Calculation method for detection distance of target single photon in turbid medium

Abstract

The invention relates to a method for calculating the detection distance of a target single photon in a turbid medium, which relates to the field of detection and comprises the following steps of: placing a light source at a coordinate position of an original point, and unidirectionally emitting a light pulse to the turbid medium; the single-photon detector receives returned photons and divides the received photons into three parts, namely photons returned by the turbid medium, photons returned by the target object hidden in the turbid medium and noise photons; respectively calculating photon flux density Green functions of the three parts; the ratio of the photon count returned by the hidden object at the target peak moment to the background photon count is used, when the ratio is larger than 1, the hidden target object can be effectively detected, and when the ratio is larger than 3, the hidden target object can be effectively imaged; the method for calculating the detection limit of the single-photon detector in the turbid medium has the advantage that the detection limit of the single-photon detector in the turbid medium can be accurately calculated.

Description

TECHNICAL FIELD

[0001] The present application 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

[0002] In many key fields such as marine resource exploration, atmospheric target identification, and biological tissue imaging, it is of great application value to achieve active optical detection of hidden targets in turbid media (such as seawater, thick fog, biological tissue, and smoke). However, the strong scattering and absorption effects of turbid media on light pose a core challenge: incident photons undergo complex multiple scattering paths, leading to rapid diffusion of the light beam, sharp decay of energy, and severe background noise. Traditional active optical detection methods based on high-power light sources and linear detectors significantly decrease in performance in such environments, and their detection distance and signal-to-noise ratio often fail to meet actual demands.

[0003] Therefore, in view of the above problems, there is a need to provide a method for calculating the single-photon detection distance of a target in a turbid medium. SUMMARY

[0004] (I) Technical problem to be solved

[0005] The technical problem to be solved by the present application is to solve the problem that the traditional optical detection method has poor effect when detecting objects in a turbid medium.

[0006] (II) Technical solution

[0007] In order to solve the above technical problem, the present application provides a method for calculating the single-photon detection distance of a target in a turbid medium, comprising the following steps:

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

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

[0010] III. Calculate the photon flux density Green function of each part respectively;

[0011] IV. Use the ratio OBR between the photon count returned by the hidden object at the target peak time t0 and the background photon count, which is specifically:

[0012]

[0013] Wherein,

[0014] f ris the repetition frequency of the laser;

[0015] t a is the accumulation time;

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

[0017] N m is the total number of photons contained in the light pulse;

[0018] V is the minimum space voxel that the detection system can distinguish in x, y, t dimensions;

[0019] G B () is the Green function of the photon flux density returned by the target object itself hidden in the turbid medium;

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

[0021] represents taking the minimum value in the 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, and when OBR>3, the hidden target object can be effectively imaged; after confirmation of effectiveness, the maximum detection distance d D satisfies:

[0024]

[0025] wherein μ S is the reduced scattering coefficient.

[0026] As a further description of the present application, preferably, the Green function of the photon flux density G s (r, t) returned by the turbid medium itself satisfies:

[0027]

[0028] wherein,

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

[0030] t is time;

[0031] k is the diffusion coefficient;

[0032] e is the natural constant;

[0033] μ a is the absorption coefficient;

[0034] c is the speed of light;

[0035] z0is the scattering free path;

[0036] z e is the extrapolated boundary distance;

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

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

[0039]

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

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

[0042]

[0043] where p is the lateral (x, y) distance from the source and z is the longitudinal (z) distance from the source.

[0044] As a further specification of the invention, preferably the photon flux density Green function G B (r, t) hidden in the turbid medium itself returned by the target object satisfies:

[0045] G B (r, t) = ∫∫ q(r', t") G T (r - r', t - t") dt" dr'

[0046] where,

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

[0048] G T () is the photon flux density Green function of the infinite turbid medium;

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

[0050] t" represents the time of the photon reflected from the target object.

[0051] As a further specification of the invention, preferably the number of photons per unit volume per unit time q(r', t") satisfies:

[0052]

[0053] where,

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

[0055] t' is the time when the photon is irradiated to the target object;

[0056] delta(t"-t') is the Dirac function about time t", which is integrated to 1 when t"=t'.

[0057] As a further illustration of the present application, preferably, the plane infinite turbid medium transmits photon flux density Green function G T (r,t) satisfies:

[0058]

[0059] wherein q(r',t')G T (r-r',t-t') is the photon flux density returned by the target object itself hidden in the turbid medium.

[0060] As a further illustration of the present application, preferably, the photon counting distribution received by the single-photon detector satisfies:

[0061]

[0062] wherein,

[0063] is the floor operator.

