In-plane multi-point parallel vibration measurement device and method based on array single photon detection

Abstract

The invention provides an in-plane multi-point parallel vibration measurement device and method based on array single-photon detection, and relates to the field of laser measurement, and the in-plane multi-point parallel vibration measurement device comprises a laser, a transmitting optical system, a receiving optical imaging system, an array single-photon detector, an array single-photon counter and a data processing module. A laser beam output by the laser is converted into a parallel coherent light beam by the emission optical system, the light beam is reflected after irradiating a target object, and the reflected light beam is imaged on the array single-photon detector by the receiving optical imaging system; the array single-photon detector converts reflected light intensity into electric signals and inputs the electric signals into the data processing module, and the data processing module calculates in-plane multi-point parallel vibration frequency information of the target object. Vibration information of a long-distance in-plane multi-point parallel target is imaged to a focal plane of an imaging optical system in a non-contact mode, and in-plane multi-point parallel vibration frequency information of the target object is acquired and calculated by a data processing module.

Description

Technical Field

[0001] This invention belongs to the field of laser measurement system technology, and particularly relates to an in-plane multi-point parallel vibration measurement device and method based on array single-photon detection. Background Technology

[0002] Existing laser vibrometric techniques are limited by their detection mechanisms, making it difficult to achieve vibration measurements over hundreds of meters or even kilometers, let alone long-distance (kilometer-scale) multi-point parallel vibration measurements. Multi-point parallel vibration measurements require simultaneous measurement of the vibration frequencies of multiple different vibrating objects. Coherent laser vibrometrics primarily uses laser light to reflect vibration frequencies as changes in phase difference through displacement, ultimately calculating vibration information by detecting changes in light intensity. This method requires power matching between the probe and reference beams, and is therefore mostly used for cooperative target measurements to ensure echo intensity matching with the reference beam. For non-cooperative target measurements, the measurement distance is limited due to weak echo intensity. Furthermore, existing laser vibrometric techniques are mainly single-point vibration measurement technologies. Vibration measurements using incoherent methods are also limited by echo intensity, making long-distance, in-plane multi-point parallel vibration measurements impossible.

[0003] Chinese invention patent publication CN112180392A discloses an atmospheric composition detection lidar based on dispersion gating. This lidar stretches femtosecond laser light into a wide-pulse laser in the time domain through dispersion. The femtosecond spectrum is mapped onto the broadened laser pulse due to group velocity dispersion. After time-domain gating by an intensity modulator, a preset wavelength of laser light is selected. The laser wavelength is scanned by adjusting the delay of the electrical drive signal of the intensity modulator. By scanning the laser wavelength, the absorption spectrum of specific atmospheric components is obtained, thereby measuring the concentration of atmospheric gas components. This atmospheric composition detection lidar can accurately gating any wavelength of the emitted laser light, with high wavelength selection accuracy. Furthermore, by adjusting the center wavelength of the filter, it can achieve scanning and detection of multiple gases.

[0004] Chinese invention patent publication CN119354922A discloses an oral bioimaging device based on quantum entangled phase. This invention utilizes a continuous laser-pumped nonlinear waveguide to generate energy-time entangled photon pairs. Signal photons and idler photons are separated by an optical filter. The oral biosample to be tested is placed in an unbalanced interferometer. By measuring the Franson interference between the signal and idler photons with and without a biosample, two interference curves with different phases are obtained, and the entangled phase difference is calculated. The position of the sample is changed by an in-plane multi-point parallel scanning platform, and Franson interference is performed to obtain the entangled phase difference at different positions. These phase differences are combined to obtain a quantum phase image of the sample. This invention has advantages such as miniaturization, integration, and practicality, opening up new avenues for the development of quantum precision measurement and life sciences.

[0005] Single-photon detection technology is a photon-level high-sensitivity detection technology. Compared with traditional photodetectors, its sensitivity is three orders of magnitude higher, enabling the extraction of weak light signals over long distances. Combined with single-photon counting technology, it can achieve linear equivalence of light intensity and finally calculate the light intensity information. By combining arrayed single-photon detectors with arrayed single-photon counters, it is possible to achieve in-plane multi-point parallel vibration measurement of non-cooperative target objects at long distances.

