Optical orbital angular momentum interferometry demodulation technology based on angular four-point detection

Abstract

The present invention discloses an optical orbit angular momentum interferometry demodulation technology based on angular four-point detection. The present invention first selects four detection points with different angular angles from a petal-shaped interference pattern formed by optical orbit angular momentum interference, and respectively collects their light intensity signals M1, M2, M3, and M4. Then, based on light intensity normalization coefficients P1, P2, P3, and P4 related to the radial radius of the selected detection points, the light intensity signals M1, M2, M3, and M4 are converted into normalized light intensities I1, I2, I3, and I4. Then, based on the normalized light intensities and angular angles, the current interference phase #imgabs0# is calculated. Finally, the interference phase #imgabs1# caused by the measurement is compared with the initial interference phase #imgabs2# before the measurement to calculate the interference phase change #imgabs3#. The present invention has the advantages of low cost, high speed, and high efficiency.

Description

Technical Field

[0001] The present invention relates to the field of light measurement and light sensing technology, and in particular to an optical orbital angular momentum interferometry demodulation technology based on angular four-point detection. Background Art

[0002] Laser interferometry systems can accurately measure tiny optical path (phase) changes caused by measured sensors or measurement values, and are widely used in the fields of optical measurement and optical sensing technology. In traditional laser single-frequency two-way interference systems, when the optical path of the light beam in the measuring arm changes, the interference fringes formed by the interference of the two light beams of the measuring arm and the reference arm will also change accordingly. By measuring the changes in the interference fringes or the intensity of the interference light, tiny optical path (phase) changes can be accurately measured, and the sensing or measurement values can be measured accordingly. When the light beams transmitted by the reference arm and the measuring arm of the traditional laser interferometer system are replaced with optical orbital angular momentum beams with different optical orbital angular momentum orders (topological charges) l1 and l2, it becomes an optical orbital angular momentum interference system. The interference of the two-arm light beams of this interference system will form a stable petal-shaped interference pattern, and the transmission phase changes between the two arms caused by changes in the measured sensor or measurement value will be detected. This will cause the petal-shaped interference pattern to rotate. By measuring the rotation angle ΔΩ through image processing and other methods, the tiny optical path (phase) changes can be accurately measured and used to measure the sensing or measurement value.

[0003] The reference arm and measurement arm of the traditional optical orbital angular momentum interferometer system transmit optical orbital angular momentum beams with different optical orbital angular momentum orders (topological charges) l1 and l2, respectively. The electric field amplitudes are expressed as:

[0004] E r (r,Ω,z)=A l (r)exp(-il1Ω)exp(iβz)

[0005] E m (r,Ω,z)=A2(r)exp(-il2Ω)exp(iβz)

[0006] Where r, Ω, and z are the radial, angular, and transmission (longitudinal) coordinates, respectively; β is the propagation constant; and the optical orbital angular momentum order difference Δl = |l1-l2| ≠ 0. To simplify the analysis, it is assumed that the initial transmission phase difference of the two-arm beam is zero and the radial distributions of the two-arm beams are similar. Then, the radial distributions A1 and A2 of the two orbital angular momentum beams satisfy A1 = A2 = A. The transverse intensity of the two orbital angular momentum beams after interference in the optical orbital angular momentum interferometer system is:

[0007] I(r,θ)=2|A(r)| 2 [1+cos(ΔlΩ)]

[0008] If the refractive index change Δn of the measuring arm or the measuring distance change ΔL causes the double-arm transmission phase difference to be When , the intensity of the interference beam can be expressed as:

[0009] I(r,θ)=2|A(r)| 2 [1+cos(Δl(Ω+Φ)]

[0010] Where Ф is the overall rotation angle change of the interference pattern, expressed as Traditional optical orbital angular momentum interferometry systems need to collect and process two-dimensional images to accurately analyze the rotation angle Ф and use it to solve the transmission phase difference. The refractive index change Δn of the measuring arm or the measurement distance change ΔL is calculated. However, this type of surface detection method has problems such as insufficient detection resolution and low speed, making it difficult to achieve high-speed, high-precision measurement and sensing applications.

