Full-dimensional photonic spin-hall space differential imaging method
By using Fourier transform and liquid crystal polarization grating separation technology, the problem of strict polarization requirements in existing methods has been solved, realizing full-dimensional optical spatial differential imaging, which can process light fields with arbitrary polarization states and generate clear differential images.
Patent Information
- Application Number
- CN202510423738.7
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2025-04-07
- Publication Date
- 2025-11-04
- Estimated Expiration
- 2045-04-07
AI Technical Summary
Existing spin Hall spatial differential imaging methods have strict requirements on the polarization of the input field, making it difficult to achieve full-dimensional optical spatial differentiation.
The full-dimensional photonic spin Hall space differential imaging method is adopted. The arbitrary polarization state light field is processed by Fourier transform and inverse Fourier transform, and polarization separation is performed by half-wave and quarter-wave geometric phase liquid crystal polarization gratings to generate four spin components. Finally, a differential image is realized on the image plane.
It achieves effective spatial filtering and polarization separation of light fields with arbitrary polarization states, generating optical differential effects in three dimensions: amplitude, phase, and polarization. It can independently process circularly polarized basis vectors and achieve clear differential imaging.
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Figure CN120255170B_ABST
Abstract
Description
TECHNICAL FIELD
[0001] The present application belongs to the field of optical imaging, and particularly relates to a full-dimension photonic spin Hall space differential imaging method. BACKGROUND
[0002] The photonic spin Hall effect refers to a physical phenomenon that photons with different spin angular momentums are transversely separated when propagating in different optical interfaces or inhomogeneous media. Since it can sensitively detect changes in material properties and environmental conditions, the photonic spin Hall effect is widely used in precision measurement, optical sensing and quantum information processing. In particular, in edge imaging, the photonic spin Hall effect makes it possible to perform edge detection through optical differential operation, promoting the development of optical space differential imaging.
[0003] So far, various amplitude and phase type photonic spin Hall differential methods have been proposed and gradually applied in practice, and they have shown broad application prospects in the fields of biomedical imaging and precision component detection. As known, the basic spatial physical dimensions of a light field include amplitude, phase and polarization. Since the existing spin Hall space differential imaging method has strict requirements on the polarization of the input field, how to realize optical space differential based on the spin Hall effect is still a problem to be solved at present. SUMMARY
[0004] The purpose of the present application is to solve the problems of the prior art, and to provide a full-dimension photonic spin Hall space differential imaging method. The technical scheme adopted is as follows:
[0005] A full-dimension photonic spin Hall space differential imaging method, the method comprising:
[0006] acquiring an arbitrary polarization state light field, and inputting the arbitrary polarization state light field into a first lens to perform Fourier transform and obtain a frequency domain light field, the arbitrary polarization state light field comprising object image information;
[0007] inputting the frequency domain light field into a one-half wave geometric phase liquid crystal polarization grating to perform polarization separation and obtain a first left-handed circularly polarized light and a first right-handed circularly polarized light, and inputting the first left-handed circularly polarized light and the first right-handed circularly polarized light into a one-quarter wave geometric phase liquid crystal polarization grating to perform polarization separation and obtain a second left-handed circularly polarized light, a second right-handed circularly polarized light, a third left-handed circularly polarized light and a third right-handed circularly polarized light;
[0008] inputting the second left-handed circularly polarized light, the second right-handed circularly polarized light, the third left-handed circularly polarized light and the third right-handed circularly polarized light into a second lens to perform inverse Fourier transform and obtain a spatial domain light field, and inputting the spatial domain light field into a polarizer to perform polarization detection and obtain a differential image.
[0009] Preferably, the arbitrary polarization state optical field can be synthesized from two circular polarization basis vectors, i.e., expressed as:
[0010]
[0011] Among them, E in (x, y) represents the arbitrary polarization state of the light field, E LCP (x, y) represents the complex amplitude distribution of left-handed circularly polarized light in the arbitrary polarization state light field, [1i] T E represents the Jones matrix of left-handed circularly polarized light in the arbitrary polarization state optical field. RCP (x, y) represents the complex amplitude distribution of right-handed circularly polarized light in the arbitrary polarization state optical field, [1-i] T The Jones matrix represents the right-hand circularly polarized light in the arbitrary polarization state optical field.
