WO2023216438A1 - 一种部分相干分数阶涡旋光束拓扑荷数测量方法及装置 - Google Patents
一种部分相干分数阶涡旋光束拓扑荷数测量方法及装置 Download PDFInfo
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Definitions
- the invention relates to the technical field of optical measurement, and in particular, to a partially coherent fractional order vortex beam topological charge measurement method, device and computer storage medium.
- a vortex beam specifically refers to a beam carrying a helical phase. Its wave front rotates spirally in the direction of the optical axis. It can be quantitatively described by the phase factor exp(il ⁇ ), where l and ⁇ represent topological charge and orientation respectively. horn.
- the manipulation of the vortex phase of light fields has gradually extended into a new research direction, namely singularity optics.
- Allen et al. pointed out that each photon of the vortex beam carries l The orbital angular momentum of ( is the reduced Planck constant) and reveals new connections between macroscopic optics and quantum effects.
- orbital angular momentum is an eigenvalue and has transmission robustness, which determines the value of orbital angular momentum carried by each photon.
- vortex beams Compared with traditional plane waves and spherical waves, vortex beams have obvious spiral wavefront and ring-shaped intensity structural characteristics due to the singularity of the central phase.
- the unique physical properties of vortex beams make them play an important role in various fields, such as optical communications, particle manipulation, optical imaging, quantum information, astronomy, optical detection, medical diagnosis, and many other applications in different fields.
- To improve the practical applications of vortex beams, more and more new methods for generating vortex beams and detecting their topological charges have been proposed in the past five years.
- further research on vortex beam control is expected to promote the birth and scientific application of new physical phenomena, which is of important scientific significance.
- topological charge In most vortex-related studies, the value of the topological charge is only restricted to integers, that is, its spiral wavefront has a step size of 2l ⁇ , where l is an integer. In fact, the value of topological charge can also be non-integer (the phase step is not an integer multiple of 2 ⁇ ).
- a vortex beam with non-integer topological charge is called a fractional-order vortex beam [Opt.Commun.1994,112,321-327,Opt .Commun.1995,119,604-612,Nanophotonics,11(2):241–273(2022)].
- fractional-order vortex beams Different from integer-order vortex beams, fractional-order vortex beams have discontinuities at their phase transitions, the annular intensity structure is destroyed, and radial dark openings (or low-intensity gaps) appear.
- fractional-order vortex beams can be expressed as the superposition of a series of integer-order vortices [J.Opt.A-Pure Appl.Op.2004,6,259-268.].
- a vortex beam with fractional topological charge can be decomposed into a Fourier series of integer-order vortex beams with different intensity weights.
- fractional-order vortex beams can be divided into fractional-order Gaussian vortex beams, fractional-order Bessel-Gaussian beams, fractional-order Laguerre-Gaussian beams, perfect fractional-order vortex beams, and fractional-order vortex beams. Order elliptical vortex beam and partially coherent fractional order vortex beam, etc.
- fractional-order vortex beams have attracted great attention in the field of light manipulation due to their unusual properties.
- the interaction between light and matter is the most intuitive mechanism to demonstrate the potential applications of fractional-order vortex beams.
- fractional-order vortex beams Compared with integer-order vortex beams that only achieve halo rotation, fractional-order vortex beams have unique intensity distribution and can achieve cell sorting or precise control of cell orientation.
- Significantly increasing the information capacity of optical communication systems is always a great challenge, where orbital angular momentum modes are orthogonal to each other and can be considered as a new degree of freedom to solve this problem. Therefore, in optical communication systems, fractional-order vortex beams with continuous integer and non-integer orbital angular momentum states can overcome the limitation of aperture size and expand the communication capacity.
- fractional-order vortex beams Another practical application of fractional-order vortex beams is optical imaging. It has been demonstrated that beams carrying orbital angular momentum can achieve image edge enhancement. Compared with regular vortex beams that only achieve isotropic edge enhancement, fractional-order vortex beams can achieve anisotropic edge enhancement. In addition, the fractional-order vortex beam can effectively resist the influence of noise and achieve high-resolution imaging in radar imaging systems.
- topological charge In view of the wide application of vortex beams, various techniques have been proposed to measure their topological charge (topological charge). For example, the number and direction of forks in the interference pattern of a vortex beam and a plane wave can correspond to the size and sign of the topological charge, respectively.
- the vortex beam can be converted into a non-hollow spot by a phase grating of opposite topological charge, which also helps to identify the value of the topological charge.
- wavefront measurement is the most intuitive technique to obtain the topological charge value, that is, the phase integral around the singularity divided by 2 ⁇ can correspond to the value of the topological charge.
- fractional-order vortex beam destroys the orthogonality of the orbital angular momentum, and its measurement should be modeled as a complex mixed integer-order orbital angular momentum situation. Therefore, most traditional methods that are effective for integer vortex beams cannot deal with fractional-order angular momentum. Vortex topological charges become invalid when measured.
- the existing measurement solutions for fractional-order vortex beams mainly include the following measurement methods:
- the mode conversion method [Opt Commun 1999;159:13-18] converts the Laguerre fractional vortex into a Hermitian mode through mutually perpendicular cylindrical mirrors, and then qualitatively analyzes the topological charge of the fractional vortex beam.
- Machine learning-based measurement methods [Phys.Rev.Lett.2019,123,183902] use diffraction or interference patterns to identify fractional topological charges by comparing intensity shapes to theoretical values. Combined with machine learning, more accurate identification can be achieved based on intensity feature analysis.
- the above methods except for the deep learning identification method, have low accuracy.
- the deep learning method relies on the training of a large amount of data and identifies based on characteristics such as light intensity.
- the training of a fixed system is not universal. ;On the other hand, when coherence degrades, interference-based measurement schemes will also fail. After the coherence is degraded, the orbital angular momentum spectrum distribution of the vortex beam will be affected, and the quantitative relationship between the orbital angular momentum spectrum and the topological charge has not been verified.
- the fractional topological charges of partially coherent fractional vortex beams cannot be quantitatively solved and characterized.
- the technical problem to be solved by the present invention is to overcome the problems in the prior art of low accuracy and inability to quantitatively solve and characterize after coherence degradation.
- the present invention provides a partially coherent fractional order vortex beam topological charge measurement method, which includes:
- the fractional-order vortex beam to be measured is irradiated onto the scattering sample, and horizontal and vertical movement and overlapping scanning are performed, and the diffraction light intensity is collected using a detector placed in the diffraction area;
- the electric field to be measured is calculated and updated iteratively to minimize the error between the diffraction light intensity collected by the detector and the diffraction light intensity calculated based on the electric field to be measured, thereby obtaining the The target electric field to be measured of the fractional order vortex beam to be measured;
- the source field vortex phase distribution map is obtained by inverse transmission calculation based on the cross-spectral density function and the light field information of the fractional-order vortex beam to be measured, and the fraction to be measured is observed according to the source field vortex phase distribution map.
- the size and positive and negative topological charge of the first-order vortex beam is obtained by inverse transmission calculation based on the cross-spectral density function and the light field information of the fractional-order vortex beam to be measured, and the fraction to be measured is observed according to the source field vortex phase distribution map.
- the diffraction area is a Fresnel diffraction area or a Fraunhofer diffraction area.
- the overlapping rate of the overlapping scan is 60% to 70%.
- the multi-mode stacked diffraction algorithm is used to calculate the electric field to be measured and update it iteratively, so as to minimize the error between the diffraction light intensity collected by the detector and the diffraction light intensity calculated based on the electric field to be measured.
- obtaining the target electric field to be measured of the fractional order vortex beam to be measured includes:
- the random mode decomposition method is used to decompose the cross-spectral density W (r 1 , r 2 ) of the fractional-order vortex beam to be measured into multiple electric fields.
