An optimal reconstruction distance selection method, device and medium for off-axis digital holography

Abstract

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

Description

[0001] The present application relates to the field of digital holography, in particular to an optimal reconstruction distance selection method, device and medium for off-axis digital holography. BACKGROUND

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

[0003] Automatic focusing is one of the key technologies in the field of digital holographic imaging. When performing quantitative analysis on the measured object, the reconstruction accuracy of the hologram image is particularly important to ensure that the amplitude and phase of the object are accurate and not distorted. Whether the recording distance of the hologram is consistent with the reproduction distance is the key to judging the quality of the image. Therefore, the traditional manual focusing cannot meet the requirements, and the use of computer real-time measurement can greatly improve the efficiency and reliability of automatic focusing.

[0004] A significant feature of digital holography is that it can realize numerical reconstruction in a computer. However, the optimal recording distance cannot be accurately obtained when the wavefront is reconstructed. The focus plane of the image cannot be directly determined by the numerical reconstruction process alone. In order to quantify the focusing degree of the image, an external function is often needed. Various second-order total variation evaluation functions based on the characteristics of digital holography have been proposed. Most automatic focusing functions perform well in image regions containing rich details. However, speckle and stripes are high-frequency noise in the entire region, which can greatly reduce the signal-to-noise ratio of the reconstructed image, and traditional focusing functions are mostly sensitive to noise, so it is difficult to determine the focus and defocus images. SUMMARY

[0005] The purpose of the present application is to overcome the low efficiency and poor accuracy of the prior art and provide an optimal reconstruction distance selection method for off-axis digital holography.

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

[0007] An optimal reconstruction distance selection method for off-axis digital holography includes the following steps:

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

[0009] S2: performing 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 inverse fractional Fourier transform to obtain positive first-order spectrum information;

[0010] S3: setting a reconstruction distance range including a recording distance in the digital hologram, setting a plurality of candidate reconstruction distances at fixed intervals in the reconstruction distance range, and performing angular spectrum method to obtain a corresponding reconstruction amplitude image for each candidate reconstruction distance;

[0011] S4: constructing a second-order total variation evaluation function, calculating the second-order total variation evaluation function value of each reconstruction amplitude image, and normalizing the function value;

[0012] S5: taking the reconstruction distance as the horizontal coordinate and the second-order total variation evaluation function value as the vertical coordinate to draw a second-order total variation evaluation function curve, and determining the best reconstruction distance according to the properties of the measured object and the second-order total variation evaluation function value.

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

[0014]

[0015] In the formula, is a coordinate point in the recording plane coordinate system of the digital hologram, represents a light wave diffracted and propagated to the recording plane, represents a conjugate light wave diffracted and propagated to the recording plane, represents a reference light wave, represents a conjugate reference light wave.

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

[0017]

[0018] In the formula, is a fractional order, is a fractional Fourier transform, is a coordinate point in the recording plane coordinate system of the digital hologram, is a hologram, represents a light wave diffracted and propagated to the recording plane, represents a conjugate light wave diffracted and propagated to the recording plane, represents a reference light wave, represents a conjugate reference light wave.

[0019] Further, in step S3, the reconstruction distance range of is , and the sampling number in the reconstruction distance range is , the sampling interval is calculated , the candidate reconstruction distances are obtained respectively , , … .

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

[0021]

[0022]

[0023]

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

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

[0026]

[0027] In the formula, represents the pixel value of the amplitude image at position when the reconstruction distance is z, represents the pixel value of the amplitude image at position when the reconstruction distance is z, represents the pixel value of the amplitude image at position when the reconstruction distance is z, represents the pixel value of the amplitude image at position when the reconstruction distance is z, represents the pixel value of the amplitude image at position when the reconstruction distance is z.

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

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

[0030] The second aspect of the present application is an off-axis digital holographic optimal reconstruction distance selection device, comprising a memory, a processor, and a program stored in the memory, wherein the processor implements any one of the off-axis digital holographic optimal reconstruction distance selection methods when executing the program.

[0031] The third aspect of the present application is a storage medium having a program stored thereon, wherein the program implements any one of the off-axis digital holographic optimal reconstruction distance selection methods when executed.

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

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

[0034] 2) The second-order total variation can enhance robustness by better smoothing noise. It can maintain important image features while filtering out high-frequency noise in the process of smoothing the image, so it shows better focusing effect under the condition of noise. BRIEF DESCRIPTION OF DRAWINGS

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

[0036] Figure 2 is a flowchart of a second-order total variation-based fractional Fourier transform off-axis digital holographic automatic focusing method provided in the embodiment of the present application.

[0037] Figure 3 is a raw hologram collected in the embodiment of the present application.

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

[0039] Figure 5 is a distribution graph of +1-order spectrum information obtained after 0.8-order inverse Fourier transform in the embodiment of the present application.

