CN116224365A - Photon counting scanning three-dimensional penetration imaging method based on asynchronous polarization modulation - Google Patents

Photon counting scanning three-dimensional penetration imaging method based on asynchronous polarization modulation Download PDF

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CN116224365A
CN116224365A CN202310011870.8A CN202310011870A CN116224365A CN 116224365 A CN116224365 A CN 116224365A CN 202310011870 A CN202310011870 A CN 202310011870A CN 116224365 A CN116224365 A CN 116224365A
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polarization modulation
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刘芮
田昕
肖滢
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Wuhan University WHU
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    • G01—MEASURING; TESTING
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Abstract

The invention provides a photon counting scanning three-dimensional penetration imaging method based on asynchronous polarization modulation. Aiming at the scattering effect and attenuation of the strong scattering medium to the optical signal, a point-to-point scanning imaging mechanism is adopted to avoid image blurring caused by the scattering effect, and a single-pixel photon counter is utilized to capture the weak ballistic photon signal. And calculating the flight time of the ballistic photon signal by using a polarization modulation ranging method, correcting the depth blurring problem introduced by asynchronous polarization modulation by using a time remolding method, and finally reconstructing a relative depth image of the target object. The method can realize three-dimensional imaging of the target object through the strong scattering medium, has clear imaging effect, has robustness to different strong scattering media, and provides convenience for three-dimensional photon counting imaging in a scattering environment.

Description

Photon counting scanning three-dimensional penetration imaging method based on asynchronous polarization modulation
Technical Field
The invention belongs to the field of photon counting three-dimensional imaging, and relates to a photon counting scanning three-dimensional penetration imaging method based on asynchronous polarization modulation, which is suitable for various photon counting three-dimensional imaging application scenes penetrating through a strong scattering medium.
Background
Compared with the traditional photon counting three-dimensional imaging, the photon counting three-dimensional penetration imaging technology can be applied to detection and analysis of targets through complex and unknown scattering media, and has been applied to the fields of biomedicine, remote sensing detection and the like.
In the conventional three-dimensional photon counting imaging technology, a method of calculating a distance using a time-of-flight technique can be divided into two types: direct and indirect processes. The method comprises the steps of obtaining the flight time of an echo signal of a target through a timing circuit, and then calculating a three-dimensional point cloud image. In direct-based three-dimensional transmission imaging, it is necessary to model and reverse derive the scattering process and then reconstruct the three-dimensional image using deconvolution of the space-time detection data. However, this method requires a prior calibration of the scattering medium and its spatial resolution is limited by scattering effects. The indirect method can be mainly divided into three types: time gating, intensity correlation and gain modulation. Among them, only time gating methods have been studied for three-dimensional penetration imaging, which filters back-scattered noise by setting a specific gating time for echo information. However, this method still suffers from scattering effects, and in a strongly scattering environment, the quality of the three-dimensional reconstruction of the object is poor. In order to solve the above-mentioned problems, a photon counting three-dimensional penetration imaging technique suitable for a strongly scattering environment is required.
The photon counting scanning three-dimensional penetration imaging method based on asynchronous polarization modulation utilizes a point-to-point scanning imaging mechanism to avoid image blurring caused by scattering effect. Through effective detection and time-dependent modulation of the scattered ballistic photon signals, a relationship between the photon number and the target distance can be established, thereby realizing three-dimensional penetration imaging of the target in a strong scattering environment. How to accurately model the detected ballistic photon signals and how to solve the problem of signal period aliasing caused by asynchronous modulation is a key problem of a photon counting scanning three-dimensional penetration imaging method based on asynchronous polarization modulation.
Disclosure of Invention
Aiming at the defects of the prior art, the invention uses a point-to-point scanning imaging mechanism to carry out photon counting three-dimensional imaging on a target in a strong scattering environment to directly avoid imaging blurring caused by scattering effect, and provides a three-dimensional penetration imaging method based on asynchronous polarization modulation aiming at the strong scattering environment.