- W is the i-th electric field after decomposition of the fractional-order vortex beam to be measured
- NR is a positive integer selected according to different degrees of coherence
- r1 and r2 are spatial coordinates.
- a multi-mode stacked diffraction algorithm is used to calculate the electric field to be measured and iteratively update it so as to minimize the error between the diffraction light intensity collected by the detector and the diffraction light intensity calculated based on the electric field to be measured, thereby Obtaining the target electric field to be measured of the fractional order vortex beam to be measured includes:
- Step 1 Assume that the cross-spectral density of the fractional-order vortex beam to be measured irradiating the scattering sample is Assume that the transmittance function of the j-th irradiation on the scattering sample is P(rR j ), r represents the coordinate, and R j represents the relative displacement between the fractional order vortex beam to be measured and the scattering sample, j represents the j-th irradiation on the sample area;
- Step 2 Calculate each exit field of the fractional-order vortex beam to be measured after passing through the scattering sample as
- Step 3 Update the diffraction field using the diffracted light intensity collected by the detector, and update the exit field according to the diffraction field
- Step 4 Update each electric field to be measured
- ⁇ and ⁇ are constants, represents the i-th emitted light electric field corresponding to the j-th scanning position after the update, is the i-th emergent light field corresponding to the j-th scanning position, O′ i j (r) is the update of the i-th incident light electric field irradiated onto the scattering sample corresponding to the j-th scanning position, O i j (r) is The j-th scanning position corresponds to the i-th incident light electric field irradiated on the scattering sample, P′ j (rR j ) is the update transmittance function of the j-th irradiation on the scattering sample, * represents the conjugate;
- Step: 5 Use the gradient descent algorithm to determine whether the error between the diffraction light intensity collected by the detector and the currently calculated diffraction light intensity reaches a preset minimization threshold. If it reaches the minimization threshold, the target is obtained The electric field to be measured, otherwise repeat steps 2-5 until the minimum threshold is reached.
- the reconstruction of the cross-spectral density function of the fractional-order vortex beam to be measured based on the target electric field to be measured includes:
- l is an integer, it is expressed as a partially coherent integer-order vortex phase.
- l is a fraction, it is expressed as a partially coherent fractional-order vortex phase.
- obtaining the light field information of the fractional-order vortex beam to be measured includes:
- the source field vortex phase distribution map is obtained by inverse transmission calculation based on the cross-spectral density function and the light field information of the fractional-order vortex beam to be measured, and the source field vortex phase distribution map is observed.
- the topological charge size and sign of the fractional-order vortex beam to be measured include:
- the topological charge of the fractional order vortex beam can be obtained by observing the phase transition of the source plane according to the source field vortex phase distribution diagram or performing loop integration on the phase.
- the invention also provides a partially coherent fractional order vortex beam topological charge measuring device, which includes:
- the spatial light modulator is used to generate a partially coherent fractional-order vortex beam, which is the fractional-order vortex beam to be measured;
- the displacement platform is used to move the scattering sample and conduct horizontal and vertical movement and overlapping scanning
- a detector placed in the diffraction area is used to collect the diffracted light intensity
- a computer configured to use a multi-mode stacked diffraction algorithm to calculate the electric field to be measured and update it iteratively, so as to minimize the error between the diffracted light intensity collected by the detector and the diffracted light intensity calculated based on the electric field to be measured, Thereby, the target electric field to be measured of the fractional order vortex beam to be measured is obtained, and the cross-spectral density function of the fractional order vortex beam to be measured is reconstructed according to the target electric field to be measured and the fractional order vortex beam to be measured is obtained.
- the light field information is calculated according to the cross-spectral density function and the light field information of the fractional-order vortex beam to be measured to obtain the source field vortex phase distribution diagram, and the source field vortex phase distribution diagram is observed.
- the magnitude and sign of the topological charge of the fractional order vortex beam to be measured is calculated according to the cross-spectral density function and the light field information of the fractional-order vortex beam to be measured to obtain the source field vortex phase distribution diagram, and the source field vortex phase distribution diagram is observed.
- the invention also provides a computer-readable storage medium.
- a computer program is stored on the computer-readable storage medium.
- the computer program is executed by a processor, the above-mentioned partially coherent fractional order vortex beam topological charge measurement is implemented. steps of the method.
- the method of the present invention for measuring the topological charge size and sign of a partially coherent fractional order vortex beam is to irradiate the fractional order vortex beam to be measured on the sample, then measure the diffracted light intensity, and determine the value to be measured through multi-mode stacked diffraction.
- This method has the advantages of high optical efficiency, high precision, and does not require additional optical devices.
- the present invention applies multi-mode stack imaging technology to partially coherent fractional order vortex beam measurement. This technology has the advantages of reconstructing light source mode information.
- the advantages of high precision and large field of view ensure that the measured light field can be calculated for reverse transmission, thereby obtaining source field phase information, and can accurately measure the topological charge of partially coherent fractional order vortex beams.
- This technology also solves the key scientific problem that the electric field mode is difficult to separate in space, making partially coherent optical mode multiplexing an available new dimension of spatial division multiplexing, greatly increasing the capacity of optical communications, and playing an important role in optical communications, optical encryption and decryption, etc. has important applications.
- Figure 1 is a flow chart for the implementation of topological charge measurement of partially coherent fractional order vortex beams according to the present invention
- Figure 2 is a schematic diagram of collecting diffracted light intensity
- Figure 3 is a schematic diagram of overlapping scanning
- Figure 4 is an experimental optical path diagram for the generation and measurement of partially coherent fractional order vortex beams
- the core of the invention is to provide a method, device and computer storage medium for measuring the topological charge of a partially coherent fractional-order vortex beam, which has high precision and quantitatively solves and characterizes the fractional-order topological charge of a partially coherent fractional-order vortex beam.
- Figure 1 is a flow chart for realizing the topological charge of the partially coherent fractional order vortex beam provided by the present invention. the specific operation steps are as follows:
- S101 Illuminate the fractional-order vortex beam to be measured onto the scattering sample, perform horizontal and vertical movement and overlapping scanning, and use a detector placed in the diffraction area to collect the diffraction light intensity;
- the fractional-order vortex beam to be measured is irradiated on the strongly scattering sample, and the fractional-order vortex beam to be measured or the sample moves along x and y for overlapping scanning.
- the overlap rate of the overlapping scan is 60% to 70%
- the CCD is placed on the Fourier plane or far field of the sample to collect the diffraction light intensity (the diffraction area is the Fresnel diffraction area or Fraunhofer area). Hefei diffraction area), collect a series of light intensities, and rely on the Fourier transform constraints of time space and spectrum space.
- the relative phase between adjacent areas can be calculated from the information redundancy generated by the overlap of adjacent areas, and the reconstruction Imaging to achieve high-resolution imaging of the light source to be measured and the object to be measured. Since no lens is used, its theoretical resolution can be higher than that of conventional optical systems. This solution not only solves the convergence problem in the reconstruction algorithm, but also achieves both a large field of view and high resolution.
- S102 Use the multi-mode stacked diffraction algorithm to calculate the electric field to be measured and iteratively update it to minimize the error between the diffraction light intensity collected by the detector and the diffraction light intensity calculated based on the electric field to be measured, thereby obtaining The target electric field to be measured of the fractional order vortex beam to be measured;
- S103 Reconstruct the cross-spectral density function of the fractional-order vortex beam to be measured according to the target electric field to be measured and obtain the light field information of the fractional-order vortex beam to be measured;
- S104 Perform inverse transmission calculation according to the cross-spectral density function and the light field information of the fractional-order vortex beam to be measured to obtain a source field vortex phase distribution map, and observe the source field vortex phase distribution map according to the source field vortex phase distribution map. Measure the topological charge size and sign of the fractional order vortex beam.
