CN101957317A - Altitude distribution mode measurer of refractive index structural constants of atmospheric turbulence - Google Patents

Abstract

The invention provides an altitude distribution mode measurer of refractive index structural constants of atmospheric turbulence, which belongs to the technical field of spatial laser communication. The measurer has three floating captive balloons as a communication platform and measures the distribution mode of the refractive index structural constants of atmospheric turbulence along horizontal and oblique paths real time by means of change of the laser signals transmitted by the atmospheric channel. The device of the invention has the advantages of simple structure, convenient operation and easy application.

Description

Atmospheric turbulence refractive index structure parameter height profile pattern measurement mechanism

Technical field

The present invention relates to atmospheric turbulence refractive index structure parameter height profile pattern measurement mechanism, belong to the laser space communication technical field.

Background technology

The atmospheric turbulence refractive index structure parameter

Playing the part of crucial role in the light propagation problem, is one of basic parameter in the optics.Because the situation of atmospheric channel constantly changes in time, so the atmospheric turbulence refractive index structure parameter

It is a time dependent amount.

Because the development of aspects such as laser communication and laser guidance is rapid, require to consider the distribution pattern of atmospheric turbulence refractive index structure parameter on laser level transmission path and oblique journey transmission path in recent years.Generally speaking, in view of the complicacy of atmosphere itself, and the turbulent flow of ground layer to be subjected to the influence of face of land situation strong, the distribution of atmospheric turbulence refractive index structure parameter is heterogeneous, it is relevant with the turbulent flow terrain clearance to depend on the local atmosphere condition.Therefore, be difficult to propose a kind of universal model and illustrate the characteristic of atmospheric turbulence refractive index structure parameter.During early stage research level transmission problem, the atmospheric turbulence refractive index structure parameter is got certain value, and when the oblique journey transmission problem of research, the atmospheric turbulence refractive index structure parameter often adopts the negative power exponential model, or adopting B spline method structure turbulent atmosphere textural constant model according to the value of atmospheric strument constant under some exemplary height, degree of accuracy is very low.

The means of measurement of Atmospheric Turbulence refractive index structure parameter comprise aircraft, radar, stellar scintillation and arrival angle fluctuation and temperature fluctuation sounding etc.But they all have deficiency separately, the subject matter that microwave and acoustic radar mensuration exist is that data are that non-light-wave band is measured, inverting obtains light-wave band needs correlation parameters such as supporting measurement aqueous vapor profile, temperature profile, these parameters are difficult for the measurement meeting and bring very big difficulty to data processing, measuring height is subjected to Power Limitation in addition, and mobility is poor; And micro-temperature sensor to carry out the measurement shortcoming of profile be because the influence of balloon wind-engaging is bigger, the zone of detection is often uncontrollable, can not satisfy the real-time of measurement and the requirement of occupied space.Domestic and international many scholars have proposed atmospheric turbulence refractive index structure parameter height profile pattern at present, and some is the empirical mode that sums up on a large amount of observation data bases in these patterns, basically be the result of a statistical average, because the restriction of observation method and cost is not particularly fully understood so far yet to the above atmospheric turbulence refractive index structure parameter distribution pattern of liftoff hundreds of rice.

When light beam transmits in atmosphere, be subjected to the influence of atmospheric turbulence refractive index fluctuation and produce turbulence effects such as flicker, drift, these propagation effects can be used for the measurement of Atmospheric Turbulence refractive index structure parameter.Therefore, development adopts the method for Laser Atmospheric Transmission to come the measurement of Atmospheric Turbulence refractive index structure parameter to have great significance and have broad application prospects with the height profile variation.

Summary of the invention

In order to realize measuring in real time distribution pattern, the present invention proposes a kind of atmospheric turbulence refractive index structure parameter height profile pattern measurement mechanism at the atmospheric turbulence refractive index structure parameter in certain altitude upper edge horizontal route and oblique journey path.

