Single-pixel OAM mode common-path interferometry method

Abstract

A single-pixel OAM mode common-path interference method uses the 0th-order OAM fundamental mode as the reference component and performs necessary phase shifts. Other-order OAM modes, including the 0th-order OAM fundamental mode, are used as modulation bases to sample the wavefront of the unknown light field and configure the resolution of spatial wavefront imaging. M × N , the sampling rate of single-pixel imaging s , the number of phase shift steps φ, select one of the OAM mode types as the modulation basis for imaging the target spatial wavefront; calculate and generate s × M × N The resolution is M × N The OAM modulation mode generates a resolution of M × N The selected OAM mode 0th order fundamental mode; the generated 0th order OAM fundamental mode is phase shifted in multiple steps according to the number of phase shift steps; the generated s × M × N The OAM modes are superimposed on the phase-shifted 0th-order OAM fundamental mode, causing intermodal interference between the two modes to produce the final modulation mode.

Description

Technical Field

[0001] The present invention belongs to the intersection field of spatial wavefront measurement and single-pixel imaging, and in particular relates to a method for common-path interference between single-pixel OAM modes. Background Art

[0002] Single-pixel wavefront imaging is an emerging wavefront measurement technology that combines single-pixel imaging with interferometry. Unlike traditional array-based wavefront imaging, single-pixel wavefront imaging reconstructs the wavefront by correlating a structured pattern with a series of corresponding complex-valued coefficients. Thanks to the high sensitivity and wide spectral bandwidth of single-pixel detectors, this technology holds broad application prospects in interferometry and holography, as well as in optical communications, optical imaging, and quantum information storage and measurement.

[0003] At the beginning of the development of single-pixel wavefront imaging, researchers focused on using the real-valued modulation basis used in intensity-based single-pixel imaging to modulate the wavefront. However, amplitude-only modulation can lead to ambiguity when distinguishing complex values ​​from their complex conjugates. Recently, researchers have introduced vortex beams as a natural complex basis for single-pixel wavefront imaging, aiming to eliminate the complex conjugate ambiguity. Because each photon in a vortex beam carries orbital angular momentum (OAM), the different OAM modes have infinite values ​​and are mutually orthogonal, providing a new dimension in the spatial domain of light waves. Interferometry is also a key step in single-pixel wavefront imaging. Initially, researchers used two-path interferometry methods such as Mach-Zehnder interferometers or Michelson interferometers to generate interference, enabling single-pixel detectors, which only obtain signal intensity information, to obtain complex wavefront coefficients. However, this method requires an additional reference optical path, which increases the complexity of the system. Later, researchers artificially partitioned the pixels of the phased array of modulators so that the interfering signal beam and reference beam are generated on the same optical path, making single-pixel wavefront imaging more compact and stable. However, these common-path interferometry methods still have certain shortcomings. When introducing reference light, some pixels of the phased array need to be sacrificed, so that the pixel resources of the phased array are not fully utilized, or the wavefront imaging resolution is reduced, or the field of view of the wavefront imaging is reduced, resulting in low wavefront imaging performance. Summary of the Invention

[0004] For single-pixel wavefront imaging based on OAM modes, the purpose of the present invention is to provide a single-pixel OAM mode common-path interference method, which is characterized by using the 0th-order OAM fundamental mode as the reference component and performing necessary phase shifts, and using other-order OAM modes including the 0th-order OAM fundamental mode as the modulation basis to sample the wavefront of the unknown light field, fully utilizing the pixel resources of the phased array to achieve high-resolution wavefront complex amplitude and large-field-of-view imaging.

