A method for improving dynamic range of four-wave lateral shearing interferometer by using double gratings

Abstract

The application discloses a method for improving dynamic range of four-wave lateral shearing interferometer by using double gratings, and belongs to the field of optical detection. The method simultaneously measures a same wave front by using two gratings with different periods, and then synthesizes wave front slopes of the two gratings, so as to achieve the purpose of improving the dynamic range of the four-wave lateral shearing interferometer. The method has the advantages that the dynamic range of the four-wave lateral shearing interferometer can be greatly improved without changing the shearing rate of a single grating. The method is clear and convenient to operate.

Description

Technical Field

[0001] This invention belongs to the field of advanced optical detection, specifically relating to a method for improving the dynamic range of a four-wave transverse shearing interferometer using dual gratings. Background Technology

[0002] The four-wave transverse shearing interferometer is a grating-type transverse shearing interferometer. The measured light is diffracted by a grating, with over 90% of the diffracted light energy concentrated in four first-order diffracted beams. These four beams propagate forward along their respective diffraction angles and eventually coherently superimpose to form interference fringes. By performing a Fourier transform on a single frame of interference fringes, extracting the corresponding spectral information through a frequency domain window, and then performing an inverse Fourier transform, the wavefront slopes in the two orthogonal directions (x and y) can be obtained. Finally, the wavefront distribution of the measured wavefront can be reconstructed using the wavefront slopes and a wavefront reconstruction algorithm. The four-wave transverse shearing interferometer has many advantages, including achromaticity, vibration resistance, and a large dynamic range. It has already been applied in a range of fields, including biomedicine, laser diagnostics, and adaptive optics, and is increasingly attracting the attention of scientists worldwide.

[0003] The detection sensitivity and dynamic range of a four-wave transverse shearing interferometer are determined by the shearing amount. A larger shearing amount results in a smaller effective aperture and higher detection sensitivity, but a smaller dynamic range. Conversely, a smaller shearing amount results in a larger effective aperture and dynamic range, but lower detection sensitivity. Therefore, traditional four-wave transverse shearing interferometers change the phase detection sensitivity and dynamic range by altering the shearing amount. The formula for calculating the shearing amount in a four-wave transverse shearing interferometer is shown below:

[0004]

[0005] Where s is the shearing amount, λ represents the center wavelength, z is the physical distance between the grating and the camera target surface, and p is the grating amplitude and the grating period.

[0006] Therefore, the traditional way to further increase the dynamic range of a four-wave transverse shearing interferometer is to reduce the distance z between the grating and the camera target surface or to increase the amplitude grating period p. However, the value of z is determined by the mechanical devices of the camera and the grating, and is usually around 2 to 3 mm. Increasing the grating period p will reduce the spatial resolution of the four-wave transverse shearing interferometer. While increasing the dynamic range, it will also lose some mid-to-high frequency information in the surface results. Summary of the Invention

[0007] The purpose of this invention is to overcome the shortcomings of current technology and propose a method for improving the dynamic range of a four-wave transverse shearing interferometer using dual gratings.

[0008] To achieve the above objectives, the technical solution adopted by the present invention is as follows: a method for improving the dynamic range of a four-wave transverse shearing interferometer using dual gratings, the method comprising the following steps:

[0009] Step 1: Two four-wave transverse shearing interference fringe patterns were acquired simultaneously, and their intensity expressions are as follows:

[0010]

[0011]

[0012] Where I1 and I2 are the interference fringes of two different grating-period four-wave transverse shearing interferometers, I0 is the background light intensity distribution of the interference fringes, p1 and p2 are the grating periods, z1 and z2 are the distances between the two gratings and the camera, and W is the wavefront distribution to be measured. and These represent the wavefront slopes in the X and Y directions, respectively. and represent the wavefront slopes in the X45° and -45° directions, respectively. For simplification, the spatial variables (x, y) are omitted in equations (1) and (2).

[0013] Step 2: Perform Fourier transforms on equations (1) and (2) respectively to obtain the spectral distributions of light intensities I1 and I2. Take out the positive first-order spectra in the X and Y directions respectively, and perform inverse Fourier transforms to obtain:

[0014]

[0015]

[0016]

[0017]

[0018] Step 3: Divide equation (3) by equation (5), and divide equation (4) by equation (6) to get:

[0019]

[0020]

[0021] Step 4: Solve for the arguments in equations (7) and (8) using the arctangent function:

[0022]

[0023]

[0024] Once the distances z1 and z2 between the grating and the camera are determined, they are difficult to change. Therefore, the grating should be fixed at a suitable position in front of the camera target beforehand. Due to the limitations of the camera structure, z1 = z2. Therefore, equations (9) and (10) can be rewritten as follows:

[0025]

[0026]

[0027] According to equations (11) and (12), the synthesized grating period... This determines the detection dynamic range; when the difference between p1 and p2 is small, the dynamic range can be increased by hundreds of times.

[0028] Furthermore, the two gratings in this method have different shear values.