This device is by first captive balloon (1), second captive balloon (2), the tertiary system is stayed balloon (3), first gondola (4), second gondola (5), the 3rd gondola (6), first laser transmitting system (7), second laser transmitting system (8), first photoreceiver (9), second photoreceiver (10), the one GPS/INS Position Fixing Navigation System (11), the 2nd GPS/INS Position Fixing Navigation System (12), the 3rd GPS/INS Position Fixing Navigation System (13), ground control system (14), first hawser (15), second hawser (16), the 3rd hawser (17), the 4th hawser (18), the 5th hawser (19), the 6th hawser (20), first data line (21), second data line (22), the 3rd data line (23) is formed; Wherein first laser transmitting system (7), second laser transmitting system (8) and a GPS/INS Position Fixing Navigation System (11) are installed on first gondola (4); First photoreceiver (9) and the 2nd GPS/INS Position Fixing Navigation System (12) are installed on second gondola (5); Second photoreceiver (10) and the 3rd GPS/INS Position Fixing Navigation System (13) are installed on the 3rd gondola (6); First hawser (15), second hawser (16) are identical with the length of the 3rd hawser (17);

Described first captive balloon (1), second captive balloon (2), the tertiary system stay balloon (3) to be connected with first gondola (4), second gondola (5), the 3rd gondola (6) respectively by first hawser (15), second hawser (16), the 3rd hawser (17);

Described first gondola (4) is connected with ground control system (14) with first data line (21) by the 4th hawser (18); Second gondola (5) is connected with ground control system (14) with the 3rd data line (22) by the 6th hawser (19); The 3rd gondola (6) is connected with ground control system (14) with second data line (23) by the 5th hawser (20);

Described ground control system (14) is controlled the height of first gondola (4) also receives first gondola (4) by first data line (21) data by regaining or discharging the 4th hawser (18) and first data line (21), control the height of second gondola (5) and receive the data of second gondola (5) by regaining or discharging the 5th hawser (19) and second data line (22), by withdrawal or discharge the 6th hawser (20) and height that the 3rd data line (23) is controlled the 3rd gondola (6) also receives the data of the 3rd gondola (6) by the 3rd data line (23) by second data line (22);

The device course of work is as follows:

Step 1, by ground control system (14) control first gondola (4), second gondola (5) and the 3rd gondola (6) predetermined altitude that goes up to the air; Wherein first gondola (4) is identical with the level height of second gondola (5); The 3rd gondola (6) is different with the level height of first gondola (4);

Step 2, first gondola (4) are determined self position and attitude by a GPS/INS Position Fixing Navigation System (11), and send self position and attitude to second gondola (5) and the 3rd gondola (6); Second gondola (5) and the 3rd gondola (6) are determined position and the attitude of self respectively by the 2nd GPS/INS Position Fixing Navigation System (12) and the 3rd GPS/INS Position Fixing Navigation System (13), and send self position and attitude to first gondola (4); First laser transmitting system (7) of first gondola (4) and second laser transmitting system (8) are respectively to first photoreceiver (9) of second gondola (5) and second photoreceiver (10) the emission beacon beam of the 3rd gondola (6), after the thick tracking of communication process was stable, first laser transmitting system (7) of first gondola (4) and second laser transmitting system (8) were launched smart beacon beam to first photoreceiver (9) of second gondola (5) and second photoreceiver (10) of the 3rd gondola (6) respectively;

Step 3, first gondola (4) are sent to ground control system (14) with self-position, attitude and first laser transmitting system (7) and second laser transmitting system (8) institute emitted laser signal by first data line (21); Second gondola (5) laser signal that self-position, attitude and first photoreceiver (9) is received is sent to ground control system (14) by second data line (22); The 3rd gondola (6) laser signal that self-position, attitude and second photoreceiver (10) is received is sent to ground control system (14) by the 3rd data line (23);

Step 4, ground control system (14) data computation by received first gondola (4) and second gondola (5) goes out the atmospheric turbulence refractive index structure parameter at the horizontal route of predetermined altitude; The data computation of ground control system (14) by received first gondola (4) and the 3rd gondola (6) goes out the atmospheric turbulence refractive index structure parameter in the oblique journey path of predetermined altitude; Detailed process is:

Ground control system (14) receives the data of first photoreceiver (9) and second photoreceiver (10) transmission;

Ground control system (14) accesses view data frame by frame, calculate the light intensity total energy value, parameters such as flicker variance, average intensity and barycenter etc. of every width of cloth image after, calculate horizontal route and oblique journey path atmospheric turbulence refractive index structure parameter

Value;

(I) the atmospheric turbulence refractive index structure parameter in the oblique journey of calculating path

The atmospheric coherence length r that D.L.Fried defines when the structure function of research Wave-front phase ₀Can be expressed as refractive index structure parameter