[0006] How to use single-photon detection technology to precisely measure the parallel vibrations of multiple points in a plane at a distance from a non-cooperative target object is an important development direction for single-photon detection technology. Summary of the Invention

[0007] To solve the above-mentioned technical problems, the first aspect of the present invention proposes an in-plane multi-point parallel vibration measurement device based on array single-photon detection, the in-plane multi-point parallel vibration measurement device comprising: a laser, a transmitting optical system, a receiving optical imaging system, an array single-photon detector, an array single-photon counter, and a data processing module; The single-photon detection band laser beam output by the laser is transformed into a parallel coherent beam by the transmitting optical system. After the parallel coherent beam illuminates the target object, it is reflected by the target object. The reflected beam is imaged onto the array single-photon detector by the receiving optical imaging system. The array single-photon detector converts the light intensity information of the received reflected beam into an electrical signal. The electrical signal is input to the data processing module. The data processing module calculates the in-plane parallel vibration frequency information of the target object based on the input electrical signal.

[0008] As described in the first aspect of the present invention, the in-plane multi-point parallel vibration measurement device, wherein the emitting optical system is a beam expanding and collimating system, including multiple lenses and / or mirrors, wherein the emitting optical system receives laser light generated by a laser and such that the size of the laser beam output by the emitting optical system is greater than or equal to the surface size of the array single-photon detector, so as to completely cover the array single-photon detector.

[0009] As described in the first aspect of the present invention, the in-plane multi-point parallel vibration measurement device, wherein the laser is a pulsed laser or a continuous laser.

[0010] As described in the first aspect of the present invention, the in-plane multi-point parallel vibration measurement device, wherein the transmitting optical system is constructed as either a coaxial transceiver optical system or a non-coaxial transceiver optical system; The receiving imaging optical system is constructed as either a coaxial transceiver optical system or a non-coaxial transceiver optical system.

[0011] As described in the first aspect of the present invention, the in-plane multi-point parallel vibration measuring device is equipped with a receiving optical imaging system capable of receiving the reflected light from the entire surface of the target object and imaging the reflected light from the target object onto the focal plane of the receiving optical imaging system. The array of single-photon detectors is positioned at the focal plane of the receiving optical imaging system to receive data information carried by the reflected light from the target object.

[0012] As described in the first aspect of the present invention, in the in-plane multi-point parallel vibration measurement device, the electrical signal output by the array single-photon detector is provided to the array single-photon counter. The corresponding electrical signal is generated by the array single-photon counter into counting data and then input into the data processing module. The data processing module calculates and outputs the vibration frequency corresponding to each pixel of the target object.

[0013] A second aspect of the present invention provides an in-plane multi-point parallel vibration measurement method based on array single-photon detection, for operating the in-plane multi-point parallel vibration measurement device based on array single-photon detection described in any of the above claims, the method comprising the following steps: Step 1: The laser, which serves as the test light source, emits a laser of a specified wavelength. The laser beam is expanded and collimated by the emitting optical system and then irradiates the surface of the target object. Step 2: The laser light reflected from the surface of the target object is mapped onto the focal plane of the imaging optical system by the receiving optical imaging system; Step 3: The array single-photon detector converts the weak light signals corresponding to multiple parallel spaces within the surface of the target object into electrical signals and sends them to the array single-photon counter. Step 4: The array single-photon counter and data processing module process and calculate the electrical signal in the spatial and temporal domains to generate and output the in-plane multi-point parallel vibration information of the target object.

[0014] As described in the second aspect of the present invention, in the in-plane multi-point parallel vibration measurement method, step 3 includes: the array single-photon detector converts the received light intensity information into electrical signals according to each corresponding pixel point, and inputs them into the corresponding positions on the array single-photon counter.

[0015] As described in the second aspect of the present invention, in the in-plane multi-point parallel vibration measurement method, step 4 includes the following sub-steps: Step 4.1: The array single-photon counter timestamps the electrical signal corresponding to each pixel and inputs it into the data processing module; Step 4.2: The data processing module performs time-domain statistics on the timestamps of the photon counts corresponding to each pixel and performs photon count rate statistics at equal intervals. Step 4.3: The data processing module performs a Fast Fourier Transform (FFT) on the time series of photon count rate to obtain the frequency domain representation of the electrical signal, and calculates the vibration frequency and vibration amplitude information corresponding to each pixel of the multi-point parallel vibration target object in the surface from the frequency domain representation of the electrical signal.