- topological charge calculation can be given based on the relationship between the phase jump and the multiple of 2 ⁇ , which is consistent with the original definition of fractional-order vortex beam. Relying on the high-resolution characteristics of the stacked coherent diffraction imaging algorithm itself, high-resolution and high-precision fractional topological charge measurements can be achieved when the light source signal is weak and the transmission medium has turbulence.
- step S102 is further described in detail, as follows:
- the partially coherent light field is a random fluctuation electric field, which can be understood as the statistical average of the instantaneous electric field ⁇ E * (r 1 )E(r 2 )>, expanded with mutually orthogonal eigenmodes ⁇ mn , and can be expressed as:
- ⁇ mn the weight of the mode.
- GSM Gaussian Sher mode
- HG Hermitian-Gaussian
- H m and H n represent m-order and n-order Hermitian polynomials respectively, and N c represents the number of modes.
- This method of pattern decomposition representation is called coherent mode decomposition.
- Another decomposition method is random modular decomposition. In this approach, a partially coherent beam is represented by an incoherent superposition of spatially random complex fields:
- E n (r) represents one of the random modes.
- the cross-spectral density W (r 1 , r 2 ) of the beam to be measured is decomposed into multiple electric fields using a decomposition method.
- NR is a positive integer selected according to different coherence degrees (theoretically NR is infinite, in the actual process NR takes a finite value, when the coherence degree is low, when NR is greater than 2000, The error is negligible.
- NR can ensure higher accuracy by choosing between 4 ⁇ 4 and 10 ⁇ 10)
- r1 and r2 are the spatial coordinates.
- Step a Assume that the cross-spectral density of the light beam to be measured irradiating the scattering sample is Assume that the transmittance function of the j-th irradiation on the scattering sample is P(rR j ), r represents the coordinate, R j represents the relative displacement between the beam to be measured and the scattering sample, and j represents the j-th The first irradiation is on the sample area;
- Step b Calculate each exit field of the light beam to be measured after passing through the scattering sample as
- Step c Use the measured light intensity to update the diffraction field and exit field.
- the diffraction field is updated to in Corresponding to the diffraction field of the i-th mode, I j (k) is the diffraction light intensity of the j-th irradiation collected by the detector, and is the light intensity contributed by all electric field modes, is the amplitude of the exit field calculated iteratively, and M is the total number of modes.
- FFT stands for Fourier transform
- IFFT stands for inverse Fourier transform
- Step d Update each electric field to be measured
- ⁇ and ⁇ are constants, represents the i-th emitted light electric field corresponding to the j-th scanning position after the update, is the i-th emergent light field corresponding to the j-th scanning position, O′ i j (r) is the update of the i-th incident light electric field irradiated onto the scattering sample corresponding to the j-th scanning position, O i j (r) is The j-th scanning position corresponds to the i-th incident light electric field irradiated on the scattering sample, P′ j (rR j ) is the update transmittance function of the j-th irradiation on the scattering sample, * represents the conjugate;
- Step e Use the gradient descent algorithm to determine whether the error between the diffraction light intensity collected by the detector and the currently calculated diffraction light intensity reaches a preset minimization threshold. If it reaches the minimization threshold, the target is obtained. Measure the electric field, otherwise repeat steps b-e until the minimum threshold is reached.
- the light beam is a completely coherent light
- the only difference from the partially coherent light is that the partially coherent light needs to measure multiple electric fields, so the present invention can also measure a completely coherent fractional order vortex light beam.
- the present invention uses the iterative algorithm used in mixed-mode stacked coherent diffraction imaging to realize the reconstruction of the electric field mode: the light source illuminates the sample and records the diffraction pattern of the Fresnel diffraction area, which satisfies the Fourier transform relationship with the object plane. Cameras with diffraction surfaces can only record the amplitude of the light field, and phase information is missing. In order to solve the phase and reconstruct the information of the surface to be measured, in the iterative algorithm of coherent diffraction imaging, algorithms such as gradient descent are used to minimize the error between the photographed light intensity and the calculated light intensity. In order to solve the iterative convergence and unique solution problems, the stacked coherent diffraction imaging technology uses redundant overlapping scanning.
- the mutually constrained diffraction information greatly improves the iterative convergence speed and accuracy.
- the stacked coherent diffraction imaging iteration algorithm uses mixed mode synchronous iteration, where the "mixed mode" refers to the electric field mode of partially coherent light. This invention mainly studies the reconstruction results of the light source and extracts the information carried by the light source itself.
- this embodiment further explains steps S103 and S104 in detail, as follows:
- l is an integer, it is expressed as a partially coherent integer-order vortex phase.
- l is a fraction, it is expressed as a partially coherent fractional-order vortex phase;
- the topological charge of the fractional order vortex beam can be obtained.
- a partially coherent beam can be regarded as an incoherent superposition of a completely coherent beam.
- the partially coherent beam to be measured passes through the scattering object, and the gradient descent algorithm is used to minimize the error between the measurable information and the information to be measured, and the fractional order vortex beam to be measured is reconstructed.
- the main electric field modes and weights Based on the mathematical relationship between the electric field mode and the cross-spectral density, the cross-spectral density function of the partially coherent light beam is calculated, the cross-spectral density of the partially coherent light is reconstructed, and complete information of the partially coherent light field is obtained, including light intensity, light intensity correlation, and electric field. Correlation, phase, etc.
- the present invention can be used for low coherence fractional order vortex Optical rotation field measurement uses diffraction patterns to reconstruct the source field information, combined with the iterative algorithm of mixed-mode stacked coherent diffraction imaging to achieve accurate measurement and reverse transmission calculation of partially coherent optical electric field modes.
- This technology also solves the spatial problem of electric field modes. Key scientific issues that are difficult to separate make partially coherent optical mode multiplexing an available new dimension of spatial division multiplexing, greatly increasing the capacity of optical communications and having important applications in optical communications, optical encryption and decryption, etc.
- Specific embodiments of the present invention also provide a computer-readable storage medium.
- a computer program is stored on the computer-readable storage medium.
- the computer program is executed by a processor, the above steps S102-S104 are implemented.
- An embodiment of the present invention also provides a device for measuring the topological charge of a partially coherent fractional-order vortex beam, which includes:
- the spatial light modulator is used to generate a partially coherent fractional-order vortex beam, which is the fractional-order vortex beam to be measured;
- the displacement platform is used to move the scattering sample and conduct horizontal and vertical movement and overlapping scanning
- a detector placed in the diffraction area is used to collect the diffracted light intensity
- a computer configured to use a multi-mode stacked diffraction algorithm to calculate the electric field to be measured and update it iteratively, so as to minimize the error between the diffracted light intensity collected by the detector and the diffracted light intensity calculated based on the electric field to be measured, Thereby, the target electric field to be measured of the fractional order vortex beam to be measured is obtained, and the cross-spectral density function of the fractional order vortex beam to be measured is reconstructed according to the target electric field to be measured and the fractional order vortex beam to be measured is obtained.
- the light field information is calculated according to the cross-spectral density function and the light field information of the fractional-order vortex beam to be measured to obtain the source field vortex phase distribution diagram, and the source field vortex phase distribution diagram is observed.
- the magnitude and sign of the topological charge of the fractional order vortex beam to be measured is calculated according to the cross-spectral density function and the light field information of the fractional-order vortex beam to be measured to obtain the source field vortex phase distribution diagram, and the source field vortex phase distribution diagram is observed.
- this embodiment is the specific experimental steps for generating and measuring partially coherent fractional order vortex beams, as follows:
- the semiconductor solid-state laser (wavelength 532.8nm) is incident on the rotating ground glass piece, and the light beam diffused by the rotating ground glass piece (rotation frequency 20HZ) is collimated by the lens.
- the coherence degree of the partially coherent light can be changed.
