Interferometric signal detection system and method based on vortex light angular phase and photodetector array

Abstract

The application discloses an interference signal detection system and method based on vortex light angle phase and a photoelectric detector array, and belongs to the technical field of optical measurement and photoelectric detection. The system generates an angular interference light field by coaxial interference of a plane wave and vortex light, and accurately configures the radial distance and spatial azimuth angle of each array element of the photoelectric detector array relative to the phase singularity of the angular interference light field according to a preset amplitude and phase matching relationship. The application utilizes the unique spiral wavefront characteristics of vortex light to linearly map the dynamic phase difference caused by measurement into a spatial physical rotation of an interference pattern, thereby constructing a continuous passive spatial phase shift mechanism distributed along the azimuth angle. The photoelectric detector array is placed in the angular interference light field, and can directly output four interference signals with equal amplitude and orthogonal phase. The application realizes a completely unpolarized optical path structure, fundamentally eliminates the nonlinear error introduced by polarization crosstalk, and significantly promotes the high precision, low cost and miniaturized integration of the system.

Description

Technical Field

[0001] This invention belongs to the field of optical measurement and photoelectric detection technology, specifically relating to an interferometric signal detection system and method based on vortex optical angle phase and photoelectric detector array, which is particularly suitable for high-precision interferometric measurement applications such as displacement measurement and vibration detection. Background Technology

[0002] Precision displacement measurement, as a core supporting technology in modern precision engineering and advanced manufacturing, plays a vital role in semiconductor manufacturing, ultra-precision machine tools, micro-nano fabrication, aerospace, and large-scale scientific experimental platforms. Facing the stringent requirements of high-end equipment and precision instruments for nanometer-level positioning, optical interferometry, with its advantages of high resolution, ultra-high precision, and long stroke, has stood out among numerous displacement detection technologies and has become the mainstream solution for ultra-precision displacement measurement.

[0003] In various optical interferometric displacement measurement systems, the increase or decrease in actual displacement values ​​is closely related to displacement direction discrimination. Only with displacement direction discrimination can an optical interferometric displacement measurement system possess complete multi-dimensional measurement capabilities. Therefore, a displacement direction discrimination module that can stably output orthogonal signals and achieve accurate direction identification is one of the core components of an optical interferometric measurement system, playing an irreplaceable and crucial role. Traditional mainstream four-channel beam-splitting phase-shifting detection modules rely on the principle of polarization phase shifting, using standard optical elements such as polarization beam-splitting prisms and waveplates to control the polarization state of light, thereby generating four orthogonal interference signals. However, this approach requires high-quality polarization optical devices, resulting in a complex optical path structure, difficult assembly and adjustment, high cost, and hindering the integration and miniaturization of measurement systems. Summary of the Invention

[0004] To address the problems of complex optical path structures, high costs, and low integration in traditional interferometry, a simple, highly integrated detection system for four orthogonal interferometric signals is proposed. This invention provides an interferometric signal detection system and method based on vortex beam angular phase and a photodetector array. An angular interference optical field is formed by the coaxial interference of a coherent plane wave and a coherent vortex beam. A photodetector array is then positioned within this angular interference field to detect the interference signals, achieving the acquisition of four equal-amplitude and orthogonal interferometric signals. By simplifying the optical path structure and reducing the number of optical components, a balance between system miniaturization, high integration, and low cost is achieved.

[0005] To achieve the above objectives, the present invention adopts the following technical solution: In a first aspect, the present invention provides an interference signal detection system based on vortex light angular phase and photodetector array, comprising an optical interference unit and a photodetector unit. The optical interference unit is used to generate a plane wave and vortex light coaxially interfere to generate an angular interference light field. The photodetector unit adopts a photodetector array, which is arranged in the angular interference light field. According to a preset amplitude and phase matching relationship, the radial distance and spatial azimuth angle of each element of the photodetector array relative to the phase singularity of the angular interference light field are configured, so that the photodetector array outputs four interference signals with equal amplitude and orthogonal phase.

[0006] Furthermore, the optical interference unit includes a laser, a first reflecting mirror, a grating, a second reflecting mirror, a third reflecting mirror, a spiral phase plate, and a beam splitter. The linearly polarized light emitted by the laser is reflected by the first reflecting mirror and then incident perpendicularly on the grating to diffract, generating two first-order diffracted plane waves. One of the first-order diffracted plane waves is reflected by the third reflecting mirror and then passes through the spiral phase plate to form a vortex beam. The vortex beam and the other first-order diffracted plane wave are reflected by the second reflecting mirror and then combined at the beam splitter to undergo coaxial interference.