The technical scheme adopted by the invention is as follows: based on a point-to-point scanning imaging mechanism, the single-pixel photon counter is utilized to improve the detection capability of weak ballistic photon signals, so that the method is suitable for three-dimensional penetration imaging in a strong scattering environment, and a polarization modulation photon counting image of a target is obtained. Further, the asymmetry of echo signals in different scattering environments is effectively described by using a gamma pulse model, and the generalization of model characterization is enhanced. Meanwhile, a relation between the signal flight time and the number of detected photons is established, and the signal flight time is calculated. Then, the time remodelling method is used for solving the problem of depth blurring caused by asynchronous control of the pulse laser and the polarization modulator, and the flight time of the signal is further corrected. And finally, obtaining the relative depth of the target through the calculated signal flight time, namely realizing three-dimensional penetration imaging of the target. The imaging system device is schematically shown in fig. 1, and the method comprises the following steps:
step 1: and constructing an imaging system light path. The laser beam of the pulse laser scans the target surface point by point through a two-dimensional scanning galvanometer, and the signal period of the pulse laser is T R . The reflected signal from the target surface is captured by the receiving system portion after passing through the scattering medium. The captured echo signal photons pass through a polarization modulation module in a receiving system, which comprises a polarizer LP1, an electro-optic phase modulator EOM and an analyzer LP2, and are then received by a single-pixel photon counter;
step 2: the detection light path is adjusted to obtain a polarization modulated image. The polarization angles of the polarizer LP1 and the analyzer LP2 are adjusted to the vertical direction, respectively, and then the analyzer LP2 is rotated 45 ° in the clockwise direction. Setting the voltage signal of EOM to V t1 ＝V π 2, acquiring a first polarization modulation image k 1, wherein Vπ Is the half-wave voltage of the EOM. Setting the voltage signal of EOM to V t2 ＝[1+cos(πt/(2 G ))]2, acquiring a second polarization modulation image k 2, wherein TG Is the modulation period of EOM, and T G ＝T r . Finally, the voltage signal of EOM is set to V t3 ＝[1-sin(πt/(2T G ))]2, acquiring a third polarization modulation image k 3 ；
Step 3: based on gammaMa Maichong model models ballistic photon signals after passing through scattering medium, derives a relation between photon number of received polarization modulation images and signal flight time, and thus calculates initial flight time diagram T of ballistic photon signals reflected by target based on detected three polarization modulation images m ；
Step 4: since the pulse laser and the EOM are respectively positioned at two sides of the scattering medium, the signal period T of the pulse laser r Modulation period T with EOM G Cannot be synchronously controlled, so that ballistic photon signals reflected by different spatial points of a target can be reflected in different modulation periods T G Modulated, the initial time of flight thus calculated has errors, which can result in a reconstructed three-dimensional image of the target having depth blur. Therefore, the problem is further solved by using a time remolding method, and the polarization modulation condition of ballistic photon signals reflected by different space points of the target is judged, so that the flight time is corrected, and a corrected ballistic photon signal flight time diagram is obtained
Figure BDA0004038006910000026
Finally according to the corrected ballistic photon signal time of flight diagram +.>
Figure BDA0004038006910000027
Calculating to obtain a relative depth map D of the target R ；
Further, the specific implementation of the step 3 includes the following sub-steps:
step 3.1, utilizing the time-varying rate to be
Figure BDA0004038006910000025
Describing the detection of ballistic photons by a photon counter, where t is time, η is the quantum efficiency of the photon counter, +.>
Figure BDA0004038006910000028
For the photon transmittance of the polarization modulation module, s (t) represents the waveform of the ballistic photon signal after passing through the scattering medium, and d is the dark count noise of the photon counter. Thus (2)In a single modulation period (0, T G ]In the above, the photon count rate m of the photon counter can be expressed as:
Figure BDA0004038006910000021
step 3.2, for a single spatially scanned point, the waveform s (t) of the ballistic photon signal after passing through the scattering medium can be expressed as
Figure BDA0004038006910000022
wherein ,Ns Representing the average photon number, T, of a single signal pulse s Representing the time of flight of the initial echo photons, f (t) represents the pulse function. Considering that a strong scattering medium causes non-uniform broadening of the waveform of a pulse signal in the time domain, the waveform of an echo photon signal is described by using a gamma pulse function, the pulse function f (t) can be expressed as
Figure BDA0004038006910000023
Wherein a and b are the shape parameter and the size parameter of the gamma distribution, respectively, and Γ (·) is the gamma function. Equation (3) satisfies
Figure BDA0004038006910000029
It is known from data statistics that for most scattering media, the transmitted signal waveform can be described by a gamma pulse function at a=2. Thus, a=2 is used, while b is taken as a variable to adapt to different scattering media. Therefore, the waveform s (t) of the ballistic photon signal after scattering the medium can be further expressed as
Figure BDA0004038006910000024
Step 3.3 polarizationThe effect of EOM in the modulation module can be seen as introducing a phase shift of α=pi V to the photonic signal t /V π, wherein Vt Is the voltage signal of the EOM. The photon transmittance of the polarization module is as follows
Figure BDA0004038006910000031
Where θ is the angle between polarizer LP1 and analyzer LP2, i.e., θ=45°.