- the partially coherent beam passes through the spatial light modulator, a partially coherent fractional order vortex beam is generated.
- the partially coherent light field produced has a greater degree of coherence.
- the light beam on the rear surface of the spatial light modulator (coherence 1mm, beam waist 1mm) is our measurement object.
- the fractional-order vortex beam to be measured is transmitted for a certain distance and then focused and irradiated onto the resolution plate.
- the resolution plate is placed on the displacement platform, and the displacement distance can be controlled through MATLAB software.
- the displacement platform moves 10 steps in the x and y directions, and the step size is 20um.
- the spot size printed on the resolution plate is about 150um.
- the camera collects the diffracted light intensity at a distance of 13cm from the resolution plate. According to the collected diffracted light intensity and brought into multi-mode stacked diffraction imaging, the main modes of the partially coherent fractional-order vortex beam can be obtained. By back-transmitting these modes to the spatial light modulator plane, the topological charge can be obtained by examining the phase transition at this time.
- the pure phase spatial light modulator is a reflective pure phase spatial light modulator: HOLOEYE GAEA, with a size of 3840*2160 pixels and a pixel size of 3.74 ⁇ m.
- a pure phase spatial light modulator is used to set the measurement range, that is, by loading a vortex phase on the spatial light modulator, a partially coherent beam can be changed into a fractional order partially coherent beam.
- the displacement platform used in the present invention is a Newport Gothic bearing XYZ translation stage (step size less than 30 nm) with a displacement accuracy within 100 nm.
- the sample used in the present invention is a resolution plate (USAF), produced by Thorlabs Company of the United States.
- the light detector is CCD or CMOS.
- the CCD used is an EMCCD (electronic gain camera) professional camera.
- the specific parameters are that the size is 1024*1024 pixels and the pixel size is 13 ⁇ m.
- the CCD is driven by MATLAB software, and the above software is used to observe and save the image information received by the CCD. After the CCD is connected to the computer, MATLAB software is used to record and save the image information received by the CCD.
- embodiments of the present application may be provided as methods, systems, or computer program products. Accordingly, the present application may take the form of an entirely hardware embodiment, an entirely software embodiment, or an embodiment that combines software and hardware aspects. Furthermore, the present application may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) embodying computer-usable program code therein.
- computer-usable storage media including, but not limited to, disk storage, CD-ROM, optical storage, etc.
- These computer program instructions may also be stored in a computer-readable memory that causes a computer or other programmable data processing apparatus to operate in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including the instruction means, the instructions
- the device implements the functions specified in a process or processes of the flowchart and/or a block or blocks of the block diagram.