[0005] To achieve the above object, the present invention provides the following technical solutions:

[0006] A single-pixel OAM mode common-path interference method uses the 0th-order OAM fundamental mode as the reference component and performs necessary phase shifts, and uses other-order OAM modes, including the 0th-order OAM fundamental mode, as the modulation basis to sample the wavefront of the unknown light field. The method specifically includes the following steps:

[0007] Step 1: Configure the resolution parameters M×N of spatial wavefront imaging, the sampling rate s of single pixel imaging, and the number of phase shift steps Select one of the OAM mode types as the modulation basis for imaging the target spatial wavefront;

[0008] Step 2: Under the conditions selected in step 1, calculate and generate s×M×N OAM modulation patterns with a resolution of M×N, and generate the 0th-order fundamental mode of the selected OAM mode with a resolution of M×N;

[0009] Step 3: Perform multi-step phase shifting on the 0th-order OAM fundamental mode generated in step 2 according to the number of phase shifting steps; superimpose the phase-shifted 0th-order OAM fundamental mode on the s×M×N OAM modes generated in step 2 (first, perform phase shifting on the 0th-order OAM mode in Matlab, and then add the phase-shifted 0th-order OAM mode to the other-order OAM modes respectively), so that the two modes undergo inter-modal interference (the two modes here refer to the 0th-order OAM mode and each of the other-order OAM modes, including the 0th-order OAM mode, that is, inter-modal interference occurs between the 0th-order OAM mode and the other-order OAM modes, including the 0th-order OAM mode, and then a final series of modulation modes are generated), and the final modulation modes;

[0010] Step 4: Load the modulation pattern to the phased array (final modulation mode), the single-pixel detector collects the signal intensity; the signal generated in step 3 is The final modulation patterns after phase shifting are sequentially loaded into the phased array to modulate the target spatial wavefront. At the same time, the single-pixel detector collects the signal intensity value of the center point of the Fourier plane of the modulated light wavefront corresponding to each pattern.

[0011] Step 5: Reconstruct the target spatial wavefront: Obtain the complex coefficient spectrum of the target spatial wavefront based on the phase shifting technique, and restore the target spatial wavefront using the single-pixel reconstruction algorithm.

[0012] Furthermore, in step 1, OAM modes include Laguerre-Gaussian modes, Bessel modes, vector vortex modes, and perfect vortex modes. Different OAM modes have corresponding 0th-order OAM modes, such as the 0th-order Laguerre-Gaussian mode and the 0th-order Bessel mode. They all belong to the 0th-order OAM mode, and the specific name for the 0th-order OAM mode is the 0th-order OAM fundamental mode.

[0013] Furthermore, the multi-step phase shift in step 3 is a phase shift of one step or a phase shift of three or more steps.

[0014] Furthermore, the phased array in step 4 is a complex amplitude modulator indirectly realized by a digital micromirror array, a ferroelectric liquid crystal spatial light modulator and an amplitude liquid crystal spatial light modulator through a Lee method or a superpixel method, or a complex amplitude modulator indirectly realized by a pure phase liquid crystal spatial light modulator through a pure phase hologram.

[0015] Furthermore, the size of the center point of the Fourier plane of the modulated light wavefront in step 4 is r≤1.27λf / d, where λ is the wavelength of the light beam, f is the focal length of the collecting lens, and d is the diameter of the light beam.

[0016] Furthermore, in step 5, the single-pixel reconstruction algorithm includes a second-order correlation operation and a compressed sensing reconstruction algorithm. The beneficial effect of the present invention is that the present invention proposes a single-pixel OAM mode common-path interference technology, which uses the 0th-order OAM fundamental mode as a reference beam and performs necessary phase shifts, uses other-order OAM modes including the 0th-order OAM fundamental mode as a modulation basis, samples the wavefront of the unknown light field, and fully utilizes the pixel resources of the phased array to achieve high-resolution complex amplitude of the wavefront and large-field imaging. Compared with the existing method of artificially dividing the pixels of the phased array of the modulation device, the present invention fully utilizes the number of pixels of the phased array while ensuring that the imaging field of view is not reduced, and achieves the advantages of full-resolution wavefront imaging of the phased array pixels. The present invention can also be extended to wider bands, such as infrared, terahertz, X-ray and other bands, especially wavefront complex amplitude imaging when array detectors are expensive or do not yet exist. It has broad application prospects in the fields of interferometry and holography that require the use of OAM beams, such as optical communications, optical imaging, quantum information storage and measurement, and other fields. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] Figure 1 The intermodal interference principle diagram when the 0th-order Bessel fundamental mode is subjected to three-step phase shifting to select the Bessel mode as the modulation basis;

