CN103424750A - Device and method for measuring atmospheric turbulence intensity profile by receiving laser beacon - Google Patents

Abstract

The invention discloses a method and a method for measuring an atmospheric turbulence intensity profile by receiving a laser beacon. The device comprises a flat reflecting mirror for receiving backwards scattered lights of the laser beacon and reflecting received light beams to an off-axis type receiving telescope; lights received by the receiving telescope are reflected by a triangular prism and then enter into a following light path; the following light path splits the light beams and transmits the split light beams to a photoelectric detector; the photoelectric detector images the received light beams and converts light signals into electric signals; the electric signals are subjected to acquisition and conversion of a data acquisition and processing unit, and are converted into digital signals; after the laser beacon images at different distances in the space are processed, the atmospheric turbulence intensity profile can be calculated. The advantages of the method and method for measuring the atmospheric turbulence intensity profile by receiving the laser beacon are that the measurement time is not limited, the range resolution is high, and the obtained data are more genuine and more believable as a spherical wave based calculation method is adopted and a slope matrix is constructed to reflect the atmospheric turbulence intensity.

Description

A kind of apparatus and method that receive laser beacon measurement of Atmospheric Turbulence intensity profile

Technical field

The invention belongs to the optical gauge technical field, relate to a kind of apparatus and method that receive laser beacon measurement of Atmospheric Turbulence intensity profile.

Background technology

When laser beam is transmitted in atmosphere, air index fluctuating due to being risen and fallen by atmospheric density can make the light beam of transmission therein produce the effects such as beam drift, beam spread, light intensity flicker, phase fluctuation, destroy the coherence of laser beam, have a strong impact on the propagation quality of light beam.In atmospheric optics research, atmospheric turbulence intensity C _n ²It is a basic parameter that characterizes the atmospheric turbulence characteristic.The atmospheric turbulence intensity profile measure obtained, can describe the details of turbulent flow in atmosphere subtly, thereby provide basic parameter for the Laser Atmospheric Transmission effect study.

At present, the method for measurement of Atmospheric Turbulence intensity profile has: micro-temperature sensor sounding method, microwave radar, acoustic radar and optical means (SCIDAR, MASS).Micro-temperature sensor sounding method employing sounding balloon is hung micro-temperature sensor and is carried out the sounding measurement, and this method has very high spatial resolution, and still, due to the impact of balloon wind-engaging, measuring route is uncontrolled, and in addition, the time of measuring a profile is also longer.Microwave radar passes through the back scattering power calculation atmospheric turbulence intensity of instrumentation radar signal, but the temperature and humidity on path need to be provided, more time-consuming, and humidity is on the very difficult deduction of the impact of measuring, so precision is not high yet.Acoustic radar measuring principle and microwave radar are similar, but, because sound wave is mechanical wave, can only measure atmospheric boundary layer, and, due to the restriction of acoustical power, make measuring height limited.The SCIDAR method is by the correlativity of light intensity or PHASE DISTRIBUTION on the certain area of detection, obtain the atmospheric turbulence intensity profile, but require two light sources that keep at a certain distance away as beacon, requirement to beacon is comparatively harsh, and require the telescope bore larger, generally, more than 1m, to its application, brought very large restriction.MASS is a kind of atmospheric turbulence intensity profile measurement mechanism of low resolution, can only provide the atmospheric turbulence intensity value of 6 to 7 height, and spatial resolution is low.

Summary of the invention

The problem that the present invention solves is to provide a kind of apparatus and method that receive laser beacon measurement of Atmospheric Turbulence intensity profile, can obtain in real time the atmospheric turbulence intensity profile, and it is controlled to have measuring route, the advantage that range resolution is high.

