Off-axis digital holographic phase reconstruction method and device based on phase-shifted fractional Fourier transform

Abstract

The present invention relates to the field of digital holographic measurement, and in particular to a phase-shifted fractional Fourier transform off-axis digital holographic phase reconstruction method and device. The method comprises obtaining an off-axis digital hologram containing object information; shifting the off-axis digital hologram by one pixel to obtain a phase-shifted off-axis digital hologram; performing a differential on the two off-axis digital holograms to obtain a differential hologram without a DC component; performing a fractional Fourier transform, bandpass filtering, and an inverse fractional Fourier transform on the differential hologram to obtain a complex amplitude result containing real image information; obtaining a reference off-axis digital hologram without object information, repeating the above process to obtain a complex amplitude result containing only carrier information and background information; and dividing the two complex amplitude results to obtain the object's phase information through an inverse trigonometric function operation. The present invention can achieve high-resolution phase reconstruction of an object without phase compensation, simplifies the calculation process, and saves time and space costs.

Description

Technical Field

[0001] The present invention belongs to the technical field of digital holographic measurement, and in particular relates to an off-axis digital holographic phase reconstruction method and device using phase-shift fractional Fourier transform. Background Art

[0002] On-axis digital holography can fully utilize frequency domain resources and the spatial bandwidth utilization of CCDs to achieve high-resolution reconstruction. However, due to the influence of spectral aliasing, the extraction of the real image spectrum is greatly increased, and complex and spatially inefficient methods are required to complete phase reconstruction. Off-axis digital holography introduces angled reference light to separate the real image spectrum from the aliased spectrum in the frequency domain through methods such as bandpass filters. Although the imaging resolution is reduced due to undesirable factors such as bandwidth limitations and noise introduction, only a single hologram is required to restore the object information, improving the time or space efficiency of the system. It does not require a complex system to collect holograms, and the reconstruction process is relatively simple and accurate.

[0003] In the phase recovery process of off-axis digital holography, the resolution is mainly limited by the off-axis angle of the reference light. An insufficient off-axis angle of the reference light can easily lead to the overlap of the +1-order spectrum and the 0-order spectrum, which is seriously interfered by the 0-order spectrum, resulting in a low resolution of the off-axis digital holographic recovery result and reduced phase reconstruction quality.

[0004] To suppress the zero-order spectrum, Yasuhiro Takaki et al. published "Hybridholographic microscopy free of conjugate and zero-order images" in the journal Applied Optics. They used two gratings to block the object beam and the reference beam respectively, and used a liquid crystal phase modulator to phase modulate the object beam. Effective suppression of the zero-order spectrum was achieved through phase shifting. However, the introduction of grating and liquid crystal phase modulator components into the system greatly increased the complexity and difficulty of adjustment of the optical system. In addition, inaccurate phase shift accuracy would affect the suppression effect of the zero-order spectrum, resulting in low phase reconstruction quality.

[0005] Liu Yiwei et al. published "Single-frame reconstruction for improvement of off-axis digital holographic imaging based on image interpolation" in the journal Optics Letters. Their paper, "Optimization of Single-frame Off-Axis Digital Holographic Imaging Reconstruction Based on Image Interpolation," leverages the Kronecker convolution's ability to generate multiple spectral levels, resulting in a significant separation of the derived spectrum from the zero-order spectrum in the frequency domain. This effectively reduces the interference of the zero-order spectrum on the reconstruction result, significantly improving resolution. However, Kronecker convolution can lead to spectral expansion, increasing the computational burden. Furthermore, for holograms with complex edges or high noise levels, the resulting multi-level spectrum may introduce new spectral aliasing, affecting the accuracy of phase reconstruction and image quality. Summary of the Invention

[0006] In view of this, the present invention aims to provide an off-axis digital holographic phase reconstruction method based on phase-shifted fractional Fourier transform, so as to solve the technical problems that the existing off-axis digital holographic phase reconstruction method based on phase-shifted fractional Fourier transform will reduce the phase reconstruction quality and increase the computational complexity when suppressing the 0th-order spectrum.

