CN116132816A - Fourier Panoramic Ghost Imaging Method Based on Logarithmic Linear Transform - Google Patents

Abstract

The invention discloses a Fourier panoramic ghost imaging method based on logarithmic linear transformation, comprising: step 1, obtaining a non-uniform sampling strategy based on logarithmic linear transformation; step 2, constructing a ring Fu Fourier basis pattern sequence; step 3, reconstructing the panoramic ghost imaging image based on the annular Fourier basis pattern sequence. The present invention designs a ring-shaped Fourier base pattern, uses a phase shift method to perform differential processing and performs Fourier inverse transformation to quickly reconstruct a target, thereby improving the reconstruction speed of panoramic ghost imaging.

Description

Fourier Panoramic Ghost Imaging Method Based on Logarithmic Linear Transform

technical field

The invention belongs to the technical field of photoelectric imaging, and in particular relates to a Fourier panoramic ghost imaging method based on logarithmic linear transformation.

Background technique

Panoramic ghost imaging is a new correlative imaging method to achieve a large circumferential 360° field of view. It uses a curved mirror to reflect the annular speckle pattern used to modulate the light source to the surrounding 360° target scene, and then collects it with a barrel detector. The reflected light intensity fluctuations are correlated with the corresponding rectangular speckle sequence based on the logarithmic polar coordinate transformation mapping, and the panoramic target scene without distortion can be directly reconstructed. Compared with traditional panoramic imaging methods, panoramic ghost imaging has the advantages of strong anti-interference ability, imaging resolution beyond the diffraction limit, imaging in different bands, and high detection sensitivity. It can be used to solve the problems and challenges encountered by traditional panoramic imaging technologies. To expand the application requirements of panoramic imaging. However, based on the theory of panoramic target reconstruction based on traditional second-order correlation characteristics, the existing panoramic ghost imaging requires a large number of sampling times and reconstruction time, which cannot achieve fast and high-quality imaging, and it is difficult to take into account large field of view, high quality and real-time performance, which hinders The practical progress of panoramic ghost imaging.

Contents of the invention

In order to achieve fast and high-quality panoramic ghost imaging and solve the problem of large field of view, high quality and real-time performance of ghost imaging, this invention proposes a Fourier panoramic ghost imaging method based on logarithmic linear transformation to achieve non-uniform sampling strategy , the concept of Fourier single-pixel imaging is introduced into the theory of panoramic ghost imaging, and a Fourier panoramic ghost imaging method is proposed, which obtains the Fourier spectrum information of the target through the annular Fourier base pattern with phase shift, and then directly performs Fast Fourier inverse transform can complete the imaging; realize high-quality Fourier panoramic ghost imaging at low sampling rate, and further reduce the sampling time to improve the real-time performance of Fourier panoramic ghost imaging.

To achieve the above object, the present invention provides the following scheme:

A Fourier panoramic ghost imaging method based on logarithmic linear transformation, comprising:

Step 1. Obtain a non-uniform sampling strategy based on logarithmic linear transformation;

Step 2, constructing a circular Fourier base pattern sequence based on the non-uniform sampling strategy;

Step 3. Reconstructing a panoramic ghost imaging image based on the circular Fourier basis pattern sequence.

Preferably, the method for obtaining the non-uniform sampling strategy includes:

Initialize Fourier panoramic ghost imaging parameters;

Based on the Fourier panoramic ghost imaging parameters and the logarithmic linear transformation, a non-uniform sampling strategy is designed.

