A Digital Holographic Reconstruction Distance Optimization Method Based on Phase Evaluation Function

Abstract

The present invention discloses a method for optimizing the reconstruction distance of digital holography based on a phase evaluation function, belonging to the technical field of optical microscopic measurement. The present invention includes the steps of: 1) obtaining the recording distance of a digital hologram of the three-dimensional topography of the surface of a microstructure to be measured; 2) setting a reconstruction distance range including the recording distance in the digital hologram, and setting a plurality of candidate reconstruction distances within the reconstruction distance range; 3) performing diffraction reconstruction and unwrapping for each candidate reconstruction distance to obtain the distorted phase corresponding to each candidate reconstruction distance; 4) substituting the distorted phase into the evaluation function, and taking the candidate reconstruction distance corresponding to the minimum value of the evaluation function as the optimization result. The present invention is based on phase information, and can quickly obtain the reconstruction distance during digital holographic phase extraction through the evaluation function.

Description

Technical Field

[0001] The present invention relates to the technical field of optical microscopic measurement, and particularly relates to a method for optimizing the reconstruction distance of digital holography based on a phase evaluation function. Background Art

[0002] Digital holography technology realizes the digitization of the whole process of three-dimensional object recording, storage and reproduction, and has the advantages of non-contact, real-time, non-destructive detection, high resolution and fast response speed. Therefore, it has been widely used in the fields of microstructure topography measurement, particle field detection, cell observation and microelectromechanical systems. According to the principle of digital holography measurement, the diffraction reconstruction distance of the hologram must be accurately set during numerical diffraction reconstruction to determine the accurate ideal reproduction image plane, and the accuracy of the reconstruction distance determines the accuracy of the reproduced light wave.

[0003] Currently, during the hologram reconstruction process, the reconstruction distance is mostly determined by measuring the hologram recording distance. Due to the uncertainty of the measurement, there is usually a small error between the reconstruction distance and the recording distance. Therefore, phase distortion occurs during diffraction reconstruction, resulting in problems such as a decrease in the quality of the reconstructed image and a reduction in measurement accuracy. Based on the phase evaluation function, the present invention provides a method for optimizing the reconstruction distance of digital holography, which finds the optimal reconstruction distance through the evaluation function curve to improve the accuracy of numerical diffraction reconstruction of digital holography. Summary of the Invention

[0004] In order to overcome the problems such as the distortion of the reproduced image caused by the reconstruction distance error during the hologram reproduction process, the present invention proposes a method for optimizing the reconstruction distance of digital holography based on a phase evaluation function, which is applicable to the measurement of the microscopic topography structures of three-dimensional surfaces of complex microstructures, such as sinusoidal gratings, stepped parts, constant phase surfaces, etc.

[0005] In order to achieve the above object, the present invention adopts the following technical steps:

[0006] A method for optimizing the reconstruction distance of digital holography based on a phase evaluation function includes the following steps:

[0007] 1) Obtain the recording distance of the digital hologram of the three-dimensional topography of the surface of the microstructure to be measured;

[0008] 2) Set a reconstruction distance range including the recording distance in the digital hologram, and set several candidate reconstruction distances within the reconstruction distance range;

[0009] 3) Perform diffraction reconstruction and unwrapping on each candidate reconstruction distance to obtain the distorted phase corresponding to each candidate reconstruction distance;

[0010] 4) Substitute the distorted phase into the evaluation function, and take the candidate reconstruction distance corresponding to the minimum value of the evaluation function as the optimization result.

[0011] Furthermore, the method for obtaining the digital hologram is as follows:

[0012] Calculate the complex amplitude of the object wave:

[0013]

[0014] The complex amplitude of the object wave interferes with the reference wave R to generate a digital hologram:

[0015] I(x, y) = |O(x, y)| 2 + |R(x, y)| 2 + OR * + O * R

[0016] where (x o , y o ) are the coordinate points in the object plane coordinate system, (x, y) are the coordinate points in the digital hologram recording plane coordinate system, d o is the recording distance, λ is the wavelength of the light wave, O represents the light wave that has propagated to the recording plane after diffraction, O * represents the conjugate light wave that has propagated to the recording plane after diffraction, o represents the light wave modulated by the surface of the object to be measured, j is the imaginary unit, k is the wave number; I(.) represents the digital hologram, |.| represents taking the modulus, and R * represents the conjugate reference wave.

