Optimal reconstruction distance selection method and device for off-axis digital holography and medium

Abstract

The invention relates to an optimal reconstruction distance selection method and device for off-axis digital holography and a medium, and the method comprises the following steps: operating an off-axis digital holographic optical path system, and obtaining a to-be-processed off-axis hologram; performing fractional order Fourier transform on the off-axis hologram to obtain time-frequency domain information of the off-axis hologram; carrying out filtering processing on the positive first-order time-frequency domain information, and then carrying out fractional order inverse Fourier transform to obtain positive first-order frequency spectrum information; setting a reconstruction distance range, and setting a plurality of candidate reconstruction distances by taking a fixed step length as an interval; executing an angular spectrum method to obtain a corresponding reconstructed amplitude image; constructing a second-order total variation evaluation function, and calculating a second-order total variation function value of each reconstructed amplitude image; and drawing a second-order total variation evaluation function curve by taking the reconstruction distance as an abscissa and the second-order total variation function value as an ordinate, and determining the optimal reconstruction distance according to the attribute of the measured object. Compared with the prior art, the method has the advantages of high accuracy, strong robustness and the like.

Description

Technical Field

[0001] The present invention relates to the technical field of digital holography, and in particular to a method, a device and a medium for selecting an optimal reconstruction distance of off-axis digital holography. Background Art

[0002] Digital holography has the characteristics of full field of view, non-destructive, high precision, digital focusing, and can simultaneously determine multiple information, such as quantitative intensity and phase of the image. Digital holography has been widely used in quantitative imaging of living cells, microscopic particle tracking, and surface morphology detection. In particular, off-axis digital holography has attracted widespread interest from researchers in fields such as biology and biomedicine, mainly because it only requires one hologram to restore object information. This not only improves the measurement efficiency of the system, but also reduces the impact of the environment on multi-frame measurements. Therefore, it is more suitable for real-time imaging of moving objects.

[0003] Autofocus is one of the key technologies in the field of digital holographic imaging. When conducting quantitative analysis on the object to be measured, the reconstruction accuracy of the holographic image is particularly important to ensure accurate and undistorted object amplitude and phase. Whether the recording distance and the reproduction distance of the hologram are consistent becomes the key to judging the image quality. Traditional manual focusing can no longer meet the needs, so combined with the digital characteristics of the holographic technology itself, the use of computer real-time measurement can greatly improve the efficiency and reliability of autofocus.

[0004] A notable feature of digital holography is that it can be numerically reconstructed in a computer. When reconstructing the wavefront, the optimal recording distance of digital holography cannot be accurately obtained. The focal plane of the image cannot be directly determined by the numerical reconstruction process alone. In order to quantify the degree of focus of the image, it is often necessary to intervene through external functions. Various second-order total variation evaluation functions based on the characteristics of digital holography have been proposed. Most autofocus functions show good performance for image areas containing rich details. However, speckle and fringes appear as high-frequency noise in the entire area, which will greatly reduce the signal-to-noise ratio of the reconstructed image. In addition, most traditional focusing functions are sensitive to noise, and it is difficult to determine the focused and defocused images. Summary of the invention

[0005] The purpose of the present invention is to provide a method for selecting the optimal reconstruction distance of off-axis digital holography in order to overcome the defects of low efficiency and poor accuracy in the above-mentioned prior art.