The present invention is achieved through the following technical solutions:

A kind of device that receives laser beacon measurement of Atmospheric Turbulence intensity profile, comprise the flat reflective mirror that the rear orientation light to laser beacon is received, the flat reflective mirror by the beam reflection that receives in the shaft type receiving telescope, the light that receiving telescope receives enters follow-up light path by the triangular prism reflection, follow-up light path will transfer in photodetector after the light beam light splitting, photodetector is by the light beam imaging of reception and light signal is converted to electric signal, electric signal is through data acquisition and processing unit collection, be converted to digital signal, after being processed by the laser beacon image to different distance place, space, calculate the atmospheric turbulence intensity profile.

The angle of pitch of described flat reflective mirror can be according to optical path adjusting, the rear orientation light that can receive along different paths, the different distance place focuses on formation Rayleigh laser beacon aloft.

Described receiving telescope comprises ellipsoid concave mirror, convex mirror and catoptron, the beam reflection that the ellipsoid concave mirror will be reflected by the flat reflective mirror is to convex mirror, convex mirror by beam reflection to catoptron, catoptron by beam reflection to triangular prism, triangular prism by beam reflection in follow-up light path.

Described receiving telescope is the receiving telescope system formed from the shaft type receiving telescope by two covers or the symmetry more than two covers; The light beam that every cover receives from the shaft type receiving telescope is after follow-up light path, and its laser beacon received all forms light spot image on each comfortable photodetector.

Described follow-up light path comprises the first convex lens group, optical filter, wedge and the second convex lens group, the light beam entered in follow-up light path is collimated by the first convex lens group, by optical filter filtering light beam parasitic light, through wedge, light beam is divided into to two bundles, finally by the second convex lens group, light beam is converged in photodetector.

Compared with prior art, the present invention has following useful technique effect:

The device of reception laser beacon measurement of Atmospheric Turbulence intensity profile provided by the invention, Rayleigh laser beacon for aerial formation, by the rear orientation light of two covers (or many covers) from the shaft type receiving telescope to a distance laser beacon, received, by the light beam splitting received, form two hot spot (or many hot spots) images by follow-up light path on detector.The fluctuating of two facula mass center spacings of statistics calculates the difference arrival angle fluctuation variance of this distance.Receive successively again the laser beacon rear orientation light at other different distance places, photodetector is become to two hot spot (or many hot spots) images, the fluctuating of two facula mass center spacings of statistics is also calculated the difference arrival angle fluctuation variance of these distances, finally by certain inversion algorithm, calculates the atmospheric turbulence intensity profile.The device of this reception laser beacon measurement of Atmospheric Turbulence intensity profile not only can obtain the atmospheric turbulence intensity profile in real time, and it is controlled to have measuring route, the advantage that range resolution is high.

The device of reception laser beacon measurement of Atmospheric Turbulence intensity profile provided by the invention, used two (or a plurality of) small-sized from shaft type telescope formation differential received system.Make whole device more portable and smart, reduced cost.Two of whiles are small-sized from shaft type telescope and transmitter-telescope formation coaxial system, are conducive to the adjusting of light path.

The elevation angle of receiving beam is controlled in the pitching that existing beam control system is directly controlled receiving telescope, makes beam control system too huge.And the present invention uses the flat reflective mirror to control the sensing of light beam, simplified control system.

The device of reception laser beacon measurement of Atmospheric Turbulence intensity profile provided by the invention, Measuring Time is unrestricted, and measuring route is adjustable flexibly, and range resolution is high, can to the atmospheric turbulence intensity profile of desired path, be measured at any time; The computing method of employing based on spherical wave, and structure slope inverse matrix atmospheric turbulence intensity profile, algorithm is stable, and the data that obtain are more genuine and believable.

The accompanying drawing explanation

Fig. 1 is for receiving the structural representation of laser beacon measurement of Atmospheric Turbulence intensity profile device;

The schematic diagram of the type of focusing that Fig. 2 is laser beacon;

Wherein: 1 is optical table; 2 is the flat reflective mirror; 3 is receiving telescope, and 31 is the ellipsoid concave mirror, and 32 is convex mirror, and 33 is catoptron; 4 is triangular prism; 5 is follow-up light path, and 51 is the first convex lens group, and 52 is optical filter, and 53 is wedge, and 54 is the second convex lens group; 6 is that photodetector, 7 is data acquisition and processing unit.