[0007] To achieve the above object, the technical solution created by the present invention is implemented as follows:

[0008] A phase-shift fractional Fourier transform off-axis digital holographic phase reconstruction method comprises the following steps:

[0009] S1: Acquire a first original off-axis digital hologram containing information of the object being measured;

[0010] S2: Shifting the first original off-axis digital hologram by one pixel in one direction using a carrier digital phase shifting technique to obtain a first phase-shifted off-axis digital hologram;

[0011] S3: performing a differential operation on the first original off-axis digital hologram and the first phase-shifted off-axis digital hologram to obtain a first differential hologram without a DC component;

[0012] S4: performing a two-dimensional fractional Fourier transform, a bandpass filter, and a two-dimensional inverse fractional Fourier transform on the first differential hologram in sequence to obtain a first complex amplitude result containing real image information;

[0013] S5: Acquire a second original off-axis digital hologram that does not contain information about the object being measured;

[0014] S6: Shifting the second original off-axis digital hologram by one pixel in one direction using a carrier digital phase shifting technique to obtain a second phase-shifted off-axis digital hologram;

[0015] S7: performing a differential operation on the second original off-axis digital hologram and the second phase-shifted off-axis digital hologram to obtain a second differential hologram without a DC component;

[0016] S8: performing a two-dimensional fractional Fourier transform, a bandpass filter, and a two-dimensional inverse fractional Fourier transform on the second differential hologram in sequence to obtain a second complex amplitude result containing only carrier information and background information;

[0017] S9: Divide the first complex amplitude result by the second complex amplitude result to obtain complex amplitude information of the object under test after removing the carrier frequency and background information, and perform inverse trigonometric function calculation on the complex amplitude information to obtain phase information of the object under test.

[0018] Furthermore, the expression of the first original off-axis digital hologram is:

[0019]

[0020] in, represents the first original off-axis digital hologram, represents the DC component of the first original off-axis digital hologram, represents the modulation term of the interference fringes, Indicates the phase information of the object being measured; The first original off-axis digital hologram is represented by x Carrier frequency of direction; The first original off-axis digital hologram is represented by y The carrier frequency of the direction, Represents background phase information;

[0021] The expression of the first phase-shifted off-axis digital hologram is:

[0022]

[0023] in, and Both represent the first phase-shifted off-axis digital hologram after moving one pixel. Indicates the phase information of the object being measured after phase shift.

[0024] Furthermore, the expression of the first differential hologram is:

[0025]

[0026] in, i Represents an imaginary number.

[0027] Furthermore, the expression of the first complex amplitude result is:

[0028]

[0029] in, p represents the fractional order parameter, represents the fractional Fourier transform operator, represents the inverse fractional Fourier transform operator, represents the horizontal coordinate variable in the fractional domain of the fractional Fourier transform, represents the vertical coordinate variable in the fractional domain of the fractional Fourier transform, Represents a bandpass filtering operation on the fractional domain of the fractional Fourier transform.

[0030] Furthermore, the expression of the second complex amplitude result is:

[0031]

[0032] Furthermore, the complex amplitude information of the object under test after removing the carrier frequency and background information The expression is:

[0033]

[0034] Furthermore, the expression of the phase information of the object being measured is:

[0035]

[0036] in, Represents complex amplitude information The imaginary part of Represents complex amplitude information The real part of .

