A method for reconstructing the structure of an object based on a single interferogram

Abstract

This invention discloses a method for object structure reconstruction based on a single interferogram, comprising: obtaining the amplitude and phase of the Fraunhofer diffraction light from the interferogram of the microstructure under test using Fourier transform; unwrapping the aforementioned phase using a suitable unwrapping algorithm to obtain the unwrapped phase; performing a second-order fitting on the unwrapped phase to obtain the phase factor of the Fraunhofer diffraction light; and performing a two-dimensional inverse Fourier transform on the ratio of the complex Fraunhofer diffraction amplitude of the microstructure under test to the aforementioned phase factor to achieve reconstruction of the microstructure under test. This invention achieves rapid reconstruction of complex microstructures based on a single interferogram, extracts the phase factor from a single interferogram, and achieves accurate reconstruction of the microstructure with only a single exposure; thus improving reconstruction efficiency. Furthermore, this invention simplifies the interferogram acquisition process, has a large adjustment range for the object plane position during interferogram acquisition, and shows significant potential in promoting the compactness of interferometric systems.

Description

Technical Field

[0001] This invention relates to a structural reconstruction method, and more particularly to a method for reconstructing the structure of an object based on a single interferogram. Background Technology

[0002] Interferometry, with its advantages of being non-contact and highly sensitive, has become an important means of reconstructing complex microstructures. Complex microstructure reconstruction techniques based on single-frame interferograms have emerged in this context, providing a novel solution for real-time monitoring of dynamic processes. Among these, optical holography is a lensless imaging technique widely used to reconstruct complex two-dimensional or three-dimensional microstructures. This method only requires a Fourier transform of the hologram to achieve rapid reconstruction of complex microstructures, but it requires precise control over the positions of the object and the receiving plane.

[0003] In 1982, Takeda et al. proposed the Fourier Transform Method (FTM), which for the first time extracted phase from a single carrier frequency interferogram, becoming a classic method for phase recovery. In 2014, Oren Raz et al. proposed the double-blind Fourier holography (DBFH) method based on the above method, which is one of the commonly used methods for reconstructing complex two-dimensional structures. The implementation of this method is relatively complex and time-consuming.

[0004] Furthermore, Chinese patent ZL 2023 1 1758306.9 discloses an interferometric diffraction measurement device for microstructures and a method for restoring their structure. This restoration method requires acquiring two interferograms: one for a known reference structure and one for the microstructure under test. First, the phase propagation factor is extracted from the known microstructure interferogram. Then, a two-dimensional inverse Fourier transform is performed on the ratio of the complex Fraunhofer diffraction amplitude of the microstructure under test to this phase propagation factor, thereby achieving rapid restoration of the microstructure. However, the application of this method is significantly limited by the need to additionally acquire an interferogram of a known reference structure. Summary of the Invention

[0005] Purpose of the invention: The purpose of this invention is to propose a method for object structure reconstruction based on a single interferogram, which can achieve accurate reconstruction of microstructures with only a single exposure. The method is simple in structure and highly efficient.

[0006] Technical solution: This invention includes the following steps:

[0007] S1. Collect the interference pattern of the diffracted light and the reference light of the microstructure under test, and obtain the amplitude and phase of the Fraunhofer diffracted light from the interference pattern of the microstructure under test;

[0008] S2. Use the unwrapping algorithm to unwrap the above phases to obtain the unwrapped phases;

[0009] S3. Perform a second fitting on the unwrapped phase to obtain the phase factor of the Fraunhofer diffraction light;

[0010] S4. Perform an inverse Fourier transform on the ratio of the Fraunhofer diffraction complex amplitude of the microstructure to be measured to the aforementioned phase factor to reconstruct the microstructure to be measured.

[0011] The phase of the Fraunhofer diffraction light of the microstructure under test is obtained by performing a Fourier transform on the interference pattern of the microstructure under test to obtain the phase of the Fraunhofer diffraction light of the microstructure under test.

[0012] The method for obtaining the unwrapped phase is as follows: the unwrapped phase is unwrapped using the branch cutting method, branch cutting lines are placed, and the phase is unwrapped to obtain the unwrapped phase.

[0013] The unpacking phase is the phase difference between the diffracted light wave and the reference light wave at the CCD observation plane. in and These are the phases of the object wave and the reference wave on the observed plane, respectively.

