CN111965838B - Parameter selection method of multimode fiber laser speckle suppression scheme based on vibration mode - Google Patents

Parameter selection method of multimode fiber laser speckle suppression scheme based on vibration mode Download PDF

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CN111965838B
CN111965838B CN202010849983.1A CN202010849983A CN111965838B CN 111965838 B CN111965838 B CN 111965838B CN 202010849983 A CN202010849983 A CN 202010849983A CN 111965838 B CN111965838 B CN 111965838B
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孙剑峰
周鑫
刘迪
陆威
李思宁
王骐
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Harbin Institute of Technology
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Abstract

The invention relates to a parameter selection method of a multimode fiber laser speckle suppression scheme based on a vibration mode. The method comprises the following steps: based on the multimode fiber coupling theory, under the condition that the mode coupling of a vibration area is far greater than that of a non-vibration area, an output power model of each transmission mode is obtained, and the model shows that the coupling power of each mode is in direct proportion to the square of the vibration amplitude and cosine change is carried out around stable power at the frequency of 2 omega; based on a multimode fiber vibration output power statistical model, a Gm-APD trigger probability model is obtained, and a multi-frame statistical Gm-APD detection model of multimode fiber coupling emission is established based on a multimode fiber mode coupling theory, the Gm-APD trigger probability model and the multimode fiber output power statistical model. The invention provides a theoretical method for parameter selection for inhibiting the influence of speckles generated by multimode fibers on an imaging result, and the model building thought can also be used for other linear detectors.

Description

Parameter selection method of multimode fiber laser speckle suppression scheme based on vibration mode
Technical Field
The invention relates to a parameter selection method of a multimode fiber laser speckle suppression scheme based on a vibration mode, and belongs to the technical field of laser imaging radar systems.
Background
The laser transmitted by the optical fiber coupling is used for long-distance flash type area array imaging and has two obvious advantages, firstly, the transmission by adopting the optical fiber coupling mode is favorable for optimizing the overall layout of a laser radar system and the miniaturization and diversification of the system layout, for example, for the transmission system adopting the space coupling mode, the position relation between a transmitting lens and the laser is relatively fixed, and the arrangement mode of the laser is more free and the overall layout of the structure is more favorable by adopting the optical fiber coupling mode; secondly, for the scheme of realizing larger field detection through the two-dimensional follow-up mechanism, the laser can be arranged outside the two-dimensional follow-up mechanism, so that the optimization of the two-dimensional follow-up structure design is facilitated, and the index requirements of key devices of the two-dimensional follow-up mechanism, such as a follow-up motor, are reduced.
However, laser passes through the multimode fiber to generate serious laser speckle, which affects the quality of echo images and reduces the detection performance of the laser radar, so that it is necessary to suppress the speckle. The speckle suppression method for multimode fiber is many, for example, vibrating multimode fiber, using micro-scanning mirror, space and angle dispersion irradiation, rotating diffraction optical element, rotating fiber light pipe, etc. All methods achieve good speckle suppression, but most require the insertion of necessary optical elements in the lasing path, which is challenging for compact, high quality optics and structural design. The adoption of the micro-vibration motor to externally vibrate the multimode optical fiber is a simple, convenient and effective speckle suppression method. A multimode fiber speckle suppression scheme based on an oscillating fiber scheme was proposed since the beginning of multimode fiber applications, and a mode coupling-based speckle suppression theory was proposed in 1992, but has not been used in engineering guidance for laser image speckle suppression parameter selection based on an area geiger mode avalanche photodiode (Gm-APD). In order to effectively guide the selection of vibration parameters and related system parameters in practical engineering, the multimode fiber laser speckle suppression model based on a vibration mode is provided by combining a Gm-APD detection model under the condition of reasonably assuming a speckle suppression theory, and a parameter selection method is provided for a laser speckle suppression scheme based on area array Gm-APD detection.
Disclosure of Invention
The invention aims to provide a parameter selection method of a multimode fiber laser speckle suppression scheme based on a vibration mode, so as to solve the problems of the conventional multimode fiber speckle suppression method.