[0018] Figure 2 The intermodal interference principle diagram when the 0th-order Laguerre-Gaussian mode is phase-shifted in four steps to select the Laguerre-Gaussian mode as the modulation basis;

[0019] Figure 3 is the amplitude and phase distribution diagram of a target spatial wavefront;

[0020] Figure 4 The spatial wavefront amplitude and phase reconstructed from the common-path interference simulation of single-pixel OAM modes in Example 1; in the figure, 1 is the Bessel modulation basis, 2 is the 0th-order Bessel fundamental mode after four-step phase shifting, and 3 is the final modulation pattern. Specific implementation plan

[0021] The present invention will be described in further detail below with reference to the accompanying drawings.

[0022] like Figures 1 to 4 As shown, the present invention discloses a single-pixel OAM mode common-path interference method, which uses the 0th-order OAM fundamental mode as a reference beam and performs necessary phase shifts, uses other-order OAM modes including the 0th-order OAM fundamental mode as a modulation basis, samples the wavefront of an unknown light field, and fully utilizes the pixel resources of a phased array to achieve high-resolution wavefront complex amplitude and large-field imaging. The method specifically includes the following steps:

[0023] Step 1: Configure the resolution parameters M×N of spatial wavefront imaging, the sampling rate s of single pixel imaging, and the number of phase shift steps One of the OAM mode types is selected as the modulation basis for imaging the target spatial wavefront. The OAM mode types include Laguerre-Gaussian mode, Bessel mode, vector vortex mode, perfect vortex mode, etc.

[0024] Step 2: Under the conditions selected in step 1, calculate and generate s×M×N OAM modulation patterns with a resolution of M×N, and generate the 0th-order fundamental mode of the selected OAM mode with a resolution of M×N;

[0025] Step 3: The 0th-order OAM fundamental mode generated in step 2 is phase-shifted by three or more steps according to the number of phase shift steps; the phase-shifted 0th-order OAM fundamental mode is superimposed on the generated s×M×N OAM modes, causing intermodal interference between the two modes to produce the final modulation pattern;

[0026] Step 4: Load the modulation pattern to the phased array, and the single-pixel detector collects the signal intensity; The final modulation patterns after phase shifting are sequentially loaded into the phased array to modulate the target spatial wavefront. At the same time, the detector collects the signal intensity value of the center point of the Fourier plane of the modulated light wavefront corresponding to each pattern. The phased array is composed of a digital micromirror array, a ferroelectric liquid crystal spatial light modulator, and an amplitude liquid crystal spatial light modulator, which indirectly realize a complex amplitude modulator through the Lee method or superpixel method, or a pure phase liquid crystal spatial light modulator which indirectly realizes a complex amplitude modulator through a pure phase hologram. The size of the center point of the modulated light wavefront in the Fourier plane is r≤1.27λf / d, where λ is the wavelength of the light beam, f is the focal length of the collection lens, and d is the diameter of the light beam.

[0027] Step 5: Reconstruct the target spatial wavefront: The complex coefficient spectrum of the target spatial wavefront is obtained using the phase shifting technique, and the target spatial wavefront is restored using a single-pixel reconstruction algorithm. The reconstruction algorithm can be selected from a second-order correlation algorithm or a compressed sensing reconstruction algorithm.

[0028] The present invention is further illustrated by the following three examples.

[0029] Example 1: Combination Figure 1 、 Figure 3 and Figure 4 This embodiment is described as follows. In this embodiment, the Bessel mode is selected as the modulation basis, a four-step phase shift is performed on the 0th-order Bessel fundamental mode, and a single-pixel OAM mode common-path interference method is used to load the final modulation mode using a pure phase liquid crystal spatial light modulator to achieve wavefront imaging. The steps are as follows:

[0030] Step 1: Configure the resolution of spatial wavefront imaging to 128×128, the sampling rate of single-pixel imaging to 100%, and the number of phase shift steps to four; select Bessel beam as the modulation basis for single-pixel spatial wavefront imaging.