[0006] The purpose of the present invention can be achieved by the following technical solutions:

[0007] A method for selecting an optimal reconstruction distance for off-axis digital holography comprises the following steps:

[0008] S1: Run the off-axis digital holographic optical path system to obtain the off-axis hologram to be processed;

[0009] S2: Performing fractional Fourier transform on the off-axis hologram to obtain the time-frequency domain information of the off-axis hologram, filtering the first-order time-frequency domain information, and then performing fractional inverse Fourier transform to obtain the first-order spectrum information;

[0010] S3: setting a reconstruction distance range including the recording distance in the digital hologram, setting a number of candidate reconstruction distances within the reconstruction distance range at intervals of a fixed step size, and performing an angular spectrum method on each candidate reconstruction distance to obtain a corresponding reconstructed amplitude image;

[0011] S4: construct a second-order total variation evaluation function, calculate the second-order total variation evaluation function value of each reconstructed amplitude image, and normalize the function value;

[0012] S5: With the reconstruction distance as the horizontal coordinate and the second-order total variation evaluation function value as the vertical coordinate, a second-order total variation evaluation function curve is drawn, and the optimal reconstruction distance is determined according to the properties of the measured object and the second-order total variation evaluation function value.

[0013] Furthermore, the calculation expression of the digital hologram is:

[0014] H(x,y)=|R(x,y) 2 |+|O(x,y) 2 |+O(x,y)R(x,y) * +O(x,y) * R(x,y)

[0015] Where (x, y) is the coordinate point in the coordinate system of the digital hologram recording surface, O(x, y) represents the light wave propagated to the recording surface after diffraction, and O(x, y) * represents the conjugate light wave that propagates to the recording surface after diffraction, R(x,y) represents the reference light wave, and R(x,y) * represents the conjugate reference light wave.

[0016] Furthermore, the calculation expression of fractional Fourier transform is:

[0017]

[0018] In the formula, a is the fractional order, is the fractional Fourier transform, (x, y) is the coordinate point in the coordinate system of the digital hologram recording surface, H(x, y) is the hologram, O(x, y) represents the light wave propagated to the recording surface after diffraction, and O(x, y) * represents the conjugate light wave that propagates to the recording surface after diffraction, R(x,y) represents the reference light wave, and R(x,y) * represents the conjugate reference light wave.

[0019] Furthermore, in step S3, the reconstruction distance range is [z1,z k ], set the number of samples within the reconstruction distance range to k, and calculate the sampling interval d z =(z k -z1) / (k-1), and the candidate reconstruction distances are z2=z1+d z ,z3=z2+d z ,z3=z2+d z , z4=z3+d z …z k =z1+(k-1)*d z .

[0020] Furthermore, the calculation expression of the angular spectrum method is:

[0021]

[0022] I(x,y,z)=|U(x,y,z)| 2

[0023]

[0024] In the formula, and represent Fourier transform and inverse Fourier transform respectively. is a filter for extracting the +1 or -1 order spectrum, G(f x ,f y ,z) is the transfer function of the angular spectrum diffraction method, f x and f y is the frequency domain coordinate, λ is the wavelength of light; z is the reconstruction distance, I(x,y,z) and are the reconstructed intensity and phase of the object to be measured, respectively.

[0025] Furthermore, the calculation expression of the second-order total variation evaluation function is:

[0026]

[0027] Where I(x,y,z) represents the pixel value of the amplitude image at position (x,y) when the reconstruction distance is z, I(x+2,y,z) represents the pixel value of the amplitude image at position (x+2,y) when the reconstruction distance is z, I(x+1,y,z) represents the pixel value of the amplitude image at position (x+1,y) when the reconstruction distance is z, I(x,y+1,z) represents the pixel value of the amplitude image at position (x,y+1) when the reconstruction distance is z, and I(x,y+2,z) represents the pixel value of the amplitude image at position (x,y+2) when the reconstruction distance is z.

[0028] Furthermore, when the attribute of the measured object is an amplitude object, the distance corresponding to the maximum value of the second-order total variation evaluation function is the optimal reconstruction distance.

[0029] Furthermore, when the attribute of the measured object is a phase object, the distance corresponding to the minimum value of the second-order total variation evaluation function is the optimal reconstruction distance.

[0030] A second aspect of the present invention is a device for selecting the optimal reconstruction distance of an off-axis digital hologram, comprising a memory, a processor, and a program stored in the memory, wherein the device implements any of the above methods for selecting the optimal reconstruction distance of an off-axis digital hologram when the processor executes the program.

