually orthogonal directions, it can effectively eliminate the influence of system random errors on the final reconstruction results. It can achieve high-precision measurement of multi-dimensional data of the surface shape, and can achieve high spatial resolution reconstruction, thereby improving the accuracy of the reconstructed surface shape.

[0029] (3) The interference system of the present invention adopts a common optical path interference measurement configuration, which can reduce the quality requirements of optical devices in the interference optical path, avoid the problem of transmission order limitation when using a two-dimensional grating to achieve four-wave transverse shear, and can achieve instantaneous interference measurement of the wavefront surface in a low-noise measurement environment. Since the interference is achieved using a polarization device, the noise and stray information unrelated to the measured wavefront can be effectively suppressed, effectively reducing random errors and additional system errors. Description of the drawings:

[0030] Figure 1 It is a structural schematic diagram of a multi-directional four-wave shearing interferometer.

[0031] Figure 2 It is a schematic diagram of the structure of the orthogonal shearing spectrometer component.

[0032] Figure 3 Schematic diagram of the imaging of the orthogonal shear splitting component forming only four orthogonal overlapping copies.

[0033] Figure 4 Schematic diagram of orthogonal four-wave shearing interferogram and its spectrum extraction.

[0034] Figure 5 Workflow diagram of multi-azimuth four-wave transverse shearing interferogram.

[0035] Figure 1 In: 1-laser light source, 2-beam expansion and collimation system, 3-spectroscopy element, 4-compensation element, 5-test element, 6-reflector, 7-polarizer, 8-orthogonal shearing spectrometer assembly, 9-analyzer, 10-imaging lens, 11-CCD camera, 12-automatic control unit, 13-computer, 14-first birefringent crystal, 15-second birefringent crystal. Specific implementation method:

[0036] The present invention will be described in detail below in conjunction with specific embodiments. These embodiments are used to illustrate the present invention but are not intended to limit the scope of the present invention.

[0037] The present invention provides a multi-directional four-wave shearing interferometry measurement method, comprising the following steps:

[0038] Step 1: Collect the interference pattern obtained by the interferometer, and obtain the frequency spectrum of the four-wave lateral shearing interference pattern through fast Fourier transform;

[0039] Step 2: Select from the Fourier spectrum and The shear wavefront ΔW is obtained by performing IFFT on the region x (x,y) and ΔW y (x,y);

[0040] Step 3: Before and after obtaining the shear waves in two directions, the test wavefront is used to restore the surface shape through DZF;

[0041] Step 4: After the phase data is aligned, the Zernike coefficients corresponding to the multiple sets of orthogonal differential phases are obtained by using the differential Zernike fitting algorithm, and the surface shape data of the wavefront to be measured is reconstructed by fusing the multiple sets of Zernike coefficients in different orthogonal directions;

[0042] The interferometer used in the method of the present invention is as follows Figure 1 and Figure 2 As shown. The system comprises a laser light source (1), a beam expansion and collimation system (2), a beam splitter (3), a compensation element (4), a test element (5), a reflector (6), a polarizer (7), an orthogonal shear beam splitter component (8), an analyzer (9), an imaging lens (10) and a CCD camera (11) which are arranged in sequence. The automatic control unit 12 is composed of a two-dimensional controller and a rotating table, and the rotating table is connected to the cross-shear beam splitter component (8). The automatic control unit (12) is connected to a computer (13), and the CCD camera (11) is connected to the automatic control unit (12) and the computer (13).

[0043] The orthogonal shearing beam splitter component (8) is a core device for realizing multi-directional four-wave shearing. The orthogonal shearing beam splitter component (8) comprises a first birefringent crystal (14) and a second birefringent crystal (15) arranged on the outgoing light path of the polarizer (7), which can avoid the position change of the device during multi-directional rotation. The angle between the light transmission axis direction of the polarizer (7) and the x-axis is 0°, the angle between the optical axis of the first birefringent crystal (14) and the x-axis is 45°, the second birefringent crystal (15) is rotated 45° along the vertical direction relative to the birefringent crystal (14), and the angle between the light transmission axis direction of the analyzer (9) and the x-axis is 45° or 135°.