- These computer program instructions may also be loaded onto a computer or other programmable data processing device, causing a series of operating steps to be performed on the computer or other programmable device to produce computer-implemented processing, thereby executing on the computer or other programmable device.
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Abstract
本发明将待测的部分相干分数阶涡旋光束通过散射物体，利用优化算法最小化可测量信息和待测信息的误差，并通过多模式叠层衍射算法重建出待测分数阶涡旋光束的主要电场模式和权重。基于电场模式和交叉谱密度的数学关系，计算出部分相干分数阶涡旋光束的交叉谱密度函数、重构部分相干分数阶涡旋光场的交叉谱密度、获取部分相干分数阶涡旋光场的完备信息，包括光强、光强关联、电场关联、相位等等。部分相干分数阶涡旋光场的完备信息得到后，进行逆向传输计算，得到源场涡旋相位分布，实现低相干条件下分数阶涡旋光束的精确拓扑荷测量。
Description
本发明涉及光学测量技术领域，尤其是指一种部分相干分数阶涡旋光束拓扑荷数测量方法、装置及计算机存储介质。
现有的技术中，涡旋光束具体是指一种携带螺旋相位的光束，其波前沿光轴方向螺旋旋转，可以用相位因子exp(ilθ)定量描述，其中l和θ分别表示拓扑电荷和方位角。光场涡旋相位的操纵已逐渐延伸为一个新的研究方向，即奇点光学。1992年，Allen等人指出涡旋光束的每个光子携带l
的轨道角动量(
是约化普朗克常数)，并揭示了宏观光学和量子效应之间的新联系。显然，轨道角动量是特征值并且具有传输鲁棒性，它决定了每个光子携带的轨道角动量值。与传统的平面波和球面波相比，涡旋光束由于中心相位奇异性而具有明显的螺旋波前和环形强度结构特征。涡旋光束的独特物理特性使其在各个领域发挥着重要的作用，如光通信、粒子操纵、光学成像、量子信息、天文学、光学检测、医学诊断以及其他许多不同领域的应用。为了提高涡旋光束的实际应用，人们在过去五年中提出了越来越多的产生涡旋光束和检测其拓扑荷的新方法。此外，涡旋光束调控的进一步研究有望促进新物理现象的诞生和科学应用，具有重要的科学意义。
在大多数与涡旋相关的研究中，拓扑荷的值仅被限制为整数，即其螺旋波前具有2lπ的步长，l为整数。事实上，拓扑荷的值也可以是非整数(相位步长不是2π的整数倍)，具有非整数拓扑荷的涡旋光束称为分数阶涡旋光束[Opt.Commun.1994,112,321-327,Opt.Commun.1995,119,604-612,Nanophotonics,11(2):241–273(2022)]。与整数阶涡旋光束不同，分数阶涡旋光束其相位跃变处出现不连续性，环形强度结构被破坏，出现径向暗开口(或低强度间隙)。2004年，Berry从理论上详细研究了具有分数阶涡 旋相位的光束的涡旋结构，并提到分数阶涡旋光束可以表示为一系列整数阶涡旋的叠加[J.Opt.A-Pure Appl.Op.2004,6,259-268.]。换句话说，具有分数拓扑荷的涡旋光束可以分解为具有不同强度权重的整数阶涡旋光束的傅立叶级数。当拓扑荷为半整数时，在相位阶跃不连续处出现无限长的交替强度涡旋链，当拓扑荷大于或小于半整数时消失。值得注意的是，每个光子的轨道角动量可以以
为单位携带整数或非整数值。分数阶涡旋光束的显着特点是不能在自由空间中稳定传播。然而，换句话说，它表现出丰富的演化过程，诱导复杂的幅度和相位结构并增加调节自由度。更具体地，基于其固有特性，分数阶涡旋光束可以分为分数阶高斯涡旋光束、分数阶贝塞尔-高斯光束、分数阶拉盖尔-高斯光束、完美分数阶涡旋光束、分数阶椭圆涡旋光束和部分相干分数阶涡旋光束等等。
近年来，分数阶涡旋光束由于其不寻常的特性而在光操纵领域引起了极大的关注。首先，光与物质之间的相互作用是展示分数阶涡旋光束潜在应用的最直观机制。与仅实现光环旋转的整数阶涡旋光束相比，分数阶涡旋光束具有独特的强度分布，可以实现细胞分选或细胞取向的精确控制。显着增加光通信系统的信息容量始终是一个巨大的挑战，其中轨道角动量模式相互正交，可以被视为解决这个问题的新自由度。因此，在光通信系统中，具有连续整数和非整数轨道角动量状态的分数阶涡旋光束可以克服孔径大小的限制并扩展通信容量。分数阶涡旋光束的另一个实际应用是光学成像。已经证实携带轨道角动量的光束可以实现图像边缘增强。与仅实现各向同性边缘增强的规则涡旋光束相比，分数阶涡旋光束可以实现各向异性边缘增强。此外，分数阶涡旋光束可以有效地抵抗噪声影响并在雷达成像系统中实现高分辨率成像。
鉴于涡旋光束的广泛应用，人们已经提出了各种技术来测量其拓扑荷(拓扑荷)。例如，涡旋光束与平面波的干涉图案中叉的数量和方向可以分别对应到拓扑荷的大小和符号。涡旋光束可以通过相反拓扑荷的相位光栅转换为非空心光斑，这也有助于识别拓扑荷的值。此外，波前测量是获得拓扑荷值的最直观技术，即奇点周围的相位积分除以2π可以对应于拓扑荷的值。 然而，分数阶涡旋光束破坏了轨道角动量的正交性，其测量应建模为复杂的混合整数阶轨道角动量的情况，因此，多数对整数涡旋光束有效的传统方法在应对分数阶涡旋拓扑荷测量时变得无效。
利用相干叠层衍射成像算法解决光场测量的研究在近几年得到了一定的发展，这得益于相干衍射成像算法的不断改进和革新。当光源相干度降低时，如果还利用完全相干光束的相干衍射的方法，得到的成像会模糊或者误差很大。除了光源本身可能存在的相干性退化，光学系统包括样品、相机和传输媒介的不稳定性也会等效于相干性的退化，与空间相干性的退化类似，时间相干性的退化也给重构带来的极大的麻烦。基于此，Arjun等人提出了混合态模型的叠层成像算法。Arjun等人在叠层衍射成像算法的基础上引入实模和鬼模式的概念[Phy.Rev.Lett.2020,125,086101]，提出了适用于宽光谱光源的解决方案，该算法允许对多个波长的光谱、探针以及光谱对应的图像同时重构。
目前已有的针对分数阶涡旋光束的测量方案要方法主要有一下测量方法：
1.基于改进的干涉法[Opt.Commun.2015,334,235-239,Opt.Commun.2012,285,383-388]将分数阶涡旋光束旋转180°后与自身进行干涉，根据干涉结果定性观测拓扑荷数。
2.模式转换法[Opt Commun 1999；159:13-18]将拉盖尔分数阶涡旋通过相互垂直的柱面镜进行转化为厄米模式进而定性分析分数阶涡旋光束拓扑荷。
3.动态双缝法[Photonics Res.2016,4,187-190]将分数阶涡旋光束通过可变双缝进行干涉后，观测光强的变化从而确定分数阶涡旋光束拓扑荷数。
4.基于机器学习的测量方法[Phys.Rev.Lett.2019,123,183902]使用衍射或干涉图案通过将强度形状与理论值进行比较来识别分数阶拓扑荷。结合机器学习，基于强度特征分析可以获得更精确的识别。
对于分数阶拓扑荷的测量问题，上述方法除深度学习识别法以外，精度 都较低，而深度学习法依赖大量数据的训练，基于光强等特性进行识别，固定系统的训练不具有普适性；另一方面，当相干性退化后，基于干涉的测量方案也将失效。相干性退化后，涡旋光束的轨道角动量谱分布将会受到影响，轨道角动量谱与拓扑荷的定量关系也未得到验证。目前部分相干分数阶涡旋光束的分数阶拓扑荷尚无法定量求解和表征。
发明内容
为此，本发明所要解决的技术问题在于克服现有技术中精度低、相干性退化后无法定量求解和表征的问题。
为解决上述技术问题，本发明提供了一种部分相干分数阶涡旋光束拓扑荷数测量方法，包括：
将将待测分数阶涡旋光束照射到散射样品上，并进行横向和竖向移动交叠扫描，利用置于衍射区域的探测器采集衍射光强；
