CN113446963A - Angle measuring system based on phased array and measuring method thereof - Google Patents

Angle measuring system based on phased array and measuring method thereof Download PDF

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CN113446963A
CN113446963A CN202110635585.4A CN202110635585A CN113446963A CN 113446963 A CN113446963 A CN 113446963A CN 202110635585 A CN202110635585 A CN 202110635585A CN 113446963 A CN113446963 A CN 113446963A
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light modulator
spatial light
phased array
angle
charge coupler
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CN113446963B (en
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周俊鹤
王琪琪
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Tongji University
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    • G01MEASURING; TESTING
    • G01BMEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
    • G01B11/00Measuring arrangements characterised by the use of optical techniques
    • G01B11/26Measuring arrangements characterised by the use of optical techniques for measuring angles or tapers; for testing the alignment of axes

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Abstract

The invention relates to an angle measuring system based on a phased array and a measuring method thereof, wherein the system comprises a laser, a collimator, a spectroscope, a reflector, a charge coupler detector, a rotary table and a spatial light modulator, wherein the collimator is right opposite to the laser, the collimator and the charge coupler detector are respectively positioned at two opposite sides of one pair of spectroscopes, the reflector and the spatial light modulator are respectively positioned at two opposite sides of the other pair of spectroscopes, and the spatial light modulator is arranged on the rotary table; the spatial light modulator is used for carrying out phase modulation on light beams transmitted to the spatial light modulator through the optical phased array, so that light spots on the charge coupler detector are moved, and the two light spots at the bottom end are coincided again; and calculating the rotation angle of the angle measurement system according to the phase modulation quantity of the spatial light modulator and the distances among the light spots in the charge coupled device detector. Compared with the prior art, the invention has the advantages of effectively enlarging the system measurement range, improving the measurement angle resolution and the like.

Description

Angle measuring system based on phased array and measuring method thereof
Technical Field
The invention relates to the technical field of angle measurement, in particular to an angle measurement system based on a phased array and a measurement method thereof.
Background
Accurate and precise small angle measurements are critical for the mounting of precision mechanical components, optical systems, and the like. The small angle measurement has the characteristics of small measurement range, high measurement precision requirement, high resolution and the like. In order to realize precise angle measurement, optical angle measurement methods proposed at present mainly include an internal reflection method, a laser interferometry, and the like.
For example, document 1 "two-dimensional high-precision small-angle deflection measurement of multiple reflections of a plane mirror" (dunalixin, gumchun, fang qing chun, etc.. photoelectric engineering 37.1(2010):26-30.) proposes a small-angle measurement system based on multiple reflections of a plane mirror. The system is characterized in that the reference mirror and the movable mirror are reflected for multiple times, the angle of the movable mirror changes along with the change of the deflection angle of a measured object every time, and the position of a light spot of a corresponding detector also changes. The deflection angle of the measured object can be obtained through the displacement change of the light spot on the detector, but the defect is that the detector range is limited, and the light spot cannot be detected by the detector when the deflection angle is too large.
For example, document 2, "Small-angle measurement with high sensitivity total-internal-reflection heterodyne interferometer" (J.Y.Lin, Y.C.Liao. optics Express 53.9(2014): 1903-. In the heterodyne interference, a specific optical axis direction of one half-wave plate and two quarter-wave plates is combined into a phase shifter. When a diamond prism is placed between the phase shifter and the analyzer displaying the appropriate transmission axis azimuth angle, it will modify and enhance the double total internal reflection of the s-and p-polarization phase difference. The phase difference enhancement is related to the incident angle, and the small angle can be conveniently and accurately measured by estimating the phase difference. Because the power of the internal reflection method is detected by a single photoelectric detector after multiple times of reflection, factors such as beam divergence, prism installation deflection and the like can bring power loss in the measurement process, and measurement errors are caused.
For example, in the document 3 "Full-circle range and micro-radial resolution and measurement of angular range", the improved micro-radio resolution Full-circle range angle measurement system based on laser self-mixing effect is proposed (c.wang, x.fan, y.guo, et al. optics Express 26.8(2018): 10371-. Compared with the traditional angle measurement method by the laser self-mixing interferometry, the measurement resolution and distance are greatly improved.
