Synchronous rotation encoding single-pixel imaging method for high-speed rotating object and medium

By using a synchronous rotation-coded single-pixel imaging method, the problem of exposure time mismatch in imaging rotating objects is solved, achieving efficient imaging of high-speed rotating objects with significantly improved image quality and speed.

CN115719312BActive Publication Date: 2026-05-22HEFEI UNIV OF TECH
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Patent Information

Authority / Receiving Office
CN · China
Patent Type
Patents(China)
Current Assignee / Owner
HEFEI UNIV OF TECH
Filing Date
2022-11-21
Publication Date
2026-05-22

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Abstract

The application discloses a synchronous rotation encoding single-pixel imaging method for a high-speed rotating object and a medium, and the method comprises the following steps: generating synchronous rotation encoding patterns in sequence; burning the synchronous rotation encoding patterns into a high-speed DMD; when the rotating object rotates counterclockwise by one degree, the high-speed DMD projects a synchronous rotation encoding pattern to the center position of the surface of the rotating object to be measured; then, the light intensity signals reflected by the surface of the rotating object are collected until the synchronous rotation encoding pattern is projected completely; finally, all the collected light intensity signal values are input into a computer, and the image is reconstructed through image recovery program processing. The application can solve the problem of poor image quality of the reconstructed rotating object by using synchronous rotation encoding, and the synchronous rotation encoding pattern suitable for the imaging of the rotating object is designed according to the relationship between the rotating angle of the object and the synchronous rotation encoding pattern by using four-step phase shift Fourier single-pixel imaging technology.
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Description

Technical Field

[0001] This invention relates to the field of single-pixel dynamic imaging technology, specifically to a method and medium for synchronous rotational encoding of single-pixel imaging of high-speed rotating objects. Background Technology

[0002] Current single-pixel imaging technology suffers from a mismatch between the object's rotation period and the exposure time for each illumination mode when imaging rotating objects. This leads to biased experimental data and poor image reconstruction, necessitating a calibration scheme to address this issue. Existing Fourier single-pixel imaging technology, limited by the speed of the spatial light modulator and requiring a large number of encoded patterns to reconstruct the object, results in excessively long image reconstruction times, making it unsuitable for imaging rotating objects.

[0003] In general, current single-pixel imaging technology has a mismatch between the rotation period of the object and the exposure time of each lighting mode when imaging rotating objects.

[0004] Existing Fourier single-pixel imaging technology is limited by the speed of spatial light modulators and requires a large number of encoded patterns to recover objects, resulting in excessively long recovery times for a single image and the inability to image rotating objects. Summary of the Invention

[0005] The present invention proposes a synchronous rotational encoding single-pixel imaging method for high-speed rotating objects, which can at least solve one of the above-mentioned technical problems.

[0006] To achieve the above objectives, the present invention adopts the following technical solution:

[0007] A method for synchronous rotation-coded single-pixel imaging of a high-speed rotating object, comprising:

[0008] First, a series of synchronous rotational coded patterns with a pre-defined sequence are generated by the program. Then, these synchronous rotational coded patterns are burned into a high-speed DMD. Next, when the rotating object rotates counterclockwise by one degree, the high-speed DMD projects a synchronous rotational coded pattern onto the center of the surface of the rotating object under test, ensuring that the modulated signal reflected by the surface of the rotating object contains information about the surface of the rotating object. Then, the light intensity signal reflected from the surface of the rotating object is collected until the synchronous rotational coded pattern is completely projected. Finally, all the collected light intensity signal values ​​are input into a computer and processed by an image restoration program to reconstruct the image of the rotating object.

[0009] Furthermore, the step of pre-generating a series of synchronized rotational coding patterns in a predetermined order specifically includes generating a series of synchronized rotational coding patterns in a predetermined order through a program. The synchronized rotational coding patterns are generated based on four-step phase shifts and the rotation angle of the object, and the generation formula is as follows:

[0010]

[0011] Where P(x,y;f,θ) is the preset synchronous rotation coding pattern, A is the average light intensity, B is the contrast, x and y are the coordinates of the target object, f is the Fourier frequency of the preset synchronous rotation coding pattern, θ is the rotation angle of the target object, indicating that when the object rotates by an angle θ, the preset synchronous rotation coding pattern corresponding to that angle will be projected onto the object surface; f x =fsinθ,f y = fcosθ, where f x Let f be the transverse component frequency, f y Let f be the longitudinal component frequency; the four-step phase shift values ​​φ = 0, π / 2, π, 3π / 2.