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

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

[0042] The markings in the diagram are as follows: 1. Light source, 2. Beam expander and collimator, 3. Beam splitter, 4. First reflecting mirror, 5. Second reflecting mirror, 6. Measurement object, 7. Beam splitter, 8. CCD camera, 9. Computer. Detailed Implementation

[0043] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments. These embodiments are based on the technical solution of the present invention and provide detailed implementation methods and specific operating procedures. However, the scope of protection of the present invention is not limited to the following embodiments.

[0044] Example 1

[0045] This invention provides a method for selecting the optimal reconstruction distance in off-axis digital holography, such as... Figure 2 As shown.

[0046] Specifically, the following steps are included:

[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 this invention is as follows: Figure 1 As shown, Figure 1 This is a structural diagram of an off-axis digital hologram device. Light source 1 is a helium-neon laser with a wavelength λ of 632.8 nm. The beam emitted from light source 1 is split into two beams by beam splitter 3 after beam expansion and collimation 2. One beam is the object beam, which is reflected by the second mirror 5 and illuminates object 6. The other beam is the reference beam, which is reflected by the first mirror 4 and then merged with the object beam at beam splitter 7. The interference angle is adjusted by adjusting either the first mirror 4 or the second mirror 5. Finally, the object beam and the reference beam interfere on a CCD camera 9 to form an off-axis hologram. The pixel size of the CCD camera is 4.65 μm. The digitized hologram is 4.65µm in size and is then 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]

[0051] in, The coordinates of the points in the digital hologram recording plane coordinate system. This refers to the light wave that has propagated to the recording plane after diffraction. This represents the conjugate light wave that propagates to the recording plane after diffraction. Indicates the reference light wave, This represents the conjugate reference light wave.

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

[0053]

[0054] In the formula, It is of fractional order. For fractional Fourier transform, The coordinates of the points in the digital hologram recording plane coordinate system. It is a hologram. This refers to the light wave that has propagated to the recording plane after diffraction. This represents the conjugate light wave that propagates to the recording plane after diffraction. Indicates the reference light wave, This represents the conjugate reference light wave.

[0055] In this embodiment, the object under test is a resolution testing target. The acquired original hologram is shown below. Figure 3 As shown. A 0.8th order fractional Fourier transform is performed on the hologram to obtain the time-frequency domain information of the off-axis hologram. Then, the +1 order time-frequency domain information is filtered, and the result is as follows. Figure 4 As shown. A 0.8 inverse Fourier transform is performed to obtain +1 level spectral information, and the calculation results are as follows. Figure 5 As shown.

[0056] S3: Set the reconstruction distance range including the recording distance in the digital hologram. Within the reconstruction distance range, set several candidate reconstruction distances at fixed step intervals, and perform angular spectrum method on each candidate reconstruction distance to obtain the corresponding reconstruction amplitude image.

[0057] Reconstruction distance range is Set the number of samples within the reconstruction distance range to Calculate the sampling interval The candidate reconstruction distances were obtained as follows: , , … .

[0058] The distance from the resolution test target to the CCD camera was roughly measured to be 144 mm using a soft ruler. The focusing range [140 mm, 148 mm] was then estimated, and the number of samples within the search range was set to 160. The sampling interval d was then calculated. z =0.05 mm, and the reconstructed distances are z1=140 mm, z2=140.05 mm, ... z k =148 mm.

[0059] The hologram is processed, and the reconstructed distances are z1=140 mm, z2=140.05 mm,..., z k =148 mm, the hologram is sequentially subjected to numerical reconstruction by the angular spectrum method to obtain object light field distributions U1, U2,..., U 160 .

[0060] According to the obtained object light field distributions , ,..., , amplitude images under different reconstruction distances are calculated , ,..., .

[0061] The function values , ,..., are calculated by using the automatic second-order total variation evaluation function, and the function values are normalized.

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

[0063]

[0064]

[0065]

[0066] In the formula, and represent the Fourier transform and the inverse Fourier transform, respectively. is a filter for extracting +1 or -1 order spectrum, is a transfer function of the angular spectrum diffraction method, and are frequency domain coordinates, , λ is the wavelength of light; z is the reconstruction distance, and are the reconstruction 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: Draw a second-order total variation evaluation function curve with the reconstruction distance as the horizontal coordinate and the second-order total variation evaluation function value as the vertical coordinate, and determine the best reconstruction distance according to the properties of the measured object.

[0069] The function values , ,..., and the function value is normalized. The calculation expression of the second-order total variation evaluation function is:

[0070]

[0071] wherein, represents a pixel value of the amplitude image at position when the reconstruction distance is z, represents a pixel value of the amplitude image at position when the reconstruction distance is z, represents a pixel value of the amplitude image at position when the reconstruction distance is z, represents a pixel value of the amplitude image at position when the reconstruction distance is z, represents a pixel value of the amplitude image at position when the reconstruction distance is z.