[0016] As described in the second aspect of the present invention, the in-plane multi-point parallel vibration measurement method further includes the following sub-steps in step 4.2: The photon count rate follows the formula below; Where N ij (t) represents the photon count value at the i-th horizontal and j-th vertical point corresponding to time t. ij f is the amplitude. ij The vibration frequency, Let be the average photon count rate at the i-th point in the horizontal direction and the j-th point in the vertical direction.

[0017] The method of this invention relates to an in-plane multi-point parallel vibration measurement device and method based on array single-photon detection. It combines an array single-photon detector and an imaging optical system to non-contactly image the vibration information of a distant in-plane multi-point parallel target onto the array single-photon detector located at the focal plane of the imaging optical system. The array single-photon counter timestamps the electrical signal corresponding to each pixel and inputs it into the data processing module. The data processing module performs statistical analysis on the timestamps of the photon counts corresponding to each pixel in the time domain. Through the array single-photon detector, the array single-photon counter, and the data processing module, the in-plane multi-point parallel vibration frequency information of the target object is finally detected, collected, and calculated. Attached Figure Description

[0018] Figure 1 This is a block diagram of the in-plane multi-point parallel vibration measurement device based on array single-photon detection proposed in this invention. Figure 2 This is a schematic diagram of the principle of multi-point parallel vibration measurement in the plane based on array single-photon detection proposed in this invention. Detailed Implementation

[0019] To achieve in-plane multi-point parallel vibration measurement of a distant, non-cooperative target object, this invention proposes an in-plane multi-point parallel vibration measurement device and method based on array single-photon detection. The system uses an optical imaging system to map the in-plane multi-point parallel vibration information of the target object onto an array single-photon detector, converting it into an electrical signal. Then, through an array single-photon counter and a data processing module, the photon count rate is statistically calculated and the in-plane multi-point parallel light intensity change of the target object is equivalently solved, and finally the in-plane multi-point parallel vibration frequency is calculated.

[0020] The specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings.

[0021] Example 1 This invention aims to achieve in-plane multi-point parallel vibration measurement of distant, non-cooperative target objects. It proposes an in-plane multi-point parallel vibration measurement device and method based on array single-photon detection. The system uses an optical imaging system to map the in-plane multi-point parallel vibration information of the target object onto an array single-photon detector and convert it into an electrical signal. Then, through an array single-photon counter and a data processing module, the photon count rate is statistically calculated and the in-plane multi-point parallel light intensity change of the target object is equivalently solved. Finally, the in-plane multi-point parallel vibration frequency is calculated.

[0022] The specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings.

[0023] Example 1 As attached Figure 1 As shown, this invention provides an in-plane multi-point parallel vibration measurement device based on array single-photon detection. The first aspect of the present invention proposes an in-plane multi-point parallel vibration measurement device based on array single-photon detection, the in-plane multi-point parallel vibration measurement device comprising: a laser, a transmitting optical system, a receiving optical imaging system, an array single-photon detector, an array single-photon counter, and a data processing module; The single-photon detection band laser beam output by the laser is transformed into a parallel coherent beam by the transmitting optical system. After the parallel coherent beam illuminates the target object, it is reflected by the target object. The reflected beam is imaged onto the array single-photon detector by the receiving optical imaging system. The array single-photon detector converts the light intensity information of the received reflected beam into an electrical signal. The electrical signal is input to the data processing module. The data processing module calculates the in-plane parallel vibration frequency information of the target object based on the input electrical signal.

[0024] As described in the first aspect of the present invention, the in-plane multi-point parallel vibration measurement device, wherein the emitting optical system is a beam expanding and collimating system, including multiple lenses and / or mirrors, wherein the emitting optical system receives laser light generated by a laser and such that the size of the laser beam output by the emitting optical system is greater than or equal to the surface size of the array single-photon detector, so as to completely cover the array single-photon detector.