[0011] There are also patents for phase demodulation technology both domestically and internationally: a four-step phase shift method based on absolute phase recovery (Chinese Patent CN 102155924 A), a high-precision four-step phase shift calibration method for variable frequency interferometry (Chinese Patent CN 104316204A), a polarization four-step phase shift method for digital speckle interferometry (Chinese Patent CN 108827176 A), a surface structured light phase decomposition method based on four-step phase shifting with variable phase shifting (Chinese Patent CN 110207621 A), and a four-step phase shift principal value phase extraction method (Chinese Patent CN 112184788 A). These patents primarily investigate phase demodulation algorithms for traditional single-frequency, dual-path laser interferometers. However, these methods generally require the acquisition of four interference patterns to correctly demodulate the phase, resulting in a complex, costly, and inefficient process. Summary of the Invention

[0012] Purpose of the invention: To address the problems existing in the prior art, the present invention provides a low-cost, high-speed, and high-efficiency optical orbital angular momentum interferometry demodulation method, device, and storage medium based on angular four-point detection.

[0013] Technical solution: The optical orbital angular momentum interferometry demodulation method based on angular four-point detection described in the present invention includes:

[0014] (1) Obtaining a petal-shaped interference pattern to be demodulated;

[0015] (2) Select four detection points with different angular angles from the petal-shaped interference pattern and collect their light intensity signals M1, M2, M3, and M4 respectively, where the angular angles Ω1, Ω2, Ω3, and Ω4 of the four detection points satisfy 2πrad ≥ Ω4 > Ω3 > Ω2 > Ω1 ≥ 0rad;

[0016] (3) converting the light intensity signals M1, M2, M3, M4 into normalized light intensities I1, I2, I3, I4 based on light intensity normalization coefficients P1, P2, P3, P4 related to the radial radius of the selected detection point;

[0017] (4) Calculate the interference phase based on normalized light intensity and angular angle

[0018] (5) Comparison of the interference phase caused by the measured and the initial interference phase before measurement Obtain the interference phase change caused by the measured The change in the measured quantity is calculated from this.

[0019] Furthermore, the interference phase is calculated in step (4) The method is:

[0020] When Ω1=0rad, Ω2=(π / 2) / Δl rad, Ω3=(π) / Δl rad and Ω4=(3π / 2) / Δl rad, the interference phase The demodulation formula is expressed as:

[0021]

[0022] When the angular angles Ω1, Ω2, Ω3, and Ω4 are other values, the interference phase The demodulation formula is expressed as:

[0023]

[0024] Wherein, Δl represents the difference in the order of the optical orbital angular momentum of the two optical orbital angular momentum beams forming the petal-shaped interference pattern to be demodulated.

[0025] Furthermore, the light intensity signals M1, M2, M3, and M4 are collected by photodetectors or charge coupled devices.

[0026] Furthermore, the angular angles Ω1, Ω2, Ω3 and Ω4 and the light intensity normalization coefficients P1, P2, P3, P4 are obtained by a preset or initialization method.

[0027] The initialization method is specifically as follows:

[0028] (1) An optical path that changes uniformly with time t is introduced into the reference arm or measurement arm of the interferometer system that forms the petal-shaped interference pattern to be demodulated, causing the petal-shaped interference pattern to rotate n times (n is an integer). The obtained rotation angle Ф(t) ranges from 0 to 2×n×π, and the corresponding transmission phase difference is Δl represents the difference in the order of the two optical orbital angular momentum beams forming the petal-shaped interference pattern to be demodulated, and the time t varies from 0 to T, where T is the rotation end time and the rotation speed is ω = 2 × n × π / T;

[0029] (2) collecting light intensity signals M1'(t), M2'(t), M3'(t), and M4'(t) that vary with time at any four angular positions of the petal-shaped interference pattern;

[0030] (3) Calculate the light intensity normalization coefficients P1, P2, P3 and P4 according to the light intensity signals M1'(t), M2'(t), M3'(t) and M4'(t). The calculation formula is P n =QUAD(M n (t)) / T, n=1, 2, 3, 4, QUAD is the integral function, for the light intensity M in time T n (t)Integral.

[0031] (4) Use Fourier transform and shift correlation methods to determine the angular angles Ω1, Ω2, Ω3 and Ω4.