Embodiment

Below in conjunction with specific embodiment, the present invention is described in further detail, and the explanation of the invention is not limited.

Referring to Fig. 1, a kind of device that receives laser beacon measurement of Atmospheric Turbulence intensity profile, the rear orientation light that comprises 2 pairs of laser beacons of flat reflective mirror is received and is reflexed in shaft type receiving telescope 3, the light that receiving telescope 3 receives enters follow-up light path 5 by triangular prism 4 reflections, follow-up light path 5 will transfer to after the light beam light splitting in photodetector 6, photodetector 6 is by the light beam imaging of reception and light signal is converted to electric signal, electric signal gathers through data acquisition and processing unit 7, be converted to digital signal, after being processed by the laser beacon image to different distance place, space, calculate the atmospheric turbulence intensity profile.

During 2 pairs of Rayleigh laser beacon rear orientation lights that form in a distance, space of flat reflective mirror are received and are reflexed to receiving telescope 3.Described receiving telescope 3 comprises ellipsoid concave mirror 31, convex mirror 32 and catoptron 33, the beam reflection that ellipsoid concave mirror 31 will be reflected by flat reflective mirror 2 is to convex mirror 32, convex mirror 32 by beam reflection to catoptron 33, catoptron 33 by beam reflection to triangular prism 4, triangular prism 4 by beam reflection in follow-up light path 5.Follow-up light path 5 comprises the first convex lens group 51, optical filter 52, wedge 53 and the second convex lens group 54, the light beam entered in follow-up light path 5 is collimated by the first convex lens group 51, by optical filter 52 filtering light beam parasitic lights, through wedge 53, light beam is divided into to two bundles, finally by the second convex lens group 54, light beam is converged in photodetector 6, described photodetector 6 is image intensifying type CD camera or electron multiplication CCD camera.

Further, described receiving telescope 3 is the receiving telescope system formed from the shaft type receiving telescope by two covers or the symmetry more than two covers; The light beam that every cover receives from the shaft type receiving telescope is after follow-up light path 5, and its laser beacon received all forms light spot image on each comfortable photodetector 6.

The laser beacon received such as the receiving telescope system 3 formed from the shaft type receiving telescope by two cover symmetries forms two light spot images on photodetector 6.Except the receiving telescope system formed from the shaft type receiving telescope by two cover symmetries, can be also three covers, quadruplet or the more symmetrical receiving telescope system formed from the shaft type receiving telescope; Now, the laser beacon received forms three light spot images, the more light spot image of four light spot images on photodetector 6.

When being measured, at first to first distance h ₁After the laser beacon rear orientation light at place completes the sampling of certain frame number, the while is according to the difference arrival angle fluctuation variance of first distance of light spot image calculated signals that gathers gained; Then h successively adjusts the distance ₂, h ₃, h ₄..., h _nLaser beacon rear orientation light at place is sampled, and provides distance h according to the light spot image calculated signals that gathers gained simultaneously ₂, h ₃, h ₄..., h _nDifference arrival angle fluctuation variance at place.Obtain n difference arrival angle fluctuation variance data after complete to n distance samples, these data are carried out to Inversion Calculation and can obtain the atmospheric turbulence intensity profile.

The mode that aerial laser beacon forms comprises: (1) expands focusing to the Emission Lasers Shu Jinhang of laser instrument institute, expand the parameter of focusing system and adjust the transmission direction of laser beam by adjusting, thereby along predetermined direction, at preposition, form laser beacon; (2) carry laser instrument (or other light emitting sources) on platform (such as aircraft, balloon etc.) aloft, and make laser instrument (or other light emitting sources) launch in a certain direction light beam in precalculated position, now aerial platform carries the light beam that laser instrument (or other light emitting sources) launches and can regard beacon as; (3) carry corner reflector (or other reflection units) on platform (such as aircraft, balloon etc.) aloft, and make corner reflector (or other reflection units) along certain direction, then utilize laser instrument (or other light emitting sources) irradiation corner reflector (or other reflection units), now by the light beam of corner reflector (or other reflection units) reflection, can regard beacon as.