[0037] An off-axis digital holographic phase reconstruction device using phase-shifted fractional Fourier transform, comprising:

[0038] A first hologram acquisition unit, configured to acquire a first original off-axis digital hologram containing information of the object being measured;

[0039] A first phase shifting unit is configured to shift the first original off-axis digital hologram by one pixel in one direction using a carrier digital phase shifting technique to obtain a first phase-shifted off-axis digital hologram;

[0040] a first differential unit, configured to perform a differential operation on the first original off-axis digital hologram and the first phase-shifted off-axis digital hologram to obtain a first differential hologram without a DC component;

[0041] a first fractional Fourier transform unit, configured to sequentially perform a two-dimensional fractional Fourier transform, bandpass filtering, and a two-dimensional inverse fractional Fourier transform on the first differential hologram to obtain a first complex amplitude result containing real image information;

[0042] A second hologram acquisition unit is used to acquire a second original off-axis digital hologram that does not contain information about the object being measured;

[0043] A second phase shifting unit is used to shift the second original off-axis digital hologram by one pixel in one direction using a carrier digital phase shifting technology to obtain a second phase-shifted off-axis digital hologram;

[0044] a second differential unit, configured to perform a differential operation on the second original off-axis digital hologram and the second phase-shifted off-axis digital hologram to obtain a second differential hologram without a DC component;

[0045] a second fractional Fourier transform unit, configured to sequentially perform a two-dimensional fractional Fourier transform, a bandpass filter, and a two-dimensional inverse fractional Fourier transform on the second differential hologram to obtain a second complex amplitude result containing only carrier information and background information;

[0046] an interference term removal unit, configured to perform a division operation on the first complex amplitude result and the second complex amplitude result to obtain complex amplitude information of the object under test after removing the carrier frequency and background information;

[0047] The phase information calculation unit is used to perform inverse trigonometric function calculation on the complex amplitude information of the measured object after removing the carrier frequency and background information, so as to obtain the phase information of the measured object.

[0048] Compared with the prior art, the present invention can achieve the following beneficial effects:

[0049] This invention uses pixel shifting and differential operations based on spatial carrier phase shifting technology to simply and efficiently remove zero-order terms. Combined with fractional Fourier transform filtering technology, this method selects optimal fractional-order parameters for filtering in the hologram's fractional Fourier transform domain, thereby precisely eliminating the carrier and performing high-resolution reconstruction, achieving single-frame, high-quality reconstruction of the object's phase and amplitude. Without increasing the complexity of the acquisition optical path, this invention eliminates the need for phase compensation, simplifies the calculation process, saves time and space costs, significantly improves the effective bandwidth ratio, achieves higher-resolution reconstruction, and obtains more comprehensive target information. This provides both theoretical and experimental foundations for high-resolution imaging measurement using off-axis digital holography. BRIEF DESCRIPTION OF THE DRAWINGS

[0050] The accompanying drawings, which constitute part of the present invention, are intended to provide a further understanding of the present invention. The exemplary embodiments of the present invention and their descriptions are intended to explain the present invention and do not constitute an undue limitation of the present invention. In the accompanying drawings:

[0051] Figure 1 A schematic flow chart of the off-axis digital holographic phase reconstruction method using phase-shifted fractional Fourier transform according to an embodiment of the present invention;

[0052] Figure 2 Schematic diagram of information distribution in the fractional domain of different p-order fractional Fourier transforms according to an embodiment of the present invention; Figure 2 a, b, c, and d are the spectra of the traditional fractional Fourier transform when the fractional order parameter p is selected as 0.6, 0.7, 0.8, and 0.9 respectively. Figure 2 e, f, g, and h are the frequency spectra of the method of the present invention when the fractional order parameter p is selected as 0.6, 0.7, 0.8, and 0.9 respectively;

[0053] Figure 3 Schematic diagram of experimental results of simulations of different methods described in the embodiments of the present invention; Figure 3 a in the figure is the resolution image simulated by the method proposed in the present invention. Figure 3 b in the figure is the off-axis hologram generated by simulation data. Figure 3 The c in the figure is the spectrum diagram generated by Fourier transform method. Figure 3 d, e, and f in the figure are respectively the phase information recovered by Fourier transform method, the red rectangular area selection, and the phase height profile along the red dotted line in the red area. Figure 3 The g in it is the spectrum diagram generated by the traditional fractional Fourier transform method. Figure 3 Here, h, i, and j are respectively the phase information recovered by the traditional fractional Fourier transform method, the red rectangular area selection, and the phase height profile along the red dotted line in the red area. Figure 3 The k in the figure is the spectrum graph generated by the method proposed in the present invention. Figure 3 Here, l, m, and n are the phase information recovered by Fourier transform method, the red rectangular area selected, and the phase height profile along the red dotted line within the red area. DETAILED DESCRIPTION

[0054] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below with reference to the accompanying drawings and specific embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and do not constitute a limitation of the present invention.