[0032] Among them, the calculation method of Fourier transform is: first calculate M n '(t)'s spectrum F n '(f)=FT(M n '(t)), where n = 1, 2, 3, 4, and FT() is the Fourier transform function; then the frequency point f corresponding to the maximum spectrum amplitude except zero frequency is calculated Mn =MAX(ABS(F n '(f))), where f≠0, MAX is the maximum value function, and ABS is the absolute value function; finally, the frequency point f is calculated Mn Phase (angular angle) Ω n =PHASE(F n '(f Mn )), where PHASE is used to calculate the spectrum F n '(f) in f Mn The phase of the frequency point.

[0033] The shift correlation calculation method is as follows: first set Ω1 to 0; then calculate the cross-correlation value C of the light intensity collected at different detection points. n (t) = CORR (M n '(t), M1'(t)), where n = 2, 3, 4, CORR is the cross-correlation function; finally, the angular angle Ω of different detection points is calculated. i =ω×MAX(C n (t)), where MAX is the maximum value function, which is used to calculate the time corresponding to the maximum value of the cross-correlation function.

[0034] Furthermore, the method of normalizing the light intensity signals M1, M2, M3, and M4 to light intensities I1, I2, I3, and I4 is as follows: n =M n / P n , n=1,2,3,4.

[0035] The optical orbital angular momentum interferometry demodulation device based on angular four-point detection of the present invention includes a processor and a computer program stored in a memory and runnable on the processor, and the processor implements the above method when executing the program.

[0036] The storage medium of the present invention contains computer-executable instructions, and the computer-executable instructions are used to perform the above method when executed by a computer processor.

[0037] Beneficial effect: Compared with the prior art, the present invention has the following significant advantages: the present invention measures the light intensity at four detection points at any angle of the petal-shaped interference pattern, and the interference phase change can be calculated by normalizing the four-point light intensity. Since four photodetectors replace the traditional image acquisition and processing methods for orbital angular momentum interference signal demodulation, and only four detection points at any different angular directions on an interference pattern are needed to correctly demodulate the phase, the demodulation process is greatly simplified. Therefore, the present invention has the unique characteristics of low cost, fast detection speed and high efficiency, providing a new solution for the field of laser sensing and measurement. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] Figure 1 A schematic flow chart of the optical orbital angular momentum interferometry demodulation method based on angular four-point detection provided by the present invention;

[0039] Figure 2 A structural diagram of the optical orbital angular momentum interferometry demodulation device based on angular four-point detection provided by the present invention;

[0040] Figure 3 A simplified diagram of the conjugate orbital angular momentum interferometry system based on the Michelson structure used in the implementation case;

[0041] Figure 4 It is the petal-shaped interference light field generated when the first-order conjugate orbital angular momentum beam interferes;

[0042] Figure 5 To measure the rotation of the interference light field when the phase of the beam transmitted by the measuring arm changes;

[0043] Figure 6 is the distribution of the four detection points in the interference light field (first-order conjugate orbital angular momentum beam);

[0044] Figure 7 During initialization, the reflector of the measuring arm moves at a uniform speed, and the normalized light intensity signals of the four detection points are obtained;

[0045] Figure 8 is the uniform displacement curve of the measuring arm reflector (first-order conjugate orbital angular momentum beam);

[0046] Figure 9 The interference light intensity signal (first-order conjugate orbital angular momentum beam) detected at the four detection points;

[0047] Figure 10 is the normalized interference light intensity signal (first-order conjugate orbital angular momentum beam);

[0048] Figure 11 is the demodulated transmission phase curve (first-order conjugate orbital angular momentum beam);

[0049] Figure 12 is the reconstructed displacement curve of the measuring arm mirror (first-order conjugate orbital angular momentum beam);

[0050] Figure 13 is the distribution of the four detection points in the interference light field (second-order conjugate orbital angular momentum beam);

[0051] Figure 14 The interference light intensity signal (2nd-order conjugate orbital angular momentum beam) detected at the four detection points;

[0052] Figure 15 is the normalized interference light intensity signal (second-order conjugate orbital angular momentum beam);

[0053] Figure 16 is the demodulated transmission phase curve (second-order conjugate orbital angular momentum beam);

[0054] Figure 17 is the reconstructed displacement curve of the measuring arm reflector (second-order conjugate orbital angular momentum beam);