[0044] The rotating table is equipped with corresponding control software, which can control the angle and rotation speed. The software system controls the rotation angle of the rotating table through a two-dimensional controller as a medium, and uses the software to set the initial value and step value of the rotating table rotation angle. The CCD camera completes an image acquisition every time it steps. The rotating table drives the shear wave plate to rotate one circle to collect multiple sets of orthogonal shearing interference patterns, realizing multi-directional four-wave shearing. The working principle is explained as follows: According to the transmission characteristics of the orthogonal shearing spectrometer component 8, the phase distribution of each linearly polarized light beam is a replica of the original wavefront to be measured, and its spatial frequency can be regarded as f0, and when the orthogonal shearing spectrometer component rotates, orthogonal wavefront shearing in different directions can be achieved. When the test light beam returned from the surface of the optical element to be measured passes through the orthogonal shearing spectrometer component, the subsequent transmission characteristics can be described as the following two parts:

[0045] (1) The four overlapping linearly polarized lights emitted by the orthogonal shear beam splitter (8) are incident on the analyzer. When the polarization angle of the analyzer (9) is 45° or 135°, the Jones vector expressions of the four emitted light waves are:

[0046]

[0047]

[0048] In the above equations (1), (2), (3) and (4), θ is the incident angle of the light wave, α is the rotation angle of the second birefringent crystal 15, and α=ω(n o -n e )Z / 2c,n o , n e are the refractive indices of the O light and the E light that produce the lateral shear displacement in the first birefringent crystal 14, ωZ / 2c represents the resonance ratio, and s represents the shear amount. Then the shear wavefront in the x direction can be expressed as ΔW x (x,y)=W(xs,y)-W(x+s,y), the shear wave front in the y direction can be expressed as ΔW y (x,y)=W(x,ys)-W(x,y+s).

[0049] (2) The orthogonal shearing beam splitter (8) generates a four-wave beam with a lateral displacement. The intensity of the beam after exiting is expressed as:

[0050]

[0051] The steps of the method of the present invention are described in detail as follows:

[0052] Figure 5 In the figure, the workflow of the multi-directional four-wave transverse shearing interferogram is given. First, by obtaining the four-wave transverse shearing interferogram I in any set of orthogonal directions, i(i = 1, 2, 3, ..., N); secondly, the spectrum is obtained by FFT calculation, and the +1 level spectrum in any i direction and the +1 level spectrum in the i+90° direction are taken, and then IFT is performed to obtain the shear wavefront W in the i direction respectively. i , i+90° shear wave front W i+90° ; Then, the coefficient ɑ is obtained by using the differential Zernike polynomial fitting method and the least squares method i (i=1,2,3,…,N), and fuse the coefficients to get the optimal coefficient ɑ; finally, complete the wavefront reconstruction.

[0053] In step 1, after the four light waves pass through the polarizer (9), four-wave lateral shearing interference is generated, and the four-wave lateral shearing interference pattern can be connected to the imaging panel of the CCD camera (11). When the four light waves pass through the polarizer (9), the polarization angles are 45° or 135° respectively, and E x+ ,E x- ,E y+ and E y- The four-wave lateral shearing interference pattern is superimposed orthogonally to produce polarization interference. The intensity of the four-wave lateral shearing interference pattern is obtained by multiplying the superposition of the complex amplitudes by their conjugates, as shown in formula (5).

[0054] By performing a fast Fourier transform of equation (5), the spectrum of the four-wave lateral shearing interferogram is then obtained.

[0055]

[0056] Among them, the Fourier spectrum of the four-wave transverse shearing interferogram mainly includes the central spectrum δ(u,v), F x (u,v) and F y (u,v),F x (u,v),F y (u,v) are translations in the x and y directions respectively, and the carrier frequency is 2f0. x (u,v) and F y (u,v) are the two-dimensional Fourier spectra of the complex amplitude of the shear wavefront in the x and y directions, respectively.

[0057] Step 2: Select from the Fourier spectrum of the four-wave transverse shearing interferogram and The shear wavefront ΔW can be obtained by performing IFFT on the region x (x,y) and ΔW y (x,y).

[0058] Step 3: Before and after obtaining the shear waves in two directions, the test wavefront can be further restored by DZF. In the pattern wavefront reconstruction, the wavefront is decomposed into a set of basis functions, and Zernike polynomials are usually used as the basis functions for this reconstruction. The original wavefront can be represented by the first N Zernike polynomials of the following form:

[0059]

[0060] Using equation (7), the shear wavefront ΔW x (x,y) and ΔW y (x,y) can be expressed as

[0061]

[0062] Assume that the differential Zernike polynomial is

[0063]

[0064] You can get

[0065]

[0066] In matrix formula it can be described as follows:

[0067] ΔW=ΔZa (11)

[0068] Among them, the differential wavefront matrix and the differential Zernike matrix are shown below respectively.