[0007] Furthermore, the photodetector array includes four photodetector elements, which are arranged around the phase singularity of the angular interference light field.

[0008] Furthermore, the photodetector array elements are photodiodes, photomultiplier tubes, or other point-type photodetectors.

[0009] Furthermore, the preset amplitude matching relationship expression is:

[0010] in, r n Let be the radial distance between the nth photodetector element and the phase singularity of the angular interference light field. i n For the first n Spatial azimuth angle of photodetector array element in angular interference light field R 0 represents the length of the major semi-axis of the equal-intensity trajectory, which is determined by the set target light intensity. c Let be the ellipticity of the angular interference light field, which is the ratio of the major axis to the minor axis of the angular interference light field. c 1.

[0011] Furthermore, the preset phase matching relationship expression is:

[0012] in, i 1 represents the initial mechanical installation azimuth angle of the first photodetector array element. lLet be the topological charge of the vortex beam. p The direction of phase shift increase of the output signal of the four-channel detector array element is given by its value. p ∈ {1, -1}, k n For the first n Each photodetector element in l The jump coefficient between equivalent phases is independently determined for each photodetector element. k n ∈ {0, 1, …, l -1}.

[0013] Secondly, the present invention provides an interferometric signal detection method based on vortex optical angle phase and photodetector array, based on the system of the first aspect, comprising the following steps: S1. Generate a coherent plane wave and a coherent vortex beam, and make the two coherent beams coaxially interfere in space to form an angular interference light field; S2. Arrange the photodetector array in the angular interference light field. The photodetector array includes four photodetector elements, which are set around the phase singularity of the angular interference light field. The radial distance between each photodetector element and the phase singularity of the angular interference light field, as well as the spatial azimuth angle in the angular interference light field, are set according to the preset amplitude matching relationship and phase matching relationship, so that the photodetector array outputs four equal-amplitude and orthogonal interference signals.

[0014] Furthermore, in step S1, a coherent plane wave and a coherent vortex beam are generated by the combination of a single-frequency laser, a spiral phase plate and optical elements, forming an angular interference light field.

[0015] Furthermore, in step S1, a combination of a single-frequency laser, a spatial light modulator, and optical elements generates a coherent plane wave and a coherent vortex beam, forming an angular interference light field.

[0016] Furthermore, the four photodetector array elements are fixed on the same 3D printed bracket.

[0017] Compared with the prior art, the present invention has at least the following beneficial technical effects: 1) This invention utilizes the coaxial interference of coherent plane waves and coherent vortex light in space to form an angular interference light field. Based on this, according to a preset amplitude and phase matching relationship, the radial distance and spatial azimuth angle of each element in the photodetector array relative to the phase singularity of the angular interference light field are precisely configured. By placing this photodetector array at a specific position in the aforementioned angular interference light field, the detection of four equal-amplitude and orthogonal phase interference signals can be directly achieved. This invention avoids complex beam splitting and phase-shifting optical structures, simplifies the system design, and improves the system integration.

[0018] 2) This invention is low-cost, reduces the number of optical components, and fundamentally eliminates nonlinear errors introduced by polarization crosstalk. Traditional interferometric measurement systems rely on discrete polarization phase-shifting modules to acquire four orthogonal signals. This architecture not only results in a large sensor probe size, but also makes it highly susceptible to nonlinear periodic errors due to inherent manufacturing defects and polarization leakage in polarization devices. This invention innovatively achieves an optical path design without any polarization optical components, significantly reducing the number of optical components. Its core mechanism lies in introducing optical orbital angular momentum (OAM) into the interferometric measurement system: the vortex beam carrying OAM has a unique spiral wavefront containing an azimuth phase term. When this vortex beam coaxially interferes with a plane wave, the dynamic phase difference between them caused by displacement is linearly mapped to the physical rotation of the angular interference field around its phase singularity in space. This unique angular phase characteristic essentially provides a naturally distributed, continuous, passive spatial phase-shifting mechanism along the azimuth direction. This invention utilizes this mechanism to circumvent complex waveplate and polarizing prism groups, which not only significantly promotes the miniaturization of the system, but also cuts off the path of nonlinear error introduced by polarization crosstalk from the physical source.