[0014] The method for obtaining the phase factor is as follows: perform a quadratic fitting on the unwrapped phase and extract the coefficients P of the two quadratic terms. 20 P 02 Substituting this into the phase factor expression, we get the phase factor C(x,y)=exp(i(P 02 x 2 +P 20 y 2 )).

[0015] The inverse Fourier transform of S4 is:

[0016]

[0017] Where IFT{·} denotes the two-dimensional inverse Fourier transform. Let be the amplitude of the Fraunhofer diffraction light.

[0018] The interference pattern acquisition system includes a coherent light source. The coherent light emitted by the coherent light source passes through a linear polarizer and a beam expander and collimator system, and is then split into two beams by a beam splitter prism. One beam passes through an attenuator and a first plane mirror to form a reference beam, while the other beam is reflected by a second and a third plane mirror to the device generating the microstructure under test, forming diffracted light. After passing through a second biconvex lens, the diffracted light interferes with the reference beam after being combined with the second beam splitter prism, and then enters the CCD.

[0019] The image-side focal plane of the second biconvex lens is shifted backward after passing through the second beam-splitting prism.

[0020] The CCD photosensitive surface is placed on the translated image plane.

[0021] The device for generating the microstructure under test is a reflective spatial light modulator.

[0022] Beneficial effects: This invention uses a single interferogram to achieve rapid reconstruction of complex microstructures. Phase factors can be extracted from a single interferogram, and accurate reconstruction of microstructures can be achieved with only a single exposure, thus improving reconstruction efficiency. In addition, this invention simplifies the interferogram acquisition process. Compared with traditional optical holography, which requires precise control of the object plane and image plane, this reconstruction method has a larger adjustment range for the object plane position when acquiring the interferogram and shows significant potential in promoting the compactness of interferometric systems. Attached Figure Description

[0023] Figure 1 This is a schematic diagram of the measuring device of the present invention;

[0024] Figure 2 This is a flowchart of the restoration method of the present invention;

[0025] Figure 3 The complex microstructure to be tested is loaded onto the DMD of this invention;

[0026] Figure 4 This is an interferogram of the complex microstructure under test collected in the experiment of this invention;

[0027] Figure 5 This is the Fourier transform of the interferogram of the microstructure under test in this invention;

[0028] Figure 6 This is the encapsulated phase diagram of the Fraunhofer diffraction light of the microstructure under test in this invention;

[0029] Figure 7 This is the unwrapped phase diagram of the Fraunhofer diffraction light of the microstructure under test in this invention;

[0030] Figure 8 This is a secondary fitting phase diagram of the Fraunhofer diffraction phase of the microstructure under test in this invention;

[0031] Figure 9 This is the reconstruction result of the microstructure to be tested in this invention. Detailed Implementation

[0032] The invention will now be further described with reference to the accompanying drawings.

[0033] like Figure 2As shown, the object structure reconstruction method based on a single interferogram in this embodiment is based on the Fraunhofer diffraction integral formula, that is, the complex amplitude of the Fraunhofer diffraction light of an object is the product of the Fourier transform of the object and a phase propagation factor. Its core is to perform a quadratic fitting on the phase of the unwrapped Fraunhofer diffraction light, extract the coefficients of the quadratic term to determine the aforementioned phase factor, and then perform a two-dimensional inverse Fourier transform on the ratio of the complex amplitude of the Fraunhofer diffraction light to this phase factor to reconstruct the object under test. Specifically, it includes the following steps:

[0034] S1. Using a CCD to acquire data about the microstructure under test. o (x o y o The interference patterns of the diffracted light and the reference light are used to obtain the amplitude of the Fraunhofer diffracted light by performing a Fourier transform on the interference pattern of the microstructure to be measured. and package phase

[0035] like Figure 1 As shown, the interference pattern acquisition system includes a helium-neon laser coherent light source 1, a linear polarizer 2, a beam expander and collimator system, a first beam splitter prism 5, an attenuator 6, a first reflector 7, a second reflector 8, a third reflector 13, a reflective spatial light modulator DMD 9, a second biconvex lens 10, a second beam splitter prism 11, and a CCD 12; the beam expander and collimator system includes a biconcave lens 3 and a first biconvex lens 4. The reflective spatial light modulator 9 is a microstructure generation device; light irradiates the microstructure under test, causing diffraction, and the CCD photosensitive surface is placed on the image-side focal plane of the second biconvex lens 10.