[0017] Furthermore, several candidate reconstruction distances are set within the reconstruction distance range, specifically:

[0018] The reconstruction distance range is equally divided into L - 1 parts, and the boundary values of the reconstruction distance range and each equally divided point are used as candidate reconstruction distances, denoted as where represents the l-th candidate reconstruction distance, Δd i represents the reconstruction interval, represents the recording distance.

[0019] Furthermore, diffraction reconstruction is performed using the conjugate wave of the original reference wave.

[0020] Furthermore, the method for calculating the distortion phase corresponding to each candidate reconstruction distance is as follows:

[0021] 3.1) For each candidate reconstruction distance perform left and right offsets to obtain a pair of offset candidate reconstruction distances and respectively take and as the reconstruction distance d iPerform diffraction reconstruction and unwrapping to obtain the complex amplitude of the conjugate real image. The formula is as follows:

[0022]

[0023] where (x, y) are the coordinate points in the coordinate system of the digital hologram recording plane, represents the coordinate points in the reconstructed image plane coordinate system when the reconstruction distance is d i The complex amplitude of the conjugate real image is represented by U +1 The complex amplitude of the conjugate real image is represented by U, λ is the wavelength of the light wave, j is the imaginary unit, and k is the wave number. is the Fourier transform, and O * represents the conjugate light wave that has propagated to the recording plane through diffraction;

[0024] 3.2) Calculate the reconstructed distorted phase based on the complex amplitude of the conjugate real image:

[0025]

[0026] where Im(.) represents the imaginary part of a complex number, and Re(.) represents the real part of a complex number. represents the distorted phase of the coordinate points in the reconstructed image plane coordinate system when the reconstruction distance is d i ;

[0027] 3.3) Respectively take and as the reconstruction distance d i , and obtain a set of reconstructed distorted phases and

[0028] 3.4) Substitute the set of reconstructed distorted phases obtained in step 3.3) into the evaluation function to obtain the evaluation value of the candidate reconstruction distance:

[0029]

[0030] where max(.) represents taking the maximum phase value, and φ (l) represents the evaluation value corresponding to the l-th reconstruction distance . Finally, obtain the evaluation value sequence [φ (1) , φ (2) , …, φ (l) , …, φ (L) corresponding to all candidate reconstruction distances.

[0031] Furthermore, the adjustment offset of the left and right offsets described in step 3.1) is less than the reconstruction pitch.

[0032] Compared with the prior art, the advantages of the present invention are as follows: The present invention proposes a method for optimizing the reconstruction distance of digital holography based on phase. By using the distorted phase information generated at each distance within the reconstruction distance range including the recording distance, the optimized distance for reconstructing the three-dimensional topography of the microstructure surface is obtained through an evaluation function, thereby improving the numerical diffraction reconstruction accuracy of the hologram. Description of the Drawings

[0033] Figure 1 It is a flowchart of a method for optimizing the reconstruction distance of digital holography shown in an embodiment of the present invention;

[0034] Figure 2 To delimit the reconstruction distance range and the reconstruction spacing Δd i and a schematic diagram for adjusting the offset Δd;

[0035] Figure 3 It is a schematic diagram of the distortion generated when the reconstruction distance is not equal to the recording distance;

[0036] Figure 4 It is a curve diagram of the evaluation function in an embodiment of the present invention. (a) is for the recording distance d o = 80.91 mm, and (b) is for the recording distance d o = 80.85 mm. Detailed Embodiment

[0037] The present invention will be further described in detail below through embodiments in conjunction with the drawings. The following embodiments are only used to more clearly illustrate the technical solution of the present invention, and cannot be used to limit the protection scope of the present invention. Some of the block diagrams shown in the drawings are functional entities, which do not necessarily correspond to physically or logically independent entities. These functional entities can be implemented in software form, or implemented in one or more hardware modules or integrated circuits, or implemented in different networks and / or processor devices and / or microcontroller devices.

[0038] The flowchart shown in the drawings is only an exemplary illustration and does not necessarily include all steps. For example, some steps can be decomposed, while some steps can be combined or partially combined. Therefore, the actual execution order may be changed according to the actual situation.

[0039] In this embodiment, all programs and algorithms are written in the environment of Matlab2018b, and the hardware conditions for running are a Core i7 processor with a main frequency of 1.8 GHz and a memory of 8 GB.