[0055] Figure 18 The distribution of the four detection points in the interference light field (2nd-order conjugate orbital angular momentum beam vibration measurement);

[0056] Figure 19 is the vibration curve of the measuring arm reflector;

[0057] Figure 20 Interference light intensity signals detected at four detection points (2nd-order conjugate orbital angular momentum beam vibration measurement);

[0058] Figure 21 is the normalized interference light intensity signal (second-order conjugate orbital angular momentum beam vibration measurement);

[0059] Figure 22 is the demodulated phase curve;

[0060] Figure 23 is the reconstructed vibration curve of the measuring arm mirror. DETAILED DESCRIPTION

[0061] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0062] Example 1

[0063] This embodiment provides an optical orbital angular momentum interferometry demodulation method based on angular four-point detection, such as Figure 1 As shown, the following steps are included:

[0064] (1) Obtain the petal-shaped interference pattern to be demodulated.

[0065] The petal-shaped interference pattern to be demodulated is output by the optical orbital angular momentum interferometer system. The reference arm and the measurement arm transmit optical orbital angular momentum beams with different optical orbital angular momentum orders (topological charges) l1 and l2, respectively. According to the interference principle, the petal-shaped interference pattern can be expressed as:

[0066] I(r,θ)=2|A(r)| 2 [1+cos(Δl(Ω+Φ)]

[0067] Where Δl = |l1-l2|≠0 represents the order difference of the optical orbital angular momentum between the reference arm and the measurement arm, r represents the radial radius, A represents the radial amplitude, Ω represents the angular angle, and Φ represents the overall rotation angle change of the interference pattern.

[0068] (2) Four detection points are selected from the petal-shaped interference pattern to collect their light intensity signals M1, M2, M3, and M4 respectively, where the angular angles Ω1, Ω2, Ω3, and Ω4 of the four detection points satisfy 2πrad ≥ Ω4 > Ω3 > Ω2 > Ω1 ≥ 0rad.

[0069] Among them, the four detection points can be expressed as (r1, Ω1), (r2, Ω2), (r3, Ω3), (r4, Ω4) using the center coordinates. n ,r n(n=1, 2, 3, 4) are the angular angle and radial radius of the nth acquisition point respectively. A photoelectric detector or a charge-coupled device is used to collect light intensity signals. The collected light intensity signals M1, M2, M3, and M4 are expressed as:

[0070] M n =2|A(r n )| 2 [1+cos(Δl(Ω n +Φ))],n=1,2,3,4

[0071] The angular angles Ω1, Ω2, Ω3, and Ω4 and the corresponding light intensity normalization coefficients P1, P2, P3, and P4 can be obtained by a preset or initialization method. The initialization method is as follows: an optical path that changes uniformly with time t is introduced into the reference arm or the measurement arm of the interferometer system that forms the petal-shaped interference pattern to be demodulated, so as to cause the petal-shaped interference pattern to rotate n times. The obtained rotation angle Φ(t) ranges from 0 to 2×n×π, and the corresponding transmission phase difference is Δl represents the difference in the order of the two optical orbital angular momentum beams forming the petal-shaped interference pattern to be demodulated; light intensity signals M1', M2', M3', and M4' are collected at any four angular positions of the petal-shaped interference pattern; and the light intensity normalization coefficient P is calculated based on the light intensity signals M1', M2', M3', and M4'. n =2|A(r n )| 2 =QUAD(M n (t)) / T, where QUAD is the integral function for the light intensity M in time T. n (t) Integration; use Fourier transform and shift correlation methods to determine the angular angles Ω1, Ω2, Ω3 and Ω4.

[0072] (3) The light intensity signals M1, M2, M3, M4 are converted into normalized light intensities I1, I2, I3, I4 based on the light intensity normalization coefficients P1, P2, P3, P4 related to the radial radius of the selected detection point.