A parameter selection method of a multimode fiber laser speckle suppression scheme based on a vibration mode comprises the following steps:
based on a multimode fiber coupling theory, under the condition that the mode coupling of a vibration area is far larger than the mode coupling of a non-vibration area, obtaining an output power model of each transmission mode, wherein the model shows that the coupling power of each mode is in direct proportion to the square of vibration amplitude, and cosine change is carried out around stable power at the frequency of 2 omega;
secondly, obtaining a Gm-APD triggering probability model based on a statistical model of multimode fiber vibration output power;
and step three, establishing a multi-frame statistic Gm-APD detection model of multimode fiber coupling emission based on a multimode fiber mode coupling theory, a Gm-APD trigger probability model and a multimode fiber output power statistic model.
Further, in step one, assuming that the phase change of each transmission mode is consistent when the fiber is deformed, the redistribution of speckle will be mainly caused by mode coupling, and the power change of the q-th transmission mode can be expressed as,
Figure BDA0002644388870000021
in the formula, hqkIs the coupling coefficient between mode q and mode k, PqIs the initial power of mode q, PkIs the initial power of mode k, Q is the total number of transmission modes in the multimode fiber,
when the multimode fiber is bent, speckle varies with the coupling coefficient, which can be expressed as the coupling coefficient between mode q and mode k,
Figure BDA0002644388870000022
in the formula KqkIs a constant, beta, determined by the structure of the fiberqAnd betakThe transmission constants for mode q and mode k respectively,
the deformation of the multimode optical fiber during vibration is expressed by a sine function along with the time,
V(t)＝V0sin(ωt) (3)
in the formula, V0Is the vibration amplitude, ω is the vibration frequency, t is the time,
the deformation function in the vibration area-L/2 can be expressed by cosine function by taking the vibration center as a zero point,
f(z)＝Vcos(πz/L),-L/2≤z≤L/2 (4)
mode coupling occurs due to bending of the optical fiber in the non-vibration region, and thus
Figure BDA0002644388870000031
F (beta) if the mode coupling in the vibration region is much larger than that in the non-vibration regionq-βk) It can be simplified to that,
Figure BDA0002644388870000032
the formula is substituted into the formula (2) to obtain the product,
Figure BDA0002644388870000033
the power fluctuation of the pattern q is represented as,
Figure BDA0002644388870000034
in the formula of gamma1Is constant, equation (8) indicates that the coupled power of mode q is proportional to the square of the vibration amplitude and varies in cosine around a stable power at a frequency of 2 ω, and thus, the power of mode q can be expressed as,
Figure BDA0002644388870000036
in the formula Pq_vIs the average power of the q-mode during the vibration process.
Furthermore, in the second step, the fluctuation of the corresponding transmitting power of any pixel of the area array detection laser radar is determined by the surrounding pixels, if the speckle is larger than the field of view of a single pixel, the pixel is not only the pixel adjacent to the current pixel,
when the refractive index step multimode fiber is vibrated rapidly, the emission power density equation corresponding to a single pixel detected by an area array is expressed as,
Figure BDA0002644388870000035
in the formula, Ps/<Ps>Is the normalized power for a single pixel,<Ps>is the average power corresponding to a single pixel, M' is the degree of freedom of the speckle pattern of the entire spot, r (-) is the gamma equation, assuming that after effective speckle suppression, the spots are uniformly distributed, then<Ps>＝<P>H, H is the total number of the pixels of the detector,
suppose PsThe transmission power corresponding to a single pixel during a vibration period is expressed as,
Figure BDA0002644388870000044
in the formula Ps1The corresponding single-pixel laser emission power when the optical fiber is not vibrated can be obtained by the formula (10), gamma1≠γ2，γ1Corresponding to a certain transmission mode, gamma2Corresponding to a single pixel, gamma1And gamma2The relationship is approximately in a linear direct proportion,
assuming that the bending state of the optical fiber is not changed when the laser light passes through the vibration region of the multimode optical fiber, a single pulse power time-varying expression can be obtained according to the formula (11),
Figure BDA0002644388870000045
wherein h (t) is a laser pulse waveform, f is a laser pulse frequency, 2 ω Δ t0I is the ordinal number of the emitted light,
for an extended lambertian target, the echo power may be expressed as.