Preferably, the non-uniform sampling strategy includes:

表示p-q坐标系中以低频中心点向p方向扩展的第u层选择间隔的半径，

表示以低频中心点向q方向扩展的第v层选择间隔的半径；p(u)和q(v)分别表示p方向第u个选择的频谱坐标和q方向第v个选择的频谱坐标；m0表示低频区域的p方向半径，n0表示低频区域的q方向半径，U表示频谱在p方向上的采样点数，V表示频谱在q方向上的采样点数，(f_p0,f_q0)表示全景傅里叶频谱的中心点坐标，α₁表示采样的频谱系数在p向间隔增长因子，α₂表示采样的频谱系数在q向间隔增长因子。In the formula,

Indicates the radius of the u-th layer selection interval extending from the low-frequency center point to the p direction in the pq coordinate system,

Indicates the radius of the selection interval of the vth layer extending from the low-frequency center point to the q direction; p(u) and q(v) represent the spectrum coordinates of the uth selection in the p direction and the spectrum coordinates of the vth selection in the q direction, respectively; m0 Indicates the radius of the p-direction of the low-frequency region, n0 represents the radius of the q-direction of the low-frequency region, U represents the number of sampling points of the spectrum in the direction of p, V represents the number of sampling points of the spectrum in the direction of q, (f _p0 , f _q0 ) represents the panoramic Fourier The coordinates of the center point of the leaf spectrum, α ₁ represents the growth factor of the sampled spectral coefficients in the p-direction interval, and α ₂ represents the growth factor of the sampled spectral coefficients in the q-direction interval.

Preferably, the method for constructing the circular Fourier base pattern sequence comprises:

Designing a panoramic Fourier base pattern model based on the non-uniform sampling strategy;

The circular Fourier basis pattern sequence is constructed based on the panoramic Fourier basis pattern model.

Preferably, the panoramic Fourier base pattern model includes:

P _uv ＝a+b×cos(2πf _p(u) p(u)+2πf _q(v) q(v)+φ),

In the formula, (p(u), q(v)) represents the spatial coordinates corresponding to the spectral coefficients selected by the non-uniform sampling strategy; (f _p(u) , f _q(v) ) represents the spectral coefficients selected by the non-uniform sampling strategy ; φ represents the initial phase; P _uv represents the corresponding panoramic Fourier basis pattern model under the corresponding spectral coefficient; a represents the average light intensity, and b represents the contrast.

Preferably, the sequence of circular Fourier basis patterns comprises:

In the formula, r _p represents the radius of the pth ring of the annular Fourier speckle structure, θ _q represents the angle corresponding to the qth pixel, Q represents the average number of units divided by each ring, ε represents the inter-ring growth coefficient, and r ₀ Indicates the outer ring radius of the central concave blind hole area, rc ₁ indicates the center radius of the first ring, rc _p indicates the center radius of the p-th ring, and ξ _p indicates the corresponding value of the p-th ring in the logarithmic polar coordinate system.

Preferably, the method for reconstructing the panoramic ghost imaging image includes:

Modulating a light source based on the annular Fourier base pattern sequence, and irradiating the curved mirror with the modulated light source;

The light source is reflected by the curved mirror to obtain reflected light, and the reflected light illuminates the target scene in the surrounding 360° field of view;

Diffuse reflection occurs in the reflected light after illuminating the target scene of the surrounding 360 ° field of view, and the light intensity with target information after the diffuse reflection is collected;

performing differential processing on the light intensities corresponding to the annular Fourier base pattern sequences with different initial phases to obtain a Fourier spectrum;

Inverse Fourier transform is performed on the Fourier spectrum to obtain the panoramic ghost imaging image.

Preferably, the calculation method of the light intensity includes:

In the formula, T _i represents the light intensity value obtained by modulating the light source with the i-th annular Fourier base pattern S _i whose initial phase is φ _j , and o(x, y) represents the irradiated surrounding 360° omnidirectional annular target.

The beneficial effects of the present invention are:

(1) A Fourier panoramic ghost imaging method based on logarithmic linear transformation disclosed in the present invention, by designing a circular Fourier base pattern, using the phase shift method to perform differential processing and performing inverse Fourier transform to quickly reconstruct The goal is to improve the reconstruction speed of panoramic ghost imaging.