Integration on transmission path to spherical wave, has

$r_0={\left[0.423k^2{\∫}_0^L{C}_n^2{(h/L)}^{5/3}\mathrm{dh}\right]}^{-3/5}$

Wherein k is the wave number of light wave, and L is an optical path length, and h is a height.This formula is applicable to oblique journey measurement, and integration gets

$r_0={\left[0.423k^2{\∫}_0^L{C}_n^2{(1-h/L)}^{5/3}\mathrm{dh}\right]}^{-3/5}$

In actual applications, refractive index structure parameter

In the adjacent space interval, equate, so

${r_0}^{-5/3}\left(z_i\right)={0.423k}^2{\mathrm{\Σ}}_{j=1}^i{C}_n^2\left(z_j\right){\∫C}_n^2{(1-\frac{h}{z_i})}^{5/3}\mathrm{dh}$

Wherein z represents height.

So atmospheric coherence length r for differing heights ₀(h) and the relation of atmospheric turbulence refractive index structure parameter can describe with matrix

${\left[R_0\right]}_n={\left[H\right]}_{\mathrm{nn}}{\left[C_n^2\right]}_n$

Wherein [H] _NnIt is matrix of coefficients by the decision of measuring height sequence.As long as measure the r of differing heights ₀(h), just can obtain measured atmospheric turbulence refractive index structure parameter by following formula.

(II) the atmospheric turbulence refractive index structure parameter in calculated level path

The atmospheric coherence length r that D.L.Fried defines when the structure function of research Wave-front phase ₀Can be expressed as refractive index structure parameter

Integration on transmission path to plane wave, has

$r_0={\left[{0.423k}^2{\∫}_0^L{C}_n^2\mathrm{dh}\right]}^{-3/5}$

Wherein k is the wave number of light wave, and L is an optical path length.Integration gets

${r_0}^{-5/3}={0.423k}^2\underset{j=1}{\overset{J}{\mathrm{\Σ}}}\left(C_{\mathrm{jn}}^2\mathrm{\Δ}{L}_j\right)$

Utilize the approximate transmission theory of light in turbulent atmosphere that laser is passed through of Tatarskii utilization Rytov, after plane wave passes turbulent atmosphere one segment distance, will cause the amplitude fluctuation of light wave, be flicker.Its logarithm intensity variance

General expression formula be

${\mathrm{\&sigma;}}_L^2=1.23C_n^2{\mathrm{<figure-callout\; id="7"\; label="K"\; filenames="HSA00000252658200011.png"\; state="\{\{state\}\}">K</figure-callout>}}^{7/6}{L}^{11/6}$

In the formula, K is the wave number of light wave, and L is the distance of transmission.

So atmospheric coherence length r for differing heights ₀(h) and the relation of atmospheric turbulence refractive index structure parameter can describe with matrix

${\left[R_0\right]}_n={\left[H\right]}_{\mathrm{nn}}{\left[C_n^2\right]}_n$

Wherein [H] _NnIt is matrix of coefficients by the decision of measuring height sequence.As long as measure the r of differing heights ₀(h), just can obtain measured atmospheric turbulence refractive index structure parameter by following formula.

Step 5, change the height of first gondola (4), second gondola (5) and the 3rd gondola (6) as required, repeated execution of steps 1 just can be calculated at the atmospheric turbulence refractive index structure parameter of differing heights upper edge horizontal route with oblique journey path by meter to step 4.

Beneficial effect

1) the present invention utilizes three captive balloons to go up to the air simultaneously, controls its lift-off height and then in real time according to the transmission of laser in atmospheric turbulence, utilizes scintigraphy to obtain the distribution of atmospheric turbulence refractive index structure parameter with height change;

2) the measuring method advanced person, the novelty that adopt of the present invention, be beneficial to popularization;

3) this apparatus structure is simple, and is with low cost, easy to operate.