[0073] The method for normalizing the light intensity signals M1, M2, M3, and M4 to light intensities I1, I2, I3, and I4 is as follows: n =M n / P n , n=1,2,3,4. After normalization, the light intensities I1, I2, I3, and I4 are expressed as:

[0074] I n =[1+cos(Δl(Ω n +Φ))],n=1,2,3,4

[0075] (4) Calculate the interference phase based on normalized light intensity and angular angle Among them, the interference phase is calculated The method is:

[0076] When Ω1=0rad, Ω2=(π / 2) / Δl rad, Ω3=(π) / Δl rad and Ω4=(3π / 2) / Δl rad, the interference phase The demodulation formula is expressed as:

[0077]

[0078] When the angular angles Ω1, Ω2, Ω3, and Ω4 are other values, the interference phase The demodulation formula is expressed as:

[0079]

[0080] When the detection area of the detection point is small, at a specific center coordinate (r n ,Ω n ) of the detection area and the total light intensity and center coordinate point (r n ,Ω n ) is proportional to the light intensity; when the detection areas of the four detection points are the same, the ratio of the total light intensity measured by the four detection points to the light intensity of the central coordinate point is the same. Since the same light intensity ratio can be used in the interference phase Therefore, when the detection area of the detection point is small and the detection areas of the four detection points are the same, the total light intensity detected by the detection point is used instead of the center coordinate point (r n ,Ω n ) does not affect the interference phase In addition, the normalized light intensity values have exactly the same DC values, which can also be offset in the above calculation.

[0081] (5) Comparison of the interference phase caused by the measured and the initial interference phase before measurement Obtain the interference phase change caused by the measured The change in the measured quantity is calculated from this.

[0082] Example 2

[0083] Figure 2 This is a structural diagram of an optical orbital angular momentum interferometry demodulation device based on angular four-point detection provided by an embodiment of the present invention. This embodiment of the present invention provides services for the implementation of the method of the above-mentioned embodiment 1 of the present invention. Figure 2 A block diagram of an exemplary device 12 suitable for use in implementing embodiments of the present invention is shown. Figure 2The device 12 shown is only an example and should not bring any limitation to the functionality and scope of use of the embodiments of the present invention.

[0084] like Figure 2 As shown, device 12 is implemented as a general-purpose computing device. Components of device 12 may include, but are not limited to, one or more processors or processing units 16, a system memory 28, and a bus 18 that connects various system components, including system memory 28 and processing unit 16.

[0085] Bus 18 represents one or more of several types of bus structures, including a memory bus or memory controller, a peripheral bus, an accelerated graphics port, a processor, or a local bus using any of a variety of bus architectures. Examples of these architectures include, but are not limited to, an Industry Standard Architecture (ISA) bus, a Micro Channel Architecture (MAC) bus, an Enhanced ISA bus, a Video Electronics Standards Association (VESA) local bus, and a Peripheral Component Interconnect (PCI) bus.

[0086] Device 12 typically includes a variety of computer system readable media. These media can be any available media that can be accessed by device 12, including volatile and non-volatile media, removable and non-removable media.

[0087] System memory 28 may include computer system readable media in the form of volatile memory, such as random access memory (RAM) 30 and / or cache memory 32. Device 12 may further include other removable / non-removable, volatile / non-volatile computer system storage media. By way of example only, storage system 34 may be configured to read and write non-removable, non-volatile magnetic media ( Figure 2 Not shown, often called a "hard drive"). Although Figure 2 Not shown, a magnetic disk drive for reading and writing to a removable non-volatile magnetic disk (e.g., a "floppy disk"), and an optical disk drive for reading and writing to a removable non-volatile optical disk (e.g., a CD-ROM, DVD-ROM, or other optical media) may be provided. In these cases, each drive may be connected to bus 18 via one or more data media interfaces. Memory 28 may include at least one program product having a set (e.g., at least one) of program modules configured to perform the functions of various embodiments of the present invention.

[0088] A program / utility 40 having a set (at least one) of program modules 42 may be stored, for example, in memory 28. Such program modules 42 include, but are not limited to, an operating system, one or more application programs, other program modules, and program data, each of which, or some combination thereof, may include an implementation of a network environment. Program modules 42 generally implement the functions and / or methods of the embodiments described herein.