(2) A Fourier panoramic ghost imaging method based on logarithmic linear transformation disclosed in the present invention can freely and flexibly perform non-uniform sampling on the panoramic Fourier spectrum based on logarithmic linear transformation, and improve the efficiency under the under-sampling rate. Spectrum sampling can reduce the sampling frequency of panoramic ghost imaging and reduce the sampling time of panoramic ghost imaging.

(3) A Fourier panoramic ghost imaging method based on logarithmic linear transformation disclosed in the present invention can greatly increase the imaging time of panoramic ghost imaging, improve the real-time performance of panoramic ghost imaging, and take into account both large field of view and high The resolution and real-time ghost imaging provides an effective way to meet the imaging needs of more large field of view applications and accelerate the practical process of ghost imaging.

Description of drawings

In order to illustrate the technical solution of the present invention more clearly, the accompanying drawings that need to be used in the embodiments are briefly introduced below. Obviously, the accompanying drawings in the following description are only some embodiments of the present invention. Technical personnel can also obtain other drawings based on these drawings without paying creative labor.

Fig. 1 is a schematic flow chart of a method according to Embodiment 1 of the present invention;

Fig. 2 is a principle diagram of the structure of the annular Fourier base pattern according to the embodiment of the present invention; Fig. 2 (a) is a detailed enlarged view of the imaging area of the annular Fourier base pattern structure, and Fig. 2 (b) is the annular Fourier base pattern Structural diagram, Figure 2(c) is an example diagram of a circular Fourier speckle pattern;

FIG. 3 is a non-uniform sampling spectrum diagram of a panoramic Fourier spectrum based on logarithmic linear transformation according to Embodiment 1 of the present invention.

Detailed ways

The following will clearly and completely describe the technical solutions in the embodiments of the present invention with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only some, not all, embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by persons of ordinary skill in the art without making creative efforts belong to the protection scope of the present invention.

In order to make the above objects, features and advantages of the present invention more comprehensible, the present invention will be further described in detail below in conjunction with the accompanying drawings and specific embodiments.

Embodiment one

As shown in Figure 1, it is a schematic flow chart of the Fourier panoramic ghost imaging method based on logarithmic linear transformation in the present invention, including the following steps:

Step 1. Obtain a non-uniform sampling strategy based on logarithmic linear transformation;

Specifically include:

(1) Initialize Fourier panoramic ghost imaging parameters;

Assume that the spatial resolution of the Fourier panoramic ghost imaging image is P×Q, and the frequency domain resolution is also set as P×Q, and the frequency coefficients are normalized and discretely processed. The processing method is as follows:

In the formula, f _p represents the pth frequency coefficient in the p direction, and f _q represents the qth frequency coefficient in the q direction.

In this embodiment, the spatial resolution of the Fourier panoramic ghost imaging image is set to 20×10 2 , and the frequency domain resolution is also set to 20×10 2 .

(2) Based on Fourier panoramic ghost imaging parameters and logarithmic linear transformation, a non-uniform sampling strategy is designed.

Assuming that the sampling rate of the Fourier spectrum in the p direction is s _p , and the sampling rate in the q direction is s _q , the whole sampling process needs U×V×2 times, where U=P×s _p , V=Q×s _q . In this embodiment, the sampling rate in the p-direction and the sampling rate in the q-direction are both set to 0.3, and the entire sampling process requires 6×31×2 times. As shown in Figure 3, in order to achieve efficient sampling, according to the high and low distribution of the spectrogram, a non-uniform sampling strategy based on logarithmic linear transformation is constructed:

Full sampling is carried out in the low-frequency region; in the high-frequency region, spectral coefficients are selectively sampled in two directions p and q at exponential intervals. Set the coordinates of the center point of the panoramic Fourier spectrum as (f _p0 , f _q0 ), set the radius in the p direction of the low-frequency region selected for full sampling as m0, and the radius in the q direction as n0; in the high-frequency region, select the sampled spectrum The increase factor of the coefficient in the p-direction interval is α ₁ , and the increase factor in the q-direction interval is α ₂ . In this embodiment, the coordinates of the central point of the panoramic Fourier spectrum are set to (11, 52), and the radius in the p direction of the low-frequency area selected for full sampling is 2, and the radius in the q direction is 8. In the high-frequency area, the sampling The spectral coefficient of the p-direction interval growth factor is 2.2361, and the q-direction interval growth factor is 1.2605.

