Full-dimensional photon spin Hall space differential imaging method

Abstract

The invention discloses a full-dimensional photon spin Hall space differential imaging method. The method comprises the following steps: inputting an arbitrary polarization state light field into a first lens for Fourier transform to obtain a frequency domain light field; inputting the frequency domain light field into a half-wave geometric phase liquid crystal polarization grating for polarization separation to obtain first left-hand circularly polarized light and first right-hand circularly polarized light; and inputting the first left-handed circularly polarized light and the first right-handed circularly polarized light into a quarter-wave geometric phase liquid crystal polarization grating and a second lens, respectively performing polarization separation and inverse Fourier transform to obtain an airspace light field, and inputting the airspace light field into a polarizer for polarization analysis to obtain a differential image. According to the invention, optical differential effects of three dimensions of amplitude, phase and polarization can be effectively generated by a photon spin Hall effect, and full-dimension optical space differential processing of an image is realized.

Description

Technical Field

[0001] The present invention belongs to the field of optical imaging, and particularly relates to a full-dimensional photon spin Hall spatial differential imaging method. Background Art

[0002] The photon spin Hall effect refers to the physical phenomenon that photons with different spin angular momenta will undergo lateral separation when propagating through different optical interfaces or inhomogeneous media. Since it can sensitively detect changes in material properties and environmental conditions, the photon spin Hall effect has been widely applied in precision measurement, optical sensing, and quantum information processing. Especially in edge imaging, the photon spin Hall effect enables image processing for edge detection through optical differential operations, promoting the development of optical spatial differential imaging.

[0003] So far, various amplitude and phase-type photon spin Hall differential methods have been proposed and gradually applied in practice, showing broad application prospects in fields such as biomedical imaging and precision component detection. As is well known, the basic spatial physical dimensions of the light field include: amplitude, phase, and polarization. Since the existing spin Hall spatial differential imaging methods have strict requirements on the polarization of the input field, how to achieve optical spatial differentiation based on the spin Hall effect remains an urgent problem to be solved currently. Summary of the Invention

[0004] The purpose of the present invention is to solve the deficiencies of the prior art and provide a full-dimensional photon spin Hall spatial differential imaging method, specifically adopting the following technical solutions:

[0005] A full-dimensional photon spin Hall spatial differential imaging method, the method comprising:

[0006] Obtain a light field with an arbitrary polarization state, and input the light field with the arbitrary polarization state into a first lens for Fourier transform to obtain a frequency-domain light field, where the light field with the arbitrary polarization state includes object image information;

[0007] Input the frequency-domain light field into a half-wave geometric phase liquid crystal polarization grating for polarization separation to obtain a first left-handed circularly polarized light and a first right-handed circularly polarized light, and input the first left-handed circularly polarized light and the first right-handed circularly polarized light into a quarter-wave geometric phase liquid crystal polarization grating for polarization separation 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;

[0008] Input 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 for inverse Fourier transform to obtain a spatial-domain light field, and input the spatial-domain light field into a polarizer for polarization analysis to obtain a differential image.

[0009] Preferably, the arbitrary polarization state optical field can be synthesized by two circular polarization basis vectors, that is, expressed as:

[0010]

[0011] where E in (x, y) represents the arbitrary polarization state optical field, E LCP (x, y) represents the complex amplitude distribution of the left-handed circularly polarized light in the arbitrary polarization state optical field, [1i] T represents the Jones matrix of the left-handed circularly polarized light in the arbitrary polarization state optical field, E RCP (x, y) represents the complex amplitude distribution of the right-handed circularly polarized light in the arbitrary polarization state optical field, [1-i] T represents the Jones matrix of the right-handed 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] where F 1,LCP (f x , f y ) represents the corresponding 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, E LCP (f x , f y ) represents the complex amplitude distribution of the left-handed circularly polarized light in the frequency-domain optical field, F 1,RCP (f x , f y ) represents the corresponding angular spectrum of the right-handed circularly polarized light in the frequency-domain optical field on the half-wave geometric phase liquid crystal polarization grating, E RCP (f x , f y ) represents the complex amplitude distribution of the right-handed circularly polarized light in the frequency-domain optical field, exp[iπλd(f x 2 +f y 2 )] represents the Fresnel diffraction transmission 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:

[0016]

[0017] where * represents the convolution operation, Λ1 represents the period of the half-wave geometric phase liquid crystal polarization grating, F′ 1,LCP (fx , f y ) represents the angular spectrum of the left-handed circularly polarized light in the frequency-domain optical field becoming the first right-handed circularly polarized light after passing through the half-wave geometric-phase liquid crystal polarization grating. represents the left-handed circularly polarized light in the frequency-domain optical field along f x direction is translated by corresponding to a translation of -Λ1 along the x direction in space, F′ 1,RCP (f x , f y ) represents the angular spectrum of the right-handed circularly polarized light in the frequency-domain optical field becoming the first left-handed circularly polarized light after passing through the half-wave geometric-phase liquid crystal polarization grating. represents the right-handed circularly polarized light in the frequency-domain optical field along f x direction is translated by corresponding to a translation of Λ1 along the x direction in space, δ represents the Dirac function.

[0018] Preferably, the angular spectrum of the first right-handed circularly polarized light before passing through the quarter-wave geometric-phase liquid crystal polarization grating is expressed as:

[0019]

[0020] where, F FP,LCP (f x , f y ) represents the angular spectrum of the first right-handed circularly polarized light before passing through the quarter-wave geometric-phase liquid crystal polarization grating;

[0021] The angular spectrum of the first left-handed circularly polarized light before passing through the quarter-wave geometric-phase liquid crystal polarization grating is expressed as:

[0022]

[0023] where, F FP,RCP (f x , f y ) represents the angular spectrum of the first left-handed circularly polarized light before passing through the quarter-wave geometric-phase liquid crystal polarization grating;

[0024] The angular spectra of the first right-handed circularly polarized light and the first left-handed circularly polarized light after passing through the quarter-wave geometric-phase liquid crystal polarization grating are expressed as:

[0025]

[0026] The second left-handed circularly polarized light H1 is:

[0027]

[0028] The second right-handed circularly polarized light H2 is:

[0029]

[0030] The third left-handed circularly polarized light H3 is as follows:

[0031]

[0032] The third right-handed circularly polarized light H4 is as follows:

[0033]

[0034] where F′ FP,LCP (f x , f y ) represents the angular spectrum of the first right-handed circularly polarized light after passing through the quarter-wave geometric phase liquid crystal polarization grating, and F′ 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, 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-handed circularly polarized light and the first left-handed circularly polarized light on the image plane are represented as:

[0036]

[0037] where f is the focal length, M is the magnification factor, and F IP,LCP (x3, y3) represents the output electric field of the first right-handed circularly polarized light on the image plane, and F IP,RCP (x3, y3) represents the output electric field of the first left-handed 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 light field is subjected to 45° polarization analysis by the polarizer, the object-image output field of the differential image obtained is:

[0041]

[0042] The object-image output field after the -45° polarization analysis of the spatial optical field by the polarizer is:

[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 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 optical 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 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 optical 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: By performing Fourier transform and inverse Fourier transform through the first lens and the second lens, the spatial filtering of the arbitrary polarization state optical field can be effectively performed. By using the half-wave geometric phase liquid crystal polarization grating to perform polarization separation on the frequency-domain optical field and the quarter-wave geometric phase liquid crystal polarization grating to perform polarization separation on the first left-handed circularly polarized light and the first right-handed circularly polarized light, the optical differential effects in 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 achieve independent optical spatial differential processing. Description of the Drawings

[0052] Figure 1 is a flowchart of the full-dimensional photon spin Hall spatial differential imaging method provided by the first embodiment of the present invention;

[0053] Figure 2It is a schematic structural diagram of the full-dimensional photon spin Hall space differential imaging system provided by the second embodiment of the present invention;

[0054] Figure 3 It is a microscopic imaging diagram of a half-wave geometric phase liquid crystal polarization grating provided by the second embodiment of the present invention;

[0055] Figure 4 It is a microscopic imaging diagram of a quarter-wave geometric phase liquid crystal polarization grating provided by the second embodiment of the present invention;

[0056] Figure 5 It is a schematic diagram of a differential image after the amplitude field is modulated by the full-dimensional photon spin Hall space differential imaging system provided by the second embodiment of the present invention;

[0057] Figure 6 It is a schematic diagram of a differential image after the phase field is modulated by the full-dimensional photon spin Hall space differential imaging system provided by the second embodiment of the present invention;

[0058] Figure 7 It is a schematic diagram of a differential image after the polarization field is modulated by the full-dimensional photon spin Hall space differential imaging system provided by the second embodiment of the present invention. Detailed implementation manners

[0059] In order to make the objectives, technical solutions and advantages of the present invention clearer and more understandable, the present 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 only used to explain the present invention and are not used to limit the present invention.