[0069]

[0070] Then, the coefficients of the Zernike polynomials are obtained using the least squares solution of equation (11),

[0071] a=(ΔZ T ΔZ) -1 ΔZ T ΔW (13)

[0072] Finally, the coefficients of the Zernike polynomials are transformed into equation (7)

[0073]

[0074] The measured wavefront shape is reconstructed.

[0075] Step 4: The orthogonal shearing spectrometer component (8) is rotated by the automatic control unit (12) for one circle to obtain multiple sets of mutually orthogonal differential phases. After phase data registration processing, the Zernike coefficients corresponding to these multiple sets of orthogonal differential phases can be obtained using the differential Zernike fitting algorithm. By fusing these multiple sets of Zernike coefficients in different orthogonal directions, the complete surface shape data of the wavefront to be measured can be reconstructed using the fused Zernike coefficients.

[0076] Figure 2 In the embodiment, a plurality of groups of four-wave shearing interference patterns in orthogonal shearing directions can be formed by the second birefringent crystal (15). The orthogonal four-wave shearing patterns in different directions corresponding to multi-directional shearing are shown, and the four-wave shearing schematic diagrams are shown in which the shearing directions are 45° and 135°, 15° and 105°, 60° and 150°, and 0° and 90°, respectively.

[0077] Figure 3 In the figure, what is presented on the CCD camera is that the test light forms only four orthogonal overlapping copies through the orthogonal shearing splitting component, and what is shown in the embodiment is a schematic diagram of four-wave shearing copies along the shearing directions of 45°, 135°, 0° and 90°.

[0078] Figure 4 In Figure 3 When the four-wave shearing replicas along the shearing directions of 45°, 135°, 0° and 90° pass through the polarizer whose transmission axis direction and the x-axis include an angle of 45° or 135°, a four-wave lateral shearing interference pattern is formed. In the embodiment, the spectrum diagram of the corresponding direction and the coordinate position of the spectrum diagram signal extraction are obtained by Fourier transform.

[0079] The above embodiments are only illustrative of the principles and effects of the present invention. A person skilled in the art may make several modifications and improvements without departing from the inventive concept of the present invention, and all of these belong to the protection scope of the present invention.

Claims

1. A multi-directional four-wave shearing interferometry measurement method, characterized in that: The following steps are included Step 1: Collect the interference pattern obtained by the interferometer, and obtain the frequency spectrum of the four-wave lateral shearing interference pattern through fast Fourier transform; Step 2: Select from the Fourier spectrum and The shear wavefront ΔW is obtained by performing an inverse Fourier transform on the region of the x (x,y) and ΔW y (x,y); Step 3: before and after obtaining the shear waves in two directions, the test wavefront is fitted by differential Zernike polynomials to restore the surface shape; The original wavefront is represented by the first N Zernike polynomials Using equation (7), the shear wavefront ΔW x (x,y) and ΔW y (x,y) can be expressed as Assume that the differential Zernike polynomial is You can get In matrix formula it can be described as follows: ΔW=ΔZa (11) Among them, the differential wavefront matrix and the differential Zernike matrix are as follows respectively; Then, the coefficients of the Zernike polynomials are obtained using the least squares solution of equation (11), a=(ΔZ T ΔZ) -1 ΔZ T ΔW (13) Finally, the coefficients of the Zernike polynomials are transformed into equation (7) Reconstruct the measured wavefront shape; Step 4: After the phase data is aligned, the Zernike coefficients corresponding to the multiple sets of orthogonal differential phases are obtained by using the differential Zernike fitting algorithm, and the surface shape data of the wavefront to be measured is reconstructed by fusing the multiple sets of Zernike coefficients in different orthogonal directions; In the interferometer used in the method, the orthogonal shearing beam splitting component (8) comprises a first birefringent crystal (14) and a second birefringent crystal (15) arranged on the output light path of the polarizer (7), wherein the angle between the light transmission axis direction of the polarizer (7) and the x-axis is 0°, the angle between the optical axis of the first birefringent crystal (14) and the x-axis is 45°, the second birefringent crystal (15) is rotated 45° along the vertical direction relative to the birefringent crystal (14), and the angle between the light transmission axis direction of the analyzer (9) and the x-axis is 45° or 135°.

2. The method for measuring multi-directional four-wave shearing interferometry according to claim 1, characterized in that: In step 1, the Fourier spectrum of the four-wave transverse shearing interference pattern is: Among them, δ(u,v) is the central spectrum, F x (u,v),F y (u,v) are translations in the x and y directions respectively, and the carrier frequency is 2f0; F x (u,v) and F y (u,v) are the two-dimensional Fourier spectra of the complex amplitude of the shear wavefront in the x and y directions, respectively.

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