[0031] Step 2: Calculate and generate 16,384 Bessel modulation patterns with a spatial resolution of 128×128, and generate a 0th-order Bessel fundamental mode with a spatial resolution of 128×128. The light field distribution formula of the ideal Bessel pattern is used to generate the Bessel pattern, as follows:

[0032]

[0033] Where n is the order of the Bessel mode, J n is the nth-order Bessel function, C is a complex constant, k z and k r are the longitudinal and radial wave vectors, r, φ, z are the radial component, azimuthal component, and longitudinal component respectively, e is the base of the natural logarithm, i is the imaginary unit,

[0034] Specifically, the value of the order n that determines the Bessel mode is selected from -64 to 63 in steps of 0.25, and the radial wave vector k is selected from 2 to 59 in steps of 1. r , 16384 Bessel modulation patterns with a spatial resolution of 128×128 are calculated and generated, and a 0th-order Bessel fundamental mode with a spatial resolution of 128×128 is generated.

[0035] Step 3: Perform a four-step phase shift of 0, π / 2, π, and 3π / 2 on the 0th-order Bessel fundamental mode generated in step 2. Superimpose the phase-shifted 0th-order Bessel fundamental mode on the 16,384 generated Bessel modes, causing intermodal interference between the two modes to produce the final modulation pattern.

[0036] Step 4: The 65,536 phase-shifted final modulation patterns are encoded into pure phase holograms through pure phase holography. The pure phase holograms of the final modulation patterns are sequentially loaded into the pure phase liquid crystal spatial light modulator to modulate the target spatial wavefront. At the same time, the detector collects the signal intensity value of the center point of the Fourier plane of the modulated light wavefront corresponding to each pattern.

[0037] Step 5: Obtain the complex coefficient spectrum of the target spatial wavefront based on the phase shifting technique, and restore the target spatial wavefront using the TVAL3 compressed sensing reconstruction algorithm.

[0038] Example 2: Combination Figure 2 This embodiment describes the steps of wavefront imaging using a single-pixel OAM mode common-path interferometry method that selects a Laguerre-Gaussian mode as a modulation basis, performs a three-step phase shift on the 0th-order Laguerre-Gaussian base mode, and uses a digital micromirror device to load the final modulation pattern. The method is as follows:

[0039] Step 1: Select the Laguerre-Gaussian pattern as the single-pixel spatial wavefront imaging modulation basis, the number of phase shift steps is three, and other initial configurations are the same as in Example 1.

[0040] Step 2: Calculate and generate 16,384 Laguerre-Gaussian modulation patterns with a spatial resolution of 128×128, and generate a Laguerre-Gaussian 0th-order fundamental mode with a spatial resolution of 128×128. The light field distribution formula of the Laguerre-Gaussian pattern is used to generate the Laguerre-Gaussian pattern, as follows:

[0041]

[0042] Where l is the topological charge, p is the radial index, k0 is the beam, r, φ, z are the radial component, azimuthal component and longitudinal component respectively, e is the base of the natural logarithm, i is the imaginary unit, and the 1 / e radius of the Gaussian term is given by Given, w(0) is the beam waist radius, z R is the Rayleigh range, and (2p+|l|+1)tan -1 (z / z R ) is the ancient Yixiang, is an accompanying Laguerre polynomial.

[0043] Specifically, the value of the topological charge l that determines the Laguerre-Gaussian mode is selected from -60 to 60 in steps of 0.25, and the value of the radial index p is selected from 0 to 34 in steps of 1. 16384 Laguerre-Gaussian modulation patterns with a spatial resolution of 128×128 are calculated and generated, and the Laguerre-Gaussian 0th-order fundamental mode with a spatial resolution of 128×128 is generated.

[0044] Step 3: Phase shift the 0th-order Laguerre-Gaussian mode generated in step 2 in three steps: 0, 2π / 3, and 4π / 3. Superimpose the phase-shifted 0th-order Laguerre-Gaussian mode on the 16,384 generated Laguerre-Gaussian modes, causing intermodal interference between the two modes to produce the final modulation pattern.