[0040] Taking the simulated sine grating as the flat-top sample to be measured, as Figure 1 shown, the method for optimizing the reconstruction distance of digital holography based on the phase evaluation function mainly includes the following steps:

[0041] First step, the computer simulates the three-dimensional topography of the surface of the microstructure to be measured and generates the original object light wave;

[0042] The relevant parameters are as follows:

[0043] Mathematical expression:

[0044] Effective pixel area of the object (intensity values of each point are equal): 220×390

[0045] Matrix position: (402:622, 300:690)

[0046] The parameters of the hologram size (simulated recording medium CCD) are: 1024×1024

[0047] Pixel pitch: 5μm×5μm

[0048] Wavelength of the light wave: λ = 632.8nm; Recording distance: d o = 80.91mm

[0049] Second step, use the Fresnel diffraction formula to obtain the object light field on the hologram recording plane:

[0050]

[0051] Among them, is the Fourier transform; (x o , y o ) is the coordinate point in the object plane coordinate system, (x, y) is the coordinate point in the hologram recording plane coordinate system, d o is the recording distance of the hologram, λ is the wavelength of the light wave, o(.) represents the light wave modulated by the surface of the object to be measured, O(.) represents the light wave diffracted and propagated to the recording plane, j is the imaginary unit, and k is the wave number.

[0052] The digital hologram generated by interfering with the reference light wave R is expressed as:

[0053] I(x, y) = |O(x, y)| 2 + |R(x, y)| 2 + OR * + O * R

[0054] Among them, I(.) represents the digital hologram, |.| represents taking the modulus, R* represents the conjugate reference light wave, O represents the light wave diffracted and propagated to the recording plane, which is a simplified form of O(x,y); O * represents the light wave diffracted and propagated to the recording plane, which is a simplified form of O * (x,y); Similarly, R and R * are R(x,y) and R *The shorthand form of (x,y).

[0055] In the third step, use the conjugate reference light wave R * Perform numerical reconstruction by the Fresnel method:

[0056] Set the initial reconstruction distance Set the range of the reconstruction distance to [80.80, 81.00] (mm) to include the actual recording distance.

[0057] As Figure 2 shown, divide the above range into 20 equal parts with a reconstruction interval Δd i = 0.01 mm. Take the boundary values 80.80, 81.00 of the reconstruction distance range and each equal division point as candidate reconstruction distances, denoted as [80.80, 80.81, 80.82, …, 81.00] (mm), for a total of 21 candidate reconstruction distances.

[0058] Perform diffraction reconstruction using the conjugate light wave of the original reference light wave. The complex amplitude of the conjugate real image light field is:

[0059]

[0060] Ignoring the phase factor independent of x o , y o , x, y, the above formula simplifies to:

[0061]

[0062] The role of the quadratic phase factor about x, y in the above formula is to expand the reconstructed image. As Figure 3 shown. In order to obtain a clear reconstructed image, this term should be made to disappear, that is, d i = d o is the ideal reconstructed image plane. However, in actual reconstruction, it is impossible to find the exact position of the ideal reconstructed image. At this time, the quadratic phase factor about x, y in the integrand cannot be eliminated. Therefore, at the reconstruction distance d i ≠ d o the reconstructed image is expanded, causing a phase reconstruction error and distortion.

[0063] Calculate the complex amplitude of the conjugate real image light field using the Fourier transform result:

[0064]

[0065] Among them, (x, y) is the coordinate point in the coordinate system of the digital hologram recording plane, represents the coordinate point in the coordinate system of the reconstructed image plane when the reconstruction distance is d i , and U +1represents the conjugate real image complex amplitude, λ is the wavelength of the light wave, j is the imaginary unit, k is the wave number, is the Fourier transform, O * represents the conjugate light wave that propagates to the recording plane after diffraction.

[0066] Fourthly, for each candidate reconstruction distance perform left and right offsets to obtain a pair of offset candidate reconstruction distances and where Δd is the adjustment offset, which is numerically less than the reconstruction spacing Δd i , as Figure 2 shown.

[0067] Respectively take and as the reconstruction distance d i , and obtain a pair of conjugate real image complex amplitudes and After phase unwrapping, a set of reconstructed distorted phase information is obtained:

[0068]

[0069]

[0070] where, Im(.) represents the imaginary part of a complex number, Re(.) represents the real part of a complex number, represents the distorted phase of the coordinate point in the reproduction image plane coordinate system when the reconstruction distance is d i .

[0071] Fifthly, substitute the two sets of reconstructed distorted phase information obtained in the fourth step into the evaluation function:

[0072]

[0073] where, max(.) represents taking the maximum phase value, φ (l) represents the l-th reconstruction distance corresponding evaluation value;

[0074] Sixthly, repeat the fourth and fifth steps, traverse all candidate reconstruction distances [80.80, 80.81, 80.82, …, 81.00], and finally obtain the evaluation value sequence [φ (1) , φ (2) , …, φ (l) , …, φ (L) corresponding to all candidate reconstruction distances.

