Abstract

A system has been developed for calibrating and precisely pointing a germanium dual-wedge scanner for a CO2 Doppler lidar from an airborne platform. This paper describes equations implemented in pointing the scanner as well as those in the iterative calibration program, which combines available data with estimated parameters of the scanner orientation relative to the axes of the aircraft's inertial navigation system to arrive at corrected scanner parameters. In addition, this paper investigates the effect of specific error conditions on program performance and the results of the program when used on 1981 flight test data.

© 1985 Optical Society of America

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References

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  1. C. DiMarzio, C. Harris, J. W. Bilbro, E. A. Weaver, D. C. Burnham, J. N. Hallock, “Pulsed Laser Doppler Measurements of Wind Shear,” Bull. Am. Meteorol. Soc. 60, 1061 (1979).
    [CrossRef]
  2. C. DiMarzio, M. Krause, R. Chandler, J. O'Reilly, K. Shaw, J. Bilbro, E. Weaver, “Airborne Lidar Dual Wedge Scanner,” presented at Eleventh International Laser Radar Conference, University of Wisconsin-Madison, p. 123, NASA CP-2228, 21–25 June 1982.
  3. M. Born, E. Wolf, Principles of Optics (Macmillan, New York, 1964), p. 125.
  4. C. A. DiMarzio, J. W. Bilbro, “An Airborne Doppler Lidar,” presented at Heterodyne Systems and Technology Conference Part 2, Williamsburg, Va., p. 529, NASA CP-2138, Part 2, 25–27 Mar. 1980.

1979 (1)

C. DiMarzio, C. Harris, J. W. Bilbro, E. A. Weaver, D. C. Burnham, J. N. Hallock, “Pulsed Laser Doppler Measurements of Wind Shear,” Bull. Am. Meteorol. Soc. 60, 1061 (1979).
[CrossRef]

Bilbro, J.

C. DiMarzio, M. Krause, R. Chandler, J. O'Reilly, K. Shaw, J. Bilbro, E. Weaver, “Airborne Lidar Dual Wedge Scanner,” presented at Eleventh International Laser Radar Conference, University of Wisconsin-Madison, p. 123, NASA CP-2228, 21–25 June 1982.

Bilbro, J. W.

C. DiMarzio, C. Harris, J. W. Bilbro, E. A. Weaver, D. C. Burnham, J. N. Hallock, “Pulsed Laser Doppler Measurements of Wind Shear,” Bull. Am. Meteorol. Soc. 60, 1061 (1979).
[CrossRef]

C. A. DiMarzio, J. W. Bilbro, “An Airborne Doppler Lidar,” presented at Heterodyne Systems and Technology Conference Part 2, Williamsburg, Va., p. 529, NASA CP-2138, Part 2, 25–27 Mar. 1980.

Born, M.

M. Born, E. Wolf, Principles of Optics (Macmillan, New York, 1964), p. 125.

Burnham, D. C.

C. DiMarzio, C. Harris, J. W. Bilbro, E. A. Weaver, D. C. Burnham, J. N. Hallock, “Pulsed Laser Doppler Measurements of Wind Shear,” Bull. Am. Meteorol. Soc. 60, 1061 (1979).
[CrossRef]

Chandler, R.

C. DiMarzio, M. Krause, R. Chandler, J. O'Reilly, K. Shaw, J. Bilbro, E. Weaver, “Airborne Lidar Dual Wedge Scanner,” presented at Eleventh International Laser Radar Conference, University of Wisconsin-Madison, p. 123, NASA CP-2228, 21–25 June 1982.

DiMarzio, C.

C. DiMarzio, C. Harris, J. W. Bilbro, E. A. Weaver, D. C. Burnham, J. N. Hallock, “Pulsed Laser Doppler Measurements of Wind Shear,” Bull. Am. Meteorol. Soc. 60, 1061 (1979).
[CrossRef]

C. DiMarzio, M. Krause, R. Chandler, J. O'Reilly, K. Shaw, J. Bilbro, E. Weaver, “Airborne Lidar Dual Wedge Scanner,” presented at Eleventh International Laser Radar Conference, University of Wisconsin-Madison, p. 123, NASA CP-2228, 21–25 June 1982.

