A PSD-based light beam pointing change detection system and method

CN120467243BActive Publication Date: 2026-08-21XIAN TECH UNIV
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Patent Information

Application Number
CN202510616341.X
Authority / Receiving Office
CN · China
Patent Type
Patents(China)
Current Assignee / Owner
Filing Date
2025-05-14
Publication Date
2026-08-21
Estimated Expiration
2045-05-14

AI Technical Summary

Technical Problem

但这两种方式均存在以下问题:都是成本太高,计算复杂,不适合量产

Benefits of technology

[0034] I. The PSD-based beam pointing change detection system and method provided by this invention can quickly measure the magnitude of object vibration and record the data, so as to detect the change in the pointing of reflected beams caused by various micro-vibrations of optical mirrors. It has the advantages of low cost and suitability for large-scale, long-term, and long-distance detection and recording.

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Abstract

The application discloses the technical field of intelligent detection and relates to a light beam pointing change detection system and method based on a PSD, which comprises a light beam sensing module installed on the surface of an optical flat through a translation lifting adjusting mechanism, a laser installed on the surface of the optical flat through an adjustable holder, and a reflector fixed on the surface of a platform to be detected, the optical flat is fixed on the surface of an air floating platform, a PSD position sensitive detector in the light beam sensing module is electrically connected to a software processing end through a driving circuit, the light beam emitted by the laser is reflected by the reflector into the PSD position sensitive detector in the light beam sensing module, and the software processing end collects change data of the position of a light spot in the PSD position sensitive detector and calculates the vibration angle of the platform to be detected in the vertical, horizontal and two-dimensional directions. The application can quickly measure the vibration size of an object and record data and detect the change of the pointing direction of reflected light beams caused by various micro-vibrations of an optical reflector.
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Description

Technical Field

[0001] This invention relates to a beam pointing change detection system and method based on PSD, belonging to the field of intelligent detection technology. Background Technology

[0002] Currently, the degree of vibration of an object is determined by detecting the change in surface angle caused by the vibration. The main methods include using a portable digital laser vibrometer (PDV) and a Sony RS-CMOS stacked lens.

[0003] PDV (Power Distribution Vehicle) detection utilizes the Doppler effect, modulating the emitted light velocity by a vibrating object. An algorithm calculates the object's velocity, converts it into relative displacement, and then uses a mathematical formula to convert that displacement into an angular change. RS-CMOS, on the other hand, uses the principle of similar triangles. An RS-CMOS position sensor derives the object's relative displacement and uses a mathematical formula to convert that displacement into an angular change. However, both methods suffer from the following problems: high cost, complex calculations, and unsuitability for mass production. Summary of the Invention

[0004] The purpose of this invention is to overcome the shortcomings of the prior art and provide a PSD-based beam pointing change detection system and method for detecting data such as the vibration angle of an object during vibration. It has the advantages of low cost, simple operation, and suitability for long-term long-distance detection and recording.

[0005] To achieve the above objectives, the present invention is implemented using the following technical solution:

[0006] In a first aspect, the present invention provides a beam pointing change detection system based on PSD, comprising a beam sensing module mounted on the surface of an optical plate via a translation and lifting adjustment mechanism, a laser mounted on the surface of the optical plate via an adjustable clamp, and a reflector fixed on the surface of a platform to be tested. The optical plate is fixed on the surface of an air-bearing platform. The PSD position-sensitive detector in the beam sensing module is electrically connected to a software processing terminal via a driving circuit. The beam emitted by the laser is reflected by the reflector and enters the PSD position-sensitive detector in the beam sensing module. The software processing terminal calculates the vibration angle of the platform to be tested along the vertical, horizontal, and two-dimensional directions by collecting the change data of the light spot position in the PSD position-sensitive detector.

[0007] Furthermore, the translation and lifting adjustment mechanism includes a lifting platform and a sliding platform. The beam sensing module is installed on the lifting platform, and the lifting platform is installed on the sliding platform. The sliding platform is fixedly installed with the optical flat plate. The beam sensing module can move and adjust in the vertical and horizontal directions respectively under the adjustment of the lifting platform and the sliding platform.