For example, document 4 "Double-grating with multiple differences enabled small angle measurement" (j.y.wang, c.liu, s.y.qin, et al.optics Express 27.4(2019): 5289-. In this particular dual grating structure, the beam can be diffracted repeatedly, and the deflection angle is enlarged accordingly. This configuration can be inserted in front of other angle measurement systems to improve their angular resolution. Experimental results show that the angle amplification and the microradian angle resolution of more than 40 times can be correspondingly realized by adopting the double-grating structure.
The detection imaging light spots adopt a Charge Coupled Detector (CCD), the CCD range is limited, the distance between the light spots cannot be too large, and the angle detection range is limited, so that the measurement range is expanded by applying a laser beam deflection technology, and the accurate directional control of the light beam in a certain range is called as a light beam deflection technology. In the prior art, a mechanical beam deflection technology is mostly adopted, which mainly changes the direction of an optical axis by means of a mechanical rotating device so as to control the beam direction. Because of the existence of mechanical rotating parts, the problems of low angle precision, slow pointing speed, complex control system and the like exist.
Disclosure of Invention
The present invention is directed to overcome the above-mentioned drawbacks of the prior art, and to provide a phased array based angle measurement system and a measurement method thereof, which can extend the measurement range and the measurement angle resolution of the system.
The purpose of the invention can be realized by the following technical scheme:
an angle measuring system based on a phased array comprises a laser, a collimator, a spectroscope, a reflector and a charge coupler detector, and further comprises a rotary table and a spatial light modulator, wherein the collimator is over against the laser, the collimator and the charge coupler detector are respectively positioned on two opposite sides of one pair of the spectroscopes, the reflector and the spatial light modulator are respectively positioned on two opposite sides of the other pair of the spectroscopes, and the spatial light modulator is arranged on the rotary table;
the laser is used for emitting laser;
the collimator faces the laser and is used for converting the divergent laser into parallel light and outputting the parallel light to the light splitter;
the light splitter is used for separating the laser into transmission light and reflection light;
the reflecting mirror is used for reflecting the light beam incident to the reflecting mirror and then sequentially passes through the spectroscope and the spatial light modulator;
the spatial light modulator is used for carrying out phase modulation on light beams transmitted to the spatial light modulator through the optical phased array, so that light spots on the charge coupler detector are moved, and a plurality of light spots on the charge coupler detector are coincided again;
the charge coupler detector is used for acquiring light spot images, light beams form a plurality of light spots on the charge coupler detector through the spectroscope, and the distance between the light spots is measured through the charge coupler detector;
and calculating the rotation angle of the angle measurement system according to the phase modulation quantity of the spatial light modulator and the distances among a plurality of light spots in the charge coupled device detector.
Furthermore, the reflector and the spatial light modulator are both reflectors, and the laser beam is emitted after being reflected for multiple times between the reflector and the spatial light modulator.
Further, the rotating table is used for changing the left-right deflection angle of the spatial light modulator through manually adjusting the micrometer.
Further, the process of obtaining the maximum angle measurement range of the angle measurement system includes:
the light beam emitted by the laser forms a plurality of light spots on the charge coupler detector;
adjusting a rotating platform positioned below the spatial light modulator to enable two light spots at the bottommost end of the charge coupler detector to be separated to the maximum position of the charge coupler detector; when the charge coupler detector displays that the separation distance of the two light spots is maximum, adjusting an optical phased array based on the spatial light modulator to enable the light spots to be coincident again; rotating the rotating platform and loading the phased array for multiple times until the phased array fails to control the light spots to move; and finally, the maximum angle measurement range of the angle measurement system is the sum of the maximum phased array deflection distance and the distance of the detection surface of the charge coupler detector.
Further, the spectroscope is provided with a 45-degree right-angle prism inclined plane.
Furthermore, the charge coupler detector and the spatial light modulator are also connected with a computer.
The invention also provides an angle measurement method adopting the phased array based angle measurement system, which comprises the following steps:
the light beam emitted by the laser forms a plurality of light spots on the charge coupler detector;
in an initial state, two light spots at the bottommost end of the charge coupler detector are overlapped;
and after the rotating platform deflects, separating two light spots at the bottommost end of the charge coupler detector, performing phase modulation through the spatial light modulator at the moment, so that the two light spots at the bottommost end of the charge coupler detector coincide again, and calculating a deflection angle according to the phase modulation amount of the spatial light modulator.