Concrete, referring to the type of focusing that provides a kind of concrete laser beacon below Fig. 2:

The laser beam of laser instrument 12 emissions enters transmitter-telescope 14 after catoptron 13, and laser beam is emitted to flat reflective mirror 2 after being expanded by transmitter-telescope 14, and flat reflective mirror 2 focuses on beam reflection to aerial setpoint distance, forms laser beacon;

Laser instrument adopts solid Nd: the YAG laser instrument, the centre wavelength of its output is 532nm, output single pulse energy 300mJ, repetition frequency 50Hz.The laser beam laser beam of laser instrument emission is entered in transmitter-telescope by catoptron 13 emissions of two light path parallels.

Transmitter-telescope is Schmidt-Ka Sai Green formula structure, comprise secondary mirror 141 and primary mirror 142, laser beam expands and reflexes to primary mirror 142 by secondary mirror 141, then focuses on emission by primary mirror 142, primary mirror 142 focuses on the laser beam of emission after 2 reflections of flat reflective mirror, and aloft preset distance focuses on.

By the spacing between secondary mirror 141 and primary mirror 142 in the adjusting transmitter-telescope, primary mirror 142 focuses on the laser beam of emission after 2 reflections of flat reflective mirror, and aloft the different distance place focuses on, formation Rayleigh laser beacon.When measuring, can regulate transmitter-telescope major-minor mirror spacing according to sampled distance like this, make to focus at the preset distance place to form the Rayleigh laser beacon.

The angle of pitch of described flat reflective mirror can, according to optical path adjusting, make primary mirror focus on the laser beam direction transmission that edge is set after the reflection of flat reflective mirror of emission.

Below provide the measuring method that receives laser beacon measurement of Atmospheric Turbulence intensity profile, for the Rayleigh laser beacon formed at the setpoint distance place along certain path, the beacon rear orientation light is after the flat reflective mirror, be incident to from the shaft type receiving telescope, receiving telescope by beam Propagation to follow-up light path, form two light spot images by follow-up light path by transferring to detector after light beam optical filtering, beam splitting, add up the fluctuating of the two facula mass center distances of multiple image by data Collection & Processing System, calculate the difference arrival angle fluctuation variance in testing distance; Then the laser beacon of next distance is measured, successively the laser beacon at each measuring distance place carried out to above-mentioned identical operation, after obtaining difference arrival angle fluctuation variance profile data, and then utilize the data inversion of difference arrival angle fluctuation variance profile to calculate atmospheric turbulence intensity profile value.

Specifically comprise following operation:

1) receive h by two covers from the shaft type receiving telescope ₁The rear orientation light of distance laser beacon, laser beacon forms two light spot images after follow-up light path on photodetector, the N two field picture that utilizes the photodetector collection to become, calculate respectively the barycenter of two hot spots to every two field picture, establish the barycenter of two hot spots of i two field picture apart from being b _i, the focal length of receiving telescope system is f ₀, distance h ₁The difference arrival angle fluctuation variance of place's laser beacon light beam is calculated and is provided by following formula:

${\mathrm{\σ}}_{\mathrm{DIM}}^2\left(h_1\right)=\frac{\stackrel{\‾}{B_i^2}-{\stackrel{\‾}{B_i}}^2}{f_0^2}$

$\stackrel{\‾}{B_i^2}=\left(\mathrm{\Σ}{b_i}^2\right)/N$ $\stackrel{\‾}{B_i^2}={(\mathrm{\Σ}{b}_i/N)}^2---\left(1\right)$

2) then utilize two covers from shaft type receiving telescope receiving range h successively ₂, h ₃, h ₄..., h _nThe laser beacon rear orientation light at place, according to step 1) method calculate that to provide the laser beacon distance be h ₂, h ₃, h ₄..., h _nThe difference arrival angle fluctuation variance of place's light spot image;