[0031] A third aspect of the present invention is a storage medium having a program stored thereon, wherein when the program is executed, any of the above methods for selecting the optimal reconstruction distance for off-axis digital holography is implemented.

[0032] Compared with the prior art, the present invention has the following beneficial effects:

[0033] 1) The present invention calculates the second-order total variation evaluation function value for a variety of possible candidate reconstruction distances, and further considers the curvature of the pixel value change. This method is better at capturing the complex structure and texture information in the image, especially when there are curves, arcs, and nonlinear changes in the image, and can more accurately reflect the details of the image.

[0034] 2) Second-order total variation can enhance robustness by better smoothing noise. It can maintain important image features while filtering out high-frequency noise during the image smoothing process, thus showing better focusing effect in the presence of noise. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] Figure 1 It is a schematic diagram of the structure of an off-axis digital holographic system in a specific embodiment.

[0036] Figure 2 It is a flow chart of an off-axis digital holographic automatic focusing method based on second-order total variation fractional Fourier transform provided in an embodiment of the present invention.

[0037] Figure 3 is the original hologram collected in the embodiment of the present invention.

[0038] Figure 4 It is a time-frequency domain information distribution diagram after 0.8-order Fourier transform in an embodiment of the present invention.

[0039] Figure 5 It is a distribution diagram of +1 level spectrum information obtained after 0.8 order inverse Fourier transform in an embodiment of the present invention.

[0040] Figure 6 is a focusing curve in the embodiment of the present invention.

[0041] Figure 7 It is an amplitude diagram reconstructed at the optimal reconstruction distance by the angular spectrum method in the embodiment of the present invention.

[0042] Explanation of the marks in the figure: 1. light source, 2. beam expander collimator, 3. beam splitter, 4. first reflector, 5. second reflector, 6. measurement object, 7. beam splitter, 8. CCD camera, 9. computer. DETAILED DESCRIPTION

[0043] The present invention is described in detail below in conjunction with the accompanying drawings and specific embodiments. This embodiment is implemented based on the technical solution of the present invention, and provides a detailed implementation method and specific operation process, but the protection scope of the present invention is not limited to the following embodiments.

[0044] Example 1

[0045] The present invention is a method for selecting the optimal reconstruction distance of off-axis digital holography. Figure 2 shown.

[0046] The specific steps include:

[0047] S1: Run the off-axis digital holographic optical path system to obtain the off-axis hologram to be processed;

[0048] The experimental environment of the present invention is as follows Figure 1 As shown, Figure 1 The figure is a structural diagram of the off-axis digital holography device. The light source 1 is a helium-neon laser with a wavelength λ equal to 632.8nm. The light beam emitted by the light source 1 is divided into two beams by the beam splitter 3 after the beam expansion and collimation 2. One beam is the object light, which is reflected by the second reflector 5 and then illuminates the object 6. The other beam is the reference light, which is reflected by the first reflector 4 and then combined with the object light on the beam splitter 7. The interference angle is adjusted by adjusting the first reflector 4 or the second reflector 5. Finally, the object light and the reference light interfere on the CCD camera 9 to form an off-axis hologram, where the pixel size of the CCD camera is 4.65um×4.65um. The digitized hologram is input into the computer 10.

[0049] The complex amplitude of the object light wave interferes with the reference light wave R to produce a digital hologram:

[0050] H(x,y)=|R(x,y) 2 |+|O(x,y) 2 |+O(x,y)R(x,y) * +O(x,y) * R(x,y)

[0051] Where (x, y) is the coordinate point in the coordinate system of the digital hologram recording surface, O(x, y) represents the light wave propagated to the recording surface after diffraction, and O(x, y) * represents the conjugate light wave that propagates to the recording surface after diffraction, R(x,y) represents the reference light wave, and R(x,y) * represents the conjugate reference light wave.