[0025] The laser can be a pulsed laser or a continuous-wave laser. Using a continuous-wave laser offers advantages such as easier optical path fabrication, enabling longer-term, comprehensive illumination of multiple parallel targets within an area, and obtaining reflected light information from the detected targets. Because the reflected light information is a continuous light reflection signal, uniform average light reflection information can be obtained, easily filtering out atmospheric interference. However, the peak energy of a continuous-wave laser is lower than that of a pulsed laser, resulting in significantly shorter detection distance and lower energy consumption. Most continuous-wave lasers use a combination of concave and convex lenses to construct the laser beam expanding and collimating system. This transmissive emission optical system has a relatively large overall volume, and the glass or quartz lenses are also quite heavy. Furthermore, the lens dispersion at a specific wavelength of laser light must be considered, and double-sided optical coatings on the lens body are necessary to avoid increasing optical losses and reducing the detection distance for multiple parallel targets within an area.

[0026] Pulsed lasers, especially high-energy short-pulse lasers with pulse widths below milliseconds, have very high peak power. A typical laser beam expanding and collimating system uses concave and convex mirrors. This type of reflective beam expanding and collimating system only needs to consider the temperature characteristics of the reflective coating and its ability to withstand strong laser light. Reflective beam expanding and collimating systems usually have a short length along the optical axis, and the mirrors can be made of materials such as metal. The precision machining and polishing coating of metal materials are less expensive than glass lenses, offer better heat dissipation, are easier to install, and have much lower reflection loss than transmitted light loss. The position of the beam corner point or focal plane can be precisely set. Using a pulsed laser to provide comprehensive illumination of multiple parallel targets within an area results in higher measurement accuracy and a longer range.

[0027] The light beam reflected by the target object needs to pass through an optical imaging system to image the single beam reflected by the target object onto an array of single-photon detectors located on the focal plane of the optical imaging system. The array of single-photon detectors images the parallel vibration information of multiple points in the target object onto the array of single-photon detectors. The array of single-photon detectors converts the received light intensity information into electrical signals for each corresponding pixel and inputs them into the corresponding positions of the array of single-photon counters. The array of single-photon counters timestamp the electrical signals corresponding to each pixel and input them into the data processing module. The data processing module counts the timestamps of the photon counts corresponding to each pixel in the time domain and counts the photon count rate at equal intervals. The photon count rate corresponds to the light intensity distribution of the target object, and the change in light intensity frequency of each pixel in the time domain corresponds to the vibration frequency of the target object. Therefore, the array of single-photon detectors, the array of single-photon counters, and the data processing module finally detect, collect, and calculate the parallel vibration frequency information of multiple points in the target object.

[0028] The aforementioned transmitting optical system or receiving imaging optical system can be constructed as either a coaxial or non-coaxial transceiver optical system; the laser beam output by the transmitting optical system should be able to cover the entire target surface. Correspondingly, the receiving imaging optical system can simultaneously image the entire target surface. The receiving optical imaging system can receive reflected light from the entire surface of the target object. The array single-photon detector includes multiple pixels, and these pixels at different positions form a pixel array of the single-photon detector. The receiving optical imaging system can map the vibration information of multiple parallel targets within the surface to the corresponding pixel positions of the array single-photon detector. The optical signals received by the pixels are equivalent to the light intensity change frequency through photon counting. The data processing module calculates and outputs the vibration frequency corresponding to each pixel of the target object, ultimately calculating the vibration frequency and amplitude intensity at each pixel of the multiple parallel targets within the surface. As described in the first aspect of the present invention, the in-plane multi-point parallel vibration measurement device, wherein the transmitting optical system is constructed as either a coaxial transceiver optical system or a non-coaxial transceiver optical system; The receiving imaging optical system is constructed as either a coaxial transceiver optical system or a non-coaxial transceiver optical system.

[0029] As described in the first aspect of the present invention, the in-plane multi-point parallel vibration measuring device is equipped with a receiving optical imaging system capable of receiving the reflected light from the entire surface of the target object and imaging the reflected light from the target object onto the focal plane of the receiving optical imaging system. The array of single-photon detectors is positioned at the focal plane of the receiving optical imaging system to receive data information carried by the reflected light from the target object.

[0030] As described in the first aspect of the present invention, in the in-plane multi-point parallel vibration measurement device, the electrical signal output by the array single-photon detector is provided to the array single-photon counter. The electrical signal is used to generate counting data by the array single-photon counter and then input into the data processing module. The data processing module calculates and outputs the vibration frequency corresponding to each pixel of the target object.