[0036] A helium-neon laser emits a coherent beam with a center wavelength. This coherent beam passes through a linear polarizer 2 and a beam expander / collimation system, then is split into two paths by a first beam-splitting prism 5. One path passes through an attenuator 6 and a first reflecting mirror 7 to form a reference beam, while the other path is reflected by a second reflecting mirror 8 and a third reflecting mirror 13 to reach the DMD and form diffracted light. The diffracted light passes through a second biconvex lens 10 and interferes with the reference beam after being combined with it by a second beam-splitting prism 11. The image-side focal plane of the second biconvex lens 10 is shifted backward by the second beam-splitting prism 11. By placing the photosensitive surface of the CCD 12 on this shifted image plane, the interference pattern of the diffracted light and the reference light on the complex microstructure under test loaded on the DMD can be acquired. Since the intensity of the diffracted light is relatively weak, the intensity of the reference light is reduced by adjusting the attenuator to improve the visibility of the interference fringes.

[0037] S2. Use a suitable unwrapping algorithm to unwrap the above-mentioned wrapped phase to obtain the unwrapped phase: Apply the "branching method" to unwrap the wrapped phase, place branch cutting lines, and perform phase unwrapping to obtain the unwrapped phase diagram, which is the phase difference between the diffracted light wave and the reference light wave on the CCD observation plane.

[0038] S3. Perform a second-order fitting on the unwrapped phase, and extract two quadratic coefficients P 20 , P 02 . Substitute them into the phase factor expression to obtain the phase factor of the Fraunhofer diffraction light C(x, y) = exp(i(P 02 x 2 +P 20 y 2 )). The reason for obtaining the phase factor by performing a second-order fitting on the unwrapped phase is as follows: First, from the Fraunhofer diffraction integral, the phase of the phase factor is a quadratic function of the spatial position coordinates x and y on the receiving plane, and the corresponding quadratic coefficients are the same, that is, C(x, y) = exp(iP(x 2 +y 2 )); Second, although in the Fraunhofer diffraction integral formula, the Fourier transform of the object structure can also contribute to the phase of the quadratic function, the influence of the quadratic function phase of the Fourier transform can be reduced by adjusting the position of the object plane to increase the phase of the phase factor. The process of obtaining the phase factor by performing a second-order fitting on the unwrapped phase is as follows: Perform a second-order fitting on the unwrapped phase to extract two quadratic coefficients P 20 , P 02 (the two are very close), and substitute them into the phase factor expression to obtain the phase factor C(x, y) = exp(i(P 02 x 2 +P 20 y 2 )).

[0039] S4. Perform an inverse Fourier transform on the ratio of the Fraunhofer diffraction complex amplitude of the micro-structure to be measured to the phase of the phase factor to realize the restoration of the micro-structure to be measured.

[0040] The following uses an experimental example to verify the present invention.

[0041] The parameters of the main instruments in this experiment are as follows: The resolution of the DMD is 1920×1080, and the single-pixel size is 7.56μm×7.56μm; the focal length of the second double convex lens 10 is 150mm; the resolution of the CCD is 5496×3672, and the single-pixel size is 2.4μm×2.4μm. The micro-structure to be measured loaded on the DMD is as shown in Figure 3 , where the complex micro-structure to be measured is the character "国".

[0042] The method for restoring the complex micro-structure in this experiment is as follows:

[0043] S1. Collect Figure 3 a single interference pattern of the complex micro-structure to be measured as shown in Figure 4 , and the size of the picture is 800×800 pixels;

[0044] from Figure 4 The amplitude of the Fraunhofer diffraction light was obtained from the interference pattern of the microstructure under test. and package phase microstructure to be tested O o (x o y o The interference pattern is manually filtered out in the frequency domain to remove unwanted spectral components, and then an inverse Fourier transform is performed to obtain the autocorrelation function and cross-correlation function of the spatially separated microstructure under test and the reference light. o (x o y o )*R(x o y o ) or R(x o y o )*O o (x o y o ), to obtain the Fourier transform of the interferogram of the microstructure under test, as shown in the figure. Figure 5 As shown, for R(x) o y o )*O o (x o y o Perform a Fourier transform to obtain the wrapped phase map, as shown below. Figure 6 As shown, this is the complex conjugate product of the object's diffraction field and the reference wave.