[0012] Furthermore, the step of burning these synchronous rotational coded patterns into the high-speed DMD specifically includes the first step of designing and building an optical experimental system, with the computer connected to the high-speed DMD, acquisition card 1, and acquisition card 2 respectively; acquisition card 1 is connected to the stepper motor, the high-speed DMD, and acquisition card 2 respectively; acquisition card 2 is connected to a single-pixel detector to collect light intensity signals; acquisition card 1 only outputs, and acquisition card 2 only inputs.

[0013] The second step is to burn the pre-generated synchronous rotational encoding pattern into the high-speed DMD via a computer connected to the high-speed DMD.

[0014] Furthermore, the high-speed DMD projecting a synchronous rotational coded pattern onto the center of the surface of the rotating object under test specifically includes the following steps: the acquisition card 1 is controlled by a LabVIEW program to first trigger the stepper motor to rotate, then trigger the high-speed DMD to project the pattern, and then trigger the acquisition card 2 to collect the signal from the single-pixel detector. These three steps are performed in a sequential cycle. When the stepper motor rotates counterclockwise by one degree, the high-speed DMD projects a synchronous rotational coded pattern onto the center of the surface of the rotating object under test, and then the acquisition card 2 collects the light intensity signal reflected by the rotating object under test at this time from the single-pixel detector.

[0015] Furthermore, the process of acquiring the light intensity signal reflected from the surface of the rotating object until the synchronously rotating coded pattern is fully projected specifically includes:

[0016] The reflected light intensity signal is collected. For every one degree the rotating object under test rotates counterclockwise, the acquisition card 2 collects the light intensity signal diffusely reflected from the surface of the object under test by the synchronously rotating coded pattern. This signal is collected by a single-pixel detector. The light intensity signal collected by the single-pixel detector is converted into a voltage value, which is then used to determine the Fourier spectrum information of the rotating object under test.

[0017] The voltage value of the reflected light intensity signal is determined by the following formula:

[0018] D i =D n +α·R i

[0019] Among them, D i D is the voltage value converted from the acquired light intensity signal. n α is the voltage value converted from ambient light intensity, and i = 1, 2, 3, 4.

[0020] Furthermore, the reconstructed image of the rotating object specifically includes,

[0021] The collected light intensity signal voltage values ​​were imported into a computer and processed using an image restoration program.

[0022] The first step is to determine the Fourier spectrum information of the rotating object under test. Based on the collected experimental data, we know that:

[0023] C(f,θ)=P×I=[D1-D3]+j·[D2-D4]

[0024] Where C is the Fourier spectrum of the rotating object to be measured, I is the rotating object to be measured, and j is the imaginary unit;

[0025] The second step involves reconstructing the image of the rotating object based on its determined Fourier spectrum information. The calculation formula is as follows:

[0026] I(x,y)=F -1 {C(f,θ)}

[0027] Where I(x,y) is the reconstructed image of the rotating object, and F -1 It is a two-dimensional inverse Fourier transform.

[0028] In another aspect, the present invention also discloses a computer-readable storage medium storing a computer program, which, when executed by a processor, causes the processor to perform the steps of the method described above.

[0029] As can be seen from the above technical solution, the synchronous rotation encoding single-pixel imaging method for high-speed rotating objects of the present invention can solve the problem that the existing Fourier single-pixel imaging technology cannot image rotating objects. By using the synchronous rotation encoding method, the period of the rotating scene is matched with the exposure time of each lighting mode, so that low-speed rotating objects can be imaged, and even high-speed rotating objects can be imaged.

[0030] In summary, the synchronous rotational coding single-pixel imaging method for high-speed rotating objects of the present invention addresses the limitations of existing Fourier single-pixel imaging technology, which requires excessive time to recover an image due to the speed limitation of the spatial light modulator and the need for a large number of coded patterns to recover the object, thus failing to image rotating objects. The present invention, by combining Fourier single-pixel imaging with synchronous rotational coding, solves the problem of mismatch between the object's rotation period and the exposure time of each illumination mode, thereby achieving imaging of high-speed rotating objects.