[0055] It should be noted that, in the absence of conflict, the embodiments of the present invention and the features in the embodiments can be combined with each other.

[0056] In the description of the present invention, it should be understood that the terms "center", "longitudinal", "lateral", "up", "down", "front", "back", "left", "right", "vertical", "horizontal", "top", "bottom", "inside", "outside" and the like indicate orientations or positional relationships based on the orientations or positional relationships shown in the accompanying drawings, and are only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore cannot be understood as a limitation on the present invention. In addition, the terms "first", "second" and the like are only used for descriptive purposes and cannot be understood as indicating or implying relative importance or implicitly indicating the number of the indicated technical features. Thus, features defined as "first", "second" and the like may explicitly or implicitly include one or more of the features. In the description of the present invention, unless otherwise specified, "multiple" means two or more.

[0057] In the description of the present invention, it should be noted that, unless otherwise expressly specified or limited, the terms "assemble," "connect," and "connect" should be understood in a broad sense. For example, they can refer to fixed connections, detachable connections, or integral connections; they can refer to mechanical connections or electrical connections; they can refer to direct connections or indirect connections through an intermediate medium; and they can refer to internal connections between two components. Those skilled in the art can understand the specific meanings of the above terms in the present invention based on specific circumstances.

[0058] The present invention will be described in detail below with reference to the accompanying drawings and in combination with embodiments.

[0059] In a first aspect, the present invention provides an off-axis digital holographic phase reconstruction method using phase-shifted fractional Fourier transform, such as Figure 1 As shown, the following steps are included:

[0060] S1: Acquire a first original off-axis digital hologram containing information of the object being measured.

[0061] The first original off-axis digital hologram containing the information of the measured object is simulated using MATLAB, and its expression is:

[0062]

[0063] in, represents the first original off-axis digital hologram, represents the DC component of the first original off-axis digital hologram, represents the modulation term of the interference fringes, Indicates the phase information of the object being measured; The first original off-axis digital hologram is represented by x Carrier frequency of direction; The first original off-axis digital hologram is represented by y The carrier frequency of the direction, Represents background phase information.

[0064] S2: Utilizing carrier digital phase shifting technology, the first original off-axis digital hologram is shifted by one pixel in one direction to obtain a first phase-shifted off-axis digital hologram.

[0065] The off-axis digital hologram is shifted by one pixel in any direction. The present invention takes the x direction as an example for explanation. The carrier digital phase shifting technology is used to shift the first original off-axis digital hologram by one pixel in the x direction to obtain a first phase-shifted off-axis digital hologram with different phase shift amounts. The expression is:

[0066]

[0067] in, and Both represent the first phase-shifted off-axis digital hologram after moving one pixel. Indicates the phase information of the object being measured after phase shift.

[0068] During the phase shift process, the zero-order term (DC component), modulation term, and object phase can be considered as constants that do not change with spatial movement.

[0069] S3: performing a differential operation on the first original off-axis digital hologram and the first phase-shifted off-axis digital hologram to obtain a first differential hologram without a DC component.

[0070] The expression of the first difference hologram is:

[0071]

[0072] in, i Represents an imaginary number.

[0073] Since the 0th order term is a constant term and does not change with spatial movement, the first original off-axis digital hologram and the first phase-shifted off-axis digital hologram with different phase shift amounts By performing the differential operation, the 0th order term can be eliminated, thereby avoiding the interference of the 0th order term on the subsequent phase reconstruction process, and finally obtaining the first differential hologram without DC component. .