利用多模式叠层衍射算法，计算待测电场并迭代更新，以便最小化所述探测器采集的衍射光强和根据所述待测电场计算得到的衍射光强之间的误差，从而得到所述待测分数阶涡旋光束的目标待测电场；
根据所述目标待测电场重建所述待测分数阶涡旋光束的交叉谱密度函数并获取所述待测分数阶涡旋光束的光场信息；
根据所述交叉谱密度函数和所述待测分数阶涡旋光束的光场信息进行逆传输计算得到源场涡旋相位分布图，根据所述源场涡旋相位分布图观测所述待测分数阶涡旋光束拓扑荷数大小和正负。
优选地，所述衍射区域为菲涅尔衍射区或夫琅禾费衍射区。
优选地，所述交叠扫描的重叠率为60％～70％。
优选地，所述利用多模式叠层衍射算法，计算待测电场并迭代更新，以便最小化所述探测器采集的衍射光强和根据所述待测电场计算得到的衍射光强之间的误差，从而得到所述待测分数阶涡旋光束的目标待测电场前包括：
利用随机模分解方法将所述待测分数阶涡旋光束的交叉谱密度W(r
1,r
2) 分解为多个电场
其中，
和
为所述待测分数阶涡旋光束分解后的第i个电场，N
R为根据不同相干度选取的正整数，r1、r2为空间坐标。
优选地，利用多模式叠层衍射算法，计算待测电场并迭代更新，以便最小化所述探测器采集的衍射光强和根据所述待测电场计算得到的衍射光强之间的误差，从而得到所述待测分数阶涡旋光束的目标待测电场包括：
步骤1：假设所述待测分数阶涡旋光束照射到散射样品上的交叉谱密度为
假设第j次照射在所述散射样品上的透过率函数为P(r-R
j)，r表示坐标，R
j表示所述待测分数阶涡旋光束与所述散射样品之间的相对位移，j表示第j次照射在样品区域；
步骤2：计算所述待测分数阶涡旋光束经过所述散射样品后的每个出射场为
步骤3：利用所述探测器采集的衍射光强更新衍射场，并根据所述衍射场更新出射场
步骤4：更新每个待测电场
其中α,β是常数，
表示更新后的第j个扫描位置对应的第i个出射光电场，
为第j个扫描位置对应的第i个出射光场，O′
i
j(r)为更新第j个扫描位置对应的第i个照射到散射样品上入射光电场，O
i
j(r)为第j个扫描位置对应的第i个照射到散射样品上入射光电场，P′
j(r-R
j)为更新第j次照射在所述散射样品上的透过率函数，*表示取共轭；
步骤:5：利用梯度下降算法判断所述探测器采集的衍射光强和当前计算 得到的衍射光强之间的误差是否达到预设的最小化阈值，若达到所述最小化阈值，则得到目标待测电场，否则重复步骤2-5，直到达到所述最小化阈值。
优选地，所述根据所述目标待测电场重建所述待测分数阶涡旋光束的交叉谱密度函数包括：
所述交叉密度函数
其中，α
i＝1/N
R为光谱权重；
对部分相干光束，引入涡旋相位，其交叉谱密度可以表示为W
0(r
1,r
2)＝W(r
1,r
2)exp(-ilθ
1)exp(ilθ
2)，其中θ为角向坐标，l为拓扑荷，当l为整数时，表示为部分相干整数阶涡旋相位，当l为分数时，表示为部分相干分数阶涡旋相位。
优选地，所述获取所述待测分数阶涡旋光束的光场信息包括：
令r1＝r2计算得到光强I；
令r2＝0计算得到相干度μ。
优选地，所述根据所述交叉谱密度函数和所述待测分数阶涡旋光束的光场信息进行逆传输计算得到源场涡旋相位分布图，根据所述源场涡旋相位分布图观测所述待测分数阶涡旋光束拓扑荷数大小和正负包括：
对交叉谱密度函数W取W/|W|计算得到交叉谱密度相位分布函数：
根据所述交叉谱密度相位分布函数得到源场涡旋相位分布图；
根据所述源场涡旋相位分布图观测源平面的相位跃变或者对相位进行环路积分即可得出分数阶涡旋光束的拓扑荷。
本发明还提供了一种部分相干分数阶涡旋光束拓扑荷数测装置，包括：
光源，用于发射部分相干光束；
空间光调制器，用于产生部分相干分数阶涡旋光束，即为待测分数阶涡旋光束；
位移平台，用于移动散射样品，进行横向和竖向移动交叠扫描；
置于衍射区域的探测器，用于采集衍射光强；
计算机，用于利用多模式叠层衍射算法，计算待测电场并迭代更新，以便最小化所述探测器采集的衍射光强和根据所述待测电场计算得到的衍射光强之间的误差，从而得到所述待测分数阶涡旋光束的目标待测电场，根据所述目标待测电场重建所述待测分数阶涡旋光束的交叉谱密度函数并获取所述待测分数阶涡旋光束的光场信息，根据所述交叉谱密度函数和所述待测分数阶涡旋光束的光场信息进行逆传输计算得到源场涡旋相位分布图，根据所述源场涡旋相位分布图观测所述待测分数阶涡旋光束拓扑荷数大小和正负。
本发明还提供了一种计算机可读存储介质，所述计算机可读存储介质上存储有计算机程序，所述计算机程序被处理器执行时实现上述一种部分相干分数阶涡旋光束拓扑荷数测量的方法的步骤。
本发明的上述技术方案相比现有技术具有以下优点：
本发明测量部分相干分数阶涡旋光束拓扑荷数大小和正负的方法，通过将待测分数阶涡旋光束照射在样品上，然后测量衍射光强，通过多模式叠层衍射来确定待测分数阶涡旋光束的主要模式。根据这些模式进行反传输到源平面，观测相位的跃变确定分数阶涡旋的拓扑荷数。该方法具有高光效率、精度高、以及不需要额外的光学器件等优点，本发明将多模式叠层成像技术应用于部分相干分数阶涡旋光束测量中去，此技术在重建光源模式信息时具备的精度高、大视场优势，保证了所测光场可以作逆向传输计算，进而获取源场相位信息，可以精确测量部分相干分数阶涡旋光束的拓扑荷数。该技术同时解决了电场模式的在空间上难以分离的关键科学问题，使部分相干光模式复用成为可用的空分复用新维度，大大增加光通信的容量，在光通信、光学加密解密等方面有着重要的应用。
为了使本发明的内容更容易被清楚的理解，下面根据本发明的具体实施例并结合附图，对本发明作进一步详细的说明，其中：
图1是本发明部分相干分数阶涡旋光束拓扑荷数测量的实现流程图；
图2是采集衍射光强示意图；
图3是交叠扫描示意图；
图4是部分相干分数阶涡旋光束产生与测量实验光路图；
图5是TC＝2.5的部分相干分数阶涡旋光束的(a-b)焦场交叉谱密度分布及(c-d)反传输所得的源场交叉谱密度分布实验结果示意图。
本发明的核心是提供一种部分相干分数阶涡旋光束拓扑荷数测量的方法、装置及计算机存储介质，精度高，定量求解和表征了部分相干分数阶涡旋光束的分数阶拓扑荷。
为了使本技术领域的人员更好地理解本发明方案，下面结合附图和具体实施方式对本发明作进一步的详细说明。显然，所描述的实施例仅仅是本发明一部分实施例，而不是全部的实施例。基于本发明中的实施例，本领域普通技术人员在没有做出创造性劳动前提下所获得的所有其他实施例，都属于本发明保护的范围。
请参考图1，图1为本发明所提供的部分相干分数阶涡旋光束拓扑荷数的实现流程图；具体操作步骤如下：
S101:将待测分数阶涡旋光束照射到散射样品上，并进行横向和竖向移动交叠扫描，利用置于衍射区域的探测器采集衍射光强；
如图2所示，基于相干衍射成像概念的光学成像方法，待测分数阶涡旋光束照射在强散射样品上，待测分数阶涡旋光束或者样品沿着x和y进行移动进行交叠扫描(如图3)，所述交叠扫描的重叠率为60％～70％，CCD放置于样品的傅里叶平面或远场处采集衍射光强(衍射区域为菲涅尔衍射区或夫琅禾费衍射区),采集一系列光强，凭借时空间和频谱空间的傅里叶变换约束，从相邻区域重叠而产生的信息冗余度可以计算出相邻区域间的相对相位，重构成像，实现待测光源和待测对象的高分辨成像。由于不使用透镜，其理论分辨力可高于常规光学系统，这种方案不仅解决了重构算法中的收敛问题，也 实现了大视场和高分辨率兼得的效果。
S102:利用多模式叠层衍射算法，计算待测电场并迭代更新，以便最小化所述探测器采集的衍射光强和根据所述待测电场计算得到的衍射光强之间的误差，从而得到所述待测分数阶涡旋光束的目标待测电场；
S103:根据所述目标待测电场重建所述待测分数阶涡旋光束的交叉谱密度函数并获取所述待测分数阶涡旋光束的光场信息；
S104:根据所述交叉谱密度函数和所述待测分数阶涡旋光束的光场信息进行逆传输计算得到源场涡旋相位分布图，根据所述源场涡旋相位分布图观测所述待测分数阶涡旋光束拓扑荷数大小和正负。
在重构出电场的情况下，我们可以进行逆传输和逆聚焦计算，恢复出源平面处的涡旋相位，从而实现拓扑荷的计算。其中，拓扑荷计算可以基于相位跃变与2π的倍数关系给出，这一关系符合分数阶涡旋光束的原始定义。依托叠层相干衍射成像算法本身的高分辨特性，可以实现光源信号较弱、传输介质存在湍流情况下的高分辨、高精确度的分数阶拓扑荷测量。