[0031] This invention utilizes four-step phase-shift Fourier single-pixel imaging technology to design a synchronous rotation coding pattern suitable for imaging rotating objects based on the relationship between the object's rotation angle and the coding pattern.

[0032] This invention eliminates the need for calibration schemes to improve image reconstruction quality; it solves the problem of poor image quality in reconstructed images of rotating objects through synchronous rotation encoding. Novelly, this invention proposes projecting a synchronous rotation encoding pattern when the rotating object rotates one degree counterclockwise, followed by the acquisition of reflected light intensity signals. These three steps are performed sequentially and cyclically.

[0033] Experiments in this invention demonstrate that the synchronous rotation-coded single-pixel imaging method can recover rotating objects at speeds up to 422.0 rpm. Theoretically, higher rotation speeds result in shorter imaging times, thus leading to better image quality compared to lower speeds. This is a significant advantage of the method described in this invention compared to traditional SPI methods, which are typically highly susceptible to object motion.

[0034] The method proposed in this invention has significant application value for detection under conditions such as high-speed rotation of aircraft engine blades. Theoretically, the faster the rotation speed, the shorter the time required to reconstruct the image and the higher the image quality, which is a significant advantage over methods such as high-speed cameras. Attached Figure Description

[0035] Figure 1 This is a flowchart of the method of the present invention;

[0036] Figure 2 This is an example of an encoded pattern generated by synchronous rotation encoding according to an embodiment of the present invention;

[0037] Figure 3 This is a diagram of the optical experimental system architecture according to an embodiment of the present invention;

[0038] Figure 4 This is a reconstruction result of a rotating object recovered at a rotational speed of 104.6 rpm according to an embodiment of the present invention;

[0039] Figure 5 This is the reconstruction result of the rotating object recovered at a rotational speed of 422.0 rpm according to an embodiment of the present invention. Detailed Implementation

[0040] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are some embodiments of the present invention, but not all embodiments.

[0041] like Figure 1 As shown in the figure, the synchronous rotation-coded single-pixel imaging method for high-speed rotating objects described in this embodiment is implemented in the following steps:

[0042] First, a series of synchronous rotational coded patterns with a pre-defined sequence are generated by the program. Then, these synchronous rotational coded patterns are burned into a high-speed DMD. Next, when the rotating object rotates counterclockwise by one degree, the high-speed DMD projects a synchronous rotational coded pattern onto the center of the surface of the rotating object under test, ensuring that the modulated signal reflected by the surface of the rotating object contains information about the surface of the rotating object. Then, the light intensity signal reflected from the surface of the rotating object is collected until the synchronous rotational coded pattern is completely projected. Finally, all the collected light intensity signal values ​​are input into a computer and processed by an image restoration program to reconstruct the image of the rotating object.

[0043] like Figure 1 As shown, the present invention is specifically divided into four stages: synchronous rotational coding pattern generation; synchronous rotational coding pattern burning into high-speed DMD; high-speed DMD projection; acquisition of reflected light intensity signals; and reconstruction of rotating object image.

[0044] 1. Synchronous Rotation Encoding Pattern Generation: A series of synchronous rotation encoding patterns in a pre-defined order are generated programmatically. These patterns are generated based on four phase shifts and the object's rotation angle. The generation formula is as follows:

[0045]

[0046] Where P(x,y;f,θ) is the preset synchronous rotation coding pattern, A is the average light intensity, B is the contrast, x and y are the coordinates of the target object, f is the Fourier frequency of the preset synchronous rotation coding pattern, θ is the rotation angle of the target object, indicating that when the object rotates by an angle θ, the preset synchronous rotation coding pattern corresponding to that angle will be projected onto the object surface; f x =fsinθ,f y = fcosθ, where f x Let f be the transverse component frequency, f y Let f be the longitudinal component frequency; the four-step phase shift values ​​φ = 0, π / 2, π, 3π / 2.