[0052] S2: performing a fractional-order fractional Fourier transform on the off-axis hologram to obtain time-frequency domain information of the off-axis hologram, filtering the positive first-order time-frequency domain information, and then performing a fractional-order inverse Fourier transform to obtain positive first-order spectrum information;

[0053]

[0054] In the formula, a is the fractional order, is the fractional Fourier transform, (x, y) is the coordinate point in the coordinate system of the digital hologram recording surface, H(x, y) is the hologram, O(x, y) represents the light wave propagated to the recording surface after diffraction, and O(x, y) * represents the conjugate light wave that propagates to the recording surface after diffraction, R(x,y) represents the reference light wave, and R(x,y) * represents the conjugate reference light wave.

[0055] In this embodiment, the object to be measured is a resolution test target. The original hologram obtained is as follows: Figure 3 The hologram is subjected to a 0.8-order fractional Fourier transform to obtain the time-frequency domain information of the off-axis hologram. Then the +1-level time-frequency domain information is filtered, and the result is as follows: Figure 4 As shown. Perform 0.8-order inverse Fourier transform to obtain +1-level spectrum information. The calculation results are as follows Figure 5 shown.

[0056] S3: setting a reconstruction distance range including the recording distance in the digital hologram, setting a number of candidate reconstruction distances within the reconstruction distance range at intervals of a fixed step size, and performing an angular spectrum method on each candidate reconstruction distance to obtain a corresponding reconstructed amplitude image;

[0057] The reconstruction distance range is [z1,z k ], set the number of samples within the reconstruction distance range to k, and calculate the sampling interval d z =(z k -z1) / (k-1), and the candidate reconstruction distances are z2=z1+d z ,z3=z2+d z ,z3=z2+d z , z4=z3+d z …z k =z1+(k-1)*dz .

[0058] The distance from the resolution test target to the CCD camera is roughly measured with a tape measure and is 144 mm. The focus interval is estimated to be [140 mm, 148 mm]. The number of samples in the search interval is set to 160, and the sampling interval d is calculated. z =0.05mm, the reconstruction distances are z1=140mm, z2=140.05mm, …z k =148mm.

[0059] The hologram is processed and the reconstruction distances are z1 = 140 mm, z2 = 140.05 mm, ... z k =148mm The hologram is numerically reconstructed by the angular spectrum method in turn, and the object light field distribution U1, U2, ..., U 160 .

[0060] According to the obtained object light field distribution U(x,y,z1),U(x,y,z2),…,U(x,y,z 160 ), calculate the amplitude images I(x,y,z1), I(x,y,z2), ..., I(x,y,z 160 ).

[0061] The function value TV is calculated using the automatic second-order total variation evaluation function (2) (I(x,y,z1)),TV (2) (I(x,y,z2)),…,TV (2) (I(x,y,z 160 )), and normalize the function value.

[0062] The calculation expression of the angular spectrum method is:

[0063]

[0064] I(x,y,z)=|U(x,y,z)| 2

[0065]

[0066] In the formula, and represent Fourier transform and inverse Fourier transform respectively. is a filter for extracting the +1 or -1 order spectrum, G(f x ,f y ,z) is the transfer function of the angular spectrum diffraction method, f x and f y is the frequency domain coordinate, λ is the wavelength of light; z is the reconstruction distance, I(x,y,z) and are the reconstructed intensity and phase of the object to be measured, respectively.

[0067] S4: construct a second-order total variation evaluation function, calculate the second-order total variation evaluation function value of each reconstructed amplitude image, and normalize the function value;

[0068] S5: With the reconstruction distance as the horizontal coordinate and the second-order total variation evaluation function value as the vertical coordinate, a second-order total variation evaluation function curve is drawn, and the optimal reconstruction distance is determined according to the properties of the measured object.