Description of drawings

Fig. 1 is a kind of atmospheric turbulence refractive index structure parameter height profile pattern measurement mechanism synoptic diagram, and wherein 1 is first captive balloon, 2 is second captive balloon, 3 stay balloon for the tertiary system, 4 is first gondola, 5 is second gondola, 6 is the 3rd gondola, 7 is first laser transmitting system, 8 is second laser transmitting system, 9 is first photoreceiver, 10 is second photoreceiver, 11 is a GPS/INS Position Fixing Navigation System, 12 is the 2nd GPS/INS Position Fixing Navigation System, 13 is the 3rd GPS/INS Position Fixing Navigation System, 14 is ground control system, 15 is first hawser, 16 is second hawser, 17 is the 3rd hawser, 18 is the 4th hawser, 19 is the 5th hawser, 20 is the 6th hawser, 21 is first data line, 22 is second data line, 23 is the 3rd data line.

Embodiment

This device is by first captive balloon (1), second captive balloon (2), the tertiary system is stayed balloon (3), first gondola (4), second gondola (5), the 3rd gondola (6), first laser transmitting system (7), second laser transmitting system (8), first photoreceiver (9), second photoreceiver (10), the one GPS/INS Position Fixing Navigation System (11), the 2nd GPS/INS Position Fixing Navigation System (12), the 3rd GPS/INS Position Fixing Navigation System (13), ground control system (14), first hawser (15), second hawser (16), the 3rd hawser (17), the 4th hawser (18), the 5th hawser (19), the 6th hawser (20), first data line (21), second data line (22), the 3rd data line (23) is formed; Wherein first laser transmitting system (7), second laser transmitting system (8) and a GPS/INS Position Fixing Navigation System (11) are installed on first gondola (4); First photoreceiver (9) and the 2nd GPS/INS Position Fixing Navigation System (12) are installed on second gondola (5); Second photoreceiver (10) and the 3rd GPS/INS Position Fixing Navigation System (13) are installed on the 3rd gondola (6); First hawser (15), second hawser (16) are identical with the length of the 3rd hawser (17);

Described first captive balloon (1), second captive balloon (2), the tertiary system stay balloon (3) to be connected with first gondola (4), second gondola (5), the 3rd gondola (6) respectively by first hawser (15), second hawser (16), the 3rd hawser (17);

Described first gondola (4) is connected with ground control system (14) with first data line (21) by the 4th hawser (18); Second gondola (5) is connected with ground control system (14) with the 3rd data line (22) by the 6th hawser (19); The 3rd gondola (6) is connected with ground control system (14) with second data line (23) by the 5th hawser (20);

Described ground control system (14) is controlled the height of first gondola (4) also receives first gondola (4) by first data line (21) data by regaining or discharging the 4th hawser (18) and first data line (21), control the height of second gondola (5) and receive the data of second gondola (5) by regaining or discharging the 5th hawser (19) and second data line (22), by withdrawal or discharge the 6th hawser (20) and height that the 3rd data line (23) is controlled the 3rd gondola (6) also receives the data of the 3rd gondola (6) by the 3rd data line (23) by second data line (22);

The device course of work is as follows:

Step 1, by ground control system (14) control first gondola (4), second gondola (5) and the 3rd gondola (6) predetermined altitude that goes up to the air; Wherein first gondola (4) is identical with the level height of second gondola (5); The 3rd gondola (6) is different with the level height of first gondola (4);

Step 2, first gondola (4) are determined self position and attitude by a GPS/INS Position Fixing Navigation System (11), and send self position and attitude to second gondola (5) and the 3rd gondola (6); Second gondola (5) and the 3rd gondola (6) are determined position and the attitude of self respectively by the 2nd GPS/INS Position Fixing Navigation System (12) and the 3rd GPS/INS Position Fixing Navigation System (13), and send self position and attitude to first gondola (4); First laser transmitting system (7) of first gondola (4) and second laser transmitting system (8) are respectively to first photoreceiver (9) of second gondola (5) and second photoreceiver (10) the emission beacon beam of the 3rd gondola (6), after the thick tracking of communication process was stable, first laser transmitting system (7) of first gondola (4) and second laser transmitting system (8) were launched smart beacon beam to first photoreceiver (9) of second gondola (5) and second photoreceiver (10) of the 3rd gondola (6) respectively;

Step 3, first gondola (4) are sent to ground control system (14) with self-position, attitude and first laser transmitting system (7) and second laser transmitting system (8) institute emitted laser signal by first data line (21); Second gondola (5) laser signal that self-position, attitude and first photoreceiver (9) is received is sent to ground control system (14) by second data line (22); The 3rd gondola (6) laser signal that self-position, attitude and second photoreceiver (10) is received is sent to ground control system (14) by the 3rd data line (23);