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

[0073] The amplitude image reconstructed at the optimal reconstruction distance of the embodiment is shown in Figure 7 It can be seen that the reconstructed amplitude image obtained by the method has the advantages of clear profile, no artifact and high resolution. From the experimental results, the method better restores the information of the object light, proving the effectiveness of the method.

[0074] The program code for implementing the method of the present application can be written in any combination of one or more programming languages. The program code can be provided to a processor or controller of a general purpose computer, special purpose computer, or other programmable data processing apparatus to produce a machine, such that the program code, when executed by the processor or controller, implements the functions / operations specified in the flowcharts and / or block diagrams. The program code can be executed entirely on the machine, partially on the machine, partially on the machine as a standalone software package, partially on the machine and partially on a remote machine or a server, or entirely on a remote machine or server.

[0075] In the context of the present application, a machine-readable medium can be a tangible medium that can contain or store a program for use by or in connection with an instruction execution system, apparatus, or device. The machine-readable medium can be a machine-readable signal medium or a machine-readable storage medium. Machine-readable storage medium can include, but are not limited to, electronic, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or any suitable combination of the foregoing. More specific examples of machine-readable storage medium would include a one or more lines of electrical connections, a portable computer diskette, 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 disc read-only memory (CDROM), an optical storage device, a magnetic storage device, or any suitable combination of the foregoing.

[0076] The preferred embodiments of the present application have been described above in detail. It should be understood that modifications and variations can be resorted to without departing from the scope of the application. Accordingly, it is intended that the application be covered by the following claims.

Claims

1. A method for selecting the optimal reconstruction distance in off-axis digital holography, characterized in that, Includes the following steps: S1: Run the off-axis digital holographic optical path system to obtain the off-axis hologram to be processed; S2: Perform a fractional Fourier transform on the off-axis hologram to obtain the time-frequency domain information of the off-axis hologram, filter the positive first-order time-frequency domain information, and then perform a fractional inverse Fourier transform to obtain the positive first-order spectrum information. S3: Set the reconstruction distance range including the recording distance in the digital hologram. Within the reconstruction distance range, set several candidate reconstruction distances at fixed step intervals, and perform angular spectrum method on each candidate reconstruction distance to obtain the corresponding reconstruction amplitude image. S4: Construct a second-order total variation evaluation function, calculate the second-order total variation evaluation function value for each reconstructed amplitude image, and normalize the function value; S5: Plot the second-order total variation evaluation function curve with the reconstruction distance as the x-axis and the second-order total variation evaluation function value as the y-axis. Determine the optimal reconstruction distance based on the properties of the measured object and the second-order total variation evaluation function value. The calculation expression for the digital hologram is: In the formula, The coordinates of the points in the digital hologram recording plane coordinate system. This refers to the light wave that has propagated to the recording plane after diffraction. This represents the conjugate light wave that propagates to the recording plane after diffraction. Indicates the reference light wave, Indicates the conjugate reference light wave; The calculation expression for the second-order total variation evaluation function is as follows: In the formula, This indicates that when the reconstruction distance is z, the amplitude image is at position Pixel value at that location, This indicates that when the reconstruction distance is z, the amplitude image is at position Pixel value at that location, This indicates that when the reconstruction distance is z, the amplitude image is at position Pixel value at that location, This indicates that when the reconstruction distance is z, the amplitude image is at position Pixel value at that location, This indicates that when the reconstruction distance is z, the amplitude image is at position The pixel value at that location.

2. The method for selecting the optimal reconstruction distance in off-axis digital holography according to claim 1, characterized in that, The expression for calculating the fractional Fourier transform is: In the formula, It is of fractional order. For fractional Fourier transform, The coordinates of the points in the digital hologram recording plane coordinate system. It is a hologram. This refers to the light wave that has propagated to the recording plane after diffraction. This represents the conjugate light wave that propagates to the recording plane after diffraction. Indicates the reference light wave, This represents the conjugate reference light wave.

3. The method for selecting the optimal reconstruction distance in off-axis digital holography according to claim 1, characterized in that, In step S3, the reconstructed distance range is: Set the number of samples within the reconstruction distance range to Calculate the sampling interval The candidate reconstruction distances were obtained as follows: , , … .

4. The method for selecting the optimal reconstruction distance in off-axis digital holography according to claim 1, characterized in that, The calculation expression for the angular spectrum method is as follows: In the formula, and These represent the Fourier transform and the inverse Fourier transform, respectively. It is a filter that extracts +1 or -1 order spectra. It is the transfer function of angular spectrum diffraction. and These are frequency domain coordinates. λ is the wavelength of light; z is the reconstruction distance. and These represent the reconstructed intensity and phase of the object under test, respectively.

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

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

7. 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 optimal reconstruction distance selection method for off-axis digital holography as described in any one of claims 1-6.

8. A storage medium having a program stored thereon, characterized in that, When the program is executed, it implements the optimal reconstruction distance selection method for off-axis digital holography as described in any one of claims 1-6.

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