Method for calculating the range of target single-photon detection in a turbid medium

Abstract

The present application relates to a kind of target single-photon detection distance calculation method in turbid medium, it is related to detection field, including the following steps: light source is placed in the coordinate position of origin, one light pulse is emitted to turbid medium unidirectionally;Single-photon detector receives returned photon, and received photon is divided into three parts of turbid medium itself returned photon, hidden in turbid medium target object itself returned photon and noise photon;Respectively calculate three parts of photon flux density Green function;Using the ratio between the photon count of hidden object returned at target peak time and background photon count, when the ratio is greater than 1, hidden target object can be effectively detected, greater than 3, hidden target object can be effectively imaged;Confirm effective, the maximum detection distance of target object can be calculated, the present application has the advantages that single-photon detector in turbid medium can accurately calculate detection limit.

Description

Technical Field

[0001] This invention relates to the field of detection technology, and in particular to a method for calculating the single-photon detection distance of a target in a turbid medium. Background Technology

[0002] Active optical detection of targets hidden in turbid media (such as seawater, dense fog, biological tissue, and soot) is of paramount importance in many key fields, including marine resource exploration, atmospheric target identification, and biological tissue imaging. However, the strong scattering and absorption effects of turbid media pose a core challenge: incident photons undergo complex multiple scattering paths, leading to rapid beam diffusion, sharp energy attenuation, and severe background noise. Traditional active optical detection methods based on high-power light sources and linear detectors exhibit significantly reduced efficiency in such environments, and their detection range and signal-to-noise ratio often fail to meet practical requirements.

[0003] Therefore, to address the above shortcomings, a method for calculating the single-photon detection range of a target in a turbid medium is needed. Summary of the Invention

[0004] (a) Technical problems to be solved

[0005] The technical problem to be solved by the present invention is to address the issue that traditional optical detection methods are ineffective when detecting objects in turbid media.

[0006] (II) Technical Solution

[0007] To address the aforementioned technical problems, this invention provides a method for calculating the single-photon detection range of a target in a turbid medium, comprising the following steps:

[0008] I. Place the light source at the coordinate position r0 = (0,0,0) and emit a light pulse δ(r0,t) towards the turbid medium in the +z direction at time 0;

[0009] II. The single-photon detector receives the returned photons and divides them into three parts: photons returned by the turbid medium itself, photons returned by the target object hidden in the turbid medium itself, and noise photons.

[0010] III. Calculate the Green's function for the three photon flux densities respectively;

[0011] IV. Use the ratio of photon counts returned by the hidden object at the target peak time t0 to the background photon count, specifically:

[0012]

[0013] in,

[0014] f rThe repetition frequency of the laser;

[0015] t a To accumulate time;

[0016] N l The total number of photons returned to the detector;

[0017] N m The total number of photons contained in a light pulse;

[0018] V represents the smallest space voxel that the detection system can resolve in the x, y, t dimensions;

[0019] G B () represents the Green's function, which represents the photon flux density returned by the target object itself, hidden within the turbid medium.

[0020] G s () represents the Green's function of the photon flux density returned by the turbid medium itself;

[0021] This indicates taking the minimum value within that range;

[0022] n(r,t0) is the noise constant per unit time;

[0023] V. When OBR > 1, the hidden target object can be effectively detected; when OBR > 3, the hidden target object can be effectively imaged. After confirmation of effectiveness, the maximum detection range d of the hidden target object is... D satisfy:

[0024]

[0025] Where, μ S is the reduced scattering coefficient.

[0026] As a further explanation of the present invention, preferably, the photon flux density G returned by the turbid medium itself is... s The Green's function (r,t) satisfies:

[0027]

[0028] in,

[0029] r is the distance from the light source;

[0030] t represents time;

[0031] k is the diffusion coefficient;

[0032] e is the natural constant;

[0033] μ a The absorption coefficient;

[0034] c is the speed of light;

[0035] z0 is the scattering free path;

[0036] z e This is the extrapolated boundary distance;

[0037] ρ is the lateral (x, y) distance from the light source.

[0038] As a further explanation of the present invention, preferably, the diffusion coefficient k satisfies:

[0039]

[0040] Where μ a μ is the absorption coefficient. S is the reduced scattering coefficient.

[0041] As a further explanation of the present invention, preferably, the distance r from the light source satisfies:

[0042]

[0043] Where ρ is the horizontal (x, y) distance from the light source, and z is the vertical (z) distance from the light source.