[0064] (III) Beneficial effects

[0065] The above technical solutions of the present application have the following advantages:

[0066] The present application designs a calculation method, which utilizes the characteristics of the single-photon detector that can effectively capture and distinguish extremely weak target reflection echoes, so that even in strong background noise, the useful signal submerged in the noise can be extracted through precise time-dependent single-photon counting technology. Further, the detection limit of the single-photon detector in the turbid medium can be further studied, and the influencing factors and optimization strategies of the maximum effective detection distance are systematically analyzed, which 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 facing practical applications. BRIEF DESCRIPTION OF DRAWINGS

[0067] Figure 1 is the total photon counting distribution diagram of the light pulse of the present application;

[0068] Figure 2 is Figure 1 the enlarged view of the red box area in

[0069] Figure 3is a comparison chart of the photon counting distribution of the returned light of the hidden object of the present application and the photon counting distribution of the turbid medium;

[0070] Figure 4 is a chart of the relationship between the distance at which the hidden object can be effectively detected, imaged and visible to the naked eye and the reduced scattering coefficient of the present application. DETAILED DESCRIPTION

[0071] In order to make the objects, technical solutions and advantages of the embodiments of the present application clearer, the technical solutions in the embodiments of the present application will be described clearly and completely below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only a part of the embodiments of the present application, rather than all the embodiments of the present application. Based on the embodiments in the present application, all other embodiments obtained by a person of ordinary skill in the art without creative work fall within the protection scope of the present application.

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

[0073] I. A light source is placed at a coordinate position of r0=(0, 0, 0) and emits a light pulse δ(r0, t) to the turbid medium in the +z direction at time 0; at the same time, a semi-infinite turbid medium is placed in the space of z>0, i.e. at a position with a distance from the position of r0.

[0074] II. When the hidden object inside the turbid medium is irradiated with a pulsed laser, the distribution of the returned photons in the time dimension is composed of three parts: the returned photons of the turbid medium itself, the returned photons of the hidden object and noise. The photon flux density Green functions of the three parts are calculated respectively, wherein:

[0075] 1. The photon flux density distribution of the returned photons of the turbid medium itself:

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

[0077]

[0078] wherein,

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

[0080]

[0081] wherein ρ is the transverse (x, y) distance from the light source and z is the longitudinal (z) distance from the light source;

[0082] t is time;

[0083] k is the diffusion coefficient, specifically:

[0084]

[0085] where μ a is the absorption coefficient, μ S is 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 is the extrapolated boundary distance.

[0091] 2. The distribution of the returned photon flux density of the hidden object

[0092] At time t', the light source produces a photon flux density in the +z direction at the target position r' = (x', y', z) inside the turbid medium:

[0093] J + (r', t' ) = G j (r' - r0, t' )

[0094] where G j () is the Green function of the photon flux density of the semi-infinite turbid medium.

[0095] The interaction between the light and the object is simplified as a specular reflection, and the photon flux density in the -z direction produced by the interaction between the photon and the object at time t" is J - (r', t" ). Assuming that the process of the interaction between the photon and the object is instantaneous, t" = t', and then we have:

[0096] J - (r', t" ) = G j (r' - r0, t' ) R(r' ) δ(t" - t' )

[0097] where,

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

[0099] δ(t" - t' ) is the Dirac function about time t".

[0100] Assuming that J -(r',t") at position r' produces an equivalent light source q(r',t") where q(r',t") is the number of photons per unit volume per unit time, specifically:

[0101]

[0102] Since t" = t', the integral of delta(t" - t') is 1.

[0103] Then q(r',t") continues to diffuse in the turbid medium and eventually reaches the z = 0 plane, the position of the single-photon detector. At time t, the photon flux density q(r',t') G T (r - r',t - t') is produced at position r = (x,y,0) on the z = 0 plane. Here, G T () is the Green function of the transmitted photon flux density in an infinite turbid medium, specifically:

[0104]

[0105] Suppose the single-photon detector can only receive photons propagating in the -z direction, i.e., q(r',t') G T (r - r',t - t') is integrated over all positions and times to obtain:

[0106] G B (r,t) = ∫∫ q(r',t") G T (r - r',t - t") dt" dr'

[0107] 3. Noise photons

[0108] Suppose the noise is an additive noise n(r,t0) with a constant mean value per unit time, i.e., regardless of the spatial position r or the time t0, the statistical average of this noise is always the same fixed value.

[0109] III. The single-photon detector is preferably a SPAD, which is a single-photon avalanche diode, a solid-state single-photon detector based on semiconductor materials such as silicon, germanium, etc. It has small volume, low power consumption, high stability, high efficiency in capturing photons in specific wavebands (such as visible light, near-infrared), extremely short avalanche process time (nanoseconds or even picoseconds), and is suitable for high-speed photon counting.