[0012] Preferably, the angular spectrum of the frequency domain optical field on the half-wave geometric phase liquid crystal polarization grating is expressed as:
[0013]
[0014] Among them, F 1,LCP (f x f y E represents the angular spectrum of the left-handed circularly polarized light in the frequency domain optical field on the half-wave geometric phase liquid crystal polarization grating. LCP (f x f y F represents the complex amplitude distribution of left-handed circularly polarized light in the frequency domain optical field. 1,RCP (f x f y E represents the angular spectrum of right-hand circularly polarized light in the frequency domain optical field on the half-wave geometric phase liquid crystal polarization grating. RCP (f x f y ) represents the complex amplitude distribution of right-handed circularly polarized light in the frequency domain optical field, exp[iπλd(f x 2 +f y 2 ] represents the Fresnel diffraction transfer function in the frequency domain;
[0015] The angular spectrum of the frequency domain optical field after passing through the half-wave geometric phase liquid crystal polarization grating is expressed as follows:
[0016]
[0017] Where * represents the convolution operation, Λ1 represents the period of the half-wave geometric phase liquid crystal polarization grating, and F′ 1,LCP (fx f y This indicates that the angular spectrum of left-handed circularly polarized light in the frequency domain optical field becomes the first right-handed circularly polarized light after passing through the half-wave geometric phase liquid crystal polarization grating. This indicates that the left-handed circularly polarized light in the frequency domain optical field is along f x The direction has shifted. This corresponds to a translation of F′ along the x-direction in space by -Λ1. 1,RCP (f x f y This indicates that the angular spectrum of right-handed circularly polarized light in the frequency domain optical field becomes the first left-handed circularly polarized light after passing through the half-wave geometric phase liquid crystal polarization grating. This indicates that the right-hand circularly polarized light in the frequency domain optical field is along f x The direction has shifted. This corresponds to a translation of Λ1 along the x-direction in space, where δ represents the Dirac function.
[0018] Preferably, the angular spectrum of the first right-hand circularly polarized light before passing through the quarter-wave geometric phase liquid crystal polarization grating is represented as follows:
[0019]
[0020] Among them, F FP,LCP (f x f y The angular spectrum of the first right-hand circularly polarized light before it passes through a quarter-wave geometric phase liquid crystal polarization grating is represented by ).
[0021] The angular spectrum of the first left-hand circularly polarized light before passing through a quarter-wave geometric phase liquid crystal polarization grating is represented as follows:
[0022]
[0023] Among them, F FP,RCP (f x f y The angular spectrum of the first left-handed circularly polarized light before it passes through a quarter-wave geometric phase liquid crystal polarization grating is represented by ).
[0024] The angular spectra of the first right-hand circularly polarized light and the first left-hand circularly polarized light after passing through a quarter-wave geometric phase liquid crystal polarization grating are expressed as follows:
[0025]
[0026] The second left-handed circularly polarized light H1 is:
[0027]
[0028] The second right-hand circularly polarized light H2 is:
[0029]
[0030] The third left-handed circularly polarized light H3 is:
[0031]
[0032] The third right-hand circularly polarized light H4 is:
[0033]
[0034] Among them, F′ FP,LCP (f x f y F′ represents the angular spectrum of the first right-hand circularly polarized light after passing through a quarter-wave geometric phase liquid crystal polarization grating. FP,RCP (f x f y ) represents the angular spectrum of the first left-handed circularly polarized light after passing through the quarter-wave geometric phase liquid crystal polarization grating, θ = 2πs / Λ2, where s represents the lateral displacement of the quarter-wave geometric phase liquid crystal polarization grating, and Λ2 represents the grating period of the quarter-wave geometric phase liquid crystal polarization grating.
[0035] Preferably, after passing through the quarter-wave geometric phase liquid crystal polarization grating, the output electric fields of the first right-hand circularly polarized light and the first left-hand circularly polarized light are represented on the image plane as follows:
[0036]
[0037] Where f is the focal length, M is the magnification factor, and F is the focal length. IP,LCP (x3, y3) represents the output electric field of the first right-handed circularly polarized light on the image plane, F IP,RCP (x3, y3) represents the output electric field of the first left-hand circularly polarized light on the image plane, and x3, y3 represent the real space coordinates of the corresponding circularly polarized light on the image plane.
[0038] When M = -1, s = 0, λd = m·Λ1Λ2, where m is a positive integer, the incident light field before entering the polarizer is:
[0039]
[0040] Preferably, after the spatial optical field is analyzed by the polarizer at 45°, the object image output field of the differential image obtained is:
[0041]
[0042] The object-image output field after the spatial optical field is subjected to -45° polarization analysis through the polarizer is as follows:
[0043]
[0044] where, F′ IP,LCP (x3, y3) represents the representation of the output electric field of the right-handed circularly polarized light in the differential image on the image plane, and F′ IP,RCP (x3, y3) represents the representation of the output electric field of the left-handed circularly polarized light in the differential image on the image plane.
[0045] Preferably, when the displacement value λf / Λ2 is smaller than the image contour corresponding to the object-image information, the left-handed circularly polarized light in the differential image is the first-order spatial differential of the left-handed circularly polarized light in the arbitrarily polarized light field:
[0046]
[0047] where, |F′ IP,LCP | represents the first-order spatial differential of the left-handed circularly polarized light, represents the partial derivative, and x represents the abscissa in the Cartesian coordinate system in real space;
[0048] When the displacement value λf / Λ2 is smaller than the image contour corresponding to the object-image information, the right-handed circularly polarized light in the differential image is the first-order spatial differential of the right-handed circularly polarized light in the arbitrarily polarized light field:
[0049]
[0050] where, |F′ IP,RCP | represents the first-order spatial differential of the right-handed circularly polarized light.