[0047] Existing Fourier single-pixel technology is based on Generate a series of coded patterns P(x,y), the generation order of which is fixed by f for each coded pattern. x and f y Decision. The angle between the direction of the stripes on the coded pattern and the vertical position is... Rotate counterclockwise by θ until the stripes are vertical. The rotating object under test is rotated counterclockwise by θ to ensure that the modulation information reflected from its surface remains unchanged after rotation. P(x,y) is rotated counterclockwise by θ to obtain the rotated coded pattern for each degree (unit: 1°) within the rotation range of 0° to 180° or 0° to 359°. Degrees without coded patterns are filled with black coded patterns. The number of coded patterns obtained at each rotation degree varies. One coded pattern is taken for each degree starting from 0° (cyclically from 0° to 359°) until all coded patterns for a certain rotation degree are taken. The series of rotated coded patterns are then internally tangented using bilinear interpolation to better adapt to the rotational motion of the object under test.

[0048] The above describes the synchronous rotation encoding process, such as... Figure 2 This is an example of the encoded pattern generated by the synchronous rotation encoding of the present invention.

[0049] 2. To synchronously spin-encode patterns into a high-speed DMD, the first step is to design and build an optical experimental system, such as... Figure 3 As shown, the computer is connected to a high-speed DMD, acquisition card 1, and acquisition card 2 respectively; acquisition card 1 is connected to a stepper motor, a high-speed DMD, and acquisition card 2 respectively; acquisition card 2 is connected to a single-pixel detector, which is used to acquire light intensity signals.

[0050] Using two acquisition cards is to enable one acquisition card to output and the other two to input, thereby improving the efficiency of the acquisition cards.

[0051] The second step is to burn the pre-generated synchronous rotational encoding pattern into the high-speed DMD via a computer connected to the high-speed DMD.

[0052] 3. High-speed DMD projection; the target objects used in the experiment are attached to... Figure 3 The experiment begins with a LabVIEW program controlling acquisition card 1 to first trigger the stepper motor to rotate, then trigger the high-speed DMD to project an image, and then trigger acquisition card 2 to acquire the signal from the single-pixel detector. These three steps are performed sequentially in a loop. For every degree the stepper motor rotates counter-clockwise, the high-speed DMD projects a synchronously rotating coded pattern onto the center of the surface of the rotating object under test. Then, acquisition card 2 acquires the light intensity signal reflected from the rotating object at that moment, collected by the single-pixel detector.

[0053] 4. Acquire the reflected light intensity signal. For every one degree the rotating object under test rotates counterclockwise, acquisition card 2 acquires the light intensity signal diffusely reflected from the surface of the object by the synchronously rotating coded pattern, which is then collected by a single-pixel detector. The light intensity signal acquired by the single-pixel detector is converted into a voltage value, which is then used to determine the Fourier spectrum information of the rotating object under test.

[0054] The voltage value of the reflected light intensity signal is determined by the following formula:

[0055] D i =D n +α·R i

[0056] Among them, D i D is the voltage value converted from the acquired light intensity signal. n α is the voltage value converted from ambient light intensity, and i = 1, 2, 3, 4.

[0057] 5. Reconstruct the image of the rotating object, import the experimental data of light intensity signal voltage values ​​collected into the computer, and process them through an image restoration program.

[0058] The first step is to determine the Fourier spectrum information of the rotating object under test. Based on the collected experimental data, we know that:

[0059] C(f,θ)=P×I=[D1-D3]+j·[D2-D4]

[0060] Where C is the Fourier spectrum of the rotating object to be tested, I is the rotating object to be tested, and j is the imaginary unit.

[0061] The second step involves reconstructing the image of the rotating object based on its determined Fourier spectrum information. The calculation formula is as follows:

[0062] I(x,y)=F -1 {C(f,θ)}

[0063] Where I(x,y) is the reconstructed image of the rotating object, and F -1 It is a two-dimensional inverse Fourier transform.

[0064] like Figure 4 The image shows the reconstruction result of the rotating object recovered at a rotational speed of 104.6 rpm in this invention; as shown... Figure 5 The image shown is the reconstruction result of the rotating object recovered at a rotational speed of 422.0 rpm in this invention. The reconstructed image size is 128×128, and all experiments were conducted at a sampling rate of 27.47%. Figure 4 and Figure 5It can be seen that the synchronous rotation encoding single-pixel imaging method in this invention can image objects in a high-speed rotating state.