Further, the method further comprises:
and if the two light spots at the bottom end of the charge coupler detector are not overlapped again after the spatial light modulator adjusts the phase modulation amount to the maximum value, calculating the deflection angle according to the distance between the two light spots at the bottom end of the charge coupler detector.
Further, the phase modulation is carried out by adjusting the pitch angle of the optical phased array in the spatial light modulator.
Further, the calculation expression of the phase modulation amount is as follows:
Figure BDA0003105538060000041
where Phase is the amount of Phase modulation, and d is the amount of Phase modulation, and is applied to the spatial light modulator to control the direction of the beam as it exits the spatial light modulator cellxIs the spacing of the elements on the x-axis, dyIs the spacing of the elements on the y-axis, k is the wave number, k is 2 x pi/lambda, lambda is the wavelength, theta0To an angle of pitch, phi0Horizontal angle, ± deflection direction.
Compared with the prior art, the invention has the following advantages:
the angle measurement system based on the phased array, disclosed by the invention, has the advantages that the phased array is loaded by the spatial light modulator, and the maximum deflection distance and the CCD distance of the phased array are obtained, so that the measurement range of the system is effectively expanded, and the measurement angle resolution is improved.
Drawings
Fig. 1 is an optical path diagram of an angle measurement system based on a phased array according to an embodiment of the present invention;
fig. 2 is an optical path diagram of an internal device of an angle measurement system based on a phased array according to an embodiment of the present invention, where (1) is a diagram showing a first change state of an optical path, (2) is a diagram showing a second change state of an optical path, and (3) is a diagram showing a third change state of an optical path;
FIG. 3 is a diagram illustrating simulation results of the phased array based angle measurement system of the present embodiment;
fig. 4 is a diagram for verifying the experimental results of the phased array-based angle measurement system of this embodiment, where (a) is a diagram of the change of a light spot before and after the spatial light modulator loads a phased array with a pitch angle of about 2.333 degrees, (b) is a diagram of the change of a light spot before and after the spatial light modulator loads a phased array with a pitch angle of about 4.667 degrees, and (c) is a diagram of the change of a light spot before and after the spatial light modulator loads a phased array with a pitch angle of about 7 degrees.
Detailed Description
In order to make the objects, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are some, but not all, embodiments of the present invention. The components of embodiments of the present invention generally described and illustrated in the figures herein may be arranged and designed in a wide variety of different configurations.
Thus, the following detailed description of the embodiments of the present invention, presented in the figures, is not intended to limit the scope of the invention, as claimed, but is merely representative of selected embodiments of the invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
It should be noted that: like reference numbers and letters refer to like items in the following figures, and thus, once an item is defined in one figure, it need not be further defined and explained in subsequent figures.
Example 1
The embodiment provides an angle measuring system based on a phased array, which comprises a laser, a collimator, a spectroscope, a reflector, a charge coupler detector, a rotary table and a spatial light modulator, wherein the collimator is right opposite to the laser, the collimator and the charge coupler detector are respectively positioned at two opposite sides of one pair of spectroscopes, the reflector and the spatial light modulator are respectively positioned at two opposite sides of the other pair of spectroscopes, and the spatial light modulator is arranged on the rotary table;
the laser is used for emitting laser;
the collimator faces the laser and is used for converting the diffused laser into parallel light and outputting the parallel light to the light splitter;
the light splitter is used for separating the laser into transmission light and reflection light;
the reflecting mirror is used for reflecting the light beam incident to the reflecting mirror and then sequentially passes through the spectroscope and the spatial light modulator;
the rotating platform is used for changing the left and right deflection angle of the spatial light modulator through manually adjusting the micrometer;
the spatial light modulator is used for carrying out phase modulation on light beams transmitted to the spatial light modulator through the optical phased array, so that light spots on the charge coupler detector are moved, and a plurality of light spots on the charge coupler detector are coincided again;
the Charge Coupled Device (CCD) detector is used for acquiring light spot images, light beams form a plurality of light spots on the CCD detector through the spectroscope, and the distance between the light spots is measured through the CCD detector;
and calculating the rotation angle of the angle measurement system according to the phase modulation quantity of the spatial light modulator and the distances among the light spots in the charge coupled device detector.