[0008] Furthermore, the beam sensing module includes a telephoto lens and a PSD position-sensitive detector chip. The telephoto lens has a diameter of 80mm and a focal length of 500mm. The PSD position-sensitive detector chip is fixed at the focal point of the telephoto lens. The PSD position-sensitive detector chip is a two-dimensional detector chip with a target surface size of 20*20mm and a response wavelength range of 300-1100nm.

[0009] Furthermore, the light source wavelength of the laser is within the wavelength response range of the PSD position-sensitive detector chip, and the laser divergence angle is less than 1 mrad. The maximum output power of the laser is less than the damage threshold of the PSD position-sensitive detector chip.

[0010] Furthermore, the center height of the laser, the center height of the reflector, and the center height of the beam sensing module are the same.

[0011] Secondly, the present invention provides a PSD-based beam pointing change detection method, and based on the above-mentioned PSD-based beam pointing change detection system, comprising:

[0012] Fix the reflector to the surface of the platform to be tested;

[0013] Start the laser, adjust the adjustable clamp and the translation and lifting adjustment mechanism so that the light spot is reflected by the reflector onto the center of the PSD position sensitive detector chip in the beam sensing module;

[0014] On the software processing end, by collecting data on the change in the position of the light spot in the PSD position-sensitive detector, the vibration angles of the platform under test along the vertical, horizontal, and two-dimensional directions are calculated.

[0015] Furthermore, the vibration angles of the platform under test along the vertical, horizontal, and two-dimensional directions are:

[0016]

[0017] Where, Δθ x The horizontal vibration angle is Δθ. y The vertical vibration angle is Δθ. r ΔX is the angle of vibration in the two-dimensional direction, ΔY is the horizontal displacement difference of the light spot on the PSD, and f' is the focal length of the lens.

[0018] Furthermore, the software processing unit collects data on the change in the position of the light spot in the PSD position-sensitive detector, calculates the vibration angles of the platform under test along the vertical, horizontal, and two-dimensional directions, and also includes: when the light spot moves out of the PSD position-sensitive detector chip, the software processing unit records the last effective point (X1, Y1) and the re-entry point (X2, Y2) of the light spot, and calculates the horizontal and vertical displacement differences on the PSD position-sensitive detector chip during the period when the light spot moves out of the PSD by combining the horizontal and vertical time-domain compensation functions, thereby calculating the horizontal and vertical vibration angles and the two-dimensional vibration angles during the stage when the light spot moves out of the PSD.

[0019]

[0020] In the formula: The horizontal vibration angle during the PSD stage of the light spot removal process. The vertical vibration angle of the light spot as it moves out of the PSD stage. Let f' be the angle of vibration in the two-dimensional direction as the light spot moves out of the PSD stage, and f' be the focal length of the lens. This represents the horizontal displacement difference on the PSD position-sensitive detector chip during the spot removal period. φ(t) represents the vertical displacement difference on the PSD position-sensitive detector chip during the spot removal period. These are the time-domain compensation functions for the horizontal and vertical directions, respectively.

[0021] Furthermore, the calculation expressions for the horizontal and vertical time-domain compensation functions are as follows:

[0022]

[0023] In the formula: ξ x ω is the equivalent damping coefficient in the horizontal direction. x φ is the natural angular frequency of horizontal vibration. x ξ is the horizontal phase offset angle. y ω is the equivalent damping coefficient in the vertical direction. y For the natural angular frequency of vertical vibration, φ y This is the vertical phase offset angle.

[0024] Furthermore, the calculation expressions for the equivalent damping coefficients in the horizontal and vertical directions are as follows:

[0025]

[0026] In the formula: x n y n These are the horizontal and vertical displacement amplitudes in the nth vibration cycle, respectively, and N is the number of decay cycles;

[0027] The calculation expressions for the natural angular frequencies of the horizontal and vertical vibrations are as follows:

[0028]

[0029] In the formula: T x T y These are the vibration periods in the horizontal and vertical directions, respectively.

[0030] The calculation expressions for the horizontal and vertical phase offset angles are as follows:

[0031]

[0032] In the formula: X(t0) is the horizontal displacement of the light spot at the instant it moves out of the PSD. Let Y(t0) be the horizontal velocity at the moment the displacement disappears, and let Y(t0) be the vertical displacement of the light spot as it moves out of the PSD. Let be the vertical velocity at the moment the displacement disappears.

