CN104007088A - Method for measuring geometrical factors of backscattering laser radar - Google Patents
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Abstract
The invention discloses a method for measuring geometrical factors of a backscattering laser radar. According to the method, after an aerosol backscattering coefficient is measured by using a CCD camera, the aerosol backscattering coefficient is substituted into a backscattering laser radar equation (please see the equation in the specification), in the equation, P(z) is an atmospheric backscattering echo signal at the position of a laser radar receiving distance z, C is an energy-containing constant of a laser radar system, eta(z) is a geometrical factor, beta1(z) and beta2(z) are the aerosol backscattering coefficient and an atmospheric molecule backscattering coefficient at the position of the distance z respectively, alpha1(z) and alpha2(z) are an aerosol extinction coefficient and an atmospheric molecule extinction coefficient of the distance z, and dz is height resolution; the geometrical factors of the backscattering laser radar are obtained through an iteration method. The measured geometrical factors are extremely high in accuracy and easy to measure, the measured geometrical factors are used for correcting signals of the backscattering laser radar, and therefore atmospheric parameter and pollutant concentration detection accuracy in a transition area is greatly improved; the method can be widely applied to detection of atmospheric pollutants of a short distance section through the backscattering laser radar.
Description
Technical field
The present invention relates to a kind of measuring method of laser radar geometric factor, especially a kind of measuring method of back scattering laser radar geometric factor.
Background technology
Back scattering laser radar is a kind of powerful of pollutant in atmospheric sounding parameter, atmosphere, but because its emitter and receiving trap are at same position, and having caused has the existence of blind area and zone of transition in section closely.So-called blind area is exactly the region that Airborne Lidar does not detect utilizing emitted light bundle backscatter signal; So-called zone of transition is exactly the region that Airborne Lidar measures part transmitting light beam backscatter signal.Conventional geometric factor η describes the integrated degree that detects transmitting light beam backscatter signal, η=0 is called blind area, 0 < η < 1 is called zone of transition, and η=1 is complete reception area, is exactly complete reception area after zone of transition.Geometric factor is the function of laser radar system device hardware location, laser beam emission angle and opening of the telescope, and is not easy by Measurement accuracy.The zone of transition distal-most end distance of general laser radar is about 800 meters of left and right, and this has just limited back scattering laser radar in the closely application of occasion, and the detection of the section atmosphere pollution scope of environmental protection and the special concern of institute of meteorological department just closely.
The method of existing measurement back scattering laser radar geometric factor is to select gasoloid level equally distributed night, allows laser radar work in the horizontal direction, measures the geometric factor of back scattering laser radar by Slope Method.Though this measuring method also can obtain the geometric factor of back scattering laser radar, but have because being subject to the restriction of weather conditions, and be difficult to the defect of utilizing in real time geometric factor to revise the signal of back scattering laser radar, restricted the investigative range of back scattering laser radar.
For avoiding this difficult problem, the applicant has done some trials and effort, if Chinese invention patent application CN103344611A is in the method for a kind of side direction lidar measurement aerosol parameters based on CCD imaging technique of announcement on October 9th, 2013.Though the method has been avoided the impact of geometric factor in back scattering laser radar, it is well suited for for surveying the atmospheric aerosol space distribution of surface layer; Yet, when it faces existing back scattering laser radar, still feel inadequate.
Summary of the invention
The technical problem to be solved in the present invention is the limitation that overcomes above-mentioned various technical schemes, and the measuring method of the back scattering laser radar geometric factor that the easy Accurate Determining of a kind of geometric factor and practicality are good is provided.
For solving technical matters of the present invention, the technical scheme adopting is: the measuring method of back scattering laser radar geometric factor comprises uses CCD camera to record gasoloid backscattering coefficient, particularly,
First by gasoloid backscattering coefficient substitution Backscattering lidar equation
In, the P in equation (z) is the atmospheric backscatter echoed signal at laser radar receiving range z place, and C is the constant that laser radar system comprises energy, and η (z) is geometric factor, β
1(z), β
2(z) be respectively gasoloid backscattering coefficient and the atmospheric molecule backscattering coefficient at distance z place, α
1(z), α
2(z) be respectively Aerosol Extinction and the atmospheric molecule extinction coefficient at distance z place, dz is height resolution, re-uses the geometric factor that process of iteration obtains back scattering laser radar.