[0029] The present invention has the following beneficial technical effects:

[0030] This method does not require changing the grating period or the distance between the grating and the camera, that is, it does not require changing the shearing amount of a single grating. Instead, it significantly improves the dynamic range of the four-wave transverse shearing interferometer simply by combining two gratings with different shearing amounts. The method is clear and easy to operate. Attached Figure Description

[0031] Figure 1 Schematic diagram of the optical path of a dual-grating four-wave transverse shearing interferometer system;

[0032] Figure 2 Two shear interference fringe patterns were obtained;

[0033] Figure 3 Spectral distribution of interference fringes;

[0034] Figure 4 The wavefront slopes in the X and Y directions obtained from fringe I1;

[0035] Figure 5 Wavefront slopes in the X and Y directions obtained from fringe I2;

[0036] Figure 6 After the two gratings are combined, the wavefront slopes in the X and Y directions are obtained. Detailed Implementation

[0037] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings used in the embodiments will be briefly introduced below. It should be understood that the following drawings only show some embodiments of the present invention and should not be regarded as a limitation on the scope. For those skilled in the art, other related drawings can be obtained based on these drawings without creative effort.

[0038] Step 1: Schematic diagram of the dual-grating detection system (as shown below) Figure 1As shown, two four-wave transverse shearing interferometers, namely CCD1 and CCD2, are used to detect the same surface under test. The corresponding grating periods of these two interferometers are p1 and p2, respectively, and the distances between the grating and the camera target surface are z1 and z2, respectively. The surface shape of the surface under test is W. The expressions of the interference fringes obtained by CCD1 and CCD2 are shown in Equations (1) and (2), respectively. Figure 2 As shown.

[0039]

[0040]

[0041] Step 2: Perform Fourier transforms on the interference fringes to obtain the spectral distributions of light intensities I1 and I2.

[0042] Step 3: Extract the positive first-order spectra in the X and Y directions using a small frequency domain window, and move them to the center of the frequency domain, as shown below. Figure 3 As shown, an inverse Fourier transform is then performed to obtain new time-domain information as shown in equations (3) to (6). Figure 4 As shown in Figure 5;

[0043]

[0044]

[0045]

[0046]

[0047] Step 4: Combine the wavefront slopes of the two gratings, that is, divide equation (3) by equation (5) and equation (4) by equation (6) to obtain the new spatial distribution function as shown in equations (7) and (8):

[0048]

[0049]

[0050] The wavefront slope of the synthesized dual gratings is obtained using the arctangent function, as follows: Figure 6 As shown, the phase envelope number is significantly reduced after dual-grating synthesis compared to single-grating conditions, and can even be reduced to zero. This achieves the effect of reducing phase envelope and expanding the detection dynamic range.

[0051] The arguments of equations (7) and (8) are obtained by solving the arctangent function:

[0052]

[0053]

[0054] Once the distances z1 and z2 between the grating and the camera are determined, they are difficult to change. Therefore, the grating should be fixed at a suitable position in front of the camera target beforehand. Due to the limitations of the camera structure, z1 = z2. Therefore, equations (9) and (10) can be rewritten as follows:

[0055]

[0056]

[0057] According to equations (11) and (12), the synthesized grating period... This determines the detection dynamic range; when the difference between p1 and p2 is very small, the dynamic range can be increased by hundreds of times.

[0058] Those skilled in the art will readily understand that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for improving the dynamic range of a four-wave transverse shearing interferometer using dual gratings, characterized in that: The method includes the following steps: Step 1: Two four-wave transverse shearing interference fringe patterns were acquired simultaneously, and their intensity expressions are as follows: Where I1 and I2 are the interference fringes of two different grating-period four-wave transverse shearing interferometers, I0 is the background light intensity distribution of the interference fringes, p1 and p2 are the grating periods, z1 and z2 are the distances between the two gratings and the camera, and W is the wavefront distribution to be measured. and These represent the wavefront slopes in the X and Y directions, respectively. and represent the wavefront slopes in the X 45° and -45° directions, respectively. For simplification, the spatial variables (x, y) are omitted in equations (1) and (2). Step 2: Perform Fourier transforms on equations (1) and (2) respectively to obtain the spectral distributions of light intensities I1 and I2. Take out the positive first-order spectra in the X and Y directions respectively, and perform inverse Fourier transforms to obtain: Step 3: Divide equation (3) by equation (5), and divide equation (4) by equation (6) to get: Step 4: Solve for the arguments in equations (7) and (8) using the arctangent function: Choose a suitable position in front of the camera target and fix the grating. Determine the distances z1 and z2 between the grating and the camera. Usually, z1 = z2. Therefore, equations (9) and (10) can be rewritten as follows: According to equations (11) and (12), the synthesized grating period... The detection dynamic range is determined by selecting p1 and p2 with small differences to improve the dynamic range.

2. The method for improving the dynamic range of a four-wave transverse shearing interferometer using dual gratings according to claim 1, characterized in that, The two gratings in this method have different shear values.

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