[0110] In actual detection, suppose the time spread of the pulsed light source is less than the time resolution of the detector, which can be regarded as a pulse function, and the pulse contains N mphotons. The smallest spatio-temporal volume that the detection system can resolve in x, y, t dimensions is V, V = ΔxΔyΔt, where Δx, Δy, Δt are the smallest intervals that the detection system can resolve in x, y, t dimensions, respectively. The distribution of photons at the return detector is:

[0111] J(r, t) = V · N m 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:

[0113] Where:

[0114] f r is the laser repetition frequency (assuming the detector can respond completely, then f r is also the detector count frequency);

[0115] t a is the accumulation time;

[0116] is the floor operator

[0117] represents taking the minimum value in the range.

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

[0119]

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

[0121]

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

[0123] To verify the effectiveness of the calculation method, the following test experiments are performed:

[0124] ​Let μ S = 1 m -1 , μ a = 0.02 m -1 , the target is a flat plate with reflectivity 1 and area 1 m2, placed at the plane z = 3 m. The laser single pulse photon number N m = 1 × 10 9 , the repetition frequency f r = 1 × 10 6 Hz, the accumulation time t a = 1 s, and the incident position and detection position are both (0, 0, 0). The average number of noise photons n(r, t0) in a time interval of 64 ps is 5, and the photon counting distribution C(r, t) received by the SPAD is shown in Figs. Figure 1 , Figure 2 and Figure 3 , wherein the hidden object peak is in the red dashed box in Fig. Figure 1 .

[0125] After the above calculation formula of OBR is brought in, OBR > 3 is calculated, which means that the target can be effectively imaged.

[0126] Subsequently, the data is fitted to obtain Figure 4 , which conforms to the power-law distribution of the above maximum imaging distance d I and the maximum detection distance d D formula, and then the above formula can be obtained:

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

[0128] As shown in Fig. Figure 4 , the fitting goodness R 2 of d I and d D and μ S distribution is 0.9998 and 0.9999, respectively, indicating that the fitting result is very consistent with the data point distribution. In the formula, b I and b D are both close to -1, and μ S -1 is a scattering free path z0, that is, the average distance traveled by a photon between two scatterings in a turbid medium. Therefore, the formula also indicates that the distance at which the hidden object can be effectively detected and imaged is about 10 times and 5 times the scattering free path, respectively. In Figure 4 , the imaging distance is about 5.54 times the visibility distance.

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

[0130] Finally, it should be noted that: the above examples are only used to illustrate the technical solutions of the present application, but not to limit them; although the present application has been described in detail with reference to the foregoing examples, those skilled in the art should understand that: it can still modify the technical solutions recorded in the foregoing examples, or make equivalent replacement for part of the technical features; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the spirit and scope of the technical solutions of the embodiments of the present application.

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 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; 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 ratio of photon counts returned by the hidden object at the target peak time t0 to the background photon count, specifically: in, f r The repetition frequency of the laser; t a To accumulate time; N l The total number of photons returned to the detector; N m The total number of photons contained in a light pulse; V represents the smallest space voxel that the detection system can resolve in the x, y, t dimensions; G B () represents the Green's function, which represents the photon flux density returned by the target object itself, hidden within the turbid medium. G s () represents the Green's function of the photon flux density returned by the turbid medium itself; This indicates taking the minimum value within that range; n(r,t0) is the noise constant per unit time; 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: Where, μ s 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 G returned by the turbid medium itself s The Green's function (r,t) satisfies: in, r is the distance from the light source; t represents time; k is the diffusion coefficient; e is the natural constant; μ a The absorption coefficient; c is the speed of light; z0 is the scattering free path; z e This is the extrapolated boundary distance; ρ is the lateral (x, y) distance from the light source.

3. The method for calculating the single-photon detection range of a target in a turbid medium according to claim 2, characterized in that: The diffusion coefficient k satisfies: Where μ a μ is the absorption coefficient. S 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: The distance r from the light source satisfies: Where ρ is the horizontal (x, y) distance from the light source, and z is the vertical (z) distance from the light source.

5. The method for calculating the single-photon detection range of a target in a turbid medium according to claim 4, characterized in that: The Green's function G, representing the photon flux density returned by the target object itself within the turbid medium. B (r,t) satisfies: G B (r,t)=∫∫q(r′,t″)G T (r-r′,t-t″)dt″dr′ in, q() represents the number of photons per unit volume per unit time; G T () is the Green's function for the transmitted photon flux density in an infinitely turbid medium; r′ represents the position of the target object; t″ represents the time it takes for the 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: The number of photons q(r′,t″) per unit time per unit volume satisfies: in, R(r′) is the reflectivity of the target object at position r′; t′ is the time it takes for a photon to reach the target object; δ(t″-t′) is the Dirac function with respect to time t″, and its integral is 1 when t″=t′.

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 G of the transmitted photon flux density in a planar infinitely large turbid medium T (r,t) satisfies: q(r′,t′)G T (rr′,tt′) represents the photon flux density returned by the target object itself 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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