Further improvement as the measuring method of back scattering laser radar geometric factor:
Preferably, the step of using process of iteration to obtain back scattering laser radar geometric factor is:
Step 1, the initial geometric factor of setting the back scattering laser radar of zone of transition is η ' (z)=1;
Step 2, by the geometric factor substitution Backscattering lidar equation of setting
In, use Fernald method to obtain gasoloid backscattering coefficient β '
1(z);
Step 3, by the gasoloid backscattering coefficient β ' obtaining
1(z) compare with the gasoloid backscattering coefficient that uses CCD camera to record, draw ratio beta '
1(z)/β
1(z);
Step 4, if ratio beta '
1(z)/β
1(z) <0.98, the geometric factor that resets the back scattering laser radar of zone of transition be last geometric factor be multiplied by ratio beta '
1(z)/β
1(z) after, repeating step 2~3, until ratio beta '
1(z)/β
1(z)>=0.98, obtains the geometric factor of back scattering laser radar.
Preferably, the distance of CCD camera and utilizing emitted light interfascicular is 5~200m; Be beneficial to the consistance of measurement effect.
Preferably, the half-light subnumber of CCD camera under-20 degree is less than 1 photon number/pixel, always subtended angle is greater than 60 degree, resolution angle is less than 0.03 degree/pixel; Be beneficial to the more accurate measurement effect of acquisition.
Preferably, the wavelength of back scattering laser radar is 532nm, pulse energy >=50mJ; Be easy to obtain accurate measurement effect.
Preferably, the process of using CCD camera to record gasoloid backscattering coefficient is:
Step 1, first CCD side direction laser radar is operated in the horizontal direction of atmosphere in the more even time period, selected scattering angle is that the gasoloid that 179~180 degree places are reference point is all 1 than phase function value and atmospheric molecule than phase function value, record again the gasoloid backscattering coefficient value in reference point, and assert that this value all equates with the gasoloid backscattering coefficient value at each scattering angle place in horizontal direction, afterwards
Step 1.1, with reference to the gasoloid backscattering coefficient value on point and gasoloid than substitution side direction laser radar equation formula together with the vertical range D of phase function value and bias angle theta, angular breadth d θ, CCD camera and the laser radar transmitting light beam of each pixel of CCD camera
in, the signal intensity that the P in equation (θ) receives for respective pixel in the direction of θ drift angle, P
0for the power of laser radar transmitting light beam, the optical transmittance that K is receiving system, the useful area that A is optical system, T
t, T
rbe respectively the transmitance on laser vertical direction and tilted direction, β (θ) is gasoloid lateral scattering coefficient, and it is by β (θ)=β
1(θ) f
1(θ)+β
2(θ) f
2(θ) form the β in formula
1(θ) be gasoloid backscattering coefficient, β
2(θ) be atmospheric molecule backscattering coefficient, f
1(θ) be that gasoloid is than phase function, f
2(θ) be atmospheric molecule than phase function, Inversion Calculation goes out gasoloid on reference point consecutive point than phase function value by the following method,
If reference point scattering angle is θ
c, gasoloid backscattering coefficient is β
1(θ
c), the optical thickness of atmosphere is τ
c, get constant
the side direction laser radar signal β ' of band decay (θ) is defined as
The expression formula of the side direction laser radar signal of band decay is in theory,
β′(θ)=[β
1(θ)f(θ)
1+β
2(θ)f
2(θ)]exp-(Δτ+τ
c(1/cos(π-θ)-1/cos(π-θ
c))+Δτ/cos(π-θ))dθ
②,
Δ τ in formula is that scattering angle is from θ
cto the SEQUENCING VERTICAL optical thickness at θ place, from reference point, utilization numerical algorithm, fit equation is formula and 2. formula 1., and numerical value solves gasoloid on reference point consecutive point than phase function f
1(θ
c+ d θ),
Step 1.2, using consecutive point as new reference point, the direction diminishing to scattering angle is chosen new consecutive point, repeating step 1.1, the gasoloid that numerical solution makes new advances on consecutive point is than phase function f
1(θ
c+ d θ), until the gasoloid that obtains all selected scattering angle in investigative range is than phase function value, obtain gasoloid than phase function f