Figure BDA0002644388870000041
In the formula z0Is the target distance, c is the speed of light, ρ is the target reflectivity, T is the atmospheric one-way transmittance, D is the receiving optical system aperture, θ is the laser incidence angle,
the triggering probability of the Gm-APD obeys the Poisson probability distribution, the Gm-APD divides the gate into intervals of equal time length, the triggering probability at each time interval is expressed as,
Figure BDA0002644388870000042
in the formula, N0J is the total time interval in the gate, TrIs the transmittance, eta, of the receiving optical systemGIs the quantum efficiency of the detector, NhAs indicated by the general representation of the,
Figure BDA0002644388870000043
n number of noise photons per time interval, shIs at the echo position j1To j2The number of echo photons of (a) is,
neglecting the influence of speckle caused by the target on the Gm-APD, according to the formula (10) and the formula (12), the triggering probability of the Gm-APD caused by vibrating the optical fiber is,
Figure BDA0002644388870000051
in the formula, ppoissonIs Poisson probability, NsPhotoelectrons generated for laser signals, NnPhotoelectrons generated for noise signals, p (N)s) Is the probability density equation of laser echo photoelectrons obtained according to the formula (10),<Ns>is the average photoelectron produced by the laser echo.
Further, in step three, the probability of failing to trigger the Gm-APD can be expressed as,
Figure BDA0002644388870000052
the trigger probability is expressed as 1-pelec(0) Therefore, the formula (14) can be improved,
Figure BDA0002644388870000053
in the formula, n0＝0,nh＝n(h>0)；sh|iIs the number of laser echo photons detected at the ith time, where sh|i＝0(h<j1Or h>j2) At j, in1～j2The number of echo photons of the range can be measured by Ps_r(t | i) is calculated to be,
the trigger probability over the Gm-APD integration time can be considered as the average trigger probability over multiple detections, expressed as,
Figure BDA0002644388870000054
in the formula, TEXFor integration time, TDIn order to repeat the cycle for the laser light,
and (3) analyzing the triggering probability errors among all pixel points on the image according to a formula (19), and selecting the optimal system parameters by taking the minimum triggering probability error among all the pixel points as a target.
The main advantages of the invention are: the invention designs a parameter selection method of a multimode fiber laser speckle suppression scheme based on a vibration mode, and an established model clearly describes the relationship between the echo detection probability of an area array Gm-APD laser radar transmitted by multimode fiber coupling and parameters such as vibration motor amplitude, frequency, detector integration time, laser repetition period and the like, and provides a theoretical method for parameter selection for suppressing the influence of speckles generated by multimode fiber on an imaging result. Meanwhile, the model thought established by the method can also be used for other linear detectors, such as an ICCD detector, and the detection model of the corresponding detector replaces the Poisson trigger model of the formula (16) to obtain the final corresponding detection model.
Drawings
FIG. 1 is a schematic view of multimode fiber vibration;
FIG. 2 is a schematic diagram illustrating the effect of vibration amplitude on speckle suppression, wherein R isERepresenting relative error of initial intensity;
fig. 3 is a schematic diagram illustrating the effect of vibration frequency on speckle suppression.
Detailed Description
The technical solutions in the embodiments of the present invention will be described clearly and completely with reference to the accompanying drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
A parameter selection method of a multimode fiber laser speckle suppression scheme based on a vibration mode comprises the following steps:
based on a multimode fiber coupling theory, under the condition that the mode coupling of a vibration area is far larger than the mode coupling of a non-vibration area, obtaining an output power model of each transmission mode, wherein the model shows that the coupling power of each mode is in direct proportion to the square of vibration amplitude, and cosine change is carried out around stable power at the frequency of 2 omega;
secondly, obtaining a Gm-APD triggering probability model based on a statistical model of multimode fiber vibration output power;
and step three, establishing a multi-frame statistic Gm-APD detection model of multimode fiber coupling emission based on a multimode fiber mode coupling theory, a Gm-APD trigger probability model and a multimode fiber output power statistic model.