[0051] The beneficial effects of the present invention are as follows: Through the Fourier transform and inverse Fourier transform by the first lens and the second lens, the spatial filtering of the arbitrarily polarized light field can be effectively performed. Through the polarization separation of the frequency-domain light field by the half-wave geometric phase liquid crystal polarization grating and the polarization separation of the first left-handed circularly polarized light and the first right-handed circularly polarized light by the quarter-wave geometric phase liquid crystal polarization grating, the optical differential effects in the three dimensions of amplitude, phase, and polarization can be effectively generated by the photon spin Hall effect to separate the circular polarization basis vectors (circularly polarized light) and realize independent optical spatial differential processing. Description of the Drawings
[0052] Figure 1 is the flowchart of the full-dimensional photon spin Hall spatial differential imaging method provided by the first embodiment of the present invention;
[0053] Figure 2This is a schematic diagram of the structure of the full-dimensional photonic spin Hall spatial differential imaging system provided in the second embodiment of the present invention;
[0054] Figure 3 This is a microscopic image of a half-wave geometric phase liquid crystal polarization grating provided in the second embodiment of the present invention;
[0055] Figure 4 This is a microscopic image of a quarter-wave geometric phase liquid crystal polarization grating provided in the second embodiment of the present invention;
[0056] Figure 5 This is a schematic diagram of the differential image after the amplitude field is modulated by the full-dimensional photon spin Hall space differential imaging system according to the second embodiment of the present invention;
[0057] Figure 6 This is a schematic diagram of the differential image after the phase field is modulated by the full-dimensional photon spin Hall space differential imaging system according to the second embodiment of the present invention;
[0058] Figure 7 This is a schematic diagram of the differential image after the polarization field is modulated by the full-dimensional photon spin Hall space differential imaging system, provided in the second embodiment of the present invention. Detailed Implementation
[0059] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.
[0060] To illustrate the technical solution described in this invention, specific embodiments are described below.
[0061] Example 1
[0062] Please see Figure 1 This is a flowchart of the full-dimensional photon spin Hall space differential imaging method provided in the first embodiment of the present invention. The full-dimensional photon spin Hall space differential imaging method includes the following steps:
[0063] Step S10: Obtain an arbitrary polarization state light field, and input the arbitrary polarization state light field into the first lens to perform a Fourier transform to obtain a frequency domain light field;
[0064] The arbitrary polarization state light field includes object image information. By inputting the arbitrary polarization state light field into the first lens and performing a Fourier transform, the arbitrary polarization state light field in the spatial domain can be effectively converted into a frequency domain light field in the frequency domain.
[0065] In this step, the arbitrary polarization state optical field can be synthesized from two circular polarization basis vectors, that is, expressed as:
[0066]
[0067] Among them, E in (x, y) represents the arbitrary polarization state of the light field, E LCP (x, y) represents the complex amplitude distribution of left-handed circularly polarized light in the arbitrary polarization state light field, [1i] T E represents the Jones matrix of left-handed circularly polarized light in the arbitrary polarization state optical field. RCP (x, y) represents the complex amplitude distribution of right-handed circularly polarized light in the arbitrary polarization state optical field, [1-i] T The Jones matrix represents the right-hand circularly polarized light in the arbitrary polarization state optical field.
[0068] Step S20: Input the frequency domain optical field into a half-wave geometric phase liquid crystal polarization grating for polarization separation to obtain a first left-hand circularly polarized light and a first right-hand circularly polarized light. Then, input the first left-hand circularly polarized light and the first right-hand circularly polarized light into a quarter-wave geometric phase liquid crystal polarization grating for polarization separation to obtain a second left-hand circularly polarized light, a second right-hand circularly polarized light, a third left-hand circularly polarized light, and a third right-hand circularly polarized light.
[0069] The light field after Fourier transform by the first lens is incident on the half-wave geometric phase liquid crystal polarization grating. Before the light beam reaches the quarter-wave geometric phase liquid crystal polarization grating, it will be completely separated into two spin components, namely, the first left-hand circularly polarized light and the first right-hand circularly polarized light. After the two spin components pass through the quarter-wave geometric phase liquid crystal polarization grating, the first left-hand circularly polarized light and the first right-hand circularly polarized light each split into two spin components, generating four spin components, namely, the first left-hand circularly polarized light splits into the second left-hand circularly polarized light and the second right-hand circularly polarized light, and the first right-hand circularly polarized light splits into the third left-hand circularly polarized light and the third right-hand circularly polarized light.