[0019] The interference signal detection method provided by this invention utilizes the spiral phase wavefront characteristics of a vortex beam to achieve spatial angular phase shift. After coaxial interference of two beams, the spatial phase distribution characteristics can be directly used for detection by a detector array, applicable to laser interferometers and grating interferometers. Addressing the unique problem in grating interferometry—the transverse ellipticization distortion of the beam caused by grating diffraction, leading to inconsistent maximum amplitudes of the output signals from the four detector array elements—this detection method, through in-depth analysis of the spatial distribution law of the angular interference light field and based on a preset amplitude matching relationship, physically compensates for the inconsistency in the maximum amplitudes of the output signals from the four detector array elements caused by spatial light field distortion, fundamentally ensuring that the system can acquire high-precision four equal-amplitude orthogonal signals. This detection method also has significant assembly and adjustment advantages: during system assembly, it is only necessary to observe whether the DC components of the four signals are consistent using an oscilloscope, or to observe whether the synthesized Lissajous trajectory is a standard circle, to quickly determine whether the center of the angular interference light field and the center of the detector array are coaxially coincident. Attached Figure Description

[0020] Figure 1 This is a schematic diagram of the overall structure of the system of the present invention; Figure 2 This is a schematic diagram of the spatial layout of a photodetector array in an angular interference light field with a topological charge of 1. Figure 3 (a) is a schematic diagram of four equal-amplitude and orthogonal phase interference signals output by a photodetector array; Figure 3 (b) represents the differential orthogonal signal between the two photodetector array elements.

[0021] In the attached diagram: 1-Laser; 2-First reflector; 3-Grate; 4-Second reflector; 5-Third reflector; 6-Helical phase plate; 7-Plane wave; 8-Vortex beam; 9-Beam splitter; 10-Photodetector array; 11-Optical interference unit; 12-First photodetector element; 13-Second photodetector element; 14-Third photodetector element; 15-Fourth photodetector element; i 1-Azimuth angle of the first photodetector element; i 2-Azimuth angle of the second photodetector array element; i 3-Azimuth angle of the third photodetector element; i 4 - Azimuth angle of the fourth photodetector element; X1 - Output signal of the first photodetector element; X2 - Output signal of the second photodetector element; X3 - Output signal of the third photodetector element; X4 - Output signal of the fourth photodetector element; X5 - Differential output signal of the first and third photodetector elements; X6 - Differential output signal of the second and fourth photodetector elements. Figure 2 middle w x Let be the minor axis of the angular interference light field; w y Let be the major axis of the angular interference light field; O The point is the phase singularity of the angular interference light field; r 1 represents the radial distance between the first photodetector element and the phase singularity of the angular interference light field; r 2 represents the radial distance between the second photodetector element and the phase singularity of the angular interference light field; r 3 represents the radial distance between the third photodetector element and the phase singularity of the angular interference light field; r 4 represents the radial distance between the fourth photodetector array element and the phase singularity of the angular interference light field. Detailed Implementation

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

[0023] To enable those skilled in the art to better understand the technical solutions of this invention, the technical solutions of the embodiments of this invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this invention, and not all embodiments. Based on the embodiments of this invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of this invention.

[0024] It should be noted that when an element is referred to as being "set on" another element, it can be directly on the other element or may be interposed with another element. When an element is considered to be "connected" to another element, it can be directly connected to the other element or may be interposed with another element. The terms "upper," "lower," "front," "rear," "left," "right," "top," "bottom," "inner," and "outer," etc., used herein to indicate orientation or positional relationships are based on the orientation or positional relationships shown in the accompanying drawings and are only for the convenience of describing the invention and simplifying the description, and are not intended to indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation, and therefore should not be construed as a limitation of the invention.

[0025] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains. The terminology used herein in the specification of this invention is for the purpose of describing particular embodiments only and is not intended to be limiting of the invention. The term "and / or" as used herein includes any and all combinations of one or more of the associated listed items.

[0026] Reference Figure 1 An interferometric signal detection system based on vortex optical angle phase and photodetector array includes an optical interferometer unit and a photodetector unit, wherein the photodetector unit adopts a photodetector array 10.