[0065] Experiments in this invention demonstrate that the synchronous rotation-coded single-pixel imaging method can recover rotating objects at speeds up to 422.0 rpm. Theoretically, higher rotation speeds result in shorter imaging times, thus leading to better image quality compared to lower speeds. This is a significant advantage of the method described in this invention compared to traditional SPI methods, which are typically highly susceptible to object motion.

[0066] In this embodiment of the invention, the high-speed DMD can be replaced by various spatial light modulators such as projectors, LCDs, and DMDs to modulate the projection pattern; the single-pixel detector can be replaced by optoelectronic devices such as photocells and photodiodes that can linearly respond to light intensity information; the stepper motor can be replaced by other devices with similar functions to stepper motors; LabVIEW program control can be replaced by microcontrollers and FPGA development boards for control operations; when encoding the target image using projection patterns, it can be based on Fourier transform, cosine transform, Hadamard transform, Radon transform, etc.

[0067] In another aspect, the present invention also discloses a computer-readable storage medium storing a computer program, which, when executed by a processor, causes the processor to perform the steps of any of the methods described above.

[0068] In another aspect, the present invention also discloses a computer device, including a memory and a processor, wherein the memory stores a computer program, and when the computer program is executed by the processor, the processor performs the steps of any of the methods described above.

[0069] In another embodiment provided in this application, a computer program product containing instructions is also provided, which, when run on a computer, causes the computer to perform the steps of any of the methods described in the above embodiments.

[0070] It is understood that the system provided in the embodiments of the present invention corresponds to the method provided in the embodiments of the present invention, and the explanation, examples and beneficial effects of the relevant content can be referred to the corresponding parts of the above methods.

[0071] Those skilled in the art will understand that all or part of the processes in the above embodiments can be implemented by a computer program instructing related hardware. The program can be stored in a non-volatile computer-readable storage medium, and when executed, it can include the processes of the embodiments described above. Any references to memory, storage, databases, or other media used in the embodiments provided in this application can include non-volatile and / or volatile memory. Non-volatile memory can include read-only memory (ROM), programmable ROM (PROM), electrically programmable ROM (EPROM), electrically erasable programmable ROM (EEPROM), or flash memory. Volatile memory can include random access memory (RAM) or external cache memory. By way of illustration and not limitation, RAM is available in various forms, such as static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), dual data rate SDRAM (DDRSDRAM), enhanced SDRAM (ESDRAM), synchronous link DRAM (SLDRAM), RAMbus direct RAM (RDRAM), direct memory bus dynamic RAM (DRDRAM), and RAMbus dynamic RAM (RDRAM), etc.

[0072] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0073] The above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit it. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for synchronous rotation-coded single-pixel imaging of a high-speed rotating object, characterized in that, Includes the following steps, First, a series of synchronous rotational encoding patterns with a pre-set sequence are generated by the program; then, these synchronous rotational encoding patterns are burned into the high-speed DMD; then, when the rotating object rotates counterclockwise by one degree, the high-speed DMD projects a synchronous rotational encoding pattern onto the center position of the surface of the rotating object under test, ensuring that the modulation signal reflected by the surface of the rotating object under test contains the surface information of the rotating object under test. Next, the light intensity signal reflected from the surface of the rotating object is collected until the synchronous rotation coded pattern is fully projected; finally, all the collected light intensity signal values ​​are input into the computer and processed by the image restoration program to reconstruct the image of the rotating object. The synchronous rotation coding pattern is generated based on four phase shifts and the object's rotation angle. The generation formula is as follows: in A preset synchronous rotation encoding pattern is used, where A is the average light intensity, B is the contrast, and x and y are the coordinates of the target object. The Fourier frequency of the preset synchronous rotation coding pattern is θ; θ is the rotation angle of the target object, indicating that when the object rotates by an angle of θ, the preset synchronous rotation coding pattern corresponding to that angle will be projected onto the object surface. = , = In the formula for transverse component frequency, for Longitudinal component frequency; four-step phase shift value =0, π / 2, π, 3π / 2.