Based on equations (1), (4) and (5), the relationship between photon count rate m of the photon counter and the time of flight of the initial echo photons can be obtained:
Figure BDA0004038006910000032
wherein ,Tm ＝T d +T s Representing the polarization modulation time, T d Is the time interval between the signal period of the pulsed laser and the modulation period of the EOM.
Step 3.4, based on the negative logarithmic maximum likelihood function under the weak light condition, the three polarization modulation images k obtained in the step 2 1 ，k 2 and k3 According to
Figure BDA0004038006910000033
Three photon count rate images m can be obtained 1 ，m 2 and m3 Where N is the number of laser pulses, l=1, 2,3.
Then, the following three equations can be obtained according to equation (6):
Figure BDA0004038006910000034
Figure BDA0004038006910000035
Figure BDA0004038006910000036
based on the formula (7-9), N s and Tm Can be found:
Figure BDA0004038006910000037
Figure BDA0004038006910000038
wherein ,
Figure BDA0004038006910000039
initial time of flight diagram T m T as found by all spatial scan points m Composition is prepared.
Further, the specific implementation of the step 4 includes the following sub-steps:
step 4.1 when the ballistic photon signals reflected by all spatial points of the target are not in the same modulation period T G When modulated, the echo signals of partial space points no longer satisfy the formula (1), but satisfy the following formula
Figure BDA00040380069100000310
Based on formulas (1) and (12), T in formula (6) s and Tm The relationship of (2) can be summarized as:
Figure BDA00040380069100000311
t described in formula (13) s and Tm The uncertainty of the relationship of (2) may lead to ambiguity in the calculated three-dimensional depth of the target. Accordingly, there is a need to solve the above problems using a time remodeling method, the schematic diagram of which is shown in fig. 2.
In assuming a true flight of ballistic photon signalsIn the case where the line time does not exceed half the polarization modulation period, i.e. T s ≤T G And/2, when max (T m )-min(T m )≤T G When in the process of/2, determining that ballistic photon signals reflected by all space points of the target are in the same modulation period T G Modulated without correcting the initial time of flight calculated in step 3.4, i.e
Figure BDA00040380069100000312
When max (T m )-min(T m )≤T G When/2, determining that ballistic photon signals reflected by all spatial points of the target are not in the same modulation period T G Modulated, at this time for the initial time-of-flight pattern T calculated in step 3.4 m Correcting to obtain a corrected ballistics photon signal flight time diagram +.>
Figure BDA00040380069100000313
Figure BDA00040380069100000314
wherein ,Tm (i, j) is T m The value of the target spatial point (i, j),
Figure BDA0004038006910000041
is->
Figure BDA0004038006910000042
The value of the target spatial point (i, j).
Step 4.2, base
Figure BDA0004038006910000043
The relative depth map of the target can be calculated:
Figure BDA0004038006910000044
compared with the prior art, the invention has the following advantages and beneficial effects: according to the invention, a point-to-point scanning imaging mechanism is utilized to carry out photon counting three-dimensional imaging on a target in a strong scattering environment so as to directly avoid imaging blurring caused by scattering effect. Further, the asymmetry of echo signals in different scattering environments is effectively described by using a gamma pulse model, and the generalization of model characterization is enhanced. Meanwhile, the time remolding method is used for solving the problem of depth blurring caused by asynchronous control of a pulse laser and a polarization modulator, and the flight time of the signal is further corrected. The method can be applied to three-dimensional imaging in different strong scattering environments, and the final imaging result has clear spatial information, accurate depth information and higher depth resolution.
Drawings
FIG. 1 is a schematic diagram of a photon counting scanning three-dimensional penetration imaging system apparatus based on asynchronous polarization modulation.
Fig. 2 is a schematic diagram of a temporal remodeling method.
FIG. 3 is a schematic view of an imaging environment of an embodiment.
Fig. 4 is an intensity image of an embodiment.
Fig. 5 is a light-transmitting real-time photograph of both sides of a scattering medium used in the imaging process of the embodiment.