In step one, specifically, when the multimode fiber is disturbed, the energy of each transmission mode is disturbed due to mode coupling and phase modulation of each order guided mode, which causes energy redistribution and speckle mode change. Assuming that the phase changes of the transmission modes are identical when the fiber is deformed, and the redistribution of speckle will be mainly caused by mode coupling, the power change of the q-th transmission mode can be expressed as,
Figure BDA0002644388870000061
in the formula, hqkIs the coupling coefficient between mode q and mode k, PqIs the initial power of mode q, PkIs the initial power of mode k, Q is the total number of transmission modes in the multimode fiber,
when the multimode fiber is bent, speckle varies with the coupling coefficient, which can be expressed as the coupling coefficient between mode q and mode k,
Figure BDA0002644388870000071
in the formula KqkIs a constant, beta, determined by the structure of the fiberqAnd betakThe transmission constants of mode q and mode k, respectively, have been studied to show that mode coupling hardly occurs in non-adjacent modes, i.e. the coupling coefficient between non-adjacent modes can be approximated to 0.
FIG. 1 is a schematic diagram of multimode fiber vibration. The deformation of the multimode optical fiber during vibration is expressed by a sine function along with the time,
V(t)＝V0sin(ωt) (3)
in the formula, V0Is the vibration amplitude, ω is the vibration frequency, t is the time,
the deformation function in the vibration area-L/2 can be expressed by cosine function by taking the vibration center as a zero point,
f(z)＝Vcos(πz/L),-L/2≤z≤L/2 (4)
mode coupling occurs due to bending of the optical fiber in the non-vibration region, and thus
Figure BDA0002644388870000072
Since the deformation of the non-vibration region is constant, the first term and the third term on the right of the equal sign of equation (5) are constants. F (beta) if the mode coupling in the vibration region is much larger than that in the non-vibration regionq-βk) It can be simplified to that,
Figure BDA0002644388870000073
the formula is substituted into the formula (2) to obtain the product,
Figure BDA0002644388870000074
the power fluctuation of the pattern q is represented as,
Figure BDA0002644388870000081
in the formula of gamma1Is constant, equation (8) indicates that the coupled power of mode q is proportional to the square of the vibration amplitude and varies in cosine around a stable power at a frequency of 2 ω, and thus, the power of mode q can be expressed as,
Figure BDA0002644388870000083
in the formula Pq_vIs the average power of the q-mode during the vibration process.
In step two, considering that mode coupling occurs between adjacent modes, the redistribution of power at any point in the beam during fiber vibration can be considered to be the result of mode coupling of points with each other at frequency 2 ω in a very small spot cell. Therefore, the fluctuation of the corresponding transmitting power of any pixel of the area array detection laser radar is determined by surrounding pixels, if the speckle is larger than the visual field of a single pixel, the pixel is not only the pixel adjacent to the current pixel,
when the refractive index step multimode fiber is vibrated rapidly, the emission power density equation corresponding to a single pixel detected by an area array is expressed as,
Figure BDA0002644388870000082
in the formula, Ps/<Ps>Is the normalized power for a single pixel,<Ps>is the average power corresponding to a single pixel, M' is the degree of freedom of the speckle pattern of the entire spot, r (-) is the gamma equation, assuming that after effective speckle suppression, the spots are uniformly distributed, then<Ps>＝<P>H, H is the total number of the pixels of the detector,
considering that equation (10) is an average result for a sufficiently long time, the observation time is much longer than the fiber vibration period. Suppose PsThe transmission power corresponding to a single pixel during a vibration period is expressed as,
Figure BDA0002644388870000084
in the formula Ps1The corresponding single-pixel laser emission power when the optical fiber is not vibrated can be obtained by the formula (10), gamma1≠γ2，γ1Corresponding to a certain transmission mode, gamma2Corresponding to a single pixel, gamma1And gamma2The relationship is approximately in a linear direct proportion,
assuming that the bending state of the optical fiber is not changed when the laser light passes through the vibration region of the multimode optical fiber, a single pulse power time-varying expression can be obtained according to the formula (11),
Figure BDA0002644388870000095
wherein h (t) is a laser pulse waveform, f is a laser pulse frequency, 2 ω Δ t0Is the first pulse when it passes through the vibration regionThe phase of the initial oscillation, i is the ordinal number of the emitted light,
for an extended lambertian target, the echo power may be expressed as.