[0027] The optical interference unit is used to generate two coherent beams, a plane wave 7 and a vortex beam 8, and to make the plane wave 7 and the vortex beam 8 coaxially interfere in space to form an angular interference light field; such as Figure 1 As shown, in one embodiment, the optical interference unit includes a combination of a laser 1, a spiral phase plate 6, and optical elements, including a first reflecting mirror 2, a grating 3, a second reflecting mirror 4, a third reflecting mirror 5, and a beam splitter 9. Linearly polarized light emitted from the laser 1 is reflected by the first reflecting mirror 2 and then incident perpendicularly onto the grating 3, where it undergoes diffraction, generating two first-order diffracted plane waves. One first-order diffracted plane wave is reflected by the third reflecting mirror 5 and passes through the spiral phase plate 6 to form a vortex beam 8. The other first-order diffracted plane wave is reflected by the second reflecting mirror 4 to form a plane wave 7. The plane wave 7 and the vortex beam 8 are combined at the beam splitter 9 and undergo coaxial interference, ultimately incident on a photodetector array 10, where the photodetector array 10 collects the interference signal.

[0028] The photodetector array 10 is used to receive light intensity signals in the angular interference light field, such as Figure 2As shown, the photodetector array 10 is arranged in an angular interference light field. Each photodetector element in the array 10 is positioned around the phase singularity of the angular interference light field. During the arrangement process, it is only necessary to observe whether the DC components of the four signals are consistent using an oscilloscope, or to observe whether the synthesized Lissajous trajectory is a standard circle, to quickly determine whether the center of the angular interference light field, i.e., the phase singularity, coincides coaxially with the center of the detector array. The radial distance of each photodetector element from the phase singularity and its spatial azimuth angle with the angular interference light field are set according to preset amplitude matching and phase matching relationships, so that the photodetector array 10 outputs four equal-amplitude and orthogonal phase interference signals, such as... Figure 3 As shown in (a), the output signals X1 and X3 of the first and third photodetector array elements, as well as X2 and X4 of the second and fourth photodetector array elements, are differentially processed to eliminate signal distortion caused by common-mode noise, increase the effective signal amplitude, and eliminate DC bias. The resulting differential output signals X5 and X6 of the first and third photodetector array elements are shown below. Figure 3 As shown in (b), the first to fourth photodetector array elements are fixed using the same 3D-printed bracket, and the structural parameters of the 3D-printed bracket are set according to the size specifications of the photodetector unit.

[0029] This detection system utilizes the unique spiral wavefront characteristics of a vortex beam carrying optical orbital angular momentum (OAM), with its core comprising the azimuth phase term exp( ilth )(in l For topological load number, i (Azimuth angle). When vortex light and plane wave coaxially interfere, the dynamic phase difference caused by displacement is linearly mapped to the physical rotation of the angular interference light field around its phase singularity in space. This unique angular phase characteristic, in its physical essence, constructs a naturally distributed, continuous, and passive spatial phase shift mechanism along the azimuth direction. Based on this mechanism, this system achieves an optical path architecture without any polarization optical elements, completely avoiding complex waveplates and polarization prism groups. This not only significantly reduces the number of optical elements to promote system miniaturization, but also physically cuts off the path of nonlinear error introduced by polarization crosstalk, realizing the miniaturization, low cost, and high integration of a high-precision interferometric signal detection system.

[0030] This system is applicable to a variety of interferometric measurement scenarios, including displacement measurement, vibration detection, and surface morphology measurement.

[0031] A plane wave and a vortex beam coaxially interfere to form an angular interference light field. The fabricated photodetector array is arranged in the angular interference light field according to a preset geometric layout. For example, when the displacement stage carrying grating 3 moves, the angular interference light field physically rotates around the phase singularity in the spatial dimension. Each photodetector element receives the light intensity signals and generates sinusoidal signals. Due to the satisfaction of amplitude matching and phase matching relationships, the four photodetector elements will output four sinusoidal signals with equal amplitude and orthogonal phase. Through differential demodulation and subsequent circuitry, the displacement and displacement direction can be demodulated.

[0032] An interferometric signal detection method based on vortex optical angle phase and photodetector array includes the following steps: Step 1: The optical interference unit generates two coherent beams, a plane wave 7 and a vortex beam 8, and causes the plane wave 7 and the vortex beam 8 to coaxially interfere in space, forming an angular interference light field; Step 2: The photoelectric detection unit uses the spatial distribution of the angular interference light field to obtain interference signals with equal amplitude and orthogonal phase: Based on the preset amplitude and phase matching relationship, the radial distance and spatial azimuth angle of each photoelectric detector element in the photoelectric detector array relative to the phase singularity of the angular interference light field are precisely configured, and the photoelectric detector array outputs four interference signals with equal amplitude and orthogonal phase.