[0074] The present invention effectively removes the zero-order term (also known as the 0-order spectrum or DC component) through pixel shift and differential operations of the spatial carrier phase shift technology, and the remaining interference term is used for the subsequent fractional Fourier transform and phase reconstruction process.

[0075] S4: performing two-dimensional fractional Fourier transform, bandpass filtering and two-dimensional inverse fractional Fourier transform on the first differential hologram in sequence to obtain a first complex amplitude result containing real image information.

[0076] Fractional Fourier transform is a generalized form of Fourier transform, and the off-axis hologram after difference I ( x,y ) can be expressed as:

[0077]

[0078]

[0079] in, Represents the kernel function of the two-dimensional fractional Fourier transform, used to define the spatial coordinates To fractional field coordinates The mapping relationship, α represents the rotation angle in the kernel function, j Represents a complex exponential function The imaginary unit in is used to map the real phase transform into the complex domain.

[0080] After performing two-dimensional fractional Fourier transform, bandpass filtering and two-dimensional fractional Fourier inverse transform on the first differential hologram without DC component, the first complex amplitude result containing real image information is obtained. for:

[0081]

[0082] in, p represents the fractional order parameter, represents the fractional Fourier transform operator, represents the inverse fractional Fourier transform operator, represents the horizontal coordinate variable in the fractional domain of the fractional Fourier transform, represents the vertical coordinate variable in the fractional domain of the fractional Fourier transform, Represents a bandpass filtering operation on the fractional domain of the fractional Fourier transform.

[0083] By adjusting the fractional order parameters p , optimize the separation between the real image and the interference components in the fractional domain, so that Can retain target information more efficiently.

[0084] S5: Acquire a second original off-axis digital hologram that does not contain information about the object being measured.

[0085] The second original off-axis digital hologram is obtained by MATLAB simulation. Since the second original off-axis digital hologram does not contain the information of the measured object, it is used as the original reference off-axis digital hologram.

[0086] S6: Utilizing carrier digital phase shifting technology to shift the second original off-axis digital hologram by one pixel in one direction to obtain a second phase-shifted off-axis digital hologram.

[0087] S7: Differentiate the second original off-axis digital hologram and the second phase-shifted off-axis digital hologram to obtain a second differential hologram without a DC component.

[0088] S8: Perform two-dimensional fractional Fourier transform, bandpass filtering and two-dimensional inverse fractional Fourier transform on the second differential hologram in sequence to obtain a second complex amplitude result containing only carrier information and background information.

[0089] The process of steps S6 to S8 refers to steps S2 to S4. After the second differential hologram undergoes two-dimensional fractional Fourier transform, bandpass filtering, and two-dimensional fractional Fourier inverse transform, the second complex amplitude result containing only carrier information and background information is obtained. for:

[0090]

[0091] From the second complex amplitude result, it can be seen that the item containing only the information of the measured object is located in the low-frequency region.

[0092] S9: Divide the first complex amplitude result by the second complex amplitude result to obtain complex amplitude information of the object under test after removing the carrier frequency and background information, and perform inverse trigonometric function calculation on the complex amplitude information to obtain phase information of the object under test.

[0093] Perform division operation on the first complex amplitude result and the second complex amplitude result to obtain the complex amplitude information of the object being measured after removing the carrier frequency and background information. for:

[0094]

[0095] Since the carrier information and background information in the two complex amplitude results are the same or known, these interference items can be effectively eliminated through division operation, thereby extracting the complex amplitude information related only to the object under test itself, which only contains the amplitude and phase information of the object under test.