[0045] S2. Use a suitable unwrapping algorithm to unwrap the above phase to obtain its unwrapped phase. Using the "branch-cutting method" to unwrap the package, branch cutting lines are placed, and phase unwrapping is performed to obtain the unwrapped phase diagram, as shown below. Figure 7 As shown, this represents the phase difference between the diffracted light wave and the reference light wave on the CCD observation plane. in and These represent the phases of the object wave and the reference wave on the observation plane, respectively. When the reference light is incident perpendicularly on the observation plane, When the reference light is incident at an oblique angle, its phase is a linear function of x and y. The phase of the reference light only affects the position of the microstructure.

[0046] S3. Perform a second fitting on the unwrapped phase to obtain the phase factor of its Fraunhofer diffraction. The phase factor is key to the structure reconstruction in this experiment. The phase factor C(x,y)=exp(i(P) 02 x 2 +P 20 y 2 The function is composed of quadratic functions of x and y, and its fitted phase diagram is as follows: Figure 8 As shown. The coefficients P of the quadratic term fitted to the phase difference obtained from unwrapping are... 20 =-1.278e+07, P 02 = -1.257e+07, thus obtaining the Fraunhofer diffraction phase factor.

[0047] S4. According to the Fraunhofer integral formula The inverse Fourier transform of the ratio of the complex amplitude to the phase factor of the Fraunhofer diffraction of the microstructure under test in this experiment was used to reconstruct the microstructure under test.

[0048]

[0049] Where IFT{·} denotes the two-dimensional inverse Fourier transform.

[0050] Following the steps above, we obtained... Figure 3 The results of the reconstruction of the microstructure, such as Figure 9 As shown, the restored structure not only reproduces the original microstructure well in terms of size and structure, but also achieves a high degree of similarity (SSIM) in the experimental results compared to the original structure, with an SSIM of over 90%. Therefore, the experimental system and restoration method of this invention can be used to measure and rapidly and accurately restore complex microstructure interference diffraction phenomena.

Claims

1. A method for reconstructing the structure of an object based on a single interferogram, characterized in that, Includes the following steps: S1. Collect the interference pattern of the diffracted light and the reference light of the microstructure under test, and obtain the amplitude and phase of the Fraunhofer diffracted light from the interference pattern of the microstructure under test. The phase of the Fraunhofer diffracted light of the microstructure under test is obtained by performing a Fourier transform on the interference pattern of the microstructure under test to obtain the phase of the Fraunhofer diffracted light of the microstructure under test. S2, using unwrapping algorithm to the above phase, get unwrapping phase, the method for obtaining the unwrapping phase is: using branch cut method to unwrap the wrapped phase, placing branch cut line, phase unwrapping, get unwrapping phase, the unwrapping phase is: the phase difference between the reference light wave and the diffraction light wave on the CCD observation plane wherein and respectively are the phase of the object wave and the reference wave on the observation plane; S3. Perform a second-order fitting on the unwrapped phase to obtain the phase factor of the Fraunhofer diffraction light. The method for obtaining the phase factor is as follows: perform a second-order fitting on the unwrapped phase and extract the coefficients P of the two quadratic terms. 20 P 02 Substituting this into the phase factor expression, we obtain the phase factor. ; S4. Perform an inverse Fourier transform on the ratio of the Fraunhofer diffraction complex amplitude of the microstructure to be measured to the aforementioned phase factor to reconstruct the microstructure to be measured.

2. The method for reconstructing object structure based on a single interferogram according to claim 1, characterized in that, The inverse Fourier transform of S4 is: in, This represents the two-dimensional inverse Fourier transform. Let be the amplitude of the Fraunhofer diffraction light.

3. The method for reconstructing object structure based on a single interferogram according to claim 1, characterized in that, The interference pattern acquisition system includes a coherent light source. The coherent light emitted by the coherent light source passes through a linear polarizer and a beam expander and collimator system, and is then split into two beams by a first beam splitter prism. One beam passes through an attenuator and a first plane mirror to form a reference beam, while the other beam is reflected by a second and a third plane mirror to the device generating the microstructure under test, forming diffracted light. After passing through a second biconvex lens, the diffracted light interferes with the reference beam after being combined with the second beam splitter prism, and then enters the CCD.

4. The method for reconstructing object structure based on a single interferogram according to claim 3, characterized in that, The image-side focal plane of the second biconvex lens is shifted backward after passing through the second beam-splitting prism.

5. The method for reconstructing object structure based on a single interferogram according to claim 4, characterized in that, The CCD photosensitive surface is placed on the translated image plane.

6. The method for reconstructing object structure based on a single interferogram according to claim 3, characterized in that, The device for generating the microstructure under test is a reflective spatial light modulator.

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