[0060] In order to illustrate the technical solutions described in the present invention, the following will be described through specific embodiments.

[0061] Embodiment 1

[0062] Please refer to Figure 1 , which is a flowchart of the full-dimensional photon spin Hall space differential imaging method provided by the first embodiment of the present invention. The full-dimensional photon spin Hall space differential imaging method includes the following steps:

[0063] Step S10, obtaining an optical field with an arbitrary polarization state, and inputting the optical field with the arbitrary polarization state into a first lens for Fourier transform to obtain a frequency-domain optical field;

[0064] Among them, the optical field with an arbitrary polarization state includes object image information. By inputting the optical field with an arbitrary polarization state into a first lens for Fourier transform, the optical field with an arbitrary polarization state in the spatial domain can be effectively converted into a frequency-domain optical field in the frequency domain.

[0065] In this step, the optical field with an arbitrary polarization state can be synthesized by two circular polarization basis vectors, that is, expressed as:

[0066]

[0067] Among them, E in (x, y) represents the optical field of any polarization state, and E LCP (x, y) represents the complex amplitude distribution of the left-handed circularly polarized light in the optical field of any polarization state, [1i] T represents the Jones matrix of the left-handed circularly polarized light in the optical field of any polarization state, and E RCP (x, y) represents the complex amplitude distribution of the right-handed circularly polarized light in the optical field of any polarization state, [1 - i] T represents the Jones matrix of the right-handed circularly polarized light in the optical field of any polarization state.

[0068] Step S20: Input the optical field in the frequency domain into a half-wave geometric phase liquid crystal polarization grating for polarization separation to obtain a first left-handed circularly polarized light and a first right-handed circularly polarized light, and input the first left-handed circularly polarized light and the first right-handed circularly polarized light into a quarter-wave geometric phase liquid crystal polarization grating for polarization separation 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;

[0069] Among them, the optical field after Fourier transform by the first lens is incident on the half-wave geometric phase liquid crystal polarization grating, and before the light beam reaches the quarter-wave geometric phase liquid crystal polarization grating, it will be completely separated into two spin components, that is, the first left-handed circularly polarized light and the first right-handed circularly polarized light. After the two spin components pass 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, that is, 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.

[0070] In this step, the angular spectrum of the optical field in the frequency domain on the half-wave geometric phase liquid crystal polarization grating is expressed as:

[0071]

[0072] Among them, F 1,LCP (f x , f y ) represents the corresponding angular spectrum of the left-handed circularly polarized light in the optical field in the frequency domain on the half-wave geometric phase liquid crystal polarization grating, and E LCP (f x , f y ) represents the complex amplitude distribution of the left-handed circularly polarized light in the optical field in the frequency domain, and F 1,RCP (f x , fy ) represents the corresponding angular spectrum of the right-handed circularly polarized light in the frequency-domain optical field on the half-wave geometric-phase liquid crystal polarization grating, E RCP (f x , f y ) represents the complex amplitude distribution of the 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 after passing through the half-wave geometric-phase liquid crystal polarization grating at plane 1 is expressed as:

[0074]

[0075] where, * represents the convolution operation, Λ1 represents the period of the half-wave geometric-phase liquid crystal polarization grating, F′ 1,LCP (f x , f y ) represents the angular spectrum of the left-handed circularly polarized light in the frequency-domain optical field becoming the first right-handed circularly polarized light after passing through the half-wave geometric-phase liquid crystal polarization grating, represents the left-handed circularly polarized light in the frequency-domain optical field translated along the f x direction by corresponding to a translation of -Λ1 along the x direction in space, F′ 1,RCP (f x , f y ) represents the angular spectrum of the right-handed circularly polarized light in the frequency-domain optical field becoming the first left-handed circularly polarized light after passing through the half-wave geometric-phase liquid crystal polarization grating, represents the right-handed circularly polarized light in the frequency-domain optical field translated along the f x direction by corresponding to a translation of Λ1 along the x direction in space, δ represents the Dirac function.