[0089] The device 12 may also communicate with one or more external devices 14 (e.g., a keyboard, a pointing device, a display 24, etc.), one or more devices that enable a user to interact with the device 12, and / or any device that enables the device 12 to communicate with one or more other computing devices (e.g., a network card, a modem, etc.). Such communication may occur through an input / output (I / O) interface 22. Furthermore, the device 12 may also communicate with one or more networks (e.g., a local area network (LAN), a wide area network (WAN), and / or a public network such as the Internet) through a network adapter 20. Figure 2 As shown, network adapter 20 communicates with the other modules of device 12 via bus 18. It should be understood that although not shown, other hardware and / or software modules may be used in conjunction with device 12, including but not limited to microcode, device drivers, redundant processing units, external disk drive arrays, RAID systems, tape drives, and data backup storage systems.

[0090] The processing unit 16 executes various functional applications and data processing by running programs stored in the system memory 28, such as implementing the method provided in the first embodiment of the present invention.

[0091] Example 3

[0092] This embodiment provides a storage medium containing computer-executable instructions. When the computer-executable instructions are executed by a computer processor, they are used to perform the method of the first embodiment.

[0093] The computer storage medium of the embodiment of the present invention can adopt any combination of one or more computer-readable media. Computer-readable media can be computer-readable signal media or computer-readable storage media. Computer-readable storage media can be, for example, but not limited to, electrical, magnetic, optical, electromagnetic, infrared, or semiconductor systems, devices or components, or any combination thereof. More specific examples (non-exhaustive list) of computer-readable storage media include: an electrical connection with one or more wires, a portable computer disk, a hard disk, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or flash memory), an optical fiber, a portable compact disk read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination thereof. In this document, a computer-readable storage medium can be any tangible medium containing or storing a program that can be used by an instruction execution system, device or device or used in combination with it.

[0094] A computer-readable signal medium may include a data signal propagated in baseband or as part of a carrier wave, which carries computer-readable program code. Such propagated data signals may take various forms, including but not limited to electromagnetic signals, optical signals, or any suitable combination thereof. A computer-readable signal medium may also be any computer-readable medium other than a computer-readable storage medium that can transmit, propagate, or transport a program for use by or in conjunction with an instruction execution system, apparatus, or device.

[0095] Program code embodied on a computer readable medium may be transmitted using any appropriate medium, including but not limited to wireless, wireline, optical fiber cable, RF, etc., or any suitable combination of the foregoing.

[0096] The computer program code for performing the operations of the present invention can be written in one or more programming languages, or a combination thereof, including object-oriented programming languages such as Java, Smalltalk, C++, and conventional procedural programming languages such as "C" or similar programming languages. The program code can be executed entirely on the user's computer, partially on the user's computer, as a separate software package, partially on the user's computer and partially on a remote computer, or entirely on a remote computer or server. In cases involving a remote computer, the remote computer can be connected to the user's computer through any type of network, including a local area network (LAN) or a wide area network (WAN), or can be connected to an external computer (e.g., through the Internet using an Internet service provider).

[0097] Of course, the computer-executable instructions of a storage medium provided by an embodiment of the present invention are not limited to the above method operations, but can also execute related operations in the method provided by any embodiment of the present invention.

[0098] The present invention is experimentally verified below. The interference system is based on the Michelson optical orbital angular momentum interference system (such as Figure 3 As shown in the figure, take the example of (as shown in the figure). First, the laser beam is emitted by a single-frequency laser, adjusted to a linear polarization state by a polarizer, adjusted to a circular polarization state by a quarter-wave plate, and finally generated by a l-order vortex wave plate to generate a l-order orbital angular momentum beam. The l-order orbital angular momentum beam of the reference arm is converted into a -l-order orbital angular momentum beam by a cylindrical mirror and a reflector converter, and is combined with the l-order orbital angular momentum beam of the measuring arm carrying the measured displacement information in a non-polarizing beam splitter prism to generate a petal-shaped interference pattern. When l = 1, the following is generated: Figure 4 The double-petal petal-shaped interference pattern is shown in Figure 1. When the measured reflector of the measuring arm moves, the transmission phase changes, which is shown as Figure 5 The rotation of the petal-like interference pattern is shown. Figure 6 During initialization, the reflector of the measuring arm moves at a uniform speed, and the normalized light intensity signals of the four detection points are obtained.

[0099] Example 1: Demodulate the phase of the interference light field of the first-order conjugate orbital angular momentum beam and reconstruct the displacement change curve of the measuring arm reflector.