3), for spherical wave, the relation of difference arrival angle fluctuation variance and atmospheric turbulence intensity is shown below:

${\mathrm{\σ}}_{\mathrm{DIM}}^2\left(h\right)=33.2({{0.358d}_0}^{-1/3}-{{0.242d}_s}^{-1/3}){\∫}_0^h{C}_n^2\left(h^{\′}\right){(1-h^{\′}/h)}^{5/3}{\mathrm{dh}}^{\′}---\left(2\right)$

D wherein ₀For the sub-pupil diameter of receiving telescope, d _sFor the spacing at receiving telescope two Ge Zitong centers, C _n ²(h) be the atmospheric turbulence intensity at distance h place;

Utilize C (h) to mean C _n ²(h), and the definition M (h) be:

$M\left(h\right)={\∫}_0^{h}C\left(h^{\′}\right){(1-h^{\′}/h)}^{5/3}{\mathrm{dh}}^{\′}---\left(3\right)$

Wherein M (h) and difference arrival angle fluctuation variances sigma _DIM ²Difference be only a constant factor κ,

So, utilize the difference arrival angle fluctuation variance of each measured distance to calculate and provide M (h).Finally, can obtain the atmospheric turbulence intensity profile by M (h) inverting C (h);

Owing to utilizing M (h) direct inversion C (h) can bring the unstable of numerical solution, acquired results is also insincere, so, at this, first formula (3) is out of shape, then solved again.Differentiated in formula (3) both sides, the derivative S (h) that can obtain M (h) with the pass of C (h) is:

$S\left(h\right)={\∫}_0^{h}C\left(h^{\′}\right)\left[\frac{5}{3}\frac{h^{\′}}{h^2}{(1-\frac{h^{\′}}{h})}^{2/3}\right]{\mathrm{dh}}^{\′}---\left(4\right)$

Suppose can be approximately constant at each distance segment C (h),

C(h)=C _j h _j-1<h<h _j (5)

(4) in formula, each parameter is continuous variable, and (4) formula is carried out to discretize, provides distance h _iThe discrete expression of place's M (h) slope S (h) is:

$S_i=\underset{j=1}{\overset{i}{\mathrm{\&Sigma;}}}{C}_j{\&Integral;}_{h_{j-1}}^{h_j}\left[\frac{5}{3}\frac{h^{\&prime;}}{h_i^2}{(1-\frac{h^{\&prime;}}{h_i})}^{2/3}\right]{\mathrm{dh}}^{\&prime;}---\left(6\right)$

When j≤i, the integration in above formula is:

$U_{\mathrm{ij}}={[\frac{3}{8}-(\frac{3}{8}+\frac{5}{8}\frac{h^{\&prime;}}{h_i}){(1-\frac{h^{\&prime;}}{h_i})}^{5/3}]}_{h^{\&prime;}=h_{j-1}}^{h^{\&prime;}=h_j}---\left(7\right)$

As j>during i, U _IjValue is zero, and (6) formula is expressed as:

$S_i=\underset{j=1}{\overset{i}{\mathrm{\&Sigma;}}}{U}_{\mathrm{ij}}{C}_j=\underset{j=1}{\overset{n}{\mathrm{\&Sigma;}}}{U}_{\mathrm{ij}}{C}_j---\left(8\right)$

Formula (6) is asked to its inverse matrix, can obtain:

$C_i=\frac{1}{U_{\mathrm{ii}}}(S_i-\underset{j=1}{\overset{i-1}{\mathrm{\&Sigma;}}}{U}_{\mathrm{ij}}{C}_j)---\left(9\right)$

Utilize above formula to C _iCarry out ascending order and solve, can obtain atmospheric turbulence intensity C _iThe profile value.

Said method adopts the computing method based on spherical wave, and structure slope inverse matrix atmospheric turbulence intensity, and the data that obtain are more genuine and believable.