1(θ) profile;
Step 2, first CCD side direction laser radar is operated in the perpendicular direction of surface level on, and assert that gasoloid in the horizontal direction obtained by step 1 is than phase function value and equating in vertical direction, choose again the somewhere of surveying on height as a reference point, record the gasoloid backscattering coefficient value on this aspect, afterwards
Step 2.1, with reference to the gasoloid backscattering coefficient value on point and gasoloid than substitution side direction laser radar equation formula together with the vertical range D of phase function value and bias angle theta, angular breadth d θ, CCD camera and the laser radar transmitting light beam of each pixel of CCD camera
in, Inversion Calculation goes out the gasoloid backscattering coefficient value on reference point consecutive point by the following method,
If reference point scattering angle is θ
c, gasoloid backscattering coefficient is β
1(θ
c), the optical thickness of atmosphere is τ
c, get constant
the side direction laser radar signal β ' of band decay (θ) is defined as
The expression formula of the side direction laser radar signal of band decay is in theory,
β′(θ)=[β
1(θ)f(θ)
1+β
2(θ)f
2(θ)]exp-(Δτ+τ
c(1/cos(π-θ)-1/cos(π-θ
c))+Δτ/cos(π-θ))dθ
②,
Δ τ in formula is that scattering angle is from θ
cto the SEQUENCING VERTICAL optical thickness at θ place, from reference point, utilization numerical algorithm, fit equation is formula and 2. formula 1., and numerical value solves the gasoloid backscattering coefficient β on reference point consecutive point
1(θ
c+ d θ),
Step 2.2, using consecutive point as new reference point, successively hoist and lower both direction on choose new consecutive point, repeating step 2.1, the numerical solution gasoloid backscattering coefficient β on consecutive point that makes new advances
1(θ
c+ d θ), until obtain the gasoloid backscattering coefficient value on all selected height in investigative range, obtain gasoloid backscattering coefficient β
1(θ) profile;
Step 3 is that gasoloid obtains the profile of gasoloid phase function than the definition of phase function by the gasoloid phase function on θ angle with the ratio of gasoloid backscattering coefficient.
Beneficial effect with respect to prior art is:
The present invention is by the method for the side direction lidar measurement aerosol parameters based on CCD imaging technique, in the gasoloid backscattering coefficient substitution Backscattering lidar equation being recorded, use the accuracy of geometric factor of the back scattering laser radar that process of iteration obtains high and easily measure.Warp is compared with the result that prior art records, and both registrations are almost in full accord, effectively verified science of the present invention and correctness.
When the present invention measures back scattering laser radar geometric factor, do not need to select gasoloid level this exacting terms at equally distributed night, so have more practicality.The geometric factor that use records is revised the signal of back scattering laser radar, improved widely the precision of the interior atmospheric sounding parameter of zone of transition and pollutant levels, widened back scattering laser radar in the investigative range of section closely, expanded the application of back scattering laser radar, promoted the cost performance of back scattering laser radar, back scattering laser radar also be can be widely used in the closely detection of section atmosphere pollution.
Accompanying drawing explanation
Fig. 1 is the result comparison chart of using respectively the back scattering laser radar geometric factor of prior art and the present invention's mensuration.
Embodiment
Below in conjunction with accompanying drawing, optimal way of the present invention is described in further detail.
Referring to Fig. 1, the measuring method of back scattering laser radar geometric factor is as follows:
First,
The distance of selected CCD camera and utilizing emitted light interfascicular is 5~200m;
The half-light subnumber of CCD camera under-20 degree is less than 1 photon number/pixel, always subtended angle is greater than 60 degree, resolution angle is less than 0.03 degree/pixel;
The wavelength of back scattering laser radar is 532nm, pulse energy >=50mJ.