The laser emission light source outputs parallel light to be transmitted through the spectroscope after reaching the collimator; the spectroscope is arranged between the spatial light modulator and the reflector in parallel, and light is separated into transmitted light and reflected light through the spectroscope.
The spatial light modulator adopts a reflection type, namely the modulation on each point is determined according to the reflectivity of each point; the reflector and the spatial light modulator are arranged oppositely and are reflectors, and the light beams are emitted after being reflected for multiple times between the two reflectors.
The process of acquiring the maximum angle measurement range of the angle measurement system comprises the following steps:
the light beam emitted by the laser forms a plurality of light spots on the charge coupler detector;
adjusting a rotating platform positioned below the spatial light modulator to enable two light spots at the bottommost end of the charge coupler detector to be separated to the maximum position of the charge coupler detector; when the charge coupler detector displays that the separation distance of the two light spots is maximum, adjusting an optical phased array based on the spatial light modulator to enable the light spots to be coincident again; rotating the rotating platform and loading the phased array for multiple times until the phased array fails to control the light spots to move; and finally, the maximum angle measurement range of the angle measurement system is the sum of the maximum phased array deflection distance and the distance of the detection surface of the charge coupler detector.
Compared with the prior art, the CCD has a limited measuring range, the distance between light spots cannot be too large, and the angle detection range is limited; the final measurement range of the angle measurement system is the maximum deflection distance of the phased array and the CCD distance, so that the light spot measurement range is expanded.
In this embodiment, the beam splitter is provided with a 45-degree right-angle prism inclined plane, and the charge coupler detector and the spatial light modulator are further connected with a computer, and are integrally controlled by the computer.
The present embodiment further provides an angle measurement method using the above phased array based angle measurement system, including the following steps:
the light beam emitted by the laser forms a plurality of light spots on the charge coupler detector;
in an initial state, two light spots at the bottommost end of the charge coupler detector are overlapped;
after the rotating platform deflects, separating two light spots at the bottommost end of the charge coupler detector, performing phase modulation through the spatial light modulator at the moment, enabling the two light spots at the bottommost end of the charge coupler detector to coincide again, and calculating a deflection angle according to the phase modulation quantity of the spatial light modulator;
if the two light spots at the bottom end of the charge coupler detector are not overlapped again after the spatial light modulator adjusts the phase modulation amount to the maximum value, the deflection angle is further calculated according to the distance between the two light spots at the bottom end of the charge coupler detector.
And adjusting the pitch angle of an optical phased array in the spatial light modulator to perform phase modulation.
Loading a phased array phase with a pitch angle theta and a horizontal angle 0 on the basis of an optical phased array of a spatial light modulator; the phase modulation is carried out once when the light beam is reflected once by the phased array, and meanwhile, the angle deflection of the light beam is increased by theta; the effective area of the optical phased array is larger than or equal to the area of the spatial light modulator, the range of the phased array loaded by the spatial light modulator is 0-2 pi, the spatial light modulator can effectively regulate and control the phase, and meanwhile, the phase of a light beam can reach any required value.
The phased array loading phase based on the spatial light modulator is determined by the following formula:
Figure BDA0003105538060000061
where Phase is the amount of Phase modulation, and d is the amount of Phase modulation, and is applied to the spatial light modulator to control the direction of the beam as it exits the spatial light modulator cellxIs the spacing of the elements on the x-axis, dyIs the spacing of the elements on the y-axis, k is the wave number, k is 2 x pi/lambda, lambda is the wavelength, theta0To an angle of pitch, phi0Horizontal angle, ± deflection direction.
Compared with the prior art, the optical phased array is applied to a precision measurement system, and the method comprises the following specific operation steps:
1) gaussian beams are adopted for transmission, the transmitted beams are transmitted to the 45-degree right-angle prism inclined plane of the spectroscope through the collimator, half of transmitted light is directly detected by the CCD, and the other part of reflected light passes through the spatial light modulator and the reflector in sequence and is reflected to the CCD again through the 45-degree right-angle prism inclined plane.
2) The relative positions of the spatial light modulator, the spectroscope and the reflector are adjusted, and the rotating platform below the spatial light modulator is rotated clockwise, so that the CCD can detect transmitted light and reflected light.
3) When the light spots are separated to the maximum distance which can be detected by the CCD, the spatial light modulator is loaded with the phased array to control the moving position of the light spots.