[0033] Compared with the prior art, the beneficial effects achieved by the present invention are as follows:

[0034] I. The PSD-based beam pointing change detection system and method provided by this invention can quickly measure the magnitude of object vibration and record the data, so as to detect the change in the pointing of reflected beams caused by various micro-vibrations of optical mirrors. It has the advantages of low cost and suitability for large-scale, long-term, and long-distance detection and recording.

[0035] Second, this invention constructs a time-domain compensation function for the vibration trajectory by dynamically correlating data such as the vibration period and the horizontal displacement of the light spot at the moment it moves out of the PSD. This function is used to calculate the horizontal and vertical displacement differences on the PSD position-sensitive detector chip during the light spot's movement out of the PSD. Ultimately, this yields the horizontal and vertical vibration angles of the micro-vibration platform and the vibration angle in the two-dimensional direction during the light spot's movement out of the PSD. This solves the data discontinuity problem of traditional detection systems and ensures the temporal integrity of vibration monitoring. Attached Figure Description

[0036] The accompanying drawings, which form part of this specification, are used to provide a further understanding of the invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute an undue limitation of the invention. In the drawings:

[0037] Figure 1 This is a schematic diagram of a beam pointing change detection system based on PSD provided in Embodiment 1 of the present invention;

[0038] Figure 2 This is a schematic diagram of the optical path of a beam pointing change detection system based on PSD provided in Embodiment 1 of the present invention;

[0039] Figure 3 This is a test schematic diagram of a PSD-based beam pointing change detection system provided in Embodiment 1 of the present invention;

[0040] Figure 4 This is a schematic diagram of the internal structure of a beam sensing module in a PSD-based beam pointing change detection system provided in Embodiment 1 of the present invention.

[0041] Figure 5 This is a schematic diagram of the beam displacement change on the PSD chip in a beam pointing change detection system based on PSD provided in Embodiment 1 of the present invention.

[0042] In the diagram: 1. Laser; 2. Adjustable gripper; 3. Reflector; 4. Beam sensing module; 5. Lifting platform; 6. Translation platform; 7. Optical flat plate; 8. Air-bearing platform; 9. Micro-vibration platform. Detailed Implementation

[0043] The present invention will now be described in detail with reference to the accompanying drawings and embodiments. It should be noted that, unless otherwise specified, the embodiments and features described herein can be combined with each other.

[0044] The following detailed description is exemplary and intended to provide further detailed explanation of the invention. Unless otherwise specified, all technical terms used in this invention have the same meaning as commonly understood by one of ordinary skill in the art. The terminology used in this invention is for describing particular embodiments only and is not intended to limit the scope of exemplary embodiments according to the invention.

[0045] Example 1:

[0046] Please see Figure 1 A PSD-based beam pointing change detection system is used to measure the magnitude of object vibration and record data. It includes: a laser 1, an adjustable clamp 2, a reflector 3, a beam sensing module 4, a lifting platform 5, a translation stage 6, an optical plate 7, an air-bearing platform 8, and a micro-vibration platform 9. The laser 1 generates a stable, narrow laser beam; the adjustable clamp 2 holds the laser 1 and adjusts the beam spot position; the reflector 3 is fixed to the micro-vibration platform 9; the beam sensing module 4 is mounted on the lifting platform 5, which adjusts the initial vertical position of the beam spot. The lifting platform 5 is fixed to the translation stage 6 and can perform precise horizontal movements with the translation stage 6. The lifting platform 5 and the translation stage 6 are used to adjust the initial position of the reflected beam incident on the beam sensing module 4; the translation stage 6 is mounted on the optical plate 7, which is fixed to the air-bearing platform 8 to avoid interference from external vibrations that could cause inaccurate measurement results.

[0047] The beam sensing module 4 includes a telephoto lens and a PSD position-sensitive detector chip. The telephoto lens has a diameter of 80mm and a focal length of 500mm. The PSD position-sensitive detector chip is fixed at the focal point of the telephoto lens and electrically connected to the software processing end. It is used to accurately measure the position of the reflected beam of the thin laser beam after passing through the optical reflector and incident on the light spot on the PSD. The PSD position-sensitive detector chip is a two-dimensional detector chip with a target size of 20*20mm, a response wavelength range of 300-1100nm, a recommended maximum range of ±8mm, a resolution of 1µm, a linear accuracy of ±10µm, an ideal linear measurement range of ±3mm, and a linear accuracy of 0.002mm within the ideal linear range.