[0070] In this step, the angular spectrum of the frequency domain optical field on the half-wave geometric phase liquid crystal polarization grating is expressed as:
[0071]
[0072] Among them, F 1,LCP (f x f y E represents the angular spectrum of the left-handed circularly polarized light in the frequency domain optical field on the half-wave geometric phase liquid crystal polarization grating. LCP (f x f y F represents the complex amplitude distribution of left-handed circularly polarized light in the frequency domain optical field. 1,RCP (f x fy E represents the angular spectrum of right-hand circularly polarized light in the frequency domain optical field on the half-wave geometric phase liquid crystal polarization grating. RCP (f x f y ) represents the complex amplitude distribution of right-handed circularly polarized light in the frequency domain optical field, exp[iπλd(f x 2 +f y 2 ] represents the Fresnel diffraction transfer function in the frequency domain;
[0073] The angular spectrum of the frequency domain optical field at plane 1, after passing through the half-wave geometric phase liquid crystal polarization grating, is expressed as follows:
[0074]
[0075] Where * represents the convolution operation, Λ1 represents the period of the half-wave geometric phase liquid crystal polarization grating, and F′ 1,LCP (f x f y This indicates that the angular spectrum of left-handed circularly polarized light in the frequency domain optical field becomes the first right-handed circularly polarized light after passing through the half-wave geometric phase liquid crystal polarization grating. This indicates that the left-handed circularly polarized light in the frequency domain optical field is along f x The direction has shifted. This corresponds to a translation of F′ along the x-direction in space by -Λ1. 1,RCP (f x f y This indicates that the angular spectrum of right-handed circularly polarized light in the frequency domain optical field becomes the first left-handed circularly polarized light after passing through the half-wave geometric phase liquid crystal polarization grating. This indicates that the right-hand circularly polarized light in the frequency domain optical field is along f x The direction has shifted. This corresponds to a translation of Λ1 along the x-direction in space, where δ represents the Dirac function.
[0076] Step S30: Input the second left-hand circularly polarized light, the second right-hand circularly polarized light, the third left-hand circularly polarized light and the third right-hand circularly polarized light into the second lens to perform inverse Fourier transform to obtain the spatial light field, and input the spatial light field into the polarizer for polarization analysis to obtain the differential image;
[0077] Among them, the four spin components are transformed by the inverse Fourier transform of the second lens and filtered by the polarizer to obtain a differential image on the image plane.
[0078] Optionally, in the Fourier plane, the angular spectrum of the first right-hand circularly polarized light before passing through a quarter-wave geometric phase liquid crystal polarization grating is represented as follows:
[0079]
[0080] Among them, F FP,LCP (f x f y The angular spectrum of the first right-hand circularly polarized light before it passes through a quarter-wave geometric phase liquid crystal polarization grating is represented by ).
[0081] In the Fourier plane, the angular spectrum of the first left-handed circularly polarized light before passing through the quarter-wave geometric phase liquid crystal polarization grating is represented as:
[0082]
[0083] Among them, F FP,RCP (f x f y The angular spectrum of the first left-handed circularly polarized light before it passes through a quarter-wave geometric phase liquid crystal polarization grating is represented by ).
[0084] The angular spectra of the first right-hand circularly polarized light and the first left-hand circularly polarized light after passing through a quarter-wave geometric phase liquid crystal polarization grating are expressed as follows:
[0085]
[0086] The second left-handed circularly polarized light H1 is:
[0087]
[0088] The second right-hand circularly polarized light H2 is:
[0089]
[0090] The third left-handed circularly polarized light H3 is:
[0091]
[0092] The third right-hand circularly polarized light H4 is:
[0093]
[0094] Among them, F′ FP,LCP (f x f y F′ represents the angular spectrum of the first right-hand circularly polarized light after passing through a quarter-wave geometric phase liquid crystal polarization grating. FP,RCP (f x f y) represents the angular spectrum of the first left-handed circularly polarized light after passing through the quarter-wave geometric phase liquid crystal polarization grating, θ = 2πs / Λ2, where s represents the lateral displacement of the quarter-wave geometric phase liquid crystal polarization grating, and Λ2 represents the grating period of the quarter-wave geometric phase liquid crystal polarization grating.
[0095] Optionally, after passing through the quarter-wave geometric phase liquid crystal polarization grating, the output electric fields of the first right-hand circularly polarized light and the first left-hand circularly polarized light are represented on the image plane as follows:
[0096]
[0097] Where f is the focal length, M is the magnification factor, and F is the focal length. IP,LCP (x3, y3) represents the output electric field of the first right-handed circularly polarized light on the image plane, F IP,RCP (x3, y3) represents the output electric field of the first left-hand circularly polarized light on the image plane, and x3, y3 represent the real space coordinates of the corresponding circularly polarized light on the image plane.