Step 4, ground control system (14) data computation by received first gondola (4) and second gondola (5) goes out the atmospheric turbulence refractive index structure parameter at the horizontal route of predetermined altitude; The data computation of ground control system (14) by received first gondola (4) and the 3rd gondola (6) goes out the atmospheric turbulence refractive index structure parameter in the oblique journey path of predetermined altitude; Detailed process is:

The picture signal of a, ccd video camera output is at first by the video capture card collection;

B, deposit view data in calculator memory;

C, utilize image processing software to access view data frame by frame, calculate the level that calculates after the light intensity total energy value, flicker variance, average intensity and parameters such as barycenter x and barycenter y of every width of cloth image and oblique journey atmospheric turbulence refractive index structure parameter

Value;

D, utilize computer program to calculate oblique journey atmospheric turbulence refractive index structure parameter value

(I) tiltedly journey is calculated atmospheric turbulence refractive index structure parameter height profile

D.L.Fried when the structure function that the research Wave-front phase rises and falls, the atmospheric coherence length r of definition ₀Can be expressed as refractive index structure parameter

Integration on transmission path, promptly

$r_0={\left[0.423k^2{\&Integral;}_0^L{C}_n^2\mathrm{dh}\right]}^{-3/5}$

Following formula is applicable to plane wave, and wherein: k is the wave number of light wave; L is an optical path length.

$r_0={\left[0.423k^2{\&Integral;}_0^L{C}_n^2{(h/L)}^{5/3}\mathrm{dh}\right]}^{-3/5}$

Following formula is applicable to spherical wave, and wherein: k is the wave number of light wave; L is an optical path length.Because this formula is applicable to oblique journey and measures that what therefore be suitable for is the spherical wave formula, to the high-altitude integration, following formula becomes from ground

$r_0={\left[0.423k^2{\&Integral;}_0^L{C}_n^2{(1-h/L)}^{5/3}\mathrm{dh}\right]}^{-3/5}$

In actual applications, we can think refractive index structure parameter

In the adjacent space interval, equate, so following formula becomes again:

${r_0}^{-5/3}\left(z_i\right)={0.423k}^2{\mathrm{\&Sigma;}}_{j=1}^i{C}_n^2\left(z_j\right)\&Integral;C_n^2{(1-\frac{h}{z_i})}^{5/3}\mathrm{dh}$

In like manner, have for plane wave

${r_0}^{-5/3}={0.423k}^2\underset{j=1}{\overset{J}{\mathrm{\&Sigma;}}}\left(C_{\mathrm{jn}}^2\mathrm{\&Delta;}{L}_j\right)$

So atmospheric coherence length r for differing heights ₀(h) and the relation of atmospheric turbulence refractive index structure parameter can describe with matrix

${\left[R_0\right]}_n={\left[H\right]}_{\mathrm{nn}}{\left[C_n^2\right]}_n$

In the formula: [H] _NnIt is matrix of coefficients by the decision of measuring height sequence.As long as measure the r of differing heights ₀(h), just can obtain measured atmospheric turbulence refractive index structure parameter by following formula.

(II) the atmospheric turbulence refractive index structure parameter of level calculation differing heights

Utilize the approximate transmission theory of light in turbulent atmosphere that laser is passed through of Tatarskii utilization Rytov, after plane wave passes turbulent atmosphere one segment distance, will cause the amplitude fluctuation of light wave, be flicker.Its logarithm intensity variance General expression formula be

${\mathrm{\&sigma;}}_L^2=1.23C_n^2{\mathrm{<figure-callout\; id="7"\; label="K"\; filenames="HSA00000252658200011.png"\; state="\{\{state\}\}">K</figure-callout>}}^{7/6}{L}^{11/6}$

In the formula, K is the wave number of light wave, and L is the distance of transmission.

Step 5, change the height of first gondola (4), second gondola (5) and the 3rd gondola (6) as required, repeated execution of steps 1 just can be calculated at the atmospheric turbulence refractive index structure parameter of differing heights upper edge horizontal route with oblique journey path by meter to step 5.