[0031] Example 2 As attached Figure 2 As shown, a second aspect of the present invention proposes an in-plane multi-point parallel vibration measurement method based on array single-photon detection, used to operate the in-plane multi-point parallel vibration measurement device based on array single-photon detection. The method includes the following steps: Step 1: The laser, which serves as the test light source, emits a laser of a specified wavelength. The laser beam is expanded and collimated by the emitting optical system and then irradiates the surface of the target object. Step 2: The laser light reflected from the surface of the target object is mapped onto the focal plane of the imaging optical system by the receiving optical imaging system; Step 3: The array single-photon detector converts the weak light signals corresponding to multiple parallel spaces within the surface of the target object into electrical signals and sends them to the array single-photon counter. Step 4: The array single-photon counter and data processing module process and calculate the electrical signal in the spatial and temporal domains to generate and output the in-plane multi-point parallel vibration information of the target object.

[0032] As described in the second aspect of the present invention, in the in-plane multi-point parallel vibration measurement method, step 3 includes: the array single-photon detector converts the received light intensity information into electrical signals according to each corresponding pixel point, and inputs them into the corresponding positions on the array single-photon counter.

[0033] As described in the second aspect of the present invention, in the in-plane multi-point parallel vibration measurement method, step 4 includes the following sub-steps: Step 4.1: The array single-photon counter timestamps the electrical signal corresponding to each pixel and inputs it into the data processing module; Step 4.2: The data processing module performs time-domain statistics on the timestamps of the photon counts corresponding to each pixel and performs photon count rate statistics at equal intervals. Step 4.3: The data processing module performs a Fast Fourier Transform (FFT) on the time series of photon count rate to obtain the frequency domain representation of the electrical signal, and calculates the vibration frequency and vibration amplitude information corresponding to each pixel of the multi-point parallel vibration target object in the surface from the frequency domain representation of the electrical signal.

[0034] As described in the second aspect of the present invention, the in-plane multi-point parallel vibration measurement method further includes the following sub-steps in step 4.2: The photon count rate follows the formula below; Where N ij (t) represents the photon count value at the i-th horizontal and j-th vertical point corresponding to time t. ij f is the amplitude. ij The vibration frequency, Let be the average photon count rate at the i-th point in the horizontal direction and the j-th point in the vertical direction.

[0035] The following is a detailed introduction to the method of parallel vibration measurement at multiple points in a single-photon plane. Here, we divide the in-plane parallel vibration target into i horizontal vibration points and j vertical vibration points, each corresponding to point a on a target. ij The position of the vibration point a after passing through the receiving optical imaging system. ij One-to-one mapping onto in-plane parallel pixels of the array single-photon detector b ijThe array single-photon detector converts discrete individual photon signals into electrical signals, which are then transmitted to the array single-photon counter. The array single-photon counter counts the photons and can then calculate the relative light intensity change. The data processing module shows the following relationship between the photon count and the array frequency: Where N ij (t) represents the photon count value at the i-th horizontal and j-th vertical point corresponding to time t. ij f is the amplitude. ij The vibration frequency, Let be the average photon count rate at the i-th point in the horizontal direction and the j-th point in the vertical direction.

[0036] By performing a Fast Fourier Transform (FFT) on the photon counting time series, the frequency domain representation of the signal is obtained. The data processing module then identifies the frequency peaks in the frequency domain of the signal. Finally, the vibration frequency and amplitude information corresponding to each pixel of the multi-point parallel vibration target object in the plane are calculated.

[0037] The photon counting time series is calculated using the following formula: in Let be the Dirac function. When selecting the positive frequency portion of the spectrum, the vibration frequency is... Will be manifested in A significant peak appears at a certain point; therefore, the corresponding vibration frequency can be effectively extracted using a peak detection algorithm. .