[0098] When M = -1, s = 0, λd = m·Λ1Λ2, where m is a positive integer, the incident light field before entering the polarizer is:
[0099]
[0100] Furthermore, after the spatial optical field is analyzed by 45° using the polarizer, the object image output field of the obtained differential image is:
[0101]
[0102] The output field of the object image after the spatial optical field is analyzed by the polarizer at -45° is:
[0103]
[0104] Among them, F′ IP,LCP (x3, y3) represents the output electric field of the right-hand circularly polarized light in the differential image on the image plane, F′ IP,RCP (x3, y3) represents the output electric field of the left-handed circularly polarized light in the differential image on the image plane.
[0105] Furthermore, when the displacement value λf / Λ2 is less than the image contour corresponding to the object image information, the left-handed circularly polarized light in the differential image is the first-order spatial differential of the left-handed circularly polarized light in the arbitrary polarization state light field:
[0106]
[0107] Among them, |F′IP,LCP represents the first-order spatial differential of left-handed circularly polarized light, represents partial derivative, and x represents the abscissa in the Cartesian coordinate system in real space;
[0108] When the displacement value λf / Λ2 is less than the image contour corresponding to the object image information, the right-handed circularly polarized light in the differential image is the first-order spatial differential of the right-handed circularly polarized light in the arbitrary polarization state light field:
[0109]
[0110] where, 丨F′ IP,RCP 丨 represents the first-order spatial differential of right-handed circularly polarized light.
[0111] In this embodiment, through the first lens and the second lens for Fourier transform and inverse Fourier transform, the spatial filtering of the arbitrary polarization state light field can be effectively carried out. Through the half-wave geometric phase liquid crystal polarization grating for polarization separation of the frequency-domain light field and the quarter-wave geometric phase liquid crystal polarization grating for polarization separation of the first left-handed circularly polarized light and the first right-handed circularly polarized light, the optical differential effects in the three dimensions of amplitude, phase and polarization can be effectively generated by the photon spin Hall effect, so as to separate the circular polarization basis vectors (circularly polarized light) and realize independent optical spatial differential processing.
[0112] Embodiment 2
[0113] Please refer to Figures 2 to 7 , which is the structural schematic diagram of the full-dimensional photon spin Hall space differential imaging system, the microscopic imaging diagram of the liquid crystal polarization grating and the full-dimensional photon spin Hall space differential imaging diagram provided by the second embodiment of the present invention, including:
[0114] The first lens 10 is used to perform Fourier transform on the input arbitrary polarization state light field to obtain a frequency-domain light field, and the arbitrary polarization state light field includes object image information; where, the arbitrary polarization state light field includes object image information, and by inputting the arbitrary polarization state light field into the first lens 10 for Fourier transform, the arbitrary polarization state light field in the spatial domain can be effectively converted into a frequency-domain light field in the frequency domain.
[0115] The arbitrary polarization state light field can be synthesized by two circular polarization basis vectors, that is, expressed as:
[0116]
[0117] where, E in (x, y) represents the arbitrary polarization state light field, E LCP (x, y) represents the complex amplitude distribution of the left-handed circularly polarized light in the arbitrary polarization state light field at plane 0, [1i] T represents the Jones matrix of the left-handed circularly polarized light in the arbitrary polarization state light field, ERCP (x, y) represents the complex amplitude distribution of right-handed circularly polarized light at plane 0 in the arbitrary polarization state light field, [1-i] T The Jones matrix represents the right-hand circularly polarized light in the arbitrary polarization state optical field.
[0118] The half-wave geometric phase liquid crystal polarization grating 11 is used to perform polarization separation on the frequency domain light field output by the first lens 10 to obtain a first left-hand circularly polarized light and a first right-hand circularly polarized light. The light field after Fourier transformation by the first lens 10 is incident on the half-wave geometric phase liquid crystal polarization grating and will be completely separated into two spin components, namely, the first left-hand circularly polarized light and the first right-hand circularly polarized light, before the light beam reaches the quarter-wave geometric phase liquid crystal polarization grating.