Figure BDA0002644388870000091
In the formula z0Is the target distance, c is the speed of light, ρ is the target reflectivity, T is the atmospheric one-way transmittance, D is the receiving optical system aperture, θ is the laser incidence angle,
the triggering probability of the Gm-APD obeys the Poisson probability distribution, the Gm-APD divides the gate into intervals of equal time length, the triggering probability at each time interval is expressed as,
Figure BDA0002644388870000092
in the formula, N0J is the total time interval in the gate, TrIs the transmittance, eta, of the receiving optical systemGIs the quantum efficiency of the detector, NhAs indicated by the general representation of the,
Figure BDA0002644388870000093
n number of noise photons per time interval, shIs at the echo position j1To j2The number of echo photons of (a) is,
neglecting the influence of speckle caused by the target on the Gm-APD, according to the formula (10) and the formula (12), the triggering probability of the Gm-APD caused by vibrating the optical fiber is,
Figure BDA0002644388870000094
in the formula, ppoissonIs Poisson probability, NsPhotoelectrons generated for laser signals, NnPhotoelectrons generated for noise signals, p (N)s) Is obtained according to the formula (10)The probability density equation of the laser echo photoelectrons of (1),<Ns>is the average photoelectron produced by the laser echo.
In step three, the probability of failing to trigger a Gm-APD can be expressed as,
Figure BDA0002644388870000101
the trigger probability is expressed as 1-pelec(0) Therefore, the formula (14) can be improved,
Figure BDA0002644388870000102
in the formula, n0＝0,nh＝n(h>0)；sh|iIs the number of laser echo photons detected at the ith time, where sh|i＝0(h<j1Or h>j2) At j, in1～j2The number of echo photons of the range can be measured by Ps_r(t | i) is calculated to be,
the trigger probability over the Gm-APD integration time can be considered as the average trigger probability over multiple detections, expressed as,
Figure BDA0002644388870000103
in the formula, TEXFor integration time, TDIn order to repeat the cycle for the laser light,
and (3) analyzing the triggering probability errors among all pixel points on the image according to a formula (19), and selecting the optimal system parameters by taking the minimum triggering probability error among all the pixel points as a target.
One embodiment of the present invention is set forth below:
and theoretically analyzing the speckle suppression result of the adjacent pixels. The following parameters were set: wavelength 1064nm, L0.015M, R500M, target reflectance 0.3, M' 2000, θ 0 °, laser single pulse energy 5 μ J, and atmospheric transmittance 0.92km-1，D＝40mm，Tr＝0.9，ηGThe target gate width is 150m, the number of noise photons in the gate is 0.1, the target is located at 30m in the gate, the resolution of the Gm-APD is 64 multiplied by 64, the timing time interval of the Gm-APD is 1ns, the waveform of the echo pulse is Gaussian and the pulse width is 2.5 ns.
FIG. 2 shows the frequency at which the vibration frequency is 300Hz and the repetition frequency of the laser is 20kHz, TEXUnder the condition of 40ms, the triggering probability of adjacent pixel points under different vibration amplitudes is changed relatively to the error. As the amplitude increases, the relative error first falls to a minimum and then rises to a maximum, and when the maximum is reached, the error begins to fall again to a value near a steady and relatively high value. The minimum error corresponds to the optimal speckle suppression effect, and the optimal vibration amplitude is 9 mm. And the smaller the initial error, the better the suppression effect. Table 1 shows the optimal speckle suppression error result corresponding to the vibration amplitude of 9 mm. The initial errors of 0.1, 0.2, 0.3 and 0.4 can be respectively improved by 10.6 times, 10.3 times, 9.9 times and 9.5 times.