[0044] As a further explanation of the present invention, preferably, the Green's function G of the photon flux density returned by the target object itself hidden within the turbid medium. B (r,t) satisfies:

[0045] G B (r,t)=∫∫q(r′,t″)G T (rr′,tt″)dt″dr′

[0046] in,

[0047] q() represents the number of photons per unit volume per unit time;

[0048] G T () is the Green's function for the transmitted photon flux density in an infinitely turbid medium;

[0049] r′ represents the position of the target object;

[0050] t″ represents the time it takes for the photon to be reflected back from the target object.

[0051] As a further explanation of the present invention, preferably, the number of photons q(r′,t″) per unit time per unit volume satisfies:

[0052]

[0053] in,

[0054] R(r′) is the reflectivity of the target object at position r′;

[0055] t′ is the time it takes for a photon to reach the target object;

[0056] δ(t″-t′) is the Dirac function with respect to time t″, and its integral is 1 when t″=t′.

[0057] As a further explanation of the present invention, preferably, the Green's function G of the transmitted photon flux density in a planar infinitely large turbid medium is... T (r,t) satisfies:

[0058]

[0059] Where q(r′,t′)G T (rr′,tt′) represents the photon flux density returned by the target object itself hidden within the turbid medium.

[0060] As a further explanation of the present invention, preferably, the photon count distribution received by the single-photon detector satisfies:

[0061]

[0062] in,

[0063] This is the floor operator.

[0064] (III) Beneficial Effects

[0065] The above-described technical solution of the present invention has the following advantages:

[0066] This invention designs a computational method that leverages the ability of single-photon detectors to effectively capture and distinguish extremely weak target reflections. This allows for the extraction of useful signals submerged in noise, even under strong background noise, through precise time-correlated single-photon counting technology. Furthermore, it enables in-depth research into the detection limits of single-photon detectors in turbid media, particularly systematically analyzing the influencing factors and optimization strategies for their maximum effective detection distance. This not only has significant theoretical value but also provides crucial scientific basis and technical support for the design and performance evaluation of high-performance, long-distance single-photon detection systems for practical applications. Attached Figure Description

[0067] Figure 1 This is a total photon count distribution diagram of the optical pulse of the present invention;

[0068] Figure 2 yes Figure 1 Enlarged view of the area within the red box;

[0069] Figure 3This is a comparison diagram of the photon count distribution returned by the hidden object in this invention and the photon count distribution in the turbid medium;

[0070] Figure 4 This is a graph showing the relationship between the distance at which a hidden object can be effectively detected, imaged, and seen by the naked eye, and the reduced scattering coefficient. Detailed Implementation

[0071] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0072] A method for calculating the single-photon detection range of a target in a turbid medium includes the following steps:

[0073] I. Place the light source at the coordinate position r0 = (0,0,0) and emit a light pulse δ(r0,t) towards the turbid medium in the +z direction at time 0; at the same time, place a semi-infinite turbid medium in the space z>0, that is, at a distance from the position of point r0.

[0074] II. When a hidden object inside a turbid medium is irradiated with a pulsed laser, the distribution of returned photons in the time dimension consists of three parts: photons returned by the turbid medium itself, photons returned by the hidden object, and noise. Calculate the Green's function of the photon flux density for each of the three parts, where:

[0075] 1. Photon flux density distribution returned by the turbid medium itself:

[0076] The photon flux density distribution (the number of photons passing through a unit area per unit time) returned by the turbid medium itself can be calculated using the Green's function of the photon flux density reflected by the semi-infinite turbid medium:

[0077]

[0078] in,

[0079] r is the distance from the light source, specifically:

[0080]

[0081] Where ρ is the horizontal (x, y) distance from the light source, and z is the vertical (z) distance from the light source;

[0082] t represents time;

[0083] k is the diffusion coefficient, specifically:

[0084]

[0085] Where μ a μ is the absorption coefficient. S The reduced scattering coefficient;

[0086] e is the natural constant;

[0087] c is the speed of light;

[0088] z0 is the scattering free path, specifically:

[0089]

[0090] z e This represents the extrapolated boundary distance.

[0091] 2. Photon flux density distribution returned by the hidden object

[0092] Inside the turbid medium, at time t′, the photon flux density in the +z direction produced by the light source at the target position r′=(x′,y′,z) is:

[0093] J + (r′,t′)=G j (r′-r0,t′)

[0094] Among them G j () is the Green's function for the transmitted photon flux density in a semi-infinite turbid medium.