Fig. 6 is a surface reflectance reconstruction map of an embodiment.
Fig. 7 is a relative depth reconstruction map of an embodiment.
Detailed Description
In order to facilitate the understanding and practice of the invention, one of ordinary skill in the art will now recognize in view of the drawings and examples that follow, it will be understood that the examples described herein are illustrative of the invention and are not intended to be limiting.
The invention mainly aims at the application requirement of three-dimensional imaging of a target through a strong scattering medium. According to the polarization modulation ranging theory, we propose a photon counting scanning three-dimensional penetration imaging method based on asynchronous polarization modulation. Image blurring caused by scattering effect is avoided based on a point-to-point scanning imaging mechanism, the flight time of ballistic photon signals reflected by the target is calculated and corrected by shooting three polarization modulation images, and finally, a relative depth image of the target is reconstructed.
Fig. 3 is a schematic view of an imaging environment of an embodiment. In room 1, the pulsed laser scans the target object, which is a paper cup, with an intensity image as shown in fig. 4, through a two-dimensional galvanometer. The reflected light from the surface of the target object reaches the room 2 after passing through the strongly scattering medium. The strong scattering medium is ground glass, and the light-transmitting real photographing chart on two sides of the ground glass is shown in figure 5. A polarization modulation module and a single pixel photon counter of the imaging system are placed in the room 2 to capture ballistic photon signals reflected from the target surface.
The embodiment provides a photon counting scanning three-dimensional penetration imaging method based on asynchronous polarization modulation for three-dimensional imaging of a target through a strong scattering medium, which specifically comprises the following steps:
step 1: and constructing an imaging system light path. The laser beam of the pulse laser scans the target surface point by point through a two-dimensional scanning galvanometer, and the signal period of the pulse laser is T r =100 ns. The reflected signal from the target surface is captured by the receiving system portion after passing through the scattering medium. The captured echo signal photons pass through a polarization modulation module in a receiving system, which comprises a polarizer LP1, an electro-optic phase modulator EOM and an analyzer LP2, and are then received by a single-pixel photon counter;
step 2: the detection light path is adjusted to obtain a polarization modulated image. The polarization angles of the polarizer LP1 and the analyzer LP2 are adjusted to the vertical direction, respectively, and then the analyzer LP2 is rotated 45 ° in the clockwise direction. Setting the voltage signal of the EOM to
Figure BDA0004038006910000058
Acquisition of a first polarization-modulated image k 1, wherein Vπ -10V is the half-wave voltage of the EOM. Setting the voltage signal of EOM to V t2 ＝[1+cos(πt/(2T G ))]2, acquiring a second polarization modulation image k 2, wherein TG Is the modulation period of EOM, and T G ＝T r =100 ns. Finally, the voltage signal of EOM is set to V t3 ＝[1-sin(πt/(2T G ))]2, acquiring a third polarization modulation image k 3 ；
Step 3: modeling ballistic photon signals after passing through a scattering medium based on a gamma pulse model, deriving a relation between the photon number of a received polarization modulation image and signal flight time, and calculating an initial flight time diagram T of ballistic photon signals reflected by a target based on the detected three polarization modulation images m . The specific implementation comprises the following substeps:
step 3.1: the utilization time-varying rate is
Figure BDA0004038006910000056
Describing the detection of ballistic photons by a photon counter by a non-uniform poisson process of (a), where η = 0.3 is the quantum efficiency of the photon counter, +.>
Figure BDA0004038006910000057
For the photon transmittance of the polarization modulation module, s (t) represents the waveform of the ballistic photon signal after passing through the scattering medium, d=0.25 -1 Is the dark count noise of the photon counter. Thus, in a single modulation period (0, 100]In the above, the photon count rate m of the photon counter can be expressed as:
Figure BDA0004038006910000051
step 3.2, for a single spatially scanned point, the waveform s (t) of the ballistic photon signal after passing through the scattering medium can be expressed as
Figure BDA0004038006910000052
wherein ,Ns Representing the average photon number, T, of a single signal pulse s Representing the time of flight of the initial echo photons, f (t) represents the pulse function. Considering that a strong scattering medium causes non-uniform broadening of the waveform of a pulse signal in the time domain, the waveform of an echo photon signal is described by using a gamma pulse function, the pulse function f (t) can be expressed as
Figure BDA0004038006910000053
Wherein a and b are the shape parameter and the size parameter of the gamma distribution, respectively, and Γ (·) is the gamma function. The above-mentioned formula meets
Figure BDA0004038006910000059
A=2 is used while b is taken as a variable to adapt to different scattering media. Therefore, the waveform s (t) of the ballistic photon signal after scattering the medium can be further expressed as
Figure BDA0004038006910000054
/>
Step 3.3 the effect of EOM in the polarization modulation module can be seen as introducing a phase shift α=pi V to the photonic signal t /10, wherein V t Is the voltage signal of the EOM. The photon transmittance of the polarization module is as follows
Figure BDA0004038006910000055
Where θ is the angle between polarizer LP1 and analyzer LP2, i.e., θ=45°.