2. The synchronous rotation-coded single-pixel imaging method for high-speed rotating objects according to claim 1, characterized in that: Fourier single-pixel technology based on Generate a series of coded patterns The generation order is fixed for each coded pattern. and The angle between the direction of the stripes on the coded pattern and the vertical position is determined. , Rotate counterclockwise by θ until the stripes are vertical; rotate the rotating object to be measured counterclockwise. This ensures that the modulation information reflected from the surface of the rotated coded pattern remains unchanged; Rotate counterclockwise The process yields the coded pattern for each degree of rotation from 0° to 180° or from 0° to 359°. Degrees without coded patterns are filled with black coded patterns. The number of coded patterns obtained at each rotation degree varies. Starting from 0°, one coded pattern is taken for each degree, i.e., 0° to 359° are taken in a cyclic manner until all coded patterns at a certain rotation degree are taken. The series of coded patterns after rotation are internally tangent using bilinear interpolation to better adapt to the rotational motion of the object under test.

3. The synchronous rotation-coded single-pixel imaging method for high-speed rotating objects according to claim 1, characterized in that: The process of burning these synchronous rotational coded patterns into the high-speed DMD specifically includes: The first step is to design and build an optical experimental system. The computer is connected to a high-speed DMD, acquisition card 1, and acquisition card 2. Acquisition card 1 is connected to a stepper motor, a high-speed DMD, and acquisition card 2. Acquisition card 2 is connected to a single-pixel detector to collect light intensity signals. Acquisition card 1 is for output only, and acquisition card 2 is for input only. The second step is to burn the pre-generated synchronous rotational encoding pattern into the high-speed DMD via a computer connected to the high-speed DMD.

4. The synchronous rotation-coded single-pixel imaging method for high-speed rotating objects according to claim 3, characterized in that: The high-speed DMD projects a synchronous rotational coded pattern onto the center of the surface of the rotating object under test, specifically including... The LabVIEW program controls the acquisition card 1 to first trigger the stepper motor to rotate, then trigger the high-speed DMD to project an image, and then trigger the acquisition card 2 to collect the signal from the single pixel detector. The three steps are performed in this order. When the stepper motor rotates counterclockwise by one degree, the high-speed DMD projects a synchronous rotating coded pattern onto the center position of the surface of the rotating object under test. Then the acquisition card 2 collects the light intensity signal reflected by the rotating object under test at this time from the single pixel detector.

5. The synchronous rotation-coded single-pixel imaging method for high-speed rotating objects according to claim 4, characterized in that: The process of collecting the light intensity signal reflected from the surface of the rotating object, until the synchronously rotating coded pattern is fully projected, specifically includes: The reflected light intensity signal is collected. For every one degree the rotating object under test rotates counterclockwise, the acquisition card 2 collects the light intensity signal diffusely reflected from the surface of the object under test by the synchronously rotating coded pattern. This signal is collected by a single-pixel detector. The light intensity signal collected by the single-pixel detector is converted into a voltage value, which is then used to determine the Fourier spectrum information of the rotating object under test. The voltage value of the reflected light intensity signal is determined by the following formula: Among them, D i D is the voltage value converted from the acquired light intensity signal. n α is the voltage value converted from ambient light intensity, and i = 1, 2, 3, 4 is the coefficient for converting photoelectric signal into voltage value.

6. The synchronous rotation-coded single-pixel imaging method for high-speed rotating objects according to claim 4, characterized in that: The reconstructed image of the rotating object specifically includes, The collected light intensity signal voltage values ​​were imported into a computer and processed using an image restoration program. The first step is to determine the Fourier spectrum information of the rotating object under test. Based on the collected experimental data, we know that: Where C is the Fourier spectrum of the rotating object under test. The rotating object to be tested The imaginary unit; The second step involves reconstructing the image of the rotating object based on its determined Fourier spectrum information. The calculation formula is as follows: in, For reconstructing images of rotating objects, It is a two-dimensional inverse Fourier transform.

7. A computer-readable storage medium storing a computer program that, when executed by a processor, causes the processor to perform the steps of the method as claimed in any one of claims 1 to 6.