[0100] The experiment uses a single-frequency laser source with a wavelength of 1550nm. The emitted Gaussian beam is converted into a first-order orbital angular momentum beam through a first-order vortex wave plate. The distribution of the four detection points in the interference light field is shown in the figure below. Figure 6 As shown, they have the same radius but different angular distributions. To calculate the angular angles Ω1, Ω2, Ω3, and Ω4 by initialization, the measuring arm reflector can be controlled to uniformly translate multiple wavelengths, causing the petal-shaped interference pattern to rotate multiple times. The normalized light intensity signals at the four detection points are measured as follows: Figure 7 As shown, according to Figure 7 As a result, the initial angular angles Ω1, Ω2, Ω3, and Ω4 can be calculated to be 0 rad, 1.163 rad, 3.591 rad, and 4.573 rad, respectively. The uniform displacement curve of the measuring arm reflector is shown in the figure. Figure 8 The interference light intensity signals detected at the four detection points are shown as Figure 9 As shown in the figure. The interference light intensity signal after normalization is as follows Figure 10 The demodulated transmission phase curve is shown as Figure 11 The reconstructed displacement curve of the measuring arm reflector is shown in Figure 12By comparing the original displacement curve and the reconstructed displacement curve, it can be concluded that the present invention can correctly demodulate the first-order orbital angular momentum beam interference signal by measuring the light intensity signal at any four angular detection points.

[0101] Example 2: Demodulate the phase of the interference light field of the second-order conjugate orbital angular momentum beam and reconstruct the displacement change curve of the measuring arm reflector.

[0102] The distribution of the four detection points in the interference light field is as follows: Figure 13 As shown in the figure, with the same radius and different angular distributions, the calculated initial angular angles Ω1, Ω2, Ω3, and Ω4 are 0 rad, 1.918 rad, 3.862 rad, and 2.868 rad, respectively. The uniform displacement curve of the measuring arm reflector is shown in the figure. Figure 14 The interference light intensity signals detected at the four detection points are shown as Figure 7 As shown in the figure. The interference light intensity signal after normalization is as follows Figure 15 The demodulated transmission phase curve is shown as Figure 16 The reconstructed displacement curve of the measuring arm reflector is shown in Figure 17 By comparing the original displacement curve and the reconstructed displacement curve, it can be concluded that the present invention can correctly demodulate the second-order orbital angular momentum beam interference signal by measuring the light intensity signal at any four angular detection points.

[0103] Example 3: Demodulate the phase of the interference light field of the second-order conjugate orbital angular momentum beam and reconstruct the vibration curve of the measuring arm mirror.

[0104] The distribution of the four detection points in the interference light field is as follows: Figure 18 As shown in the figure, with different radii and angular distributions, the coordinates of the four detection points are (50 pixels, 0 rad), (45 pixels, π / 4 rad), (40 pixels, π / 2 rad), and (35 pixels, 3π / 4 rad). The vibration curve of the measuring arm reflector is shown in the figure. Figure 19 The interference light intensity signals detected at the four detection points are shown as Figure 20 As shown in the figure. The interference light intensity signal after normalization is as follows Figure 21 The demodulated transmission phase curve is shown as Figure 22 The reconstructed vibration curve of the measuring arm reflector is shown in Figure 23 By comparing the original vibration curve and the reconstructed vibration curve, it can be concluded that the present invention can correctly demodulate the second-order orbital angular momentum beam interference signal by measuring the light intensity signal at any four angular angles and radial radius detection points.

Claims

1. An optical orbital angular momentum interferometry demodulation method based on angular four-point detection, characterized in that include: (1) Obtaining a petal-shaped interference pattern to be demodulated; (2) Select four detection points with different angular angles from the petal-shaped interference pattern and collect their light intensity signals M1, M2, M3, and M4 respectively, where the angular angles Ω1, Ω2, Ω3, and Ω4 of the four detection points satisfy 2πrad ≥ Ω4 > Ω3 > Ω2 > Ω1 ≥ 0rad; (3) converting the light intensity signals M1, M2, M3, M4 into normalized light intensities I1, I2, I3, I4 based on light intensity normalization coefficients P1, P2, P3, P4 related to the radial radius of the selected detection point; (4) Calculate the interference phase based on normalized light intensity and angular angle (5) Comparison of the interference phase caused by the measured and the initial interference phase before measurement Obtain the interference phase change caused by the measured Among them, the interference phase is calculated in step (4) The method is: When Ω1=0rad, Ω2=(π / 2) / Δl rad, Ω3=(π) / Δl rad and Ω4=(3π / 2) / Δl rad, the interference phase The demodulation formula is expressed as: When the angular angles Ω1, Ω2, Ω3, and Ω4 are other values, the interference phase The demodulation formula is expressed as: Wherein, Δl represents the order difference of the optical orbital angular momentum of the two optical orbital angular momentum beams forming the petal-shaped interference pattern to be demodulated.