[0076] Step S30, input 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 for inverse Fourier transform to obtain a spatial-domain optical field, and input the spatial-domain optical field into a polarizer for polarization analysis to obtain a differential image;

[0077] Among them, the four spin components obtain a differential image on the image plane after the inverse Fourier transform of the second lens and the filtering of the polarizer.

[0078] Optionally, in the Fourier plane, the angular spectrum of the first right-handed circularly polarized light before passing through the quarter-wave geometric-phase liquid crystal polarization grating is expressed as:

[0079]

[0080] Among them, F FP,LCP (f x , f y ) represents the angular spectrum of the first right-handed circularly polarized light before passing through the quarter-wave geometric phase liquid crystal polarization grating;

[0081] On 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 expressed as:

[0082]

[0083] Among them, F FP,RCP (f x , f y ) represents the angular spectrum of the first left-handed circularly polarized light before passing through the quarter-wave geometric phase liquid crystal polarization grating;

[0084] The angular spectra of the first right-handed circularly polarized light and the first left-handed circularly polarized light after passing through the quarter-wave geometric phase liquid crystal polarization grating are expressed as:

[0085]

[0086] The second left-handed circularly polarized light H1 is:

[0087]

[0088] The second right-handed circularly polarized light H2 is:

[0089]

[0090] The third left-handed circularly polarized light H3 is:

[0091]

[0092] The third right-handed circularly polarized light H4 is:

[0093]

[0094] Among them, F′ FP,LCP (f x , f y ) represents the angular spectrum of the first right-handed circularly polarized light after passing through the quarter-wave geometric phase liquid crystal polarization grating, and F′ 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, where θ = 2πs / Λ2, 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-handed circularly polarized light and the first left-handed circularly polarized light on the image plane are represented as:

[0096]

[0097] where f is the focal length, M is the magnification factor, and F IP,LCP (x3, y3) represents the representation of the output electric field of the first right-handed circularly polarized light on the image plane, and F IP,RCP (x3, y3) represents the representation of the output electric field of the first left-handed 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, and λd = m·Λ1Λ2, where m is a positive integer, the incident light field before entering the polarizer is:

[0099]

[0100] Furthermore, after the spatial light field is subjected to 45° polarization analysis by the polarizer, the object-image output field of the differential image obtained is:

[0101]

[0102] The object-image output field of the spatial light field after -45° polarization analysis by the polarizer is:

[0103]

[0104] 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.

[0105] Even further, 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] where |F'IP,LCP 丨 represents the first-order spatial differential of left-handed circularly polarized light, represents partial derivative, x represents the abscissa in the Cartesian coordinate system in real space;

[0108] When the displacement value λf / Λ2 is smaller than the image profile 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] Among them, 丨F′ IP,RCP 丨 represents the first-order spatial differential of right-handed circularly polarized light.

[0111] In this embodiment, Fourier transform and inverse Fourier transform are performed by the first lens and the second lens, so that spatial filtering can be effectively performed on the light field of any polarization state, and polarization separation of the frequency domain light field is performed by the half-wave geometric phase liquid crystal polarization grating, and polarization separation of the first left-handed circularly polarized light and the first right-handed circularly polarized light is performed by the quarter-wave geometric phase liquid crystal polarization grating. The photon spin Hall effect can effectively generate optical differential effects in three dimensions of amplitude, phase and polarization to separate the circular polarization basis vectors (circularly polarized light) and realize independent optical spatial differential processing.