DiMarzio, C. A.

C. A. DiMarzio, J. W. Bilbro, “An Airborne Doppler Lidar,” presented at Heterodyne Systems and Technology Conference Part 2, Williamsburg, Va., p. 529, NASA CP-2138, Part 2, 25–27 Mar. 1980.

Hallock, J. N.

C. DiMarzio, C. Harris, J. W. Bilbro, E. A. Weaver, D. C. Burnham, J. N. Hallock, “Pulsed Laser Doppler Measurements of Wind Shear,” Bull. Am. Meteorol. Soc. 60, 1061 (1979).
[CrossRef]

Harris, C.

C. DiMarzio, C. Harris, J. W. Bilbro, E. A. Weaver, D. C. Burnham, J. N. Hallock, “Pulsed Laser Doppler Measurements of Wind Shear,” Bull. Am. Meteorol. Soc. 60, 1061 (1979).
[CrossRef]

Krause, M.

C. DiMarzio, M. Krause, R. Chandler, J. O'Reilly, K. Shaw, J. Bilbro, E. Weaver, “Airborne Lidar Dual Wedge Scanner,” presented at Eleventh International Laser Radar Conference, University of Wisconsin-Madison, p. 123, NASA CP-2228, 21–25 June 1982.

O'Reilly, J.

C. DiMarzio, M. Krause, R. Chandler, J. O'Reilly, K. Shaw, J. Bilbro, E. Weaver, “Airborne Lidar Dual Wedge Scanner,” presented at Eleventh International Laser Radar Conference, University of Wisconsin-Madison, p. 123, NASA CP-2228, 21–25 June 1982.

Shaw, K.

C. DiMarzio, M. Krause, R. Chandler, J. O'Reilly, K. Shaw, J. Bilbro, E. Weaver, “Airborne Lidar Dual Wedge Scanner,” presented at Eleventh International Laser Radar Conference, University of Wisconsin-Madison, p. 123, NASA CP-2228, 21–25 June 1982.

Weaver, E.

C. DiMarzio, M. Krause, R. Chandler, J. O'Reilly, K. Shaw, J. Bilbro, E. Weaver, “Airborne Lidar Dual Wedge Scanner,” presented at Eleventh International Laser Radar Conference, University of Wisconsin-Madison, p. 123, NASA CP-2228, 21–25 June 1982.

Weaver, E. A.

C. DiMarzio, C. Harris, J. W. Bilbro, E. A. Weaver, D. C. Burnham, J. N. Hallock, “Pulsed Laser Doppler Measurements of Wind Shear,” Bull. Am. Meteorol. Soc. 60, 1061 (1979).
[CrossRef]

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Macmillan, New York, 1964), p. 125.

Bull. Am. Meteorol. Soc. (1)

C. DiMarzio, C. Harris, J. W. Bilbro, E. A. Weaver, D. C. Burnham, J. N. Hallock, “Pulsed Laser Doppler Measurements of Wind Shear,” Bull. Am. Meteorol. Soc. 60, 1061 (1979).
[CrossRef]

Other (3)

C. DiMarzio, M. Krause, R. Chandler, J. O'Reilly, K. Shaw, J. Bilbro, E. Weaver, “Airborne Lidar Dual Wedge Scanner,” presented at Eleventh International Laser Radar Conference, University of Wisconsin-Madison, p. 123, NASA CP-2228, 21–25 June 1982.

M. Born, E. Wolf, Principles of Optics (Macmillan, New York, 1964), p. 125.

C. A. DiMarzio, J. W. Bilbro, “An Airborne Doppler Lidar,” presented at Heterodyne Systems and Technology Conference Part 2, Williamsburg, Va., p. 529, NASA CP-2138, Part 2, 25–27 Mar. 1980.