Secondly,
Use CCD camera to record gasoloid backscattering coefficient, its process is:
Step 1, first CCD side direction laser radar is operated in the horizontal direction of atmosphere in the more even time period, selected scattering angle is that the gasoloid that 180 (can be 179~180) degree place is reference point is all 1 than phase function value and atmospheric molecule than phase function value, record again the gasoloid backscattering coefficient value in reference point, and assert that this value all equates with the gasoloid backscattering coefficient value at each scattering angle place in horizontal direction; Wherein, the gasoloid backscattering coefficient value recording in reference point is use back scattering laser radar.Afterwards,
Step 1.1, with reference to the gasoloid backscattering coefficient value on point and gasoloid than substitution side direction laser radar equation formula together with the vertical range D of phase function value and bias angle theta, angular breadth d θ, CCD camera and the laser radar transmitting light beam of each pixel of CCD camera
in, the signal intensity that the P in equation (θ) receives for respective pixel in the direction of θ drift angle, P
0for the power of laser radar transmitting light beam, the optical transmittance that K is receiving system, the useful area that A is optical system, T
t, T
rbe respectively the transmitance on laser vertical direction and tilted direction, β (θ) is gasoloid lateral scattering coefficient, and it is by β (θ)=β
1(θ) f
1(θ)+β
2(θ) f
2(θ) form the β in formula
1(θ) be gasoloid backscattering coefficient, β
2(θ) be atmospheric molecule backscattering coefficient, f
1(θ) be that gasoloid is than phase function, f
2(θ) be atmospheric molecule than phase function, Inversion Calculation goes out gasoloid on reference point consecutive point than phase function value by the following method,
If reference point scattering angle is θ
c, gasoloid backscattering coefficient is β
1(θ
c), the optical thickness of atmosphere is τ
c, get constant
the side direction laser radar signal β ' of band decay (θ) is defined as
The expression formula of the side direction laser radar signal of band decay is in theory,
β′(θ)=[β
1(θ)f(θ)
1+β
2(θ)f
2(θ)]exp-(Δτ+τ
c(1/cos(π-θ)-1/cos(π-θ
c))+Δτ/cos(π-θ))dθ
②,
Δ τ in formula is that scattering angle is from θ
cto the SEQUENCING VERTICAL optical thickness at θ place, from reference point, utilization numerical algorithm, fit equation is formula and 2. formula 1., and numerical value solves gasoloid on reference point consecutive point than phase function f
1(θ
c+ d θ),
Step 1.2, using consecutive point as new reference point, the direction diminishing to scattering angle is chosen new consecutive point, repeating step 1.1, the gasoloid that numerical solution makes new advances on consecutive point is than phase function f
1(θ
c+ d θ), in horizontal direction, the number of each consecutive point is elected 3000 as, until the gasoloid that obtains all selected scattering angle in investigative range is than phase function value, obtains gasoloid than phase function f
1(θ) profile;
Step 2, first CCD side direction laser radar is operated in the perpendicular direction of surface level on, and assert that gasoloid in the horizontal direction obtained by step 1 is than phase function value and equating in vertical direction, choose again the somewhere of surveying on height as a reference point, record the gasoloid backscattering coefficient value on this aspect; Wherein, the gasoloid backscattering coefficient value recording in reference point is use back scattering laser radar.Afterwards,
Step 2.1, with reference to the gasoloid backscattering coefficient value on point and gasoloid than substitution side direction laser radar equation formula together with the vertical range D of phase function value and bias angle theta, angular breadth d θ, CCD camera and the laser radar transmitting light beam of each pixel of CCD camera
in, Inversion Calculation goes out the gasoloid backscattering coefficient value on reference point consecutive point by the following method,
If reference point scattering angle is θ
c, gasoloid backscattering coefficient is β
1(θ
c), the optical thickness of atmosphere is τ
c, get constant
the side direction laser radar signal β ' of band decay (θ) is defined as
The expression formula of the side direction laser radar signal of band decay is in theory,
β′(θ)=[β
1(θ)f(θ)
1+β
2(θ)f
2(θ)]exp-(Δτ+τ
c(1/cos(π-θ)-1/cos(π-θ
c))+Δτ/cos(π-θ))dθ
②,
Δ τ in formula is that scattering angle is from θ
cto the SEQUENCING VERTICAL optical thickness at θ place, from reference point, utilization numerical algorithm, fit equation is formula and 2. formula 1., and numerical value solves the gasoloid backscattering coefficient β on reference point consecutive point
1(θ
c+ d θ),
Step 2.2, using consecutive point as new reference point, successively hoist and lower both direction on choose new consecutive point, repeating step 2.1, the numerical solution gasoloid backscattering coefficient β on consecutive point that makes new advances
1(θ
c+ d θ), in vertical direction, the number of each consecutive point is elected 3000 as, until obtain the gasoloid backscattering coefficient value on all selected height in investigative range, obtains gasoloid backscattering coefficient β
1(θ) profile;
Step 3 is that gasoloid obtains the profile of gasoloid phase function than the definition of phase function by the gasoloid phase function on θ angle with the ratio of gasoloid backscattering coefficient.