4) When the phased array is loaded onto the spatial light modulator, as shown in FIG. 2, the deflection angle changes each time the phased array is passed. And then sequentially passes through the 45-degree right-angle prism inclined plane, the reflector and the 45-degree right-angle prism inclined plane, and the reflected light is detected by the CCD.
5) Adjusting the pitch angle of the phased array, as shown in fig. 2(2), so that the two light spots of reference numbers 1 and 2 with the closest CCD distance coincide; rotating the rotating platform again, as shown in fig. 2(3), so that the distance between the charge coupled detectors 1 and 2 becomes larger; then, the processes of fig. 2(2) and fig. 2(3) are carried out for a plurality of times until the phased array cannot change the distance between the light spots; the total measurement range of the system is the maximum deflection distance of the phased array and the CCD distance, and the signal-to-noise ratio of the system is reduced due to the loading of the phased array, so that the CCD output image is influenced.
The phased array based angle measurement system in the present embodiment was verified with a specific example. The spatial light modulator adopts a reflection type, the dimension is 800 x 600, and the size dx (10um) of each pixel point is obtained; the size of the beam splitter is 2.5 × 2.5(cm3), and the light beam enters the inclined plane of the 45-degree right-angle prism through the collimator; the rotating platform is arranged below the spatial light modulator, controls the left deflection angle and the right deflection angle of the spatial light modulator, and rotates 1.083 degrees when the micrometer rotates for one circle; mirror size 6 x 4(cm 2); CCD size 1.41312 × 0.7452(cm 2); based on the optical phased array of the spatial light modulator, the range of the loading Phase pitch angle of the phased array is about 2 × the maximum angle of each rotation of the rotary table, and Phase in a formula is determined. Because the size of the spatial light modulator is limited, when the spatial light modulator rotates for multiple times, the light spot moves to the edge of the spatial light modulator, the spatial light modulator with a larger area can be selected, and the measuring range is expanded more.
The beam splitter is located intermediate the spatial light modulator and the mirror. As shown in fig. 3, the relative change of the two light spots is recorded every time the rotary table rotates by 0.1083 °, and it can be seen that the rotation angle and the relative positions of the two light spots are in a linear relationship. Fig. 4 is a graph showing the experimental results of the phased array loaded once. In the left view of fig. 4(a), the turntable is rotated about 1.1913 ° so that the two spots are far apart from the CCD. To re-coincide the two spots as shown in the right hand diagram of figure 4(a), the spatial light modulator is loaded with a phased array with a pitch of about 2.333 deg.. The left image of fig. 4(b) shows a second rotation of the turntable of about 1.1913 deg. so that the spots are further apart from the CCD. When the spatial light modulator loads a phased array phase with a pitch angle of 4.667 degrees and a horizontal angle of 0 degrees, the light spots are coincided again at the leftmost side of the CCD, as shown in the right diagram of FIG. 4 (b). In the left image of fig. 4(c), the turntable is rotated a third time by about 1.1913 ° so that the two spots are far apart from the CCD. When the spatial light modulator is loaded with the phased array phase with the pitch angle of 7 degrees and the horizontal angle of 0 degrees as shown in the right diagram of fig. 4(c), the light spots are coincided again at the leftmost side of the CCD as shown in the right diagram of fig. 4 (c). The CCD light spot distance is maximum after the phased array coincident light spot is loaded for many times and the rotating table is rotated, so that the CCD measurement range is expanded, and the measurement result is more accurate.
According to simulation results and experimental results, the phased array-based small-angle measurement system is applied between two reflectors, and the phased array is loaded to the spatial light modulator to control the steering of light beams. The invention discloses a phased array-based small-angle measurement system, which effectively enlarges the measurement range of a CCD (charge coupled device) and improves the measurement angle resolution and the system sensitivity by loading the phased array through a spatial light modulator. The optical phased array can accurately measure small angles, and the large potential market value of the optical phased array is determined by the wide application range of the optical phased array.
The foregoing detailed description of the preferred embodiments of the invention has been presented. It should be understood that numerous modifications and variations could be devised by those skilled in the art in light of the present teachings without departing from the inventive concepts. Therefore, the technical solutions available to those skilled in the art through logic analysis, reasoning and limited experiments based on the prior art according to the concept of the present invention should be within the scope of protection defined by the claims.