[0033] The coherent plane wave and coherent vortex light in step 1 can be formed in either of the following ways: one is by a combination of a single-frequency laser, a spiral phase plate and optical elements to form an angular interference light field; the other is by a combination of a single-frequency laser, a spatial light modulator (SLM) and optical elements to form an angular interference light field.

[0034] The optical interference unit in step 1 is a combination of a laser, a spiral phase plate or a spatial light modulator (SLM), and optical elements. These optical elements include, but are not limited to, beam splitters, mirrors, collimating lenses, and diffractive optical elements. Depending on the optical measurement principle, one or more of these optical elements are selected and combined with the laser to form the optical interference unit.

[0035] The photodetector array in step 2 consists of four photodiodes, photomultiplier tubes, or other types of single-point photodetectors. The spatial arrangement of the photodetector array elements is configured based on the topological charge of the vortex light and the intensity of the target detection light. By satisfying preset amplitude matching and phase matching relationships, four equal-amplitude and orthogonal phase interference signals are output. The four photodetector array elements use the same photodetectors.

[0036] In step 2, the preset amplitude matching relationship satisfies the following formula:

[0037] in,r n For the first n The radial distance between each photodetector element and the phase singularity of the angular interference light field. i n For the first n Spatial azimuth angle of each photodetector array element in the angular interference light field R 0 represents the length of the major semi-axis of the equal-intensity trajectory, which is determined by the set target light intensity. c Let be the ellipticity of the angular interference light field, which is the ratio of the major axis to the minor axis of the angular interference light field. c 1.

[0038] In step 2, the preset phase matching relationship satisfies the following formula:

[0039] in, i 1 represents the initial mechanical installation azimuth angle of the first photoelectric detector element. l The topological charge number of the vortex beam 8. p The direction of phase shift increase of the output signal of the four-channel detector array element is given by its value. p ∈{1, -1}, k n For the nth photodetector element in l The jump coefficient between equivalent phases is independently determined for each photodetector element. k n ∈{0, 1, …, l -1}.

[0040] Example This embodiment provides a method for detecting interferometric signals, such as Figure 1 As shown, linearly polarized light emitted from laser 1 is reflected by the first reflecting mirror 2 and then incident perpendicularly onto grating 3, where it undergoes diffraction, generating two first-order diffracted plane waves. One of these first-order diffracted plane waves is a plane wave 7, while the other is reflected by reflecting mirror 5 and then passes through a spiral phase plate 6, transforming into vortex light 8. The vortex light 8 and the plane wave 7, reflected by reflecting mirror 4, are combined at beam splitter 9 and undergo coaxial interference, ultimately incident on photodetector array 10, where the interference signal is acquired. A coherent plane wave 7 and a coherent vortex light 8 are generated by optical interference unit 11 and coaxially interfered, incident on photodetector array 10. Photodetector array 10 includes a first photodetector element 12, a second photodetector element 13, a third photodetector element 14, and a fourth photodetector element 15. Due to the coaxial interference of the coherent plane wave and the coherent vortex light, an angular interference light field is formed. The original wavefront shapes of the two beams are identical, both being circular. Assuming the two beams of light have the same initial phase, both are... f If 0 = 0, then the wavefront functions of plane wave 7 and vortex light 8 can be expressed as follows: (1) (2) in, This represents the wavefront function of plane wave 7. This represents the wavefront function of vortex light 8. A 1 and A 2 represents the amplitude of the wavefront function of plane wave 7 and vortex light 8, respectively; e is the natural constant; i is the imaginary unit; k1 and k2 represent the wave vectors of plane wave 7 and vortex light 8, respectively; r represents the position vector in three-dimensional space; and π represents pi. f 0 represents the frequency of plane wave 7 and vortex light 8. t Δ represents the time variable. f This represents the frequency difference between vortex light 8 and plane wave 7. l The topological charge of the vortex beam is determined by the topological charge of the spiral phase plate 6. i In the angular interference light field, the azimuth angle is the polar coordinate system established with the phase singularity as the origin.

[0041] From the two-beam interference intensity formula (3), the beam interference intensity in the angular interference field can be obtained. I Expression (4): (3) (4) Where, Φ1=k1r- 2π f 0 t Φ2=k2r- 2π( f 0+Δ f ) t + lθ Since the two beams are completely coaxial (the wave vectors are parallel in the propagation direction), the transverse wave vector difference approaches zero, that is, (k1-k2)r can be regarded as a static optical constant phase difference Δ. 0. In a grating interferometer, the Doppler frequency shift Δ f Mechanical displacement directly from the grating x G For positive and negative first-order reflected diffracted light, the integrated phase shift is 2πΔ. feet = 4π x G / d G , d G Since it is the grating constant, the instantaneous interference intensity distribution on the detector surface is... I GIt can be represented as: (5) Among them, the DC component I DC = A 1 2 + A 2 2 AC amplitude I AC = 2 A 1 A 2.