[0096] Perform inverse trigonometric calculation on the complex amplitude information containing only the amplitude and phase information of the object being measured to obtain the phase information of the object being measured. for:

[0097]

[0098] in, Represents complex amplitude information The imaginary part, that is, the complex amplitude information The amplitude sinusoidal component corresponds to the energy distribution or intensity information of the light wave of the object being measured; Represents complex amplitude information The real part, that is, the complex amplitude information The amplitude cosine component of the optical wave is directly related to the phase delay characteristics of the light wave of the object being measured.

[0099] and The ratio of eliminates the influence of amplitude fluctuation and retains the pure phase difference information. The final result is the optical path difference distribution caused by the measured object.

[0100] The present invention first uses spatial carrier phase shift technology to eliminate the zero-order term, and then uses fractional Fourier transform filtering technology to accurately separate the spectrum, significantly improving the complex amplitude information of the measured object. The signal-to-noise ratio and The calculation is more reliable, thus achieving high-resolution phase reconstruction of the object under test.

[0101] Example 1

[0102] In this embodiment 1, the process of recording the first original off-axis digital hologram is simulated by using MATLAB. The initial parameters are set as follows: the simulated object is a 512 pixel × 512 pixel resolution image. Figure 3 As shown in a in the figure, the sampling interval is 4.8 microns and the wavelength of the laser source is 632.8 nm. The off-axis hologram generated by the simulation data is shown in Figure 3 As shown in b.

[0103] Difference hologram Perform two-dimensional fractional Fourier transform, fractional order parameter selection, bandpass filtering and inverse fractional Fourier transform, and obtain p =0.6, 0.7, 0.8, 0.9 when the corresponding information distribution in the score domain. p The fractional domain information distribution of the order fractional Fourier transform is as follows Figure 2 As shown, adjust p The value of controls the maximum separation effect between the conjugate images in the fractional domain. This effectively adjusts the image in the fractional domain, accurately extracts high-frequency information to a certain extent, and obtains a complex amplitude result containing real image information.

[0104] It should be noted that the smaller the value of p, the larger the overlapping area of ​​the two AC components and the DC component. For the traditional fractional Fourier transform filtering technology, p When the value is 0.6~0.8, the two AC components (+1 order spectrum, i.e. conjugate term) and the DC component will overlap slightly (e.g. Figure 2As shown in a, b, and c in Figure 2), the effect of phase reconstruction will be slightly affected. p When the value is 0.9, the two AC components are completely separated from the DC component (e.g. Figure 2 As shown in d in the figure, no DC component can be extracted.

[0105] The present invention uses the space carrier phase shift technology to eliminate the DC component in advance. p When the value is 0.7, the complex amplitude result containing the real image information can be completely separated from the DC component (such as Figure 2 f in the figure), in p When the values ​​are 0.8 and 0.9, the separation effect becomes better and better. p Another effect of taking 0.9 is that a large-sized bandpass filter can be selected to extract as much information as possible so that the two AC components are not affected by the conjugate term.

[0106] Figure 3 The reconstruction results in

[15] show that due to zero-order interference, both the Fourier transform and traditional fractional Fourier transform methods exhibit significant resolution degradation and carrier crosstalk, resulting in significant information loss. The Fourier transform method has difficulty identifying element 3 of group 6 (6.20μm linewidth), and the traditional fractional Fourier transform method is almost unable to identify element 5 of group 6 (4.92μm linewidth). Compared with the Fourier transform and traditional fractional Fourier transform methods, the proposed method effectively eliminates zero-order interference, maintains high resolution while increasing the bandpass filter size, improves bandwidth utilization, and achieves reconstruction of high-frequency details without carrier artifacts. Clearly, the proposed method improves the resolution of phase information, particularly achieving high-resolution target recognition of element 1 of group 7 (3.91μm linewidth).

[0107] In the second aspect, the present invention provides an off-axis digital holographic phase reconstruction device of phase-shifted fractional Fourier transform, which is used to implement the method steps described in the above embodiment. The explanation based on the same name meaning is the same as the above embodiment, and has the same technical effect as the above embodiment, and will not be repeated here.