基于以上实施例，对步骤S102进行进一步详细说明，具体如下：
部分相干光场是一种随机涨落电场，可以理解为瞬时电场的统计平均<E
*(r
1)E(r
2)>，以互相正交的本征模φ
mn展开，可以表示为：
其中，λ
mn表示模式的权重。对于经典的高斯谢尔模(GSM)部分相干光，交叉谱密度函数可以分解为厄米高斯(HG)模式的非相干叠加，即:
H
m和H
n分别表示m阶和n阶厄米多项式，N
c表示模式的数量。这种模式分解表示的方法叫做相干模式分解。另一种分解方式为随机模分解法。在这种方法中，部分相干光束由空间随机复杂场的非相干叠加表示：
其中α
n＝1/N
R表示模式权重，E
n(r)表示其中一个随机模。
以上相干分解和随机模分解原理已被广泛应用于部分相干光的实验产生，同理，也可用于部分相干光场的测量。
利用分解方法将所述待测光束的交叉谱密度W(r
1,r
2)分解为多个电场
其中，
和
为所述待测光束分解后的第i个电场，N
R为根据不同相干度选取的正整数(理论上NR为无穷大，实际过程中NR取有限值，相干度较低时当NR大于2000，误差忽略不计。当相干度/光束束腰比值在1到0.1之间时，NR选取4×4至10×10之间即可保证较高的准确性)，r1、r2为空间坐标。
步骤a：假设所述待测光束照射到散射样品上的交叉谱密度为
假设第j次照射在所述散射样品上的透过率函数为P(r-R
j)，r表示坐标，R
j表示所述待测光束与所述散射样品之间的相对位移，j表示第j次照射在样品区域；
步骤b：计算所述待测光束经过所述散射样品后的每个出射场为
步骤c：利用测量得到的光强去更新衍射场及出射场。衍射场更新为
其中
对应第i个模式的衍射场，I
j(k)为所述探测器采集的第j次照射的衍射光强，为所有电场模式贡献的光强，
为迭代计算的出射场的振幅，M为总模式数。在利用反傅里叶变换更新第i个模式的出射波
其中FFT表示傅里叶变换，IFFT表示逆傅里叶变换；
步骤d：更新每个待测电场
其中α,β是常数，
表示更新后的第j个扫描位置对应的第i个出射光电场，
为第j个扫描位置对应的第i个出射光场，O′
i
j(r)为更新第j个扫描位置对应的第i个照射到散射样品上入射光电场，O
i
j(r)为第j个扫描位置对应的第i个照射到散射样品上入射光电场，P′
j(r-R
j)为更新第j次照射在所述散射样品上的透过率函数，*表示取共轭；
步骤e：利用梯度下降算法判断所述探测器采集的衍射光强和当前计算得到的衍射光强之间的误差是否达到预设的最小化阈值，若达到所述最小化阈值，则得到目标待测电场，否则重复步骤b-e，直到达到所述最小化阈值。
若光束为完全相干光时，其与部分相干光的区别只在于，部分相干光需要测量多个电场，所以本发明也可以测量完全相干分数阶涡旋光束。
本发明使用混合模式叠层相干衍射成像中用到的迭代算法实现电场模式的重构：光源照射样品，记录菲涅尔衍射区的衍射图案，其与物平面之间满足傅里叶变换关系。衍射面的相机只能记录光场的振幅，相位信息缺失。为解得相位，重建待测面信息，在相干衍射成像的迭代算法中，使用梯度下降等算法最小化拍摄光强和计算光强之间的误差。为解决迭代收敛和唯一解问题，叠层相干衍射成像技术采用冗余地交叠扫描，互为约束的衍射信息大大提高了迭代的收敛速度和准确率。针对空间或时间部分相干光源，叠层相干衍射成像迭代算法用到了混合模式同步迭代，这里“混合模式”指的便是部分相干光的电场模式。本发明主要研究光源的重建结果，提取光源本身携带的信息。
基于以上实施例，本实施例对步骤S103和S104进行进一步详细说明，具体如下：
交叉密度函数
其中，α
i＝1/N
R为光谱权重；
对部分相干光束，引入涡旋相位，其交叉谱密度可以表示为W
0(r
1,r
2)＝W(r
1,r
2)exp(-ilθ
1)exp(ilθ
2)，其中θ为角向坐标，l为拓扑荷，当l为整数时，表示为部分相干整数阶涡旋相位，当l为分数时，表示为部分相干分数阶涡旋相位；
令r1＝r2计算得到光强I；
令r2＝0计算得到相干度μ；
对交叉谱密度函数W取W/|W|计算得到交叉谱密度相位分布函数：
根据所述交叉谱密度相位分布函数得到源场涡旋相位分布图；
通过光场逆传输或者逆聚焦至源平面，观测源平面的相位跃变或者对相位进行环路积分即可得出分数阶涡旋光束的拓扑荷。
若将部分相干涡旋光束聚焦，根据傅里叶变换原理，可以推导出源场交叉谱密度W
0(r
1,r
2)和焦场交叉谱密度W
f(ρ
1,ρ
0)关系可以简述为：
F
-1{W
f(ρ
1,ρ
0)}∝W
0(r
1,r
2)
同样地，也可以推导出任意传输距离的接受面和源平面的交叉谱密度定量联系。
部分相干光束可以看成完全相干光束的非相干叠加，将待测的部分相干光束通过散射物体，利用梯度下降算法最小化可测量信息和待测信息的误差，重建出待测分数阶涡旋光束的主要电场模式和权重。基于电场模式和交叉谱密度的数学关系，计算出部分相干光束的交叉谱密度函数、重构部分相干光的交叉谱密度、获取部分相干光场的完备信息，包括光强、光强关联、电场关联、相位等等。部分相干光场的完备信息得到后，进行逆向传输计算，得到源场涡旋相位分布，实现低相干条件下分数阶涡旋光束的精确拓扑荷，因此，本发明可以用于低相干分数阶涡旋光场测量，利用衍射图重建源场信息的方案，结合混合模式叠层相干衍射成像的迭代算法实现部分相干光电场模 式的精准测量和逆向传输计算，该技术同时解决了电场模式的在空间上难以分离的关键科学问题，使部分相干光模式复用成为可用的空分复用新维度，大大增加光通信的容量，在光通信、光学加密解密等方面有着重要的应用。
本发明具体实施例还提供了一种计算机可读存储介质，所述计算机可读存储介质上存储有计算机程序，所述计算机程序被处理器执行时实现上述步骤S102-S104。
本发明实施例还提供一种部分相干分数阶涡旋光束拓扑荷数测量的装置，包括：
光源，用于发射部分相干光束；
空间光调制器，用于产生部分相干分数阶涡旋光束，即为待测分数阶涡旋光束；
位移平台，用于移动散射样品，进行横向和竖向移动交叠扫描；
置于衍射区域的探测器，用于采集衍射光强；
计算机，用于利用多模式叠层衍射算法，计算待测电场并迭代更新，以便最小化所述探测器采集的衍射光强和根据所述待测电场计算得到的衍射光强之间的误差，从而得到所述待测分数阶涡旋光束的目标待测电场，根据所述目标待测电场重建所述待测分数阶涡旋光束的交叉谱密度函数并获取所述待测分数阶涡旋光束的光场信息，根据所述交叉谱密度函数和所述待测分数阶涡旋光束的光场信息进行逆传输计算得到源场涡旋相位分布图，根据所述源场涡旋相位分布图观测所述待测分数阶涡旋光束拓扑荷数大小和正负。
如图4所示，本实施例为部分相干分数阶涡旋光束产生与测量具体实验步骤，如下：
半导体固体激光器(波长532.8nm)入射至旋转毛玻璃片，经旋转毛玻璃片(旋转频率20HZ)扩散后的光束由透镜准直，通过改变照射在毛玻璃上光斑大小可以改变部分相干光的相干度。当部分相干光束通过空间光调制器后，则产生部分相干分数阶涡旋光束。当照射在毛玻璃上光斑很小时，产生的部 分相干光光场的相干度较大。实施例中，空间光调制器后表面的光束(相干度1mm，束腰1mm)为我们的测量对象。
待测分数阶涡旋光束传输一段距离后聚焦照射到分辨率板上，分辨率板放在位移平台上，通过MATLAB软件可以控制位移距离。此实例中位移平台x与y方向位移10步，步长为20um。打在分辨率板上光斑尺寸为150um左右。相机距离分辨率板13cm处采集衍射光强。根据采集到的衍射光强，带入多模式叠层衍射成像后，可以得到部分相干分数阶涡旋光束的主要模式。通过这些模式反传输到空间光调制器平面，检查此时的相位跃变即可得到拓扑荷数。
实验结果如图5所示，环绕一圈，相位跃变总数φ＝5.005π，计算得到TC＝φ/2＝2.5025，准确度为99.9％.。
本实施例的仪器具体为：