[0119] The angular spectrum of the frequency domain optical field on the half-wave geometric phase liquid crystal polarization grating is represented as follows:
[0120]
[0121] Among them, F 1,LCP (f x f y E represents the angular spectrum of the left-handed circularly polarized light in the frequency domain optical field on the half-wave geometric phase liquid crystal polarization grating. LCP (f x f y F represents the complex amplitude distribution of left-handed circularly polarized light in the frequency domain optical field. 1,RCP (f x f y E represents the angular spectrum of right-hand circularly polarized light in the frequency domain optical field on the half-wave geometric phase liquid crystal polarization grating. RCP (f x f y ) represents the complex amplitude distribution of right-handed circularly polarized light in the frequency domain optical field, exp[iπλd(f x 2 +f y 2 ] represents the Fresnel diffraction transfer function in the frequency domain;
[0122] The angular spectrum of the frequency domain optical field after passing through the half-wave geometric phase liquid crystal polarization grating is expressed as follows:
[0123]
[0124] Where * represents the convolution operation, Λ1 represents the period of the half-wave geometric phase liquid crystal polarization grating, and F′ 1,LCP (f x f yThis indicates that the angular spectrum of left-handed circularly polarized light in the frequency domain optical field becomes the first right-handed circularly polarized light after passing through the half-wave geometric phase liquid crystal polarization grating. This indicates that the left-handed circularly polarized light in the frequency domain optical field is along f x The direction has shifted. This corresponds to a translation of F′ along the x-direction in space by -Λ1. 1,RCP (f x f y This indicates that the angular spectrum of right-handed circularly polarized light in the frequency domain optical field becomes the first left-handed circularly polarized light after passing through the half-wave geometric phase liquid crystal polarization grating. This indicates that the right-hand circularly polarized light in the frequency domain optical field is along f x The direction has shifted. This corresponds to a translation of Λ1 along the x-direction in space, where δ represents the Dirac function.
[0125] A quarter-wave geometric phase liquid crystal polarization grating 12 is used to polarize the first left-handed circularly polarized light and the first right-handed circularly polarized light output from the half-wave geometric phase liquid crystal polarization grating 11, to obtain a second left-handed circularly polarized light, a second right-handed circularly polarized light, a third left-handed circularly polarized light, and a third right-handed circularly polarized light. After passing through the quarter-wave geometric phase liquid crystal polarization grating, the first left-handed circularly polarized light and the first right-handed circularly polarized light each split into two spin components, generating four spin components: the first left-handed circularly polarized light splits into the second left-handed circularly polarized light and the second right-handed circularly polarized light, and the first right-handed circularly polarized light splits into the third left-handed circularly polarized light and the third right-handed circularly polarized light.
[0126] The angular spectrum of the first right-hand circularly polarized light before passing through a quarter-wave geometric phase liquid crystal polarization grating is represented as follows:
[0127]
[0128] Among them, F FP,LCP (f x f y The angular spectrum of the first right-hand circularly polarized light before it passes through a quarter-wave geometric phase liquid crystal polarization grating is represented by ).
[0129] The angular spectrum of the first left-hand circularly polarized light before passing through a quarter-wave geometric phase liquid crystal polarization grating is represented as follows:
[0130]
[0131] Among them, F FP,RCP (f x f y The angular spectrum of the first left-handed circularly polarized light before it passes through a quarter-wave geometric phase liquid crystal polarization grating is represented by ).
[0132] The angular spectra of the first right-hand circularly polarized light and the first left-hand circularly polarized light after passing through a quarter-wave geometric phase liquid crystal polarization grating are expressed as follows:
[0133]
[0134] The second left-handed circularly polarized light H1 is:
[0135]
[0136] The second right-hand circularly polarized light H2 is:
[0137]
[0138] The third left-handed circularly polarized light H3 is:
[0139]
[0140] The third right-hand circularly polarized light H4 is:
[0141]
[0142] Among them, F′ FP,LCP (f x f y F′ represents the angular spectrum of the first right-hand circularly polarized light after passing through a quarter-wave geometric phase liquid crystal polarization grating. FP,RCP (f x f y ) represents the angular spectrum of the first left-handed circularly polarized light after passing through the quarter-wave geometric phase liquid crystal polarization grating, θ = 2πs / Λ2, where s represents the lateral displacement of the quarter-wave geometric phase liquid crystal polarization grating, and Λ2 represents the grating period of the quarter-wave geometric phase liquid crystal polarization grating.
[0143] After passing through the quarter-wave geometric phase liquid crystal polarization grating, the output electric fields of the first right-hand circularly polarized light and the first left-hand circularly polarized light on the image plane are represented as follows:
[0144]
[0145] Where f is the focal length, M is the magnification factor, and F is the focal length. IP,LCP (x3, y3) represents the output electric field of the first right-handed circularly polarized light on the image plane, F IP,RCP (x3, y3) represents the output electric field of the first left-hand circularly polarized light on the image plane, and x3, y3 represent the real space coordinates of the corresponding circularly polarized light on the image plane.
[0146] When M = -1, s = 0, λd = m·Λ1Λ2, where m is a positive integer, the incident light field before entering the polarizer is:
[0147]
[0148] The second lens 13 is used to perform inverse Fourier transform on the second left-hand circularly polarized light, the second right-hand circularly polarized light, the third left-hand circularly polarized light, and the third right-hand circularly polarized light output from the quarter-wave geometric phase liquid crystal polarization grating 12 to obtain a spatial optical field. In this way, by performing inverse Fourier transform on the second left-hand circularly polarized light, the second right-hand circularly polarized light, the third left-hand circularly polarized light, and the third right-hand circularly polarized light output from the quarter-wave geometric phase liquid crystal polarization grating 12, the frequency domain optical field can be effectively converted into a spatial optical field.