2. The optical orbital angular momentum interferometry demodulation method based on angular four-point detection according to claim 1, characterized in that: The light intensity signals M1, M2, M3, and M4 are collected by photodetectors or charge coupled devices.

3. The optical orbital angular momentum interferometry demodulation method based on angular four-point detection according to claim 1, characterized in that: The angular angles Ω1, Ω2, Ω3, Ω4 and the light intensity normalization coefficients P1, P2, P3, P4 are obtained by a preset or initialization method.

4. The optical orbital angular momentum interferometry demodulation method based on angular four-point detection according to claim 3, characterized in that: The initialization method is specifically as follows: (1) An optical path that changes uniformly with time t is introduced into the reference arm or measurement arm of the interferometer system that forms the petal-shaped interference pattern to be demodulated, so as to cause the petal-shaped interference pattern to rotate n times, where n is an integer. The obtained rotation angle Ф(t) ranges from 0 to 2×n×π, and the corresponding transmission phase difference is Δl represents the difference in the order of the two optical orbital angular momentum beams forming the petal-shaped interference pattern to be demodulated, and the time t varies from 0 to T, where T is the rotation end time and the rotation speed is ω = 2 × n × π / T; (2) collecting light intensity signals M1'(t), M2'(t), M3'(t), and M4'(t) that vary with time at any four angular positions of the petal-shaped interference pattern; (3) Calculate the light intensity normalization coefficients P1, P2, P3 and P4 according to the light intensity signals M1'(t), M2'(t), M3'(t) and M4'(t). The calculation formula is P n =QUAD(M n (t)) / T, n=1, 2, 3, 4, QUAD is the integral function, for the light intensity M in time T n (t) integration; (4) Determine the angular angles Ω1, Ω2, Ω3, and Ω4 using Fourier transform or shift correlation methods; Among them, the calculation method of Fourier transform is: first calculate M n '(t)'s spectrum F n '(f)=FT(M n '(t)), where n = 1, 2, 3, 4, and FT() is the Fourier transform function; then the frequency point f corresponding to the maximum spectrum amplitude except zero frequency is calculated Mn =MAX(ABS(F n '(f))), where f≠0, MAX is the maximum value function, and ABS is the absolute value function; finally, the frequency point f is calculated Mn Phase Ω n , that is, the angular angle, Ω n =PHASE(F n '(f Mn )), where PHASE is used to calculate the spectrum F n '(f) in f Mn The phase of the frequency point. The shift correlation calculation method is as follows: first set Ω1 to 0; then calculate the cross-correlation value C of the light intensity collected at different detection points. n (t) = CORR (M n '(t), M1'(t)), where n = 2, 3, 4, CORR is the cross-correlation function; finally, the angular angle Ω of different detection points is calculated. i =ω×MAX(C n (t)), where MAX is the maximum value function, which is used to calculate the time corresponding to the maximum value of the cross-correlation function.

5. The optical orbital angular momentum interferometry demodulation method based on angular four-point detection according to claim 1, characterized in that: The method of normalizing the light intensity signals M1, M2, M3, and M4 to light intensities I1, I2, I3, and I4 is as follows: n =M n / P n , n=1,2,3,4.

6. An optical orbital angular momentum interferometry demodulation device based on angular four-point detection, comprising a processor and a computer program stored in a memory and executable on the processor, characterized in that: When the processor executes the program, the method according to any one of claims 1 to 5 is implemented.

7. A storage medium containing computer-executable instructions, characterized in that: The computer executable instructions are used to perform the method according to any one of claims 1 to 5 when executed by a computer processor.

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