Finally,
First by gasoloid backscattering coefficient substitution Backscattering lidar equation
Step 1, first records gasoloid backscattering coefficient β by use CCD camera
1(θ) variable in---bias angle theta is converted to gasoloid backscattering coefficient β in Backscattering lidar equation
1(z) variable in---distance z, pass is between the two z=D/tan (π-θ), wherein, D is the vertical range of CCD camera and laser radar transmitting light beam, and the initial geometric factor that resets the back scattering laser radar of zone of transition is η ' (z)=1;
Step 2, by the geometric factor substitution Backscattering lidar equation of setting
In, use Fernald method to obtain gasoloid backscattering coefficient β '
1(z);
Step 3, by the gasoloid backscattering coefficient β ' obtaining
1(z) with the gasoloid backscattering coefficient β through conversion that uses CCD camera to record
1(z) compare, draw ratio beta '
1(z)/β
1(z);
Step 4, if ratio beta '
1(z)/β
1(z) <0.98, the geometric factor that resets the back scattering laser radar of zone of transition be last geometric factor be multiplied by ratio beta '
1(z)/β
1(z) after, repeating step 2~3, until ratio beta '
1(z)/β
1(z)>=0.98, obtains the geometric factor of the back scattering laser radar as shown in the pecked line in Fig. 1.
Obviously, those skilled in the art can carry out various changes and modification and not depart from the spirit and scope of the present invention the measuring method of back scattering laser radar geometric factor of the present invention.Like this, if of the present invention these are revised and within modification belongs to the scope of the claims in the present invention and equivalent technologies thereof, the present invention is also intended to comprise these changes and modification interior.
Claims (6)
1. a measuring method for back scattering laser radar geometric factor, comprises and uses CCD camera to record gasoloid backscattering coefficient, it is characterized in that key step is as follows:
First by gasoloid backscattering coefficient substitution Backscattering lidar equation
In, the P in equation (z) is the atmospheric backscatter echoed signal at laser radar receiving range z place, and C is the constant that laser radar system comprises energy, and η (z) is geometric factor, β
1(z), β
2(z) be respectively gasoloid backscattering coefficient and the atmospheric molecule backscattering coefficient at distance z place, α
1(z), α
2(z) be respectively Aerosol Extinction and the atmospheric molecule extinction coefficient at distance z place, dz is height resolution, re-uses the geometric factor that process of iteration obtains back scattering laser radar.
2. the measuring method of back scattering laser radar geometric factor according to claim 1, is characterized in that the step of using process of iteration to obtain back scattering laser radar geometric factor is:
Step 1, the initial geometric factor of setting the back scattering laser radar of zone of transition is η ' (z)=1;
Step 2, by the geometric factor substitution Backscattering lidar equation of setting
In, use Fernald method to obtain gasoloid backscattering coefficient β '
1(z);
Step 3, by the gasoloid backscattering coefficient β ' obtaining
1(z) compare with the gasoloid backscattering coefficient that uses CCD camera to record, draw ratio beta '
1(z)/β
1(z);
Step 4, if ratio beta '
1(z)/β
1(z) <0.98, the geometric factor that resets the back scattering laser radar of zone of transition be last geometric factor be multiplied by ratio beta '
1(z)/β
1(z) after, repeating step 2~3, until ratio beta '
1(z)/β
1(z)>=0.98, obtains the geometric factor of back scattering laser radar.
3. the measuring method of back scattering laser radar geometric factor according to claim 2, the distance that it is characterized in that CCD camera and utilizing emitted light interfascicular is 5~200m.
4. the measuring method of back scattering laser radar geometric factor according to claim 2, is characterized in that the half-light subnumber of CCD camera under-20 degree is less than 1 photon number/pixel, always subtended angle is greater than 60 degree, resolution angle is less than 0.03 degree/pixel.
5. the measuring method of back scattering laser radar geometric factor according to claim 2, the wavelength that it is characterized in that back scattering laser radar is 532nm, pulse energy >=50mJ.