Claims (7)

1. a device that receives laser beacon measurement of Atmospheric Turbulence intensity profile, it is characterized in that, comprise the flat reflective mirror (2) that the rear orientation light to laser beacon is received, flat reflective mirror (2) by the beam reflection that receives in shaft type receiving telescope (3), the light that receiving telescope (3) receives enters follow-up light path (5) by triangular prism (4) reflection, follow-up light path (5) will transfer to after the light beam light splitting in photodetector (6), photodetector (6) is by the light beam imaging of reception and light signal is converted to electric signal, electric signal gathers through data acquisition and processing unit (7), be converted to digital signal, by image after the laser beacon imaging to different distance place, space, processed, Inversion Calculation atmospheric turbulence intensity profile.

2. the device of reception laser beacon measurement of Atmospheric Turbulence intensity profile as claimed in claim 1, it is characterized in that, the angle of pitch of described flat reflective mirror (2) can be according to optical path adjusting, the rear orientation light that can receive along different paths, the different distance place focuses on formation Rayleigh laser beacon aloft.

3. the device of reception laser beacon measurement of Atmospheric Turbulence intensity profile as claimed in claim 1, it is characterized in that, describedly from shaft type receiving telescope (3), comprise ellipsoid concave mirror (31), convex mirror (32) and catoptron (33), the beam reflection that ellipsoid concave mirror (31) will be reflected by flat reflective mirror (2) is to convex mirror (32), convex mirror (32) by beam reflection to catoptron (33), catoptron (33) by beam reflection to triangular prism (4), triangular prism (4) by beam reflection in follow-up light path (5).

4. the device of reception laser beacon measurement of Atmospheric Turbulence intensity profile as described as claim 1 or 3, it is characterized in that, described receiving telescope (3) is the receiving telescope system formed from the shaft type receiving telescope by two covers or the symmetry more than two covers; The light beam that every cover receives from the shaft type receiving telescope is after follow-up light path (5), and its laser beacon received is the upper light spot image that forms of each comfortable photodetector (6) all.

5. the device of reception laser beacon measurement of Atmospheric Turbulence intensity profile as claimed in claim 1, it is characterized in that, described follow-up light path (5) comprises the first convex lens group (51), optical filter (52), wedge (53) and the second convex lens group (54), the light beam entered in follow-up light path (5) is collimated by the first convex lens group (51), by optical filter (52) filtering light beam parasitic light, through wedge (53), light beam is divided into to two bundles, finally by the second convex lens group (54), light beam is converged in photodetector (6).

6. the device of reception laser beacon measurement of Atmospheric Turbulence intensity profile as claimed in claim 1, is characterized in that, described photodetector (6) is image intensifying CCD camera or electron multiplication CCD camera, and sample frame speed is not less than 50fps.

7. the device of reception laser beacon measurement of Atmospheric Turbulence intensity profile as claimed in claim 1, is characterized in that, described image after the laser beacon imaging at different distance place, space is processed and comprised:

1) receive h by two covers from the shaft type receiving telescope ₁The rear orientation light of distance laser beacon, laser beacon forms two light spot images after follow-up light path on photodetector, the N two field picture that utilizes the photodetector collection to become, calculate respectively the barycenter of two hot spots to every two field picture, establish the barycenter of two hot spots of i two field picture apart from being b _i, the focal length of receiving telescope system is f ₀, distance h ₁The difference arrival angle fluctuation variance of place's laser beacon light beam is calculated and is provided by following formula:

${\mathrm{\&sigma;}}_{\mathrm{DIM}}^2\left(h_1\right)=\frac{\stackrel{\&OverBar;}{B_i^2}-{\stackrel{\&OverBar;}{B_i}}^2}{f_0^2}$

$\stackrel{\&OverBar;}{B_i^2}=\left(\mathrm{\&Sigma;}{b_i}^2\right)/N$ $\stackrel{\&OverBar;}{B_i^2}={(\mathrm{\&Sigma;}{b}_i/N)}^2---\left(1\right)$