[0095] Simplifying the interaction between light and an object as specular reflection, after the photon interacts with the object, the photon flux density in the -z direction at time t″ is J. - (r′,t″). Assuming the interaction between the photon and the object is instantaneous, then t″ = t′, and thus:

[0096] J - (r′,t″)=G j (r′-r0,t′)R(r′)δ(t″-t′)

[0097] in,

[0098] R(r′) is the reflectivity of the target object at position r′;

[0099] δ(t″-t′) is the Dirac function with respect to time t″.

[0100] Let J -(r′,t″) generates an equivalent light source q(r′,t″) at position r′, where q(r′,t″) is the number of photons per unit time per unit volume, specifically:

[0101]

[0102] Since t″=t′, the integral of δ(t″-t′) is 1.

[0103] Subsequently, q(r′,t″) continues to diffuse in the turbid medium and eventually reaches the z=0 plane, which is the location of the single-photon detector. At time t, a photon flux density q(r′,t′)G is generated at the position r=(x,y,0) on the z=0 plane. T (rr′,tt′). Wherein, G T () represents the Green's function for the transmitted photon flux density in an infinitely turbid medium, specifically:

[0104]

[0105] Suppose that a single-photon detector can only receive photons propagating along the -z direction, i.e., q(r′,t′)G T Integrating (rr′,tt′) over all positions and times, we get:

[0106] G B (r,t)=∫∫q(r′,t″)G T (rr′,tt″)dt″dr′

[0107] 3. Noise photons

[0108] Let the noise be additive noise n(r,t0) with a random distribution and a constant mean per unit time. That is, regardless of the spatial location r or the time t0, the statistical average value of this noise is always the same fixed value.

[0109] III. The preferred single-photon detector is a SPAD, which stands for Single-Photon Avalanche Diode. SPADs are solid-state single-photon detectors based on semiconductor materials (such as silicon and germanium). They are characterized by small size, low power consumption, high stability, high photon capture efficiency in specific wavelength bands (such as visible light and near-infrared), and extremely short avalanche process times (nanoseconds or even picoseconds), making them suitable for high-speed photon counting.

[0110] In actual detection, assuming the time broadening of the pulse source is smaller than the time resolution of the detector, it can be considered as a pulse function containing N. mA number of photons. The smallest spacetime voxel that the detection system can resolve in the x, y, t dimensions is V, where V = ΔxΔyΔt, and Δx, Δy, and Δt are the smallest intervals that the detection system can resolve in the x, y, t dimensions, respectively. The photon distribution returning to the detector is as follows:

[0111] J(r,t)=V·N m (G B (r,t)+G s (r,t))+n(r,t0)

[0112] Let the total number of photons contained in J(r,t) be N. l The photon count distribution received by the SPAD is as follows:

[0113] in:

[0114] f r Let f be the laser repetition frequency (assuming the detector can respond perfectly). r Also the detector counting frequency);

[0115] t a To accumulate time;

[0116] The floor operator

[0117] This indicates taking the minimum value within that range.

[0118] IV. The effectiveness of detection and imaging is quantitatively evaluated using the ratio of the photon count returned by the hidden object at the target peak time t0 to the background photon count, specifically:

[0119]

[0120] V. When OBR > 1, the hidden target object can be effectively detected; when OBR > 3, the hidden target object can be effectively imaged. After confirmation of effectiveness, the maximum imaging distance d of the hidden target object is... I and maximum detection distance d D satisfy:

[0121]

[0122] Where a I b I a d b D All are constants.

[0123] To verify the effectiveness of this calculation method, the following test experiment was conducted:

[0124] Let μ S =1m -1 μ a =0.02m -1 The target is a flat plate with a reflectivity of 1 and an area of ​​1 square meter, placed at a plane with z = 3 m. The laser's single-pulse photon count N is... m =1×10 9 repetition frequency f r =1×10 6 Hz, accumulation time t a =1s, the incident position and the detection position are both (0,0,0). The average number of noise photons n(r,t0) is 5 within a 64ps ​​time interval. Then the photon count distribution C(r,t) received by the SPAD is as follows: Figure 1 , Figure 2 and Figure 3 As shown, where Figure 1 The peak within the red box (dashed line) represents a hidden object.

[0125] If the calculated OBR is greater than 3 after substituting into the formula for calculating OBR, it means that the target can be effectively imaged.