[0075] Step 7: Use the candidate reconstruction distances in Step 3 as the abscissa \(X = [80.80, 80.81, 80.82, \ldots, 81.00]\) (mm), and use the sequence of evaluation values \([\varphi (1) , \varphi (2) , \ldots, \varphi (l) , \ldots, \varphi (L) \) corresponding to all the candidate reconstruction distances obtained in Step 6 as the ordinate. Visualize the data of \(X\) and \(Y\) to obtain the evaluation function curve, and select the abscissa corresponding to the minimum value point as the optimized reconstruction distance, as shown in (a) of Figure 4 .

[0076] Change the recording distance \(d o = 80.85\) mm in the embodiment, and use the method of the above Steps 1 to 7 to optimize the reconstruction distance. The obtained evaluation function curve is as shown in (b) of Figure 4 .

[0077] The above is only the specific implementation manner of the present invention, but the protection scope of the present invention is not limited thereto. Any person skilled in the art within the technical scope disclosed by the present invention can easily think of changes or substitutions, which should all be covered by the protection scope of the present invention.

Claims

1. A digital holographic reconstruction distance optimization method based on a phase evaluation function, characterized in that Including the following steps: 1) Obtain the recording distance of the digital hologram of the three-dimensional topography of the microstructure to be measured; 2) Set the reconstruction distance range including the recording distance in the digital hologram, and set several candidate reconstruction distances within the reconstruction distance range; specifically: Divide the reconstruction distance range into equal parts parts, and use the boundary values of the reconstruction distance range and each equal division point as candidate reconstruction distances, denoted as , where , represents the th candidate reconstruction distance, represents the reconstruction interval, represents the recording distance; 3) Perform diffraction reconstruction and unwrapping for each candidate reconstruction distance to obtain the distorted phase corresponding to each candidate reconstruction distance, and the calculation method is: 3.1) For each candidate reconstruction distance perform left and right offsets to obtain a pair of offset candidate reconstruction distances and ; respectively use and as the reconstruction distance to perform diffraction reconstruction and unwrapping to obtain the conjugate real-image complex amplitude. The formula is as follows: ； Wherein, is the coordinate point in the coordinate system of the digital hologram recording plane, represents that the reconstruction distance is the coordinate point in the coordinate system of the reconstructed image plane at this time, represents the conjugate real image complex amplitude, is the light wave wavelength, is the complex number unit, is the wave number, is the Fourier transform, represents the conjugate light wave that propagates to the recording plane through diffraction; 3.2) Calculate the reconstructed distorted phase according to the conjugate real image complex amplitude: ； wherein, represents the imaginary part of a complex number, represents the real part of a complex number, represents that the reconstruction distance is the distorted phase of the coordinate point in the reproduced image plane coordinate system; 3.3) Respectively take and as the reconstruction distance , and obtain a set of reconstructed distorted phases and according to steps 3.1) and 3.2); 3.4) Substitute the set of reconstructed distorted phases obtained in step 3.3) into the evaluation function to obtain the evaluation value of the candidate reconstruction distance: ； Among them, represents taking the maximum phase value, represents the th reconstruction distance corresponding evaluation value, and finally an evaluation value sequence corresponding to all candidate reconstruction distances is obtained ; 4) Substitute the distorted phase into the evaluation function, and take the candidate reconstruction distance corresponding to the minimum value of the evaluation function as the optimization result.

2. The digital holographic reconstruction distance optimization method based on a phase evaluation function according to claim 1, wherein, The method for obtaining the digital hologram is: Calculate the complex amplitude of the object light wave: ； The complex amplitude of the object wave and the reference wave interfere to generate a digital hologram: ； wherein, is a coordinate point in the object surface coordinate system, is a coordinate point in the digital hologram recording surface coordinate system, is the recording distance, is the light wave wavelength, represents the light wave diffracted and propagated to the recording surface, represents the conjugate light wave diffracted and propagated to the recording surface, represents the light wave modulated by the surface of the object to be measured, is the imaginary unit, is the wave number; represents the digital hologram, represents taking the modulus, represents the conjugate reference light wave.

3. The digital holographic reconstruction distance optimization method based on a phase evaluation function according to claim 1, wherein Perform diffraction reconstruction using the conjugate light wave of the original reference light wave.

4. The digital holographic reconstruction distance optimization method based on a phase evaluation function according to claim 1, wherein In step 3.1), the adjustment offset of the left and right offset is less than the reconstruction pitch.

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