[0045] Step 4: Select one of the Lee method and the superpixel method to encode the 49,152 resulting phase-shifted modulation patterns into binary patterns containing only 0 and 1 elements that can be loaded into a digital micromirror device. These patterns are then loaded sequentially into the digital micromirror device to modulate the target spatial wavefront. Simultaneously, the detector collects the signal intensity value at the center point of the Fourier plane of the modulated light wavefront corresponding to each pattern.

[0046] Step 5: Obtain the complex coefficient spectrum of the target spatial wavefront based on the phase shifting technique, and restore the target spatial wavefront using the TVAL3 compressed sensing reconstruction algorithm.

[0047] Example 3: Take the wavefront imaging of a space to be measured with a circular amplitude distribution and a grayscale image "house" phase distribution as an example. Figure 3 As shown. Wavefront imaging is performed according to the steps of Example 1, and the reconstructed wavefront amplitude and phase distribution are obtained as shown Figure 4 shown.

[0048] The above description is merely a preferred embodiment of the present invention. The scope of protection of the present invention is not limited to the above embodiment. All technical solutions based on the concept of the present invention are within the scope of protection of the present invention. It should be noted that for those skilled in the art, various improvements and modifications that do not depart from the principles of the present invention should also be considered within the scope of protection of the present invention.

Claims

1. A single-pixel OAM mode common-path interference method, characterized by: The 0th-order OAM fundamental mode is used as the reference component and the necessary phase shift is performed. Other-order OAM modes including the 0th-order OAM fundamental mode are used as the modulation basis to sample the wavefront of the unknown light field. The specific steps include: Step 1: Configure the resolution of spatial wavefront imaging M × N , the sampling rate of single-pixel imaging s , the phase shift step number φ, select one of the OAM mode types as the modulation basis for imaging the target spatial wavefront; Step 2: Under the conditions selected in step 1, calculate and generate s × M × N The resolution is M × N The OAM modulation mode generates a resolution of M × N The selected OAM mode 0th order fundamental mode; Step 3: perform multi-step phase shifting on the 0th order OAM fundamental mode generated in step 2 according to the number of phase shifting steps; s × M × N The OAM modes are superimposed on the phase-shifted 0th-order OAM fundamental mode, causing intermodal interference between the two modes to produce the final modulation mode. Step 4: Load the modulation pattern to the phased array, and use the single-pixel detector to collect the signal intensity; s The final modulation patterns after ×M×N phase shifts are sequentially loaded into the phased array to modulate the target spatial wavefront. At the same time, the detector collects the signal intensity value of the center point of the Fourier plane of the modulated light wavefront corresponding to each pattern. Step 5: Reconstruct the target spatial wavefront: Obtain the complex coefficient spectrum of the target spatial wavefront based on the phase shifting technique, and restore the target spatial wavefront using the single-pixel reconstruction algorithm.

2. The single-pixel OAM mode common-path interference method according to claim 1, characterized in that: In step 1, the OAM mode types include Laguerre-Gaussian mode, Bessel mode, vector vortex mode, and perfect vortex mode.

3. The single-pixel OAM mode common-path interference method according to claim 1, characterized in that: The multi-step phase shift in step 3 is a three-step phase shift.

4. The single-pixel OAM mode common-path interference method according to claim 1, characterized in that: The phased array in step 4 is a complex amplitude modulator indirectly realized by a digital micromirror array, a ferroelectric liquid crystal spatial light modulator and an amplitude liquid crystal spatial light modulator through a Lee method or a superpixel method, or a complex amplitude modulator indirectly realized by a pure phase liquid crystal spatial light modulator through a pure phase hologram.

5. The single-pixel OAM mode common-path interference method according to claim 1, characterized in that: The size of the center point of the Fourier plane of the modulated light wavefront in step 4 is r≤1.27λf / d, where λ is the wavelength of the light beam, f is the focal length of the collecting lens, and d is the diameter of the light beam.

6. The single-pixel OAM mode common-path interference method according to claim 1, characterized in that: The single pixel reconstruction algorithm in step 5 includes a second-order correlation operation and a compressed sensing reconstruction algorithm.

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