Then the non-uniform sampling strategy model based on logarithmic linear transformation is as follows:

表示p-q坐标系中以低频中心点向p方向扩展的第u层选择间隔的半径，

表示以低频中心点向q方向扩展的第v层选择间隔的半径；p(u)和q(v)分别表示p方向第u个选择的频谱坐标和q方向第v个选择的频谱坐标；m0表示低频区域的p方向半径，n0表示低频区域的q方向半径，U表示频谱在p方向上的采样点数，V表示频谱在q方向上的采样点数，(f_p0,f_q0)表示全景傅里叶频谱的中心点坐标，α₁表示采样的频谱系数在p向间隔增长因子，α₂表示采样的频谱系数在q向间隔增长因子。In the formula:

Indicates the radius of the u-th layer selection interval extending from the low-frequency center point to the p direction in the pq coordinate system,

Indicates the radius of the selection interval of the vth layer extending from the low-frequency center point to the q direction; p(u) and q(v) represent the spectrum coordinates of the uth selection in the p direction and the spectrum coordinates of the vth selection in the q direction, respectively; m0 Indicates the radius of the p-direction of the low-frequency region, n0 represents the radius of the q-direction of the low-frequency region, U represents the number of sampling points of the spectrum in the direction of p, V represents the number of sampling points of the spectrum in the direction of q, (f _p0 , f _q0 ) represents the panoramic Fourier The coordinates of the center point of the leaf spectrum, α ₁ represents the growth factor of the sampled spectral coefficients in the p-direction interval, and α ₂ represents the growth factor of the sampled spectral coefficients in the q-direction interval.

Step 2, constructing a circular Fourier base pattern sequence based on a non-uniform sampling strategy;

Specifically include:

(1) Design a panoramic Fourier base pattern model based on a non-uniform sampling strategy;

According to the spectral coefficients selected by the non-uniform sampling strategy, the panoramic Fourier basis pattern model is designed, and the calculation method is as follows:

P _uv ＝1+0.5×cos(2πf _p(u) p(u)+2πf _q(v) q(v)+φ),

In the formula, (p(u), q(v)) represents the spatial coordinates corresponding to the spectral coefficients selected by the non-uniform sampling strategy; (f _p(u) , f _q(v) ) represents the spectral coefficients selected by the non-uniform sampling strategy ; φ represents the initial phase, according to the four-step phase shift method, the possible values are: 0, π/2, π, 3π/2; P _uv represents the corresponding panoramic Fourier basis pattern model under the corresponding spectral coefficient; a Indicates the average light intensity, and b indicates the contrast.

(2) Based on the panoramic Fourier basis pattern model, a circular Fourier basis pattern sequence is constructed.

As shown in Fig. 2, the annular Fourier base pattern includes the central fovea blind hole area and the imaging area, the outer ring radius r ₀ of the central fovea blind hole area is the blind area, and the outside r ₀ is the imaging area. According to the resolution P×Q of the panoramic ghost imaging image, the imaging area is divided into P rings, and Q pixels are uniformly distributed in each ring, and ε represents the growth coefficient between rings. In this embodiment, according to the resolution of the panoramic ghost imaging image of 20×102, the imaging area is divided into 20 rings, and 102 pixels are evenly distributed in each ring.

The sequence of circular Fourier basis patterns includes:

In the formula, r _p represents the radius of the pth ring of the annular Fourier speckle structure, θ _q represents the angle corresponding to the qth pixel, Q represents the average number of units divided by each ring, ε represents the inter-ring growth coefficient, and r ₀ Indicates the outer ring radius of the central concave blind hole area, rc ₁ indicates the center radius of the first ring, rc _p indicates the center radius of the p-th ring, and ξ _p indicates the corresponding value of the p-th ring in the logarithmic polar coordinate system.