[0048] The wavelength of the laser source 1 should be within the wavelength response range of the PSD position-sensitive detector chip, the laser divergence angle should be less than 1 mrad, and the maximum output power of the laser 1 should be less than the damage threshold of the PSD position-sensitive detector chip.

[0049] The center height of laser 1, the center height of reflector 3, and the center height of beam sensing module 4 are the same;

[0050] Please refer to the following: Figure 2-5 This embodiment presents a method for detecting beam pointing change based on PSD, including the following steps:

[0051] Step 1: Based on the measurement height, install the laser 1, adjustable clamp 2, beam sensing module 4, lifting platform 5, translation platform 6, optical flat plate 7, and air-bearing platform 8 to complete the construction of the measuring device;

[0052] Step 2: Fix the reflector 3 onto the micro-vibration platform 9;

[0053] Step 3: Turn on the power of laser 1, adjust the adjustable clamp 2, lifting platform 5, and translation platform 6 so that the light spot is reflected by the reflector 3 at the center of the PSD position sensitive detector chip in the beam sensing module 4.

[0054] Step 4: When the micro-vibration platform vibrates, it causes the reflector 3 to vibrate, resulting in a change in the direction of the reflected beam. This causes a change in the position of the light spot incident on the PSD position-sensitive detector. The software processing unit collects and calculates the data on this change in light spot position to accurately measure the change in the direction of the reflected beam. Specifically: In the software processing unit, click "Align," marking the current position of the light spot as the zero point. By calculating the relative position change between the light spot and the zero point, accurate measurement of the change in the direction of the reflected beam is achieved. Set an appropriate sampling frequency in the software processing unit, turn on the micro-vibration platform 9, and use the software processing unit to measure and record the position change of the light spot on the PSD until the entire measurement process is complete.

[0055] The software processing end is based on LabVIEW software programming. It can obtain the two-dimensional position coordinates (x, y) of the light spot according to the serial communication protocol of PSD, calculate the displacement of the light spot in the horizontal and vertical directions (Δx, Δy), and then convert them into the pointing coordinates of the light beam (Δθx, Δθy), so as to realize the accurate measurement of the change in the pointing of the reflected light beam. The data processing algorithm is as follows:

[0056] In paraxial optical paths of geometric optics, it is known that:

[0057]

[0058] Where y' is the image height and f' is the focal length of the lens, and according to the law of reflection, when light is reflected, the angle of incidence equals the angle of reflection. Therefore, we can approximate the following using the above formula:

[0059]

[0060] Where, Δθ x ΔX is the horizontal vibration angle, and ΔX is the horizontal displacement difference of the light spot on the PSD.

[0061] Similarly, the angle at which the light spot vibrates in the vertical direction is:

[0062]

[0063] Where, Δθ y The vertical vibration angle is ΔY, and the vertical displacement difference of the light spot on the PSD is ΔY.

[0064] The angle at which the light spot vibrates in the two-dimensional direction is:

[0065]

[0066] Where, Δθ r Let Δr be the angle of vibration in the two-dimensional direction, and let Δr be the two-dimensional displacement difference of the light spot on the PSD.

[0067] It should be noted that during the vibration process, the amplitude may exceed the detection range of the PSD. When the light spot moves out of the PSD position-sensitive detector chip, the software processing end records the last effective point (X1, Y1) and the re-entry point (X2, Y2) of the light spot. Combining the horizontal and vertical time-domain compensation functions, the horizontal and vertical displacement differences on the PSD position-sensitive detector chip during the light spot's movement out are calculated. Thus, the horizontal and vertical vibration angles and the two-dimensional vibration angles during the light spot's movement out of the PSD are calculated.