6. the measuring method of back scattering laser radar geometric factor according to claim 1, is characterized in that the process of using CCD camera to record gasoloid backscattering coefficient is:
Step 1, first CCD side direction laser radar is operated in the horizontal direction of atmosphere in the more even time period, selected scattering angle is that the gasoloid that 179~180 degree places are reference point is all 1 than phase function value and atmospheric molecule than phase function value, record again the gasoloid backscattering coefficient value in reference point, and assert that this value all equates with the gasoloid backscattering coefficient value at each scattering angle place in horizontal direction, afterwards
Step 1.1, with reference to the gasoloid backscattering coefficient value on point and gasoloid than substitution side direction laser radar equation formula together with the vertical range D of phase function value and bias angle theta, angular breadth d θ, CCD camera and the laser radar transmitting light beam of each pixel of CCD camera
in, the signal intensity that the P in equation (θ) receives for respective pixel in the direction of θ drift angle, P
0for the power of laser radar transmitting light beam, the optical transmittance that K is receiving system, the useful area that A is optical system, T
t, T
rbe respectively the transmitance on laser vertical direction and tilted direction, β (θ) is gasoloid lateral scattering coefficient, and it is by β (θ)=β
1(θ) f
1(θ)+β
2(θ) f
2(θ) form the β in formula
1(θ) be gasoloid backscattering coefficient, β
2(θ) be atmospheric molecule backscattering coefficient, f
1(θ) be that gasoloid is than phase function, f
2(θ) be atmospheric molecule than phase function, Inversion Calculation goes out gasoloid on reference point consecutive point than phase function value by the following method,
If reference point scattering angle is θ
c, gasoloid backscattering coefficient is β
1(θ
c), the optical thickness of atmosphere is τ
c, get constant
the side direction laser radar signal β ' of band decay (θ) is defined as
The expression formula of the side direction laser radar signal of band decay is in theory,
β′(θ)=[β
1(θ)f(θ)
1+β
2(θ)f
2(θ)]exp-(Δτ+τ
c(1/cos(π-θ)-1/cos(π-θ
c))+Δτ/cos(π-θ))dθ
②,
Δ τ in formula is that scattering angle is from θ
cto the SEQUENCING VERTICAL optical thickness at θ place, from reference point, utilization numerical algorithm, fit equation is formula and 2. formula 1., and numerical value solves gasoloid on reference point consecutive point than phase function f
1(θ
c+ d θ),
Step 1.2, using consecutive point as new reference point, the direction diminishing to scattering angle is chosen new consecutive point, repeating step 1.1, the gasoloid that numerical solution makes new advances on consecutive point is than phase function f
1(θ
c+ d θ), until the gasoloid that obtains all selected scattering angle in investigative range is than phase function value, obtain gasoloid than phase function f
1(θ) profile;
Step 2, first CCD side direction laser radar is operated in the perpendicular direction of surface level on, and assert that gasoloid in the horizontal direction obtained by step 1 is than phase function value and equating in vertical direction, choose again the somewhere of surveying on height as a reference point, record the gasoloid backscattering coefficient value on this aspect, afterwards
Step 2.1, with reference to the gasoloid backscattering coefficient value on point and gasoloid than substitution side direction laser radar equation formula together with the vertical range D of phase function value and bias angle theta, angular breadth d θ, CCD camera and the laser radar transmitting light beam of each pixel of CCD camera
in, Inversion Calculation goes out the gasoloid backscattering coefficient value on reference point consecutive point by the following method,
If reference point scattering angle is θ
c, gasoloid backscattering coefficient is β
1(θ
c), the optical thickness of atmosphere is τ
c, get constant
the side direction laser radar signal β ' of band decay (θ) is defined as
The expression formula of the side direction laser radar signal of band decay is in theory,
β′(θ)=[β
1(θ)f(θ)
1+β
2(θ)f
2(θ)]exp-(Δτ+τ
c(1/cos(π-θ)-1/cos(π-θ
c))+Δτ/cos(π-θ))dθ
②,
Δ τ in formula is that scattering angle is from θ
cto the SEQUENCING VERTICAL optical thickness at θ place, from reference point, utilization numerical algorithm, fit equation is formula and 2. formula 1., and numerical value solves the gasoloid backscattering coefficient β on reference point consecutive point
1(θ
c+ d θ),
Step 2.2, using consecutive point as new reference point, successively hoist and lower both direction on choose new consecutive point, repeating step 2.1, the numerical solution gasoloid backscattering coefficient β on consecutive point that makes new advances
1(θ
c+ d θ), until obtain the gasoloid backscattering coefficient value on all selected height in investigative range, obtain gasoloid backscattering coefficient β
1(θ) profile;
Step 3 is that gasoloid obtains the profile of gasoloid phase function than the definition of phase function by the gasoloid phase function on θ angle with the ratio of gasoloid backscattering coefficient.
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