[0149] Polarizer 14 is used to filter the spatial light field output by the second lens 13 to obtain a differential image on the image plane.
[0150] After the spatial optical field is analyzed by the polarizer at 45°, the resulting differential image output field is:
[0151]
[0152] The output field of the object image after the spatial optical field is analyzed by the polarizer at -45° is:
[0153]
[0154]
[0155] Among them, F′ IP,LCP (x3, y3) represents the output electric field of the right-hand circularly polarized light in the differential image on the image plane, F′ IP,RCP (x3, y3) represents the output electric field of the left-handed circularly polarized light in the differential image on the image plane.
[0156] When the displacement value λf / Λ2 is less than the image contour corresponding to the object image information, the left-handed circularly polarized light in the differential image is the first-order spatial differential of the left-handed circularly polarized light in the arbitrary polarization state light field:
[0157]
[0158] Among them, |F′ IP,LCP | represents the first-order spatial differential of left-handed circularly polarized light. Let x denote the partial derivative, and let x represent the x-coordinate in the Cartesian coordinate system in real space.
[0159] When the displacement value λf / Λ2 is less than the image contour corresponding to the object image information, the right-handed circularly polarized light in the differential image is the first-order spatial differential of the right-handed circularly polarized light in the arbitrary polarization state light field:
[0160]
[0161] Among them, 丨F′ IP,RCP 丨 represents the first-order spatial differential of the right-handed circularly polarized light.
[0162] In this embodiment, a quadruple focal length optical system (4f system) is constructed using the first lens 10 and the second lens 13 with the same focal length to achieve spatial filtering. Two geometric phase liquid crystal polarization gratings are integrated between the first lens 10 and the second lens 13. The light field carrying the object image information sequentially passes through the half-wave geometric phase liquid crystal polarization grating and the quarter-wave geometric phase liquid crystal polarization grating, generating a large photon spin Hall effect and a small photon spin Hall effect respectively, for separating the circular polarization basis vectors and realizing independent differential processing. Since an arbitrary polarization field can be decomposed into two circular polarization basis vectors carrying conjugate phase information, polarization differential imaging is actually transformed into phase differential imaging, proving that full-dimensional photon spin space differential imaging can support differential imaging of amplitude, phase, and polarization fields.
[0163] In this embodiment, the result is simple, the regulation is flexible, and it can satisfy the differential imaging in three dimensions of amplitude, phase, and polarization based on the photon spin Hall effect. By constructing the cascaded photon spin Hall effect of two geometric phase liquid crystal polarization gratings based on the 4f system, optical differentiation in three dimensions (amplitude, phase, and polarization) of light is realized. It is applicable to fields such as optical differential imaging, material characterization, and optical information processing. When the linearly polarized light carrying the object image information is incident on the full-dimensional photon spin Hall space differential imaging system, through two cascaded photon spin Hall effects, the arbitrary polarization state light is gradually separated into four spin components. The left-handed and right-handed components are approximately equal to the first-order spatial differential of the input field under the polarization analysis of a specific polarizer. Further through the first-order spatial differential, a clear differential object image can be presented on the image plane.
Claims
1. A method for multidimensional photonic spin Hall spatial differential imaging, characterized in that, The method includes: An arbitrary polarization state light field is acquired and input into a first lens for Fourier transform to obtain a frequency domain light field, wherein the arbitrary polarization state light field includes object image information; The frequency domain optical field is input into a half-wave geometric phase liquid crystal polarization grating for polarization separation to obtain a first left-hand circularly polarized light and a first right-hand circularly polarized light. The first left-hand circularly polarized light and the first right-hand circularly polarized light are then input into a quarter-wave geometric phase liquid crystal polarization grating for polarization separation to obtain a second left-hand circularly polarized light, a second right-hand circularly polarized light, a third left-hand circularly polarized light, and a third right-hand circularly polarized light. The second left-hand circularly polarized light, the second right-hand circularly polarized light, the third left-hand circularly polarized light, and the third right-hand circularly polarized light are input into the second lens for inverse Fourier transform to obtain a spatial optical field. The spatial optical field is then input into a polarizer for polarization analysis to obtain a differential image.
2. The full-dimensional photonic spin Hall spatial differential imaging method as described in claim 1, characterized in that, The arbitrary polarization state optical field can be synthesized from two circular polarization basis vectors, that is, it can be expressed as: in, x and y This represents the x and y axes in the Cartesian coordinate system at point 0 in the plane. Represents the arbitrary polarization state of the light field. This represents the complex amplitude distribution of left-handed circularly polarized light in the arbitrary polarization state optical field. The Jones matrix represents the left-handed circularly polarized light in the arbitrary polarization state optical field. This represents the complex amplitude distribution of right-handed circularly polarized light in the arbitrary polarization state optical field. The Jones matrix represents the right-hand circularly polarized light in the arbitrary polarization state optical field.