[0112] Example 2

[0113] See also Figures 2 to 7 , is a structural schematic diagram of a full-dimensional photon spin Hall spatial differential imaging system provided by a second embodiment of the present invention, a microscopic imaging diagram of a liquid crystal polarization grating, and a full-dimensional photon spin Hall spatial differential imaging diagram, 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, wherein the arbitrary polarization state light field includes object image information; wherein 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, which can be expressed as:

[0116]

[0117] Among them, E in (x, y) represents the arbitrary polarization state light field, E LCP (x, y) represents the complex amplitude distribution of left-handed circularly polarized light at plane 0 in the arbitrary polarization state light field, [1i] T represents the Jones matrix of left-handed circularly polarized light in the arbitrary polarization state light field, ERCP (x, y) represents the complex amplitude distribution of the right-handed circularly polarized light in the plane 0 in the arbitrary polarization state light field, [1 - i] T represents the Jones matrix of the right-handed circularly polarized light in the arbitrary polarization state light 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-handed circularly polarized light and a first right-handed circularly polarized light; wherein, the light field after Fourier transform 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 before the light beam reaches the quarter-wave geometric phase liquid crystal polarization grating, that is, the first left-handed circularly polarized light and the first right-handed circularly polarized light.

[0119] The angular spectrum of the frequency-domain light field on the half-wave geometric phase liquid crystal polarization grating is expressed as:

[0120]

[0121] where, F 1,LCP (f x , f y ) represents the corresponding angular spectrum of the left-handed circularly polarized light in the frequency-domain light field on the half-wave geometric phase liquid crystal polarization grating, E LCP (f x , f y ) represents the complex amplitude distribution of the left-handed circularly polarized light in the frequency-domain light field, F 1,RCP (f x , f y ) represents the corresponding angular spectrum of the right-handed circularly polarized light in the frequency-domain light field on the half-wave geometric phase liquid crystal polarization grating, E RCP (f x , f y ) represents the complex amplitude distribution of the right-handed circularly polarized light in the frequency-domain light field, exp[iπλd(f x 2 + f y 2 )] represents the Fresnel diffraction transmission function in the frequency domain;

[0122] The angular spectrum of the frequency-domain light field after passing through the half-wave geometric phase liquid crystal polarization grating is expressed as:

[0123]

[0124] where, * represents the convolution operation, Λ1 represents the period of the half-wave geometric phase liquid crystal polarization grating, F′ 1,LCP (f x , f y) represents the angular spectrum of the left - handed circularly polarized light in the frequency - domain optical field becoming the first right - handed circularly polarized light after passing through the half - wave geometric - phase liquid - crystal polarization grating. represents that the left - handed circularly polarized light in the frequency - domain optical field is translated along the f x direction by which corresponds to a translation of - Λ1 in the x - direction in space, and F′ 1,RCP (f x , f y ) represents the angular spectrum of the right - handed circularly polarized light in the frequency - domain optical field becoming the first left - handed circularly polarized light after passing through the half - wave geometric - phase liquid - crystal polarization grating. represents that the right - handed circularly polarized light in the frequency - domain optical field is translated along the f x direction by which corresponds to a translation of Λ1 in the x - direction in space, and δ represents the Dirac function.

[0125] The quarter - wave geometric - phase liquid - crystal polarization grating 12 is used to perform polarization separation on the first left - handed circularly polarized light and the first right - handed circularly polarized light output by 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; among them, after passing through the quarter - wave geometric - phase liquid - crystal polarization grating, each of the two spin components of the first left - handed circularly polarized light and the first right - handed circularly polarized light splits into two spin components, generating four spin components, that is, the first left - handed circularly polarized light splits into a second left - handed circularly polarized light and a second right - handed circularly polarized light, and the first right - handed circularly polarized light splits into a third left - handed circularly polarized light and a third right - handed circularly polarized light.

[0126] The angular spectrum of the first right - handed circularly polarized light before passing through the quarter - wave geometric - phase liquid - crystal polarization grating is expressed as:

[0127]

[0128] where F FP,LCP (f x , f y ) represents the angular spectrum of the first right - handed circularly polarized light before passing through the quarter - wave geometric - phase liquid - crystal polarization grating;

[0129] The angular spectrum of the first left - handed circularly polarized light before passing through the quarter - wave geometric - phase liquid - crystal polarization grating is expressed as:

[0130]

[0131] where F FP,RCP (f x , f y ) represents the angular spectrum of the first left - handed circularly polarized light before passing through the quarter - wave geometric - phase liquid - crystal polarization grating;

[0132] The angular spectra of the first right-handed circularly polarized light and the first left-handed circularly polarized light after passing through the quarter-wave geometric phase liquid crystal polarization grating are expressed as:

[0133]

[0134] The second left-handed circularly polarized light H1 is:

[0135]

[0136] The second right-handed circularly polarized light H2 is:

[0137]

[0138] The third left-handed circularly polarized light H3 is:

[0139]

[0140] The third right-handed circularly polarized light H4 is:

[0141]

[0142] where F′ FP,LCP (f x , f y ) represents the angular spectrum of the first right-handed circularly polarized light after passing through the quarter-wave geometric phase liquid crystal polarization grating, and F′ 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-handed circularly polarized light and the first left-handed circularly polarized light on the image plane are expressed as:

[0144]

[0145] where f is the focal length, M is the magnification factor, F IP,LCP (x3, y3) represents the output electric field of the first right-handed circularly polarized light on the image plane, and F IP,RCP (x3, y3) represents the output electric field of the first left-handed circularly polarized light on the image plane. 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] A second lens 13 is configured to perform an inverse Fourier transform on 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 output by the quarter-wave geometric phase liquid crystal polarization grating 12 to obtain a spatial light field; wherein, by performing an inverse Fourier transform on 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 output by the quarter-wave geometric phase liquid crystal polarization grating 12, the light field in the frequency domain can be effectively converted into a light field in the spatial domain.

[0149] A polarizer 14 is configured 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 light field is subjected to 45° polarization analysis by the polarizer, the object-image output field of the obtained differential image is:

[0151]

[0152] The object-image output field after the spatial light field is subjected to -45° polarization analysis by the polarizer is:

[0153]

[0154]

[0155] 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.

[0156] When the displacement value λf / Λ2 is less than the image profile 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] 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 the real space;

[0159] When the displacement value λf / Λ2 is smaller than the image profile 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 right-handed circularly polarized light.

[0162] In this embodiment, a quadruple focal length optical system (4f system) is constructed using a first lens 10 and a 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 image information passes through the half-wave geometric phase liquid crystal polarization grating and the quarter-wave geometric phase liquid crystal polarization grating in turn, respectively generating a huge photon spin Hall effect and a tiny photon spin Hall effect, which are used to separate the circular polarization basis vectors and achieve independent differential processing. Since any 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 meet the differential imaging of amplitude, phase and polarization in three dimensions based on the photon spin Hall effect. By constructing the cascaded photon spin Hall effect of two geometric phase liquid crystal polarization gratings on the basis of the 4f system, the optical differential of light in three dimensions (amplitude, phase and polarization) is realized. It is suitable for fields such as optical differential imaging, material characterization and optical information processing. When the linearly polarized light carrying the image information is incident on the full-dimensional photon spin Hall spatial differential imaging system, through two cascaded photon spin Hall effects, the light from any polarization state 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 a specific polarizer analyzer. Further through the first-order spatial differential, a clear differential image can be presented on the image plane.

Claims

1. A full-dimensional photon spin Hall space differential imaging method, characterized in that The method includes: Obtain an optical field with an arbitrary polarization state, and input the optical field with an arbitrary polarization state into a first lens for Fourier transform to obtain a frequency-domain optical field, where the optical field with an arbitrary polarization state includes object image information; Input the frequency-domain optical field into a half-wave geometric-phase liquid crystal polarization grating for polarization separation to obtain a first left-handed circularly polarized light and a first right-handed circularly polarized light, and input the first left-handed circularly polarized light and the first right-handed circularly polarized light into a quarter-wave geometric-phase liquid crystal polarization grating for polarization separation 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; Input 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 for inverse Fourier transform to obtain a spatial-domain optical field, and input the spatial-domain optical field into a polarizer for polarization analysis to obtain a differential image.

2. The full-dimensional photon spin Hall spatial differential imaging method according to claim 1, characterized in that The optical field with an arbitrary polarization state can be synthesized by two circular polarization basis vectors, that is, expressed as: where x and y represent the horizontal and vertical axes in the Cartesian coordinate system at plane 0, and E in (x, y) represents the optical field of any polarization state, and E LCP (x, y) represents the complex amplitude distribution of left-handed circularly polarized light in the optical field of any polarization state, [1i] T represents the Jones matrix of left-handed circularly polarized light in the optical field of any polarization state, and E RCP (x, y) represents the complex amplitude distribution of right-handed circularly polarized light in the optical field of any polarization state, [1-i] T represents the Jones matrix of right-handed circularly polarized light in the optical field of any polarization state.