[0108] A single-frame phase-shifted off-axis digital holographic phase determination device, comprising:

[0109] A first hologram acquisition unit, configured to acquire a first original off-axis digital hologram containing information of the object being measured;

[0110] A first phase shifting unit is configured to shift the first original off-axis digital hologram by one pixel in one direction using a carrier digital phase shifting technique to obtain a first phase-shifted off-axis digital hologram;

[0111] a first differential unit, configured to perform a differential operation on the first original off-axis digital hologram and the first phase-shifted off-axis digital hologram to obtain a first differential hologram without a DC component;

[0112] a first fractional Fourier transform unit, configured to sequentially perform a two-dimensional fractional Fourier transform, bandpass filtering, and a two-dimensional inverse fractional Fourier transform on the first differential hologram to obtain a first complex amplitude result containing real image information;

[0113] A second hologram acquisition unit is used to acquire a second original off-axis digital hologram that does not contain information about the object being measured;

[0114] A second phase shifting unit is used to shift the second original off-axis digital hologram by one pixel in one direction using a carrier digital phase shifting technology to obtain a second phase-shifted off-axis digital hologram;

[0115] a second differential unit, configured to perform a differential operation on the second original off-axis digital hologram and the second phase-shifted off-axis digital hologram to obtain a second differential hologram without a DC component;

[0116] a second fractional Fourier transform unit, configured to sequentially perform a two-dimensional fractional Fourier transform, a bandpass filter, and a two-dimensional inverse fractional Fourier transform on the second differential hologram to obtain a second complex amplitude result containing only carrier information and background information;

[0117] an interference term removal unit, configured to perform a division operation on the first complex amplitude result and the second complex amplitude result to obtain complex amplitude information of the object under test after removing the carrier frequency and background information;

[0118] The phase information calculation unit is used to perform inverse trigonometric function calculation on the complex amplitude information of the measured object after removing the carrier frequency and background information, so as to obtain the phase information of the measured object.

[0119] It should be understood that the various forms of the processes shown above can be used to reorder, add, or delete steps. For example, the steps described in the present disclosure can be performed in parallel, sequentially, or in a different order, as long as the desired results of the technical solutions disclosed in the present disclosure can be achieved. This is not limited herein.

[0120] The above specific embodiments do not limit the scope of protection of the present invention. Those skilled in the art will appreciate that various modifications, combinations, sub-combinations, and substitutions may be made based on design requirements and other factors. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention are intended to be included within the scope of protection of the present invention.

Claims

1. A phase-shifted fractional Fourier transform off-axis digital holographic phase reconstruction method, characterized in that: The steps include: S1: Acquire a first original off-axis digital hologram containing information of the object being measured; S2: Shifting the first original off-axis digital hologram by one pixel in one direction using a carrier digital phase shifting technique to obtain a first phase-shifted off-axis digital hologram; S3: performing a differential operation on the first original off-axis digital hologram and the first phase-shifted off-axis digital hologram to obtain a first differential hologram without a DC component; S4: performing a two-dimensional fractional Fourier transform, a bandpass filter, and a two-dimensional inverse fractional Fourier transform on the first differential hologram in sequence to obtain a first complex amplitude result containing real image information; S5: Acquire a second original off-axis digital hologram that does not contain information about the object being measured; S6: Shifting the second original off-axis digital hologram by one pixel in one direction using a carrier digital phase shifting technique to obtain a second phase-shifted off-axis digital hologram; S7: performing a differential operation on the second original off-axis digital hologram and the second phase-shifted off-axis digital hologram to obtain a second differential hologram without a DC component; S8: performing a two-dimensional fractional Fourier transform, a bandpass filter, and a two-dimensional inverse fractional Fourier transform on the second differential hologram in sequence to obtain a second complex amplitude result containing only carrier information and background information; S9: Divide the first complex amplitude result by the second complex amplitude result to obtain complex amplitude information of the object under test after removing the carrier frequency and background information, and perform inverse trigonometric function calculation on the complex amplitude information to obtain phase information of the object under test.