The relationship between the photon count rate m of the photon counter and the time of flight of the initial echo photons can be obtained:
Figure BDA0004038006910000061
wherein ,Tm ＝T d +T s Representing the polarization modulation time, T d Is the time interval between the signal period of the pulsed laser and the modulation period of the EOM.
Step 3.4, based on the negative logarithmic maximum likelihood function under the weak light condition, the three polarization modulation images k obtained in the step 2 1 ，k 2 and k3 According to
Figure BDA0004038006910000062
Three photon count rate images m can be obtained 1 ，m 2 and m3 Where N is the number of laser pulses, l=1, 2,3.
Then, the following three equations can be obtained:
m 1 ＝0.25T G +0.15N s
Figure BDA0004038006910000063
Figure BDA0004038006910000064
solving the equation set consisting of the three equations, N s and Tm The method can obtain the following steps:
Figure BDA0004038006910000065
Figure BDA0004038006910000066
wherein ,
Figure BDA0004038006910000067
initial time of flight diagram T m T as found by all spatial scan points m Composition is prepared.
Step 4: since the pulse laser and the EOM are respectively positioned at two sides of the scattering medium, the signal period T of the pulse laser r Modulation period T with EOM G Cannot be synchronously controlled, so that ballistic photon signals reflected by different spatial points of a target can be reflected in different modulation periods T G Modulated, the initial time of flight thus calculated has errors, which can result in a reconstructed three-dimensional image of the target having depth blur. Thus, go inThe method comprises the steps of solving the problems by using a time remolding method, judging polarization modulation conditions of ballistic photon signals reflected by different space points of a target, correcting flight time, and obtaining a corrected ballistic photon signal flight time diagram
Figure BDA0004038006910000068
Finally according to the corrected ballistic photon signal time of flight diagram +.>
Figure BDA0004038006910000069
Calculating to obtain a relative depth map D of the target R . The specific implementation comprises the following substeps:
and 4.1, judging whether ballistic photon signals reflected by all the space points of the target are modulated in the same modulation period. Since there is max (T in this embodiment m )-min(T m )≤T G 2, therefore, it is determined that ballistic photon signals reflected by all spatial points of the target are not in the same modulation period T G Modulated, at this time for the initial time-of-flight pattern T calculated in step 3.4 m Correcting to obtain a corrected trajectory photon signal flight time chart
Figure BDA00040380069100000615
/>
Figure BDA00040380069100000610
wherein ,Tm (i, j) is T m The value of the target spatial point (i, j),
Figure BDA00040380069100000611
is->
Figure BDA00040380069100000612
The value of the target spatial point (i, j).
Step 4.2 based on
Figure BDA00040380069100000613
Can calculate the targetRelative depth map:
Figure BDA00040380069100000614
the surface reflectivity reconstruction map and the relative depth reconstruction map of the target object surface obtained based on the steps are shown in fig. 6 and fig. 7 respectively. The method provided by the invention can be seen to be based on a point-to-point scanning imaging mechanism and a polarization modulation ranging principle, a single-pixel photon counter is utilized to acquire weak ballistic photon signals after penetrating through a strong scattering medium, and a relative depth image of a target is further reconstructed, so that three-dimensional imaging of the target through the strong scattering medium can be realized.
It should be understood that parts of the specification not specifically set forth herein are all prior art.
It should be understood that the foregoing description of the embodiments is not intended to limit the scope of the invention, but rather to make substitutions and modifications within the scope of the invention as defined by the appended claims without departing from the scope of the invention.