纯相位空间光调制器为反射式纯相位空间光调制器：HOLOEYE GAEA，尺寸大小为3840*2160像素，像素大小为3.74μm。纯相位空间光调制器用于设置测量范围，即通过在空间光调制器上加载涡旋相位，可以将部分相干光束变为分数阶部分相干光束。
本发明中用到位移平台为Newport哥德式轴承XYZ平移台(步长小于30nm)位移精度为100nm以内。
本发明中用到的样品为分辨率板(USAF)，美国Thorlabs公司生产。
本发明中，光探测器为CCD或CMOS。本实施例中，使用的CCD为EMCCD(电子增益相机)专业相机，具体参数为尺寸大小为1024*1024像素，像素大小为13μm。CCD用MATLAB软件驱动，上述软件用来观察以及保存CCD接收的图像信息。CCD连接到电脑之后，用MATLAB软件记录并保存CCD接收的图像信息。
本领域内的技术人员应明白，本申请的实施例可提供为方法、系统、或计算机程序产品。因此，本申请可采用完全硬件实施例、完全软件实施例、或结合软件和硬件方面的实施例的形式。而且，本申请可采用在一个或多个 其中包含有计算机可用程序代码的计算机可用存储介质(包括但不限于磁盘存储器、CD-ROM、光学存储器等)上实施的计算机程序产品的形式。
本申请是参照根据本申请实施例的方法、设备(系统)、和计算机程序产品的流程图和/或方框图来描述的。应理解可由计算机程序指令实现流程图和/或方框图中的每一流程和/或方框、以及流程图和/或方框图中的流程和/或方框的结合。可提供这些计算机程序指令到通用计算机、专用计算机、嵌入式处理机或其他可编程数据处理设备的处理器以产生一个机器，使得通过计算机或其他可编程数据处理设备的处理器执行的指令产生用于实现在流程图一个流程或多个流程和/或方框图一个方框或多个方框中指定的功能的装置。
这些计算机程序指令也可存储在能引导计算机或其他可编程数据处理设备以特定方式工作的计算机可读存储器中，使得存储在该计算机可读存储器中的指令产生包括指令装置的制造品，该指令装置实现在流程图一个流程或多个流程和/或方框图一个方框或多个方框中指定的功能。
这些计算机程序指令也可装载到计算机或其他可编程数据处理设备上，使得在计算机或其他可编程设备上执行一系列操作步骤以产生计算机实现的处理，从而在计算机或其他可编程设备上执行的指令提供用于实现在流程图一个流程或多个流程和/或方框图一个方框或多个方框中指定的功能的步骤。
显然，上述实施例仅仅是为清楚地说明所作的举例，并非对实施方式的限定。对于所属领域的普通技术人员来说，在上述说明的基础上还可以做出其它不同形式变化或变动。这里无需也无法对所有的实施方式予以穷举。而由此所引伸出的显而易见的变化或变动仍处于本发明创造的保护范围之中。
Claims (10)
- 一种部分相干分数阶涡旋光束拓扑荷数测量方法，其特征在于，包括：将待测分数阶涡旋光束照射到散射样品上，并进行横向和竖向移动交叠扫描，利用置于衍射区域的探测器采集衍射光强；利用多模式叠层衍射算法，计算待测电场并迭代更新，以便最小化所述探测器采集的衍射光强和根据所述待测电场计算得到的衍射光强之间的误差，从而得到所述待测分数阶涡旋光束的目标待测电场；根据所述目标待测电场重建所述待测分数阶涡旋光束的交叉谱密度函数并获取所述待测分数阶涡旋光束的光场信息；根据所述交叉谱密度函数和所述待测分数阶涡旋光束的光场信息进行逆传输计算得到源场涡旋相位分布图，根据所述源场涡旋相位分布图观测所述待测分数阶涡旋光束拓扑荷数大小和正负。
- 根据权利要求1所述的部分相干分数阶涡旋光束拓扑荷数测量方法，其特征在于，所述衍射区域为菲涅尔衍射区或夫琅禾费衍射区。
- 根据权利要求1所述的部分相干分数阶涡旋光束拓扑荷数测量方法，其特征在于，所述交叠扫描的重叠率为60％～70％。
- 根据权利要求1所述的部分相干分数阶涡旋光束拓扑荷数测量方法，其特征在于，所述利用多模式叠层衍射算法，计算待测电场并迭代更新，以便最小化所述探测器采集的衍射光强和根据所述待测电场计算得到的衍射光强之间的误差，从而得到所述待测分数阶涡旋光束的目标待测电场前包括：利用随机模分解方法将所述待测分数阶涡旋光束的交叉谱密度W(r 1,r 2)分解为多个电场其中，
和
为 所述待测分数阶涡旋光束分解后的第i个电场，N R为根据不同相干度选取的正整数，r1、r2为空间坐标。
- 根据权利要4所述的部分相干分数阶涡旋光束拓扑荷数测量方法，其特征在于，所述利用多模式叠层衍射算法，计算待测电场并迭代更新，以便最小化所述探测器采集的衍射光强和当前根据所述待测电场计算得到的衍射光强之间的误差，从而得到所述待测分数阶涡旋光束的目标待测电场包括：步骤1：假设所述待测分数阶涡旋光束照射到散射样品上的交叉谱密度为假设第j次照射在所述散射样品上的透过率函数为P(r-R j)，r表示坐标，R j表示所述待测分数阶涡旋光束与所述散射样品之间的相对位移，j表示第j次照射在样品区域；
步骤2：计算所述待测分数阶涡旋光束经过所述散射样品后的每个出射场为
步骤3：利用所述探测器采集的衍射光强更新衍射场，并根据所述衍射场更新出射场
步骤4：更新每个待测电场
其中α,β是常数，表示更新后的第j个扫描位置对应的第i个出射光电场，
为第j个扫描位置对应的第i个出射光场，O′ i j(r)为更新第j个扫描位置对应的第i个照射到散射样品上入射光电场，
为第j个扫描位置对应的第i个照射到散射样品上入射光 电场，P′ j(r-R j)为更新第j次照射在所述散射样品上的透过率函数，*表示取共轭；
步骤:5：利用梯度下降算法判断所述探测器采集的衍射光强和当前计算得到的衍射光强之间的误差是否达到预设的最小化阈值，若达到所述最小化阈值，则得到目标待测电场，否则重复步骤2-5，直到达到所述最小化阈值。 - 根据权利要求5所述的部分相干分数阶涡旋光束拓扑荷数测量方法，其特征在于，所述根据所述目标待测电场重建所述待测分数阶涡旋光束的交叉谱密度函数包括：所述交叉密度函数其中，α i＝1/N R为光谱权重；
对部分相干光束，引入涡旋相位，其交叉谱密度可以表示为W 0(r 1,r 2)＝W(r 1,r 2)exp(-ilθ 1)exp(ilθ 2)，其中θ为角向坐标，l为拓扑荷，当l为整数时，表示为部分相干整数阶涡旋相位，当l为分数时，表示为部分相干分数阶涡旋相位。 - 根据权利要求6所述的部分相干分数阶涡旋光束拓扑荷数测量方法，其特征在于，所述获取所述待测分数阶涡旋光束的光场信息包括：令r1＝r2计算得到光强I；令r2＝0计算得到相干度μ。
- 根据权利要求1所述的部分相干分数阶涡旋光束拓扑荷数测量方法，其特征在于，所述根据所述待测分数阶涡旋光束的光场信息进行逆传输计算得到源场涡旋相位分布图，根据所述源场涡旋相位分布图观测所述待测分数阶涡旋光束拓扑荷数大小和正负包括：对交叉谱密度函数W取W/|W|计算得到交叉谱密度相位分布函数：根据所述交叉谱密度相位分布函数得到源场涡旋相位分布图；根据所述源场涡旋相位分布图观测源平面的相位跃变或者对相位进行环路积分即可得出分数阶涡旋光束的拓扑荷。
- 一种部分相干分数阶涡旋光束拓扑荷数测装置，其特征在于，包括：光源，用于发射部分相干光束；空间光调制器，用于产生部分相干分数阶涡旋光束，即为待测分数阶涡旋光束；位移平台，用于移动散射样品，进行横向和竖向移动交叠扫描；置于衍射区域的探测器，用于采集衍射光强；计算机，用于利用多模式叠层衍射算法，计算待测电场并迭代更新，以便最小化所述探测器采集的衍射光强和根据所述待测电场计算得到的衍射光强之间的误差，从而得到所述待测分数阶涡旋光束的目标待测电场，根据所述目标待测电场重建所述待测分数阶涡旋光束的交叉谱密度函数并获取所述待测分数阶涡旋光束的光场信息，根据所述交叉谱密度函数和所述待测分数阶涡旋光束的光场信息进行逆传输计算得到源场涡旋相位分布图，根据所述源场涡旋相位分布图观测所述待测分数阶涡旋光束拓扑荷数大小和正负。
- 一种计算机可读存储介质，其特征在于，所述计算机可读存储介质上存储有计算机程序，所述计算机程序被处理器执行时实现如权利要求4至8任一项所述一种部分相干分数阶涡旋光束拓扑荷数测量的方法的步骤。
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