2) then utilize two covers from shaft type receiving telescope receiving range h successively ₂, h ₃, h ₄..., h _nThe laser beacon rear orientation light at place, according to step 1) method calculate that to provide the laser beacon distance be h ₂, h ₃, h ₄..., h _nThe difference arrival angle fluctuation variance of place's light spot image;

3), for spherical wave, the relation of difference arrival angle fluctuation variance and atmospheric turbulence intensity is shown below:

${\mathrm{\&sigma;}}_{\mathrm{DIM}}^2\left(h\right)=33.2({{0.358d}_0}^{-1/3}-{{0.242d}_s}^{-1/3}){\&Integral;}_0^h{C}_n^2\left(h^{\&prime;}\right){(1-h^{\&prime;}/h)}^{5/3}{\mathrm{dh}}^{\&prime;}---\left(2\right)$

D wherein ₀For the sub-pupil diameter of receiving telescope, d _sFor the spacing at receiving telescope two Ge Zitong centers, C _n ²(h) be the atmospheric turbulence intensity at distance h place;

Utilize C (h) to mean C _n ²(h), and the definition M (h) be:

$M\left(h\right)={\&Integral;}_0^{h}C\left(h^{\&prime;}\right){(1-h^{\&prime;}/h)}^{5/3}{\mathrm{dh}}^{\&prime;}---\left(3\right)$

Wherein M (h) and difference arrival angle fluctuation variances sigma _DIM ²Difference be only a constant factor κ,

So, utilize the difference arrival angle fluctuation variance of each measured distance to calculate and provide M (h); Finally, can obtain the atmospheric turbulence intensity profile by M (h) inverting C (h);

Owing to utilizing M (h) direct inversion C (h) can bring the unstable of numerical solution, acquired results is also insincere, so, at this, first formula (3) is out of shape, then solved again; Differentiated in formula (3) both sides, the derivative S (h) that can obtain M (h) with the pass of C (h) is:

$S\left(h\right)={\&Integral;}_0^{h}C\left(h^{\&prime;}\right)\left[\frac{5}{3}\frac{h^{\&prime;}}{h^2}{(1-\frac{h^{\&prime;}}{h})}^{2/3}\right]{\mathrm{dh}}^{\&prime;}---\left(4\right)$

Suppose can be approximately constant at each distance segment C (h),

C(h)=C _j h _j-1<h<h _j (5)

(4) in formula, each parameter is continuous variable, and (4) formula is carried out to discretize, provides distance h _iThe discrete expression of place's M (h) slope S (h) is:

$S_i=\underset{j=1}{\overset{i}{\mathrm{\&Sigma;}}}{C}_j{\&Integral;}_{h_{j-1}}^{h_j}\left[\frac{5}{3}\frac{h^{\&prime;}}{h_i^2}{(1-\frac{h^{\&prime;}}{h_i})}^{2/3}\right]{\mathrm{dh}}^{\&prime;}---\left(6\right)$

When j≤i, the integration in above formula is:

$U_{\mathrm{ij}}={[\frac{3}{8}-(\frac{3}{8}+\frac{5}{8}\frac{h^{\&prime;}}{h_i}){(1-\frac{h^{\&prime;}}{h_i})}^{5/3}]}_{h^{\&prime;}=h_{j-1}}^{h^{\&prime;}=h_j}---\left(7\right)$

As j>during i, U _IjValue is zero, and (6) formula is expressed as:

$S_i=\underset{j=1}{\overset{i}{\mathrm{\&Sigma;}}}{U}_{\mathrm{ij}}{C}_j=\underset{j=1}{\overset{n}{\mathrm{\&Sigma;}}}{U}_{\mathrm{ij}}{C}_j---\left(8\right)$

Formula (6) is asked to its inverse matrix, can obtain:

$C_i=\frac{1}{U_{\mathrm{ii}}}(S_i-\underset{j=1}{\overset{i-1}{\mathrm{\&Sigma;}}}{U}_{\mathrm{ij}}{C}_j)---\left(9\right)$

Utilize above formula to C _iCarry out ascending order and solve, can obtain atmospheric turbulence intensity C _iThe profile value.

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