[0068]

[0069] In the formula: The horizontal vibration angle during the PSD stage of the light spot removal process. The vertical vibration angle of the light spot as it moves out of the PSD stage. The angle of vibration in the two-dimensional direction as the light spot moves out of the PSD stage. This represents the horizontal displacement difference on the PSD position-sensitive detector chip during the spot removal period. The vertical displacement difference on the PSD position-sensitive detector chip during the spot removal period is expressed as:

[0070]

[0071] Where: φ(t), The time-domain compensation functions are for the horizontal and vertical directions, respectively, and their expressions are:

[0072]

[0073] In the formula: ξ x ω is the equivalent damping coefficient in the horizontal direction. x φ is the natural angular frequency of horizontal vibration. x ξ is the horizontal phase offset angle. y ω is the equivalent damping coefficient in the vertical direction. y For the natural angular frequency of vertical vibration, φ y The vertical phase offset angle is calculated using the following formula: Based on the trajectory of the light spot within the effective detection area, dynamic parameters are extracted through vibration waveform feature analysis.

[0074] 1. Equivalent damping coefficients in horizontal and vertical directions

[0075]

[0076] In the formula: x n y n These are the horizontal and vertical displacement amplitudes of the nth vibration cycle, respectively; N is the number of decay cycles, usually taken as 3-5 complete cycles.

[0077] 2. Natural angular frequencies of horizontal and vertical vibrations

[0078]

[0079] In the formula: T x T y These are the vibration periods in the horizontal and vertical directions, respectively.

[0080] 3. Horizontal and vertical phase offset angles

[0081]

[0082] In the formula: X(t0) is the horizontal displacement of the light spot at the instant it moves out of the PSD; Y(t0) represents the horizontal velocity at the moment the displacement disappears; Y(t0) represents the vertical displacement of the light spot as it moves out of the PSD. Let be the vertical velocity at the moment the displacement disappears.

[0083] In summary, when the light spot exceeds the detection range of the PSD, the above scheme constructs a time-domain compensation function for the vibration trajectory by dynamically correlating data such as the vibration period and the horizontal displacement of the light spot at the moment it moves out of the PSD. This function calculates the horizontal and vertical displacement differences on the PSD position-sensitive detector chip during the period when the light spot moves out of the PSD, and finally obtains the horizontal, vertical, and two-dimensional vibration angles of the micro-vibration platform during the stage when the light spot moves out of the PSD. This solves the data discontinuity problem of traditional detection systems and ensures the temporal integrity of vibration monitoring.

[0084] The PSD-based beam pointing change detection system provided by this invention is simple in equipment, low in cost, capable of long-distance detection, easy to operate, and highly accurate. It can quickly measure the magnitude of object vibration and record the data, with a measurement range of ±0.916°, a measurement accuracy of 0.00023°, and a repeatability of ±0.00011°. This invention also provides a method for detecting minute angles, used to detect changes in the pointing of reflected beams caused by various micro-vibrations of an optical mirror. This method has the advantages of low cost and suitability for large-scale, long-term, and long-distance detection and recording.

[0085] As is known from common technical knowledge, this invention can be implemented through other embodiments that do not depart from its spirit or essential characteristics. Therefore, the disclosed embodiments described above are merely illustrative in all respects and are not the only ones. All modifications within the scope of this invention or its equivalents are included in this invention.

[0086] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit it. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the specific implementation of the present invention. Any modifications or equivalent substitutions that do not depart from the spirit and scope of the present invention should be covered within the scope of protection of the claims of the present invention.

Claims

1. A method for detecting beam pointing change based on PSD, characterized in that, The detection system employs a PSD-based beam pointing change detection system, which includes: a beam sensing module (4) mounted on the surface of an optical plate (7) via a translation and lifting adjustment mechanism; a laser (1) mounted on the surface of the optical plate (7) via an adjustable clamp (2); and a reflector (3) fixed on the surface of the platform to be tested. The optical plate (7) is fixed on the surface of an air-floating platform (8). The PSD position-sensitive detector in the beam sensing module (4) is electrically connected to the software processing terminal via a drive circuit. The beam emitted by the laser (1) is reflected by the reflector (3) into the PSD position-sensitive detector in the beam sensing module (4). The software processing terminal calculates the vibration angle of the platform to be tested along the vertical, horizontal, and two-dimensional directions by collecting the change data of the light spot position in the PSD position-sensitive detector. The PSD-based beam pointing change detection method includes: Fix the reflector (3) to the surface of the platform to be tested; Start the laser (1), adjust the adjustable clamp (2) and the translation and lifting adjustment mechanism so that the light spot is reflected by the reflector (3) at the center of the PSD position sensitive detector chip in the beam sensing module (4); On the software processing end, by collecting data on the change in the position of the light spot in the PSD position-sensitive detector, the vibration angles of the platform under test along the vertical, horizontal, and two-dimensional directions are calculated, including: when the light spot moves out of the PSD position-sensitive detector chip, the software processing end records the last effective point of the light spot (…). , ) and the reentry point of the light spot ( , By combining horizontal and vertical time-domain compensation functions, the horizontal and vertical displacement differences on the PSD position-sensitive detector chip during the spot removal period are calculated, thereby obtaining the horizontal and vertical vibration angles and the two-dimensional vibration angles during the spot removal stage of the PSD. ; ; ; ; ; In the formula: The horizontal vibration angle during the PSD stage of the light spot removal process. The vertical vibration angle of the light spot as it moves out of the PSD stage. The angle of vibration in the two-dimensional direction as the light spot moves out of the PSD stage. The focal length of the lens. This represents the horizontal displacement difference on the PSD position-sensitive detector chip during the spot removal period. This represents the vertical displacement difference on the PSD position-sensitive detector chip during the spot removal period. , These are the time-domain compensation functions for the horizontal and vertical directions, respectively.