[0038] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the embodiments of the present invention and are not intended to limit them. Although the embodiments of the present invention have been described in detail with reference to the above preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions to the technical solutions of the embodiments of the present invention should not depart from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. An in-plane multi-point parallel vibration measurement device based on array single-photon detection, characterized in that, The in-plane multi-point parallel vibration measurement device includes: a laser, a transmitting optical system, a receiving optical imaging system, an array of single-photon detectors, an array of single-photon counters, and a data processing module. The single-photon detection band laser beam output by the laser is transformed into a parallel coherent beam by the transmitting optical system. After the parallel coherent beam illuminates the target object, it is reflected by the target object. The reflected beam is imaged onto the array single-photon detector by the receiving optical imaging system. The array single-photon detector converts the light intensity information of the received reflected beam into an electrical signal. The electrical signal is input to the data processing module. The data processing module calculates the in-plane parallel vibration frequency information of the target object based on the input electrical signal.

2. The in-plane multi-point parallel vibration measurement device as described in claim 1, characterized in that, The transmitting optical system is a beam expanding and collimating system, including multiple lenses and / or mirrors. The transmitting optical system receives the laser generated by the laser and ensures that the size of the laser beam output by the transmitting optical system is greater than or equal to the surface size of the array single-photon detector, so as to completely cover the array single-photon detector.

3. The in-plane multi-point parallel vibration measurement device as described in claim 2, characterized in that, The laser is a pulsed laser or a continuous laser.

4. The in-plane multi-point parallel vibration measurement device as described in claim 2, characterized in that, The transmitting optical system is constructed as either a coaxial transceiver optical system or a non-coaxial transceiver optical system. The receiving imaging optical system is constructed as either a coaxial transceiver optical system or a non-coaxial transceiver optical system.

5. The in-plane multi-point parallel vibration measurement device as described in claim 2, characterized in that, The receiving optical imaging system is capable of receiving the reflected light from the entire surface of the target object and imaging the reflected light from the target object onto the focal plane of the receiving optical imaging system. The array of single-photon detectors is positioned at the focal plane of the receiving optical imaging system to receive data information carried by the reflected light from the target object.

6. The in-plane multi-point parallel vibration measurement device as described in claim 1, characterized in that, The electrical signal output by the array single-photon detector is provided to the array single-photon counter. The electrical signal is used to generate counting data by the array single-photon counter and then input into the data processing module. The data processing module calculates and outputs the vibration frequency corresponding to each pixel of the target object.

7. A method for in-plane multi-point parallel vibration measurement based on array single-photon detection, used to operate the in-plane multi-point parallel vibration measurement device based on array single-photon detection as described in any one of claims 1-6, characterized in that: The method includes the following steps: Step 1: The laser, which serves as the test light source, emits a laser of a specified wavelength. The laser beam is expanded and collimated by the emitting optical system and then irradiates the surface of the target object. Step 2: The laser light reflected from the surface of the target object is mapped onto the focal plane of the imaging optical system by the receiving optical imaging system; Step 3: The array single-photon detector converts the weak light signals corresponding to multiple parallel spaces within the surface of the target object into electrical signals and sends them to the array single-photon counter. Step 4: The array single-photon counter and data processing module process and calculate the electrical signal in the spatial and temporal domains to generate and output the in-plane multi-point parallel vibration information of the target object.

8. The in-plane multi-point parallel vibration measurement method as described in claim 7, characterized in that, Step 3 includes: the array single-photon detector converts the received light intensity information into electrical signals for each corresponding pixel, and inputs them into the corresponding positions on the array single-photon counter.

9. The in-plane multi-point parallel vibration measurement method as described in claim 7, characterized in that, Step 4 includes the following sub-steps: Step 4.1: The array single-photon counter timestamps the electrical signal corresponding to each pixel and inputs it into the data processing module; Step 4.2: The data processing module performs time-domain statistics on the timestamps of the photon counts corresponding to each pixel and performs photon count rate statistics at equal intervals. Step 4.3: The data processing module performs a Fast Fourier Transform (FFT) on the time series of photon count rate to obtain the frequency domain representation of the electrical signal, and calculates the vibration frequency and vibration amplitude information corresponding to each pixel of the multi-point parallel vibration target object in the surface from the frequency domain representation of the electrical signal.

10. The in-plane multi-point parallel vibration measurement method as described in claim 9, characterized in that, Step 4.2 also includes the following sub-steps: The photon count rate follows the formula below; Where N ij (t) represents the photon count value at the i-th horizontal and j-th vertical point corresponding to time t. ij f is the amplitude. ij The vibration frequency, Let be the average photon count rate at the i-th point in the horizontal direction and the j-th point in the vertical direction.

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