Figure BDA0002644388870000111
Table 1 optimal speckle suppression results
FIG. 3 shows the vibration amplitude at 9mm, RE＝0.3,TEXUnder the condition of 40ms, the vibration frequency and the laser repetition frequency are used for speckle suppression, and when the vibration frequency is higher than 215Hz, the relative error tends to be stable and the laser repetition frequency does not influence the speckle suppression result.
The method is used for speckle image suppression optimal parameter selection and engineering guidance based on multimode fiber laser. The method is particularly used for theoretically guiding selection of parameters such as vibration amplitude, imaging frame frequency, exposure time and the like of the optical fiber in the process of carrying out laser image speckle suppression on the vibration multimode optical fiber. The method can be used for determining the indexes of the area array laser imaging radar transmitted by the high-pulse-energy optical fiber in a coupling mode and designing a system scheme, and can also be used for the theoretical research of detection characteristics.

Claims (4)

1. A parameter selection method of a multimode fiber laser speckle suppression scheme based on a vibration mode is characterized by comprising the following steps:
based on a multimode fiber coupling theory, under the condition that the mode coupling of a vibration area is far larger than the mode coupling of a non-vibration area, obtaining an output power model of each transmission mode, wherein the model shows that the coupling power of each mode is in direct proportion to the square of vibration amplitude, and cosine change is carried out around stable power at the frequency of 2 omega;
step two, obtaining a statistical model of the multimode fiber vibration output power by using the output power model of each transmission mode in the step one, and obtaining a Gm-APD triggering probability model by using the statistical model of the multimode fiber vibration output power;
thirdly, establishing a multi-frame statistic Gm-APD detection model of multimode fiber coupling emission based on a multimode fiber mode coupling theory, the Gm-APD triggering probability model and the statistic model of multimode fiber output power,
the multi-frame statistic Gm-APD detection model describes the relation between the echo detection probability of the area array Gm-APD laser radar transmitted by multimode fiber coupling and the amplitude, frequency, detector integration time and laser repetition period parameters of the vibration motor.
2. The method according to claim 1, wherein in step one, specifically, assuming that the phase change of each transmission mode is consistent when the fiber is deformed, the redistribution of speckles will be mainly caused by mode coupling, and the power change of the mode q is expressed as,
Figure FDA0003514145050000011
in the formula, hqkIs the coupling coefficient between mode q and mode k, PqIs the initial power of mode q, PkIs the initial power of mode k, Q is the total number of transmission modes in the multimode fiber,
when the multimode fiber is bent, speckle varies with the coupling coefficient, which is expressed as the coupling coefficient between mode q and mode k,
Figure FDA0003514145050000012
in the formula KqkIs a constant, beta, determined by the structure of the fiberqAnd betakThe transmission constants for mode q and mode k respectively,
the deformation of the multimode optical fiber during vibration is expressed by a sine function along with the time,
V(t)＝V0sin(ωt) (3)
in the formula, V0Is the vibration amplitude, ω is the vibration frequency, t is the time,
the deformation function in the vibration area-L/2 is expressed by cosine function with the vibration center as zero point,
f(z)＝Vcos(πz/L),-L/2≤z≤L/2 (4)
mode coupling occurs due to bending of the optical fiber in the non-vibration region, and thus
Figure FDA0003514145050000021
F (beta) if the mode coupling in the vibration region is much larger than that in the non-vibration regionq-βk) In a simplified manner, the process is carried out,
Figure FDA0003514145050000022
the formula is substituted into the formula (2) to obtain,
Figure FDA0003514145050000023
the power fluctuation of the pattern q is represented as,
Figure FDA0003514145050000024
in the formula of gamma1Is constant, equation (8) indicates that the coupled power of mode q is proportional to the square of the vibration amplitude and varies in cosine around a stable power at a frequency of 2 ω, and thus, the power of mode q is expressed as,
Figure FDA0003514145050000025
in the formula Pq_vIs the average power of the q-mode during the vibration process.