[0069] The function value TV is calculated using the second-order total variation evaluation function (2) (I(x,y,z1)),TV (2) (I(x,y,z2)),…,TV (2) (I(x,y,z 160 )), and normalize the function value. The calculation expression of the second-order total variation evaluation function is:

[0070]

[0071] Where I(x,y,z) represents the pixel value of the amplitude image at position (x,y) when the reconstruction distance is z, I(x+2,y,z) represents the pixel value of the amplitude image at position (x+2,y) when the reconstruction distance is z, I(x+1,y,z) represents the pixel value of the amplitude image at position (x+1,y) when the reconstruction distance is z, I(x,y+1,z) represents the pixel value of the amplitude image at position (x,y+1) when the reconstruction distance is z, and I(x,y+2,z) represents the pixel value of the amplitude image at position (x,y+2) when the reconstruction distance is z.

[0072] The focusing curve of this embodiment is as follows Figure 6 As shown, it can be seen that the reconstruction distance z=144.2 mm corresponding to the maximum value of the evaluation function, z is the optimal reconstruction distance.

[0073] The amplitude image reconstructed at the optimal reconstruction distance of this embodiment is as follows: Figure 7 As shown, it can be seen that the reconstructed amplitude image obtained by the present invention has the advantages of clear contours, no artifacts and high resolution. From the experimental results, the method can better restore the information of the object light, which proves the effectiveness of the present invention.

[0074] The program code for implementing the method of the present invention can be written in any combination of one or more programming languages. These program codes can be provided to a processor or controller of a general-purpose computer, a special-purpose computer or other programmable data processing device, so that the program code, when executed by the processor or controller, enables the functions / operations specified in the flow chart and / or block diagram to be implemented. The program code can be executed entirely on the machine, partially on the machine, partially on the machine as a stand-alone software package and partially on a remote machine, or entirely on a remote machine or server.

[0075] In the context of the present invention, a machine-readable medium may be a tangible medium that may contain or store a program for use by or in conjunction with an instruction execution system, device, or equipment. A machine-readable medium may be a machine-readable signal medium or a machine-readable storage medium. A machine-readable medium may include, but is not limited to, electronic, magnetic, optical, electromagnetic, infrared, or semiconductor systems, devices, or equipment, or any suitable combination of the foregoing. A more specific example of a machine-readable storage medium may include an electrical connection based on one or more lines, a portable computer disk, a hard disk, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or flash memory), an optical fiber, a portable compact disk read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination of the foregoing.

[0076] The preferred specific embodiments of the present invention are described in detail above. It should be understood that a person skilled in the art can make many modifications and changes based on the concept of the present invention without creative work. Therefore, any technical solution that can be obtained by a person skilled in the art through logical analysis, reasoning or limited experiments based on the concept of the present invention on the basis of the prior art should be within the scope of protection determined by the claims.

Claims

1. A method for selecting the optimal reconstruction distance of off-axis digital holography, characterized in that: The following steps are involved: S1: Run the off-axis digital holographic optical path system to obtain the off-axis hologram to be processed; S2: performing a fractional Fourier transform on the off-axis hologram to obtain time-frequency domain information of the off-axis hologram, filtering the positive first-order time-frequency domain information, and then performing a fractional inverse Fourier transform to obtain the positive first-order spectrum information; S3: setting a reconstruction distance range including the recording distance in the digital hologram, setting a number of candidate reconstruction distances within the reconstruction distance range at intervals of a fixed step size, and performing an angular spectrum method on each candidate reconstruction distance to obtain a corresponding reconstructed amplitude image; S4: construct a second-order total variation evaluation function, calculate the second-order total variation evaluation function value of each reconstructed amplitude image, and normalize the function value; S5: With the reconstruction distance as the horizontal coordinate and the second-order total variation evaluation function value as the vertical coordinate, a second-order total variation evaluation function curve is drawn, and the optimal reconstruction distance is determined according to the properties of the measured object and the second-order total variation evaluation function value.