[0042] To extract high-precision displacement information, a photodetector array is needed, containing four photodetector elements, with the phases of the AC signals from the four elements differing by π / 2 sequentially. Let the... n Each photodetector array element ( n The received phase of (∈ {1,2,3,4}) is α n Extract the spatial phase term from the interference equation (5): (6) To achieve strictly orthogonal sequences, the first... n The phase of each photodetector element must be equal to the phase of the reference photodetector element (the first photodetector element), plus the target phase difference ((n-1)π / 2), and each photodetector element is allowed to perform angular translations that are integer multiples of 2π within the optical period. This is to avoid physical collisions or obstructions between the detector elements during actual mechanical installation. n Spatial phase of detector array elements α n Must meet: (7) Substituting equation (6) into equation (7), we obtain the array element azimuth layout equation for orthogonal signal detection: (8) in, i 1 represents the initial mechanical installation azimuth angle of the first photodetector array element. i n For the first n Spatial azimuth angle of photodetector array element in angular interference light field l Let be the topological charge number of the vortex beam. p The direction of phase shift increase of the output signal of the four-channel detector array element is given by its value. p ∈ {1, -1}, k n For the first n Each photodetector element in lThe jump coefficient between equivalent phases is independently determined for each photodetector element. k n ∈ {0, 1, …, l -1}.

[0043] In actual optical paths, due to the diffraction effect of the grating, a circular beam will become elliptical. Amplitude A 1 and A 2 is not ideally uniform, and the resulting AC amplitude I AC It will exhibit an elliptical Gaussian distribution. The AC amplitude of the interference signal can be described in space as: (9) in, I max Let be the peak light intensity at the point of highest energy on the interference bright ring, and r be the radial distance from any point in the angular interference light field to the phase singularity. w x Let be the major axis of the angular interference light field. w y Let be the minor axis of the angular interference light field.

[0044] To ensure that the four photodetector elements at different locations output electrical signals of exactly equal amplitude, they must be forced to lie on the same contour line of equal intensity. Let I AC = I C , I C The constant AC light intensity is designed for the target system. Taking the natural logarithm of both sides of equation (9) and rearranging the equation algebraically, the radial distance can be obtained. r n : (10) The numerator in formula (10) is uniformly defined as R 0, which represents the semi-major axis of an ellipse of equal strength, and introduces the ellipticity. c = w x / w y The final radial distance formula can be obtained as follows: (11) in, r n For the first n The radial distance between each photodetector element and the phase singularity of the angular interference light field. i n For the first n Spatial azimuth angle of photodetector array element in angular interference light fieldR 0 represents the length of the major semi-axis of the equal-intensity trajectory, which is determined by the set target light intensity. c Let be the ellipticity of the angular interference light field, which is the ratio of the major axis to the minor axis of the angular interference light field. c 1.