Claims (10)

1. The photon counting scanning three-dimensional penetration imaging method based on asynchronous polarization modulation is characterized by comprising the following steps of:
step 1, an imaging system is built;
the imaging system comprises a pulse laser, a two-dimensional scanning galvanometer, a target object, a scattering medium and a receiving system part, wherein the receiving system part comprises a polarization modulation module and a single-pixel photon counter, and the polarization modulation module comprises a polarizer LP1, an electro-optic phase modulator EOM and an analyzer LP2;
step 2, adjusting the detection light path to obtain polarization modulation images, namely adjusting the polarization angles of the polarizer LP1 and the analyzer LP2 to obtain a plurality of polarization modulation images;
step 3, based on gammaThe pulse model models ballistic photon signals after passing through a scattering medium, derives a relation between the photon number of a received polarization modulation image and the signal flight time, and thus calculates an initial flight time diagram T of ballistic photon signals reflected by a target based on a plurality of detected polarization modulation images m ；
Step 4, judging polarization modulation conditions of ballistic photon signals reflected by different space points of the target, thereby correcting the flight time and obtaining a corrected ballistic photon signal flight time diagram
Figure FDA0004038006900000011
Finally according to the corrected ballistic photon signal time of flight diagram +.>
Figure FDA0004038006900000012
Calculating to obtain a relative depth map D of the target R 。
2. An asynchronous polarization modulation based photon counting scanning three-dimensional transmission imaging method as claimed in claim 1, wherein: the specific implementation mode of the step 1 is as follows;
the laser beam of the pulse laser scans the target surface point by point through a two-dimensional scanning galvanometer, and the signal period of the pulse laser is T r The reflected signal on the target surface is captured by the receiving system after passing through the scattering medium, and the captured echo signal photons pass through a polarization modulation module in the receiving system, which comprises a polarizer LP1, an electro-optical phase modulator EOM and an analyzer LP2, and are then received by a single-pixel photon counter.
3. An asynchronous polarization modulation based photon counting scanning three-dimensional transmission imaging method as claimed in claim 1, wherein: three polarization-modulated images were acquired in step 2.
4. A photon counting scanning three-dimensional penetration imaging method based on asynchronous polarization modulation as claimed in claim 2, wherein: the specific implementation mode of the step 2 is as follows;
the polarization angles of the polarizer LP1 and the analyzer LP2 are respectively adjusted to the vertical direction, and then the analyzer LP2 is rotated 45 degrees along the clockwise direction; setting the voltage signal of EOM to V t1 ＝ π 2, acquiring a first polarization modulation image k 1, wherein Vπ Is half-wave voltage of EOM, and then the voltage signal of EOM is set as V t2 ＝[1+cos(/(2 G ))]2, acquiring a second polarization modulation image k 2 Wherein T is time, T G Is the modulation period of EOM, and T G ＝ r Finally, the voltage signal of EOM is set to V t3 ＝[1-sin(/(2 G ))]2, acquiring a third polarization modulation image k 3 。
5. An asynchronous polarization modulation based photon counting scanning three-dimensional transmission imaging method as claimed in claim 1, wherein: the specific implementation of the step 3 comprises the following sub-steps:
step 3.1, utilizing the time-varying rate to be
Figure FDA0004038006900000021
Describing the detection of ballistic photons by a photon counter by a non-uniform poisson process, where η is the quantum efficiency of the photon counter, +.>
Figure FDA0004038006900000022
S (t) represents the waveform of ballistic photon signals after passing through a scattering medium, and d is dark counting noise of a photon counter; thus, in a single modulation period (0, T G ]In the above, the photon count rate m of the photon counter can be expressed as:
Figure FDA0004038006900000023
step 3.2, for a single spatially scanned point, the waveform s (t) of the ballistic photon signal after passing through the scattering medium can be expressed as
Figure FDA0004038006900000024
wherein ,Ns Representing the average photon number, T, of a single signal pulse s Representing the time of flight of the initial echo photons, f (t) representing the pulse function; considering that a strong scattering medium causes non-uniform broadening of the waveform of a pulse signal in the time domain, the waveform of an echo photon signal is described by using a gamma pulse function, the pulse function f (t) can be expressed as
Figure FDA0004038006900000025
Wherein a and b are the shape parameter and the size parameter of the gamma distribution, Γ (·) is the gamma function, and formula (3) satisfies