3. The full-dimensional photon spin Hall spatial differential imaging method according to claim 2, wherein The angular spectrum of the frequency-domain optical field on the half-wave geometric-phase liquid crystal polarization grating is expressed as: Among them, F 1,LCP (f x , f y ) 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, E LCP (f x , f y ) represents the complex amplitude distribution of the left-handed circularly polarized light in the frequency-domain optical field, F 1,RCP (f x , f y ) represents the angular spectrum of the right-handed circularly polarized light in the frequency-domain optical field on the half-wave geometric phase liquid crystal polarization grating, E RCP (f x , f y ) represents the complex amplitude distribution of the 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; The angular spectrum of the frequency-domain optical field after passing through the half-wave geometric-phase liquid crystal polarization grating is expressed as: Among them, * represents the convolution operation, Λ1 represents the period of the half-wave geometric phase liquid crystal polarization grating, F′ 1,LCP (f x , f y ) represents the angular spectrum 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, represents that the left-handed circularly polarized light in the frequency-domain optical field is translated along the f x direction by which corresponds to a translation of -Λ1 in the x direction in space, F′ 1,RCP (f x , f y ) represents the angular spectrum that the 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, represents that the right-handed circularly polarized light in the frequency-domain optical field is translated along the f x direction by which corresponds to a translation of Λ1 in the x direction in space, and δ represents the Dirac function.

4. The full-dimensional photon spin Hall spatial differential imaging method according to claim 1, wherein The angular spectrum of the first right-handed circularly polarized light before passing through the quarter-wave geometric-phase liquid crystal polarization grating is expressed as: Among them, F FP,LCP (f x , f y ) represents the angular spectrum of the first right-handed circularly polarized light before passing through the quarter-wave geometric phase liquid crystal polarization grating; The angular spectrum of the first left-handed circularly polarized light before passing through the quarter-wave geometric-phase liquid crystal polarization grating is expressed as: Among them, F FP,RCP (f x , f y ) represents the angular spectrum of the first left-handed circularly polarized light before passing through the quarter-wave geometric phase liquid crystal polarization grating; The angular spectra of the first right-handed circularly polarized light and the first left-handed circularly polarized light after passing through the quarter-wave geometric-phase liquid crystal polarization grating are expressed as: The second left-handed circularly polarized light H1 is: The second right-handed circularly polarized light H2 is: The third left-handed circularly polarized light H3 is: The third right-handed circularly polarized light H4 is: Among them, F′ FP,LCP (f x , f y ) represents the angular spectrum of the first right-handed circularly polarized light after passing through the quarter-wave geometric phase liquid crystal polarization grating, and F′ 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.

5. The full-dimensional photon spin Hall spatial differential imaging method according to claim 1, characterized in that After passing through the quarter-wave geometric-phase liquid crystal polarization grating, the representation of the output electric fields of the first right-handed circularly polarized light and the first left-handed circularly polarized light on the image plane is: where f is the focal length, M is the magnification factor, F IP,LCP (x3, y3) represents the representation of the output electric field of the first right-handed circularly polarized light on the image plane, F IP,RCP (x3, y3) represents the representation of the output electric field of the first left-handed 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; When M = -1, s = 0, λd = m·Λ1Λ2, where m is a positive integer, the incident optical field before entering the polarizer is:

6. The full-dimensional photon spin Hall space differential imaging method according to claim 1, characterized in that After the spatial-domain optical field passes through the polarizer for 45° polarization analysis, the object image output field of the obtained differential image is: The object image output field after the spatial-domain optical field passes through the polarizer for -45° polarization analysis is: Among them, F' IP,LCP (x3, y3) represents the representation of the output electric field of 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 left-handed circularly polarized light in the differential image on the image plane.

7. The full-dimensional photon spin Hall space differential imaging method according to claim 6, characterized in that 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 optical field with an arbitrary polarization state: where, |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; 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 optical field with an arbitrary polarization state: Among them, |F' IP,RCP | represents the first-order spatial differential of right-handed circularly polarized light.

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