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Figures (15)

Fig. 1
Fig. 1

Calculating the line of sight. Figs. 14 illustrate the iterative calibration routine using trial and error to compare the set of four measured data points with trial data points calculated with aircraft orientation, scanner setting, and scanner alignment data.

Fig. 2
Fig. 2

Setting the scanner to a line of sight. Figs. 14 illustrate the iterative calibration routine using trial and error to compare the set of four measured data points with trial data points calculated with aircraft orientation, scanner setting, and scanner alignment data.

Fig. 3
Fig. 3

Calibrating the scanner. Figs. 14 illustrate the iterative calibration routine using trial and error to compare the set of four measured data points with trial data points calculated with aircraft orientation, scanner setting, and scanner alignment data.

Fig. 5
Fig. 5

In the dual-wedge scanner coordinate system, the input vector Ŝ is collinear with the x axis, which is the axis of rotation for the two wedges.

Fig. 6
Fig. 6

Using simple approximation, counterrotating two equal wedges of the scanner produces a straight line on the z axis.

Fig. 7
Fig. 7

A closer look at counterrotating equal wedges shows errors of 30 m at 10,000 m for a scan 8000 m wide.

Fig. 8
Fig. 8

Counterrotating unequal wedges produces greater distortions to the scan generated.

Fig. 9
Fig. 9

Rotating the second wedge independently produces the ellipse shown. The desired point can then be arrived at by rotating the wedges simultaneously.

Fig. 10
Fig. 10

Calculating aircraft alignment involves three rotations about the coordinate systems of heading, pitch, and roll.

Fig. 11
Fig. 11

As the iterations progress, each of the parameters approaches its correct value.

Fig. 12
Fig. 12

Results better than 14 and 10 m at 10,000 m are obtained with the two misaligned parameter sets if the rotation angles are unrounded.

Fig. 13
Fig. 13

Due to the one-tenth degree quantization in positioning the scanner, the actual errors are 15 and 12 m at 10,000 m.

Fig. 14
Fig. 14

Fore and aft looking scans create a grid of wind velocity returns in the Severe Storms measurement system.

Fig. 15
Fig. 15

Acquisition and selection of data points are restricted by scanner coverage, physical obstructions, and human limitations.

Tables (2)

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Table I Scan and Check Parameters

Tables Icon

Table II Effects of Misalignment of Input Beam

Equations (10)

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S ̂ j + 1 = r j S ̂ j + { 1 r j 2 [ 1 ( S ̂ j · N ̂ j ) 2 ] r j S ̂ j · N ̂ j } N ̂ j ,
N ̂ j = cos w j i ̂ + sin w j ( cos θ j j ̂ + sin θ j k ̂ ) ,
S ̂ 1 = i ̂ .
dev = cos 1 ( x x 2 + y 2 + z 2 ) .
S ̂ 2 = r 1 i ̂ + { 1 r 1 2 ( sin 2 w 1 ) r 1 cos w 1 } × [ ( cos w 1 ) i ̂ + ( sin w 1 ) j ̂ ] .
N ̂ 2 = ( cos w 2 ) i ̂ + ( sin w 2 cos Δ θ ) j ̂ + ( sin w 2 sin Δ θ ) k ̂ .
cos ( dev ) = r 2 x 2 + { 1 r 2 2 [ 1 r 2 2 ] [ 1 ( S ̂ 2 · N ̂ 2 ) 2 ] r 2 S ̂ 2 · N ̂ 2 } cos w 2 ,
δ = cos ( dev ) r 2 x 2 cos w 2 = cos ( dev ) r 2 [ r 1 sin 2 ( w 1 ) + cos ( w 1 ) 1 r 1 2 sin 2 w 1 ] cos w 2 ,
S ̂ 2 · N ̂ 2 = 1 r 2 2 δ 2 2 δ r 2 .
Δ θ = cos 1 { S ̂ 2 · N ̂ 2 x 2 cos w 2 y 2 sin w 2 } .

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