Claims (10)

1. An angle measuring system based on a phased array comprises a laser, a collimator, a spectroscope, a reflector and a charge coupler detector, and is characterized by further comprising a rotary table and a spatial light modulator, wherein the collimator is over against the laser, the collimator and the charge coupler detector are respectively positioned on two opposite sides of one pair of the spectroscope, the reflector and the spatial light modulator are respectively positioned on two opposite sides of the other pair of the spectroscope, and the spatial light modulator is arranged on the rotary table;
the laser is used for emitting laser;
the collimator faces the laser and is used for converting the divergent laser into parallel light and outputting the parallel light to the light splitter;
the light splitter is used for separating the laser into transmission light and reflection light;
the reflecting mirror is used for reflecting the light beam incident to the reflecting mirror and then sequentially passes through the spectroscope and the spatial light modulator;
the spatial light modulator is used for carrying out phase modulation on light beams transmitted to the spatial light modulator through the optical phased array, so that light spots on the charge coupler detector are moved, and a plurality of light spots on the charge coupler detector are coincided again;
the charge coupler detector is used for acquiring light spot images, light beams form a plurality of light spots on the charge coupler detector through the spectroscope, and the distance between the light spots is measured through the charge coupler detector;
and calculating the rotation angle of the angle measurement system according to the phase modulation quantity of the spatial light modulator and the distances among a plurality of light spots in the charge coupled device detector.
2. The phased array based angle measurement system of claim 1, wherein the reflector and the spatial light modulator are both reflectors, and the laser beam is emitted after multiple reflections between the reflector and the spatial light modulator.
3. The phased array based angle measurement system of claim 1, wherein the rotary stage is configured to change the angle of left and right deflection of the spatial light modulator by manually adjusting a micrometer.
4. The phased array based angle measurement system of claim 1, wherein the maximum angle measurement range of the angle measurement system is obtained by:
the light beam emitted by the laser forms a plurality of light spots on the charge coupler detector;
adjusting a rotating platform positioned below the spatial light modulator to enable two light spots at the bottommost end of the charge coupler detector to be separated to the maximum position of the charge coupler detector; when the charge coupler detector displays that the separation distance of the two light spots is maximum, adjusting an optical phased array based on the spatial light modulator to enable the light spots to be coincident again; rotating the rotating platform and loading the phased array for multiple times until the phased array fails to control the light spots to move; and finally, the maximum angle measurement range of the angle measurement system is the sum of the maximum phased array deflection distance and the distance of the detection surface of the charge coupler detector.
5. The phased array based angle measurement system of claim 1, wherein the beam splitter is provided with 45 degree right angle prism facets.
6. The phased array based angle measurement system of claim 1, wherein the CCD detector and the spatial light modulator are further connected to a computer.
7. An angle measuring method using a phased array based angle measuring system according to claim 1, characterized by comprising the steps of:
the light beam emitted by the laser forms a plurality of light spots on the charge coupler detector;
in an initial state, two light spots at the bottommost end of the charge coupler detector are overlapped;
and after the rotating platform deflects, separating two light spots at the bottommost end of the charge coupler detector, performing phase modulation through the spatial light modulator at the moment, so that the two light spots at the bottommost end of the charge coupler detector coincide again, and calculating a deflection angle according to the phase modulation amount of the spatial light modulator.
8. The method of claim 7, further comprising:
and if the two light spots at the bottom end of the charge coupler detector are not overlapped again after the spatial light modulator adjusts the phase modulation amount to the maximum value, calculating the deflection angle according to the distance between the two light spots at the bottom end of the charge coupler detector.
9. The method of claim 7, wherein the phase modulation is performed by adjusting a pitch angle of an optical phased array in the spatial light modulator.
10. The method of claim 9, wherein the phase modulation amount is calculated by the expression:
Figure FDA0003105538050000021
where Phase is the amount of Phase modulation, and d is the amount of Phase modulation, and is applied to the spatial light modulator to control the direction of the beam as it exits the spatial light modulator cellxIs the spacing of the elements on the x-axis, dyIs the spacing of the elements on the y-axis, k is the wave number, k is 2 x pi/lambda, lambda is the wavelength,θ0To an angle of pitch, phi0Horizontal angle, ± deflection direction.
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