Figure FDA0004038006900000026
It is known from data statistics that, for most scattering media, the transmitted signal waveform can be described by a gamma pulse function when a=2, so that a=2 is adopted, and b is taken as a variable to adapt to different scattering media; therefore, the waveform s (t) of the ballistic photon signal after scattering the medium can be further expressed as
Figure FDA0004038006900000027
Step 3.3 the effect of EOM in the polarization modulation module can be seen as introducing a phase shift α=pi V to the photonic signal t / π, wherein Vt Is a voltage signal of EOM, and the photon transmittance of the polarization module is that
Figure FDA0004038006900000028
Wherein θ is the angle between polarizer LP1 and analyzer LP2, i.e., θ=45°;
based on equations (1), (4) and (5), the relationship between photon count rate m of the photon counter and the time of flight of the initial echo photons can be obtained:
Figure FDA0004038006900000029
wherein ,Tm ＝ d + s Representing the polarization modulation time, T d Time intervals during the signal period and modulation period of the EOM for the pulsed laser;
step 3.4, based on the negative logarithmic maximum likelihood function under the weak light condition, the three polarization modulation images k obtained in the step 2 1 ，k 2 and k3 According to
Figure FDA0004038006900000031
Three photon count rate images m can be obtained 1 ，m 2 and m3 Where N is the number of laser pulses, l=1, 2,3;
then, the following three equations can be obtained according to equation (6):
Figure FDA0004038006900000032
Figure FDA0004038006900000033
Figure FDA0004038006900000034
based on the formula (7-9), N s and Tm Can be found:
Figure FDA0004038006900000035
/>
Figure FDA0004038006900000036
wherein ,
Figure FDA0004038006900000037
initial time of flight diagram T m T as found by all spatial scan points m Composition is prepared.
6. An asynchronous polarization modulation based photon counting scanning three-dimensional transmission imaging method according to claim 5, wherein: the specific implementation of the step 4 comprises the following sub-steps:
step 4.1 when the ballistic photon signals reflected by all spatial points of the target are not in the same modulation period T G When modulated, the echo signals of partial space points no longer satisfy the formula (1), but satisfy the following formula
Figure FDA0004038006900000038
Based on formulas (1) and (12), T in formula (6) s and Tm The relationship of (2) can be summarized as:
Figure FDA0004038006900000039
t described in formula (13) s and Tm The uncertainty of the relation of the target three-dimensional depth can cause the calculated target three-dimensional depth to have ambiguity, so that a time remodelling method is needed to solve the problems, and the specific implementation is as follows;
under the assumption that the true flight time of ballistic photon signals does not exceed half the polarization modulation period, i.e. T s ≤T G And/2, when max (T m )-min(T m )≤T G When in the process of/2, determining that ballistic photon signals reflected by all space points of the target are in the same modulation period T G Modulated without correcting the initial time of flight calculated in step 3.4, i.e
Figure FDA00040380069000000310
When max (T m )-min(T m )≤T G When/2, determining that ballistic photon signals reflected by all spatial points of the target are not in the same modulation period T G Modulated, at this time for the initial time-of-flight pattern T calculated in step 3.4 m Correcting to obtain a corrected ballistics photon signal flight time diagram +.>
Figure FDA0004038006900000041
Figure FDA0004038006900000042
wherein ,Tm (i, j) is T m The value of the target spatial point (i, j),
Figure FDA0004038006900000043
is->
Figure FDA0004038006900000044
A value of a target spatial point (i, j);
step 4.2 based on
Figure FDA0004038006900000045
The relative depth map of the target can be calculated:
Figure FDA0004038006900000046
7. an asynchronous polarization modulation based photon counting scanning three-dimensional transmission imaging method as claimed in claim 1, wherein: the strong scattering medium is ground glass.
8. A photon counting scanning three-dimensional penetration imaging method based on asynchronous polarization modulation as claimed in claim 2, wherein: the signal period of the pulse laser is T r ＝100。
9. An asynchronous polarization modulation based photon counting scanning three-dimensional transmission imaging method according to claim 4, wherein:
Figure FDA0004038006900000047
T g ＝100。
10. an asynchronous polarization modulation based photon counting scanning three-dimensional transmission imaging method according to claim 5, wherein: η=0.3, d=0.25 -1 。
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CN116704559A (en) * 2023-07-28 2023-09-05 南京大学 Quantum fingerprint identification method and system based on asynchronous two-photon interference
CN116704559B (en) * 2023-07-28 2023-11-03 南京大学 Quantum fingerprint identification method and system based on asynchronous two-photon interference

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