[0126] The data was then fitted to obtain... Figure 4 The maximum imaging distance d meets the above requirements. I and maximum detection distance d D Substituting the power-law distribution of the formula into the above equation, we get:

[0127] a I =4.938, b I =-0.9697, a D =10.04, b D = -0.9686

[0128] Depend on Figure 4 It can be seen that d I and d D With μ S goodness of fit of the distribution R 2 The values ​​are 0.9998 and 0.9999 respectively, indicating that the fitting results closely match the distribution of the data points. In the formula, b... I and b D Both are close to -1, while μ S -1 Let z0 be the scattering free path, which is the average distance a photon travels between two scatterings when propagating in a turbid medium. Therefore, this equation also indicates that the distances at which a hidden object can be effectively detected and imaged are approximately 10 times and 5 times the scattering free path, respectively. Figure 4 The average imaging distance is about 5.54 times the visible distance.

[0129] In summary, the calculation method provided by this invention can accurately calculate the maximum imaging distance, maximum detection distance, and visibility distance of objects hidden in turbid media. It not only has important theoretical value, but also provides key scientific basis and technical support for the design and performance evaluation of high-performance, long-distance single-photon detection systems for practical applications.

[0130] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for calculating the single-photon detection range of a target in a turbid medium, characterized in that: Includes the following steps: I. Place the light source =The coordinates of (0,0,0) are such that at time 0, the coordinates of the coordinates are shifted towards the + A turbid medium in the direction emits a light pulse δ ( , ); II. The single-photon detector receives the returned photons and divides them into three parts: photons returned by the turbid medium itself, photons returned by the target object hidden in the turbid medium itself, and noise photons. III. Calculate the Green's function for the three photon flux densities respectively; IV. Use the target peak time The ratio between the photon count returned by the hidden object and the background photon count Specifically: in, The repetition frequency of the laser; To accumulate time; The total number of photons returned to the detector; The total number of photons contained in a light pulse; For the detection system in , , The smallest space voxel that can be distinguished by dimension; Green's function is the photon flux density returned by the target object itself, which is hidden within the turbid medium. Green's function represents the photon flux density returned by the turbid medium itself. Indicates taking Minimum value within the range; The noise constant per unit time; V. When Hidden targets can be effectively detected. The hidden target object can be effectively imaged; once confirmed as effective, the maximum detection range of the hidden target object is determined. satisfy: in, is the reduced scattering coefficient.

2. The method for calculating the single-photon detection range of a target in a turbid medium according to claim 1, characterized in that: Photon flux density returned by the turbid medium itself Green's function satisfies: in, Distance from the light source; For time; The diffusion coefficient is denoted as . It is a natural constant; The absorption coefficient; The speed of light; The scattering free path; This is the extrapolated boundary distance; 3. The method for calculating the single-photon detection range of a target in a turbid medium according to claim 2, characterized in that: diffusion coefficient satisfy: in The absorption coefficient is... is the reduced scattering coefficient.

4. The method for calculating the single-photon detection range of a target in a turbid medium according to claim 3, characterized in that: Distance from light source satisfy: in, The horizontal distance from the light source ( , y )distance, The longitudinal distance from the light source ( )distance.

5. The method for calculating the single-photon detection range of a target in a turbid medium according to claim 4, characterized in that: Green's function of photon flux density returned by the target object itself within the turbid medium satisfy: in, The number of photons per unit volume per unit time; Green's function is the photon flux density transmitted through an infinitely large turbid medium. Represents the position of the target object; This represents the time it takes for a photon to be reflected back from the target object.

6. The method for calculating the single-photon detection range of a target in a turbid medium according to claim 5, characterized in that: Number of photons per unit volume per unit time satisfy: in, For the Green's function of the transmitted photon flux density in a semi-infinite turbid medium; For position The reflectivity of the target object; The time it takes for a photon to reach the target object; Regarding time The Dirac function, when Its integral is 1.

7. The method for calculating the single-photon detection range of a target in a turbid medium according to claim 6, characterized in that: Green's function of transmitted photon flux density in a planar infinitely large turbid medium satisfy: This refers to the photon flux density returned by the target object itself, which is hidden within the turbid medium.

8. The method for calculating the single-photon detection range of a target in a turbid medium according to claim 7, characterized in that: The photon count distribution received by the single-photon detector satisfies: in, This is the floor operator.

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