3. The method according to claim 1, wherein in step two, the fluctuation of the corresponding transmitting power of any pixel of the area array detection lidar is determined by surrounding pixels, and if the speckle is larger than the single-pixel field of view, the pixel is not only a pixel adjacent to the current pixel,
when the refractive index step multimode fiber is vibrated rapidly, the emission power density equation corresponding to a single pixel detected by an area array is expressed as,
Figure FDA0003514145050000026
in the formula, Ps/<Ps>Is the normalized power for a single pixel,<Ps>is the average power corresponding to a single pixel, M' is the degree of freedom of the speckle pattern of the entire spot, r (-) is the gamma equation, assuming that after effective speckle suppression, the spots are uniformly distributed, then<Ps>＝<P>H, H is the total number of the pixels of the detector,
suppose PsDoes not change during one vibration period, according to formula (9), during one vibration periodAnd, the transmission power corresponding to a single pixel is expressed as,
Ps_c(t)＝Ps1+γ2V0 2-γ2V0 2cos(2ωt)＝Ps-γ2V0 2cos(2ωt) (11)
in the formula Ps1Is the corresponding single-pixel laser emission power when the optical fiber is not vibrated, is obtained by the formula (10)1≠γ2，γ1Corresponding to transmission mode, gamma2Corresponding to a single pixel, gamma1And gamma2The relationship is approximately in a linear direct proportion,
assuming that the bending state of the optical fiber is not changed when the laser light passes through the vibration region of the multimode optical fiber, a single pulse power time-varying expression is obtained according to the formula (11),
Figure FDA0003514145050000031
wherein h (t) is a laser pulse waveform, f is a laser pulse frequency, 2 ω Δ t0I is the ordinal number of the emitted light,
for an extended lambertian target, the echo power is expressed as,
Figure FDA0003514145050000032
in the formula z0Is a target distance, c is a speed of light, ρ is a target reflectance, T is an atmospheric one-way transmittance, D is a receiving optical system aperture, θ is a laser incident angle, R is a target distance,
the triggering probability of the Gm-APD obeys the Poisson probability distribution, the Gm-APD divides the gate into intervals of equal time length, the triggering probability at each time interval is expressed as,
Figure FDA0003514145050000033
in the formula, N0J is the total time interval in the gate, TrIs the transmittance, eta, of the receiving optical systemGIs the quantum efficiency of the detector, NhAs indicated by the general representation of the,
Figure FDA0003514145050000041
n number of noise photons per time interval, shIs at the echo position j1To j2The number of echo photons of (a) is,
neglecting the influence of speckle caused by the target on the Gm-APD, according to the formula (10) and the formula (12), the triggering probability of the Gm-APD caused by vibrating the optical fiber is,
Figure FDA0003514145050000042
in the formula, ppoissonIs Poisson probability, NsPhotoelectrons generated for laser signals, NnPhotoelectrons generated for noise signals, p (N)s) Is the probability density equation of laser echo photoelectrons obtained according to the formula (10),<Ns>is the average photoelectron produced by the laser echo.
4. The method for selecting parameters of the multimode fiber laser speckle suppression scheme based on the vibration mode as claimed in claim 1, wherein in step three, the probability that Gm-APD can not be triggered is expressed as,
Figure FDA0003514145050000043
the trigger probability is expressed as 1-pelec(0) Therefore, the formula (14) is improved to,
Figure FDA0003514145050000044
in the formula, n0＝0,nh＝n(h>0)；sh|iIs the number of laser echo photons detected at the ith time interval of the h interval, where sh|i＝0(h<j1Or h>j2) At j, in1～j2Number of echo photons of range Ps_r(t | i) is calculated to be,
the trigger probability over the Gm-APD integration time, taken as the average trigger probability over multiple detections, is expressed as,
Figure FDA0003514145050000045
in the formula, TEXFor integration time, TDIn order to repeat the cycle for the laser light,
and (3) analyzing the triggering probability errors among all pixel points on the image according to a formula (19), and selecting the optimal system parameters by taking the minimum triggering probability error among all the pixel points as a target.
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