[0045] The finite photosensitive area of ​​the photodetector array elements leads to spatial phase integration, which not only affects the total signal energy but also has a very subtle impact on the AC interference contrast. Therefore, a rigorous mathematical derivation was performed, assuming that the edges of the square photodetector array elements are all parallel to the global mechanical coordinate system. X shaft and Y Axis. In the angular interference light field, the first... n Photodetector array element ( n The center position of (∈ {1, 2, 3, 4}) is strictly locked by a defined radial and azimuth formula, and its global rectangular coordinates ( X n , Y n ) for: (12) For a side length of Δ l A square photodetector array element is used to establish a local coordinate system with the center of the photodetector array element as the origin. u , v ),in u Parallel to X axis, v Parallel to Y Axis. Due to the side length Δ of the photodetector array element. l The DC bias within the target spot region is extremely small compared to the size of the angular interference light field. I DC and AC amplitude I AC It remains almost constant. However, the angular phase of the vortex light... lth ( X , Y A linear tilt will occur on the detector surface. The azimuth angle will be... i ( X , Y = arctan( Y / X At the center of the detector ( X n , Y n A first-order Taylor expansion at position ) yields the local phase distribution function, which can be approximated as: (13) Substituting the expanded local phase into the interference equation, the... n Total light intensity signal received by the photodetector array element S n ( x )for: (14) Where, Φ 0,n = 4π x G / d G – lth n + Δ 0 is the first n Ideal orthogonal phase at the center of the photodetector array element d G The grating constant is D n It is the first n The integration region of the photodetector array element. x G This represents the actual mechanical linear displacement of the grating relative to the optical reading. n The complete light intensity signal expression of the photodetector array element is: (15) Among them, sinc( x ) = (sin x ) / x , K n The signal contrast attenuation coefficient caused by the finite aperture of the photodetector array elements is related not only to the radial distance. r n It is also related to the azimuth angle of the array element. i n Modulation. From formula (15), it can be seen that the limited photosensitive area of ​​the detector does not introduce phase distortion. When the light field undergoes elliptic distortion, if the radial distances of the four array elements from the phase singularity are equal, i.e. r 1= r 2= r 3= r 4= R ,in R Since the amplitude of each signal is constant, a biaxially symmetric geometric constraint must be introduced to ensure the uniformity of the amplitude of each array element. K n The formula for equal, equal-amplitude, biaxially symmetric azimuth angles is as follows: (16) In the formula, the reference installation angle is... iThe value of 1 ranges from (0, π / 2). Since formula (16) assumes that the detector array elements are arranged in a counter-clockwise order, the phase shift increment direction coefficient in formula (8) is taken as... p = 1. To simultaneously achieve equal amplitude and orthogonal signal output, the spatial azimuth angles of the four array elements are... i n The orthogonal layout model and the equal-amplitude biaxial symmetry constraint must be satisfied simultaneously. Solving equations (8) and (16) simultaneously in the second quadrant yields the reference installation angle located in the first quadrant. i 1 is: (17) In the formula, k 2 is the second photodetector element 13 in l The jump coefficient between equivalent phases k 2∈ {0, 1, (2 l -1) / 4 }, … The rounding sign is used for rounding down. Substituting equation (17) back into equation (16), we obtain the orthogonal azimuth layout equation for radial light intensity correction: (18) The derivation of equation (18) must satisfy the following physical constraints: the first photodetector element 12 is selected as the phase reference, and its jump coefficient is set to... k 1 = 0; Based on the centrosymmetric geometric constraints between the first photodetector element 12 and the third photodetector element 14, the phase difference between them is required to be an odd multiple of π, from which the topological charge number is derived. l = 1 + 2 k 3. Due to the jump coefficient k 3 is an integer, therefore the topological load number is... l The number of jump coefficients must be odd; the sequence of jump coefficients must satisfy a recurrence relation. k 4= k 2+ k 3. Under this azimuth constraint, the ideal phase sequence of the output signals of the four detector array elements. β 1. β 2. β 3. β 4 is represented as follows: (19) As can be seen from the ideal phase sequence above, the phase difference between adjacent detector elements is π / 2. In summary, under the azimuth layout model with radial intensity correction, the four detector elements can generate interference signals with equal amplitude and orthogonal phase.

[0046] Taking into account the geometric dimensions of the photodetector array elements, the ellipticization distortion effect of the angular interference optical field caused by grating diffraction, and the computational requirements for generating four equal-amplitude orthogonal signals, this embodiment of the invention selects a spiral phase plate with an order of 1 and a working wavelength corresponding to the laser wavelength to generate the topological charge. l = 1 vortex light. Based on this, the photodetector array adopts, as follows: Figure 2 The diagram shows a symmetrical spatial layout. An initial azimuth angle is set. i = 45°, which compensates for the amplitude imbalance introduced by optical distortion, ensuring that the system meets the phase orthogonality condition at the physical level. Therefore, the complete light intensity signal expression output by each detector element is defined as follows: (twenty one) in, K The attenuation coefficient is caused by the finite aperture of the detector array element. K = sinc 2 [(√2)Δ l / 4 R ],Φ( x G ) = 4π x G / d G – π / 4 + Δ 0 represents the system's reference phase term. Thus, based on this layout model, the grating interferometric displacement measurement system can acquire four equal-amplitude and orthogonal interferometric signals.

[0047] The system structure of this invention is simple, the number of optical components is reduced, it is suitable for interferometric measurement scenarios such as high-precision displacement measurement, and it has good integration potential.