Step 3, reconstructing the panoramic ghost imaging image based on the circular Fourier basis pattern sequence.

Specifically include:

(1) Modulate the light source based on the circular Fourier base pattern sequence, and irradiate the curved mirror with the modulated light source;

(2) The light source is reflected by the curved mirror to obtain reflected light, which illuminates the target scene in the surrounding 360° field of view;

(3) The reflected light after illuminating the target scene in the surrounding 360° field of view undergoes diffuse reflection, and the light intensity with target information after the diffuse reflection is collected;

The calculation methods of light intensity include:

In the formula, T _i represents the light intensity value obtained by modulating the light source with the i-th annular Fourier base pattern S _i whose initial phase is φ _j , and o(x, y) represents the irradiated surrounding 360° omnidirectional annular target.

(4) Differentially process the light intensities corresponding to the annular Fourier base pattern sequences of different initial phases to obtain the Fourier spectrum; the calculation method is as follows:

First, U×V performs differential processing on the light intensity values corresponding to the annular Fourier base patterns with different initial phases to obtain the spectral coefficient values at the corresponding coordinates:

表示透射初始相位为0、频谱系数坐标为(p(u),q(v))的环形傅里叶基底图案所对应的光强值，

表示透射初始相位为π/2、频谱系数坐标为(p(u),q(v))的环形傅里叶基底图案所对应的光强值，

表示透射初始相位为π、频谱系数坐标为(p(u),q(v))的环形傅里叶基底图案所对应的光强值，

表示透射初始相位为3π/2、频谱系数坐标为(p(u),q(v))的环形傅里叶基底图案所对应的光强值，f_p(u),q(v)表示坐标为(p(u),q(v))的频谱系数，j表示虚部。In the formula,

Indicates the light intensity value corresponding to the circular Fourier basis pattern with the transmission initial phase of 0 and spectral coefficient coordinates of (p(u),q(v)),

Indicates the light intensity value corresponding to the circular Fourier basis pattern with the transmission initial phase of π/2 and the spectral coefficient coordinates of (p(u),q(v)),

Indicates the light intensity value corresponding to the circular Fourier basis pattern with the transmission initial phase as π and spectral coefficient coordinates as (p(u),q(v)),

Indicates the light intensity value corresponding to the annular Fourier basis pattern with the transmission initial phase of 3π/2 and the spectral coefficient coordinates of (p(u),q(v)), f _p(u),q(v) represent the coordinates is the spectral coefficient of (p(u),q(v)), and j represents the imaginary part.

(5) Inverse Fourier transform is performed on the Fourier spectrum to obtain a panoramic ghost imaging image.

The calculation method is as follows:

o'(p,q)=F ^-1 (f _pq )

In the formula, o' represents the reconstructed panoramic ghost imaging image, F ^-1 represents the inverse Fourier transform symbol, and f _pq represents the Fourier spectral coefficient matrix of the P×Q panoramic image.

The above-mentioned embodiments are only descriptions of the preferred modes of the present invention, and do not limit the scope of the present invention. Variations and improvements should fall within the scope of protection defined by the claims of the present invention.

Claims (8)

1. A Fourier panorama ghost imaging method based on logarithmic rectilinear transform, is characterized in that, comprises: Step 1. Obtain a non-uniform sampling strategy based on logarithmic linear transformation; Step 2, constructing a circular Fourier base pattern sequence based on the non-uniform sampling strategy; Step 3. Reconstructing a panoramic ghost imaging image based on the circular Fourier basis pattern sequence. 2. according to the described Fourier panoramic ghost imaging method based on logarithmic linear transform according to claim 1, it is characterized in that, the method that obtains described non-uniform sampling strategy comprises: Initialize Fourier panoramic ghost imaging parameters; Based on the Fourier panoramic ghost imaging parameters and the logarithmic linear transformation, a non-uniform sampling strategy is designed. 3. the Fourier panoramic ghost imaging method based on logarithmic linear transform according to claim 2, is characterized in that, described non-uniform sampling strategy comprises:

In the formula,

Indicates the radius of the u-th layer selection interval extending from the low-frequency center point to the p direction in the pq coordinate system,

Indicates the radius of the selection interval of the vth layer extending from the low-frequency center point to the q direction; p(u) and q(v) represent the spectrum coordinates of the uth selection in the p direction and the spectrum coordinates of the vth selection in the q direction, respectively; m0 Indicates the radius of the p-direction of the low-frequency region, n0 represents the radius of the q-direction of the low-frequency region, U represents the number of sampling points of the spectrum in the direction of p, V represents the number of sampling points of the spectrum in the direction of q, (f _p0 , f _q0 ) represents the panoramic Fourier The coordinates of the center point of the leaf spectrum, α ₁ represents the growth factor of the sampled spectral coefficients in the p-direction interval, and α ₂ represents the growth factor of the sampled spectral coefficients in the q-direction interval. 4. according to the described Fourier panoramic ghost imaging method based on logarithmic linear transform according to claim 1, it is characterized in that, the method for constructing described annular Fourier basis pattern sequence comprises: Designing a panoramic Fourier base pattern model based on the non-uniform sampling strategy; The circular Fourier basis pattern sequence is constructed based on the panoramic Fourier basis pattern model. 5. the Fourier panoramic ghost imaging method based on logarithmic linear transformation according to claim 4, is characterized in that, described panoramic Fourier base pattern model comprises: P _uv ＝a+b×cos(2πf _p(u) p(u)+2πf _q(v) q(v)+φ), In the formula, (p(u), q(v)) represents the spatial coordinates corresponding to the spectral coefficients selected by the non-uniform sampling strategy; (f _p(u) , f _q(v) ) represents the spectral coefficients selected by the non-uniform sampling strategy ; φ represents the initial phase; P _uv represents the corresponding panoramic Fourier basis pattern model under the corresponding spectral coefficient; a represents the average light intensity, and b represents the contrast. 6. according to the described Fourier panoramic ghost imaging method based on logarithmic straight line transform of claim 4, it is characterized in that, described annular Fourier base pattern sequence comprises:

In the formula, r _p represents the radius of the pth ring of the annular Fourier speckle structure, θ _q represents the angle corresponding to the qth pixel, Q represents the average number of units divided by each ring, ε represents the inter-ring growth coefficient, and r ₀ Indicates the outer ring radius of the central concave blind hole area, rc ₁ indicates the center radius of the first ring, rc _p indicates the center radius of the p-th ring, and ξ _p indicates the corresponding value of the p-th ring in the logarithmic polar coordinate system. 7. according to the described Fourier panoramic ghost imaging method based on logarithmic linear transform according to claim 1, it is characterized in that, the method for reconstructing described panoramic ghost imaging image comprises: Modulating a light source based on the annular Fourier base pattern sequence, and irradiating the curved mirror with the modulated light source; The light source is reflected by the curved mirror to obtain reflected light, and the reflected light illuminates the target scene in the surrounding 360° field of view; Diffuse reflection occurs in the reflected light after illuminating the target scene of the surrounding 360 ° field of view, and the light intensity with target information after the diffuse reflection is collected; performing differential processing on the light intensities corresponding to the annular Fourier base pattern sequences with different initial phases to obtain a Fourier spectrum; Inverse Fourier transform is performed on the Fourier spectrum to obtain the panoramic ghost imaging image. 8. the Fourier panoramic ghost imaging method based on logarithmic linear transform according to claim 7, is characterized in that, the computing method of described light intensity comprises:

In the formula, T _i represents the light intensity value obtained by modulating the light source with the i-th annular Fourier base pattern S _i whose initial phase is φ _j , and o(x, y) represents the irradiated surrounding 360° omnidirectional annular target.

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