2. The off-axis digital holographic phase reconstruction method based on phase-shifted fractional Fourier transform according to claim 1, characterized in that: The expression of the first original off-axis digital hologram is: in, represents the first original off-axis digital hologram, represents the DC component of the first original off-axis digital hologram, represents the modulation term of the interference fringes, Indicates the phase information of the object being measured; The first original off-axis digital hologram is represented by x Carrier frequency of direction; The first original off-axis digital hologram is represented by y The carrier frequency of the direction, Represents background phase information; The expression of the first phase-shifted off-axis digital hologram is: in, and Both represent the first phase-shifted off-axis digital hologram after moving one pixel. Indicates the phase information of the object being measured after phase shift.

3. The off-axis digital holographic phase reconstruction method based on phase-shifted fractional Fourier transform according to claim 2, characterized in that: The expression of the first difference hologram is: in, i Represents an imaginary number.

4. The off-axis digital holographic phase reconstruction method using phase-shifted fractional Fourier transform according to claim 3, characterized in that: The expression of the first complex amplitude result is: in, p represents the fractional order parameter, represents the fractional Fourier transform operator, represents the inverse fractional Fourier transform operator, represents the horizontal coordinate variable in the fractional domain of the fractional Fourier transform, represents the vertical coordinate variable in the fractional domain of the fractional Fourier transform, Represents a bandpass filtering operation on the fractional domain of the fractional Fourier transform.

5. The off-axis digital holographic phase reconstruction method using phase-shifted fractional Fourier transform according to claim 4, characterized in that: The expression of the second complex amplitude result is:

6. The off-axis digital holographic phase reconstruction method using phase-shifted fractional Fourier transform according to claim 5, characterized in that: Complex amplitude information of the object being measured after removing the carrier frequency and background information The expression is:

7. The off-axis digital holographic phase reconstruction method using phase-shifted fractional Fourier transform according to claim 6, characterized in that: The expression of the phase information of the measured object is: in, Represents complex amplitude information The imaginary part of Represents complex amplitude information The real part of .

8. An off-axis digital holographic phase reconstruction device using phase-shifted fractional Fourier transform, characterized in that: include: A first hologram acquisition unit, configured to acquire a first original off-axis digital hologram containing information of the object being measured; A first phase shifting unit is configured to shift the first original off-axis digital hologram by one pixel in one direction using a carrier digital phase shifting technique to obtain a first phase-shifted off-axis digital hologram; a first differential unit, configured to perform a differential operation on the first original off-axis digital hologram and the first phase-shifted off-axis digital hologram to obtain a first differential hologram without a DC component; a first fractional Fourier transform unit, configured to sequentially perform a two-dimensional fractional Fourier transform, bandpass filtering, and a two-dimensional inverse fractional Fourier transform on the first differential hologram to obtain a first complex amplitude result containing real image information; A second hologram acquisition unit is used to acquire a second original off-axis digital hologram that does not contain information about the object being measured; A second phase shifting unit is used to shift the second original off-axis digital hologram by one pixel in one direction using a carrier digital phase shifting technology to obtain a second phase-shifted off-axis digital hologram; a second differential unit, configured to perform a differential operation on the second original off-axis digital hologram and the second phase-shifted off-axis digital hologram to obtain a second differential hologram without a DC component; a second fractional Fourier transform unit, configured to sequentially perform a two-dimensional fractional Fourier transform, a bandpass filter, and a two-dimensional inverse fractional Fourier transform on the second differential hologram to obtain a second complex amplitude result containing only carrier information and background information; an interference term removal unit, configured to perform a division operation on the first complex amplitude result and the second complex amplitude result to obtain complex amplitude information of the object under test after removing the carrier frequency and background information; The phase information calculation unit is used to perform inverse trigonometric function calculation on the complex amplitude information of the measured object after removing the carrier frequency and background information, so as to obtain the phase information of the measured object.

Images