Claims (1)

1. atmospheric turbulence refractive index structure parameter height profile pattern measurement mechanism, it is characterized in that this installs by first captive balloon (1), second captive balloon (2), the tertiary system is stayed balloon (3), first gondola (4), second gondola (5), the 3rd gondola (6), first laser transmitting system (7), second laser transmitting system (8), first photoreceiver (9), second photoreceiver (10), the one GPS/INS Position Fixing Navigation System (11), the 2nd GPS/INS Position Fixing Navigation System (12), the 3rd GPS/INS Position Fixing Navigation System (13), ground control system (14), first hawser (15), second hawser (16), the 3rd hawser (17), the 4th hawser (18), the 5th hawser (19), the 6th hawser (20), first data line (21), second data line (22), the 3rd data line (23) is formed; Wherein first laser transmitting system (7), second laser transmitting system (8) and a GPS/INS Position Fixing Navigation System (11) are installed on first gondola (4); First photoreceiver (9) and the 2nd GPS/INS Position Fixing Navigation System (12) are installed on second gondola (5); Second photoreceiver (10) and the 3rd GPS/INS Position Fixing Navigation System (13) are installed on the 3rd gondola (6); First hawser (15), second hawser (16) are identical with the length of the 3rd hawser (17);

Described first captive balloon (1), second captive balloon (2), the tertiary system stay balloon (3) to be connected with first gondola (4), second gondola (5), the 3rd gondola (6) respectively by first hawser (15), second hawser (16), the 3rd hawser (17);

Described first gondola (4) is connected with ground control system (14) with first data line (21) by the 4th hawser (18); Second gondola (5) is connected with ground control system (14) with the 3rd data line (22) by the 6th hawser (19); The 3rd gondola (6) is connected with ground control system (14) with second data line (23) by the 5th hawser (20);

Described ground control system (14) is controlled the height of first gondola (4) also receives first gondola (4) by first data line (21) data by regaining or discharging the 4th hawser (18) and first data line (21), control the height of second gondola (5) and receive the data of second gondola (5) by regaining or discharging the 5th hawser (19) and second data line (22), by withdrawal or discharge the 6th hawser (20) and height that the 3rd data line (23) is controlled the 3rd gondola (6) also receives the data of the 3rd gondola (6) by the 3rd data line (23) by second data line (22);

The device course of work is as follows:

Step 1, by ground control system (14) control first gondola (4), second gondola (5) and the 3rd gondola (6) predetermined altitude that goes up to the air; Wherein first gondola (4) is identical with the level height of second gondola (5); The 3rd gondola (6) is different with the level height of first gondola (4);

Step 2, first gondola (4) are determined self position and attitude by a GPS/INS Position Fixing Navigation System (11), and send self position and attitude to second gondola (5) and the 3rd gondola (6); Second gondola (5) and the 3rd gondola (6) are determined position and the attitude of self respectively by the 2nd GPS/INS Position Fixing Navigation System (12) and the 3rd GPS/INS Position Fixing Navigation System (13), and send self position and attitude to first gondola (4); First laser transmitting system (7) of first gondola (4) and second laser transmitting system (8) are respectively to first photoreceiver (9) of second gondola (5) and second photoreceiver (10) the emission beacon beam of the 3rd gondola (6), after the thick tracking of communication process was stable, first laser transmitting system (7) of first gondola (4) and second laser transmitting system (8) were launched smart beacon beam to first photoreceiver (9) of second gondola (5) and second photoreceiver (10) of the 3rd gondola (6) respectively;

Step 3, first gondola (4) are sent to ground control system (14) with self-position, attitude and first laser transmitting system (7) and second laser transmitting system (8) institute emitted laser signal by first data line (21); Second gondola (5) laser signal that self-position, attitude and first photoreceiver (9) is received is sent to ground control system (14) by second data line (22); The 3rd gondola (6) laser signal that self-position, attitude and second photoreceiver (10) is received is sent to ground control system (14) by the 3rd data line (23);

Step 4, ground control system (14) data computation by received first gondola (4) and second gondola (5) goes out the atmospheric turbulence refractive index structure parameter at the horizontal route of predetermined altitude; The data computation of ground control system (14) by received first gondola (4) and the 3rd gondola (6) goes out the atmospheric turbulence refractive index structure parameter in the oblique journey path of predetermined altitude;

Step 5, change the height of first gondola (4), second gondola (5) and the 3rd gondola (6) as required, repeated execution of steps 1 just can be calculated at the atmospheric turbulence refractive index structure parameter of differing heights upper edge horizontal route with oblique journey path by meter to step 4.

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