[0048] Although embodiments of the present invention have been described above in conjunction with the accompanying drawings, the invention is not limited to the specific embodiments described above. The specific embodiments described above are merely illustrative and instructive, and not restrictive. Those skilled in the art, guided by this specification, can make many other forms without departing from the scope of the claims of the present invention, and all of these are within the scope of protection of the present invention.

Claims

1. An interferometric signal detection system based on vortex optical angle phase and photodetector array, characterized in that, It includes an optical interference unit and a photoelectric detection unit. The optical interference unit is used to generate a plane wave and a vortex beam to coaxially interfere and generate an angular interference light field. The photoelectric detection unit adopts a photodetector array, which is arranged in the angular interference light field. Based on the preset amplitude and phase matching relationship, the radial distance and spatial azimuth angle of each element of the photodetector array relative to the phase singularity of the angular interference light field are configured, so that the photodetector array outputs four interference signals with equal amplitude and orthogonal phase.

2. The interferometric signal detection system based on vortex optical angle phase and photodetector array according to claim 1, characterized in that, The optical interference unit includes a laser (1), a first mirror (2), a grating (3), a second mirror (4), a third mirror (5), a spiral phase plate (6), and a beam splitter (9). The linearly polarized light emitted by the laser (1) is reflected by the first mirror (2) and then incident perpendicularly on the grating (3) to diffract, generating two first-order diffracted plane waves. One of the first-order diffracted plane waves is reflected by the third mirror (5) and then passes through the spiral phase plate (6) to form a vortex light (8). The vortex light (8) and the other first-order diffracted plane wave are reflected by the second mirror (4) and then combined in the beam splitter (9) to undergo coaxial interference.

3. The interferometric signal detection system based on vortex optical angle phase and photodetector array according to claim 1, characterized in that, The photodetector array includes four photodetector elements, which are arranged around the phase singularity of the angular interference light field.

4. The interferometric signal detection system based on vortex optical angle phase and photodetector array according to claim 3, characterized in that, The photodetector array element is a photodiode, a photomultiplier tube, or other point-type photodetector.

5. The interferometric signal detection system based on vortex optical angle phase and photodetector array according to claim 1, characterized in that, The preset amplitude matching relationship expression is: in, r n Let be the radial distance between the nth photodetector element and the phase singularity of the angular interference light field. θ n For the first n Spatial azimuth angle of photodetector array element in angular interference light field R 0 represents the length of the major semi-axis of the equal-intensity trajectory, which is determined by the set target light intensity. γ Let be the ellipticity of the angular interference light field, which is the ratio of the major axis to the minor axis of the angular interference light field. γ 1.

6. The interferometric signal detection system based on vortex optical angle phase and photodetector array according to claim 1, characterized in that, The preset phase matching relationship expression is: in, θ 1 represents the initial mechanical installation azimuth angle of the first photodetector array element. l Let be the topological charge of the vortex beam. p The direction of phase shift increase of the output signal of the four-channel detector array element is given by its value. p ∈ {1, -1}, k n For the first n Each photodetector element in l The jump coefficient between equivalent phases is independently determined for each photodetector element. k n ∈ {0, 1, …, l -1}.

7. A method for detecting interferometric signals based on vortex optical angle phase and photodetector array, based on the system described in claim 1, characterized in that, Includes the following steps: S1. Generate a coherent plane wave and a coherent vortex beam, and make the two coherent beams coaxially interfere in space to form an angular interference light field; S2. Arrange a photodetector array in the angular interference light field. The photodetector array includes four photodetector elements, which are arranged around the phase singularity of the angular interference light field. The radial distance between each photodetector element and the phase singularity of the angular interference light field, as well as the spatial azimuth angle in the angular interference light field, are set according to preset amplitude matching and phase matching relationships, so that the photodetector array outputs four equal-amplitude and orthogonal interference signals.

8. The interferometric signal detection method based on vortex optical angle phase and photodetector array according to claim 7, characterized in that, In step S1, a coherent plane wave and a coherent vortex beam are generated by a combination of a single-frequency laser, a spiral phase plate, and optical elements, forming an angular interference light field.

9. The interferometric signal detection method based on vortex optical angle phase and photodetector array according to claim 7, characterized in that, In step S1, a combination of a single-frequency laser, a spatial light modulator, and optical elements generates a coherent plane wave and a coherent vortex beam, forming an angular interference light field.

10. The interferometric signal detection method based on vortex optical angle phase and photodetector array according to claim 7, characterized in that, The four photodetector array elements are fixed on the same 3D printed bracket.

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