2. The PSD-based beam pointing change detection method according to claim 1, characterized in that, The translation and lifting adjustment mechanism includes a lifting platform (5) and a translation platform (6). The beam sensing module (4) is installed on the lifting platform (5), the lifting platform (5) is installed on the translation platform (6), the translation platform (6) is fixedly installed on the optical plate (7), and the beam sensing module (4) can move and adjust in the vertical and horizontal directions respectively under the adjustment of the lifting platform (5) and the translation platform (6).

3. The PSD-based beam pointing change detection method according to claim 1, characterized in that, The beam sensing module (4) includes a telephoto lens and a PSD position-sensitive detector chip. The telephoto lens has a diameter of 80mm and a focal length of 500mm. The PSD position-sensitive detector chip is fixed at the focal point of the telephoto lens. The PSD position-sensitive detector chip is a two-dimensional detector chip with a target size of 20*20mm and a response wavelength range of 300-1100nm.

4. The PSD-based beam pointing change detection method according to claim 1, characterized in that, The light source wavelength of the laser (1) is within the wavelength response range of the PSD position sensitive detector chip, and the laser divergence angle is less than 1 mrad. The maximum output power of the laser (1) is less than the damage threshold of the PSD position sensitive detector chip.

5. The PSD-based beam pointing change detection method according to claim 1, characterized in that, The center height of the laser (1), the center height of the reflector (3), and the center height of the beam sensing module (4) are the same.

6. The PSD-based beam pointing change detection method according to claim 1, characterized in that, The vibration angles of the platform under test along the vertical, horizontal, and two-dimensional directions are: ; ; ; in, The angle of vibration in the horizontal direction. The vertical vibration angle. The angle of vibration in a two-dimensional direction. This represents the horizontal displacement difference of the light spot on the PSD. This represents the vertical displacement difference of the light spot on the PSD. This is the focal length of the lens.

7. The PSD-based beam pointing change detection method according to claim 1, characterized in that, The calculation expressions for the horizontal and vertical time-domain compensation functions are as follows: ; ; In the formula: This is the equivalent damping coefficient in the horizontal direction. The natural angular frequency of horizontal vibration. This is the horizontal phase offset angle. The equivalent damping coefficient in the vertical direction is... The natural angular frequency of vertical vibration, This is the vertical phase offset angle.

8. The PSD-based beam pointing change detection method according to claim 7, characterized in that, The calculation expressions for the equivalent damping coefficients in the horizontal and vertical directions are as follows: ; ; In the formula: , These are the horizontal and vertical displacement amplitudes in the nth vibration cycle, respectively, and N is the number of decay cycles; The calculation expressions for the natural angular frequencies of the horizontal and vertical vibrations are as follows: ; ; In the formula: , These are the vibration periods in the horizontal and vertical directions, respectively. The calculation expressions for the horizontal and vertical phase offset angles are as follows: ; ; In the formula: This represents the horizontal displacement of the light spot as it moves out of the PSD. Let be the horizontal velocity at the moment the displacement disappears. This represents the vertical displacement of the light spot the instant it moves out of the PSD. Let be the vertical velocity at the moment the displacement disappears.

Citation Information

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