3. The full-dimensional photonic spin Hall spatial differential imaging method as described in claim 2, characterized in that, The angular spectrum of the frequency domain optical field on the half-wave geometric phase liquid crystal polarization grating is represented as follows: in, This represents the angular spectrum of left-handed circularly polarized light in the frequency domain optical field on the half-wave geometric phase liquid crystal polarization grating. This represents the complex amplitude distribution of left-handed circularly polarized light in the frequency domain optical field. This represents the angular spectrum of right-handed circularly polarized light in the frequency domain optical field on the half-wave geometric phase liquid crystal polarization grating. This represents the complex amplitude distribution of right-handed circularly polarized light in the frequency domain optical field. This represents the Fresnel diffraction transfer function in the frequency domain; The angular spectrum of the frequency domain optical field after passing through the half-wave geometric phase liquid crystal polarization grating is expressed as follows: in, This represents the convolution operation. This represents the period of the half-wave geometric phase liquid crystal polarization grating. This indicates that the left-handed circularly polarized light in the frequency domain optical field becomes the first right-handed circularly polarized light after passing through the half-wave geometric phase liquid crystal polarization grating. This indicates that the left-handed circularly polarized light in the frequency domain optical field is along... The direction has shifted. Corresponding to along in space The direction has shifted. , This indicates that the right-hand circularly polarized light in the frequency domain optical field becomes the first left-hand circularly polarized light after passing through the half-wave geometric phase liquid crystal polarization grating. This indicates that the right-hand circularly polarized light in the frequency domain optical field is along... The direction has shifted. Corresponding to along in space The direction has shifted. , This represents the Dirac function.
4. The full-dimensional photonic spin Hall spatial differential imaging method as described in claim 3, characterized in that, The angular spectrum of the first right-hand circularly polarized light before passing through a quarter-wave geometric phase liquid crystal polarization grating is represented as follows: in, This represents the angular spectrum of the first right-hand circularly polarized light before it passes through a quarter-wave geometric phase liquid crystal polarization grating; The angular spectrum of the first left-hand circularly polarized light before passing through a quarter-wave geometric phase liquid crystal polarization grating is represented as follows: in, This represents the angular spectrum of the first left-handed circularly polarized light before it passes through a quarter-wave geometric phase liquid crystal polarization grating; The angular spectra of the first right-hand circularly polarized light and the first left-hand circularly polarized light after passing through a quarter-wave geometric phase liquid crystal polarization grating are expressed as follows: The second left-handed circularly polarized light for: The second right-hand circularly polarized light for: The third left-hand circularly polarized light for: The third right-hand circularly polarized light for: in, This represents the angular spectrum of the first right-hand circularly polarized light after passing through a quarter-wave geometric phase liquid crystal polarization grating. This represents the angular spectrum of the first left-handed circularly polarized light after passing through the quarter-wave geometric phase liquid crystal polarization grating. , This represents the lateral displacement of the quarter-wave geometric phase liquid crystal polarization grating. The grating period represents the quarter-wave geometric phase liquid crystal polarization grating.
5. The full-dimensional photonic spin Hall spatial differential imaging method as described in claim 4, characterized in that, After passing through the quarter-wave geometric phase liquid crystal polarization grating, the output electric fields of the first right-hand circularly polarized light and the first left-hand circularly polarized light on the image plane are represented as follows: in, Where M is the focal length and M is the magnification factor. This represents the output electric field of the first right-hand circularly polarized light on the image plane. This represents the output electric field of the first left-handed circularly polarized light on the image plane. , This represents the real space coordinates of the corresponding circularly polarized light on the image plane; When M=-1, =0, , As a positive integer, the incident light field before entering the polarizer is: 。 6. The full-dimensional photonic spin Hall spatial differential imaging method as described in claim 5, characterized in that, After the spatial optical field is analyzed by the polarizer at 45°, the resulting differential image output field is: The output field of the object image after the spatial optical field is analyzed by the polarizer at -45° is: in, This represents the output electric field of right-handed circularly polarized light in the differential image on the image plane. This represents the output electric field of the left-handed circularly polarized light in the differential image on the image plane.
7. The full-dimensional photonic spin Hall spatial differential imaging method as described in claim 6, characterized in that, When displacement value When the image profile is smaller than the image information corresponding to the object, the left-handed circularly polarized light in the differential image is the first-order spatial differential of the left-handed circularly polarized light in the arbitrary polarization state light field: in, This represents the first-order spatial differential of left-handed circularly polarized light. Indicates partial derivative, This represents the x-coordinate in a Cartesian coordinate system in real space. When displacement value When the image profile is smaller than the image information corresponding to the object, the right-hand circularly polarized light in the differential image is the first-order spatial differential of the right-hand circularly polarized light in the arbitrary polarization state light field: in, This represents the first-order spatial differential of right-handed circularly polarized light.