2. The method for selecting the optimal reconstruction distance of off-axis digital holography according to claim 1, characterized in that: The calculation expression of the digital hologram is: H(x,y)=|R(x,y) 2 |+|O(x,y) 2 |+O(x,y)R(x,y) * +O(x,y) * R(x,y) Where (x, y) is the coordinate point in the coordinate system of the digital hologram recording surface, O(x, y) represents the light wave propagated to the recording surface after diffraction, and O(x, y) * represents the conjugate light wave that propagates to the recording surface after diffraction, R(x,y) represents the reference light wave, and R(x,y) * represents the conjugate reference light wave.

3. The method for selecting the optimal reconstruction distance of off-axis digital holography according to claim 1, characterized in that: The calculation expression of the fractional Fourier transform is: In the formula, a is the fractional order, is the fractional Fourier transform, (x, y) is the coordinate point in the coordinate system of the digital hologram recording surface, H(x, y) is the hologram, O(x, y) represents the light wave propagated to the recording surface after diffraction, and O(x, y) * represents the conjugate light wave that propagates to the recording surface after diffraction, R(x,y) represents the reference light wave, and R(x,y) * represents the conjugate reference light wave.

4. The method for selecting the optimal reconstruction distance of off-axis digital holography according to claim 1, characterized in that: In step S3, the reconstruction distance range is [z1,z k ], set the number of samples within the reconstruction distance range to k, and calculate the sampling interval d z =(z k -z1) / (k-1), and the candidate reconstruction distances are z2=z1+d z ,z3=z2+dz, z3=z2+dz, z4=z3+dz…z k =z1+(k-1)*d z .

5. The method for selecting the optimal reconstruction distance of off-axis digital holography according to claim 1, characterized in that: The calculation expression of the angular spectrum method is: I(x,y,z)=|U(x,y,z) 2 In the formula, and represent Fourier transform and inverse Fourier transform respectively. is a filter for extracting the +1 or -1 order spectrum, G(f x ,f y ,z) is the transfer function of the angular spectrum diffraction method, f x and f y is the frequency domain coordinate, λ is the wavelength of light; z is the reconstruction distance, I(x,y,z) and are the reconstructed intensity and phase of the object to be measured, respectively.

6. The method for selecting the optimal reconstruction distance of off-axis digital holography according to claim 1, characterized in that: The calculation expression of the second-order total variation evaluation function is: Wherein, I(x,y,z) represents the pixel value of the amplitude image at position (x,y) when the reconstruction distance is z, I(x+2,y,z) represents the pixel value of the amplitude image at position (x+2,y) when the reconstruction distance is z, I(x+1,y,z) represents the pixel value of the amplitude image at position (x+1,y) when the reconstruction distance is z, I(x,y+1,z) represents the pixel value of the amplitude image at position (x,y+1) when the reconstruction distance is z, and I(x,y+2,z) represents the pixel value of the amplitude image at position (x,y+2) when the reconstruction distance is z.

7. The method for selecting the optimal reconstruction distance of off-axis digital holography according to claim 1, characterized in that: When the attribute of the measured object is an amplitude object, the distance corresponding to the maximum value of the second-order total variation evaluation function is the optimal reconstruction distance.

8. The method for selecting the optimal reconstruction distance of off-axis digital holography according to claim 1, characterized in that: When the attribute of the measured object is a phase object, the distance corresponding to the minimum value of the second-order total variation evaluation function is the optimal reconstruction distance.

9. An optimal reconstruction distance selection device for off-axis digital holography, comprising a memory, a processor, and a program stored in the memory, characterized in that: When the processor executes the program, it implements the method for selecting the optimal reconstruction distance of off-axis digital holography as described in any one of claims 1-8.

10. A storage medium having a program stored thereon, characterized in that: When the program is executed, it implements the method for selecting the optimal reconstruction distance of off-axis digital holography as described in any one of claims 1-8.

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