Abstract

A simple analytical solution has been found that enables prediction of the effects of line-of-sight motion of a sensor on clutter leakage after first differencing. The effect of finite footprint size is included, and the crucial importance of the ratio of this quantity to the background correlation length is given. For small motions the clutter leakage as a fraction of the value of background standard deviation is given by the very simple formula 2[1exp(L/d)], where L is the footprint size, and d is the background correlation length.

© 1983 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. Y. Ikatura et al., Infrared Phys. 14, 17 (1974).
    [CrossRef]
  2. C. Hester, “Wiener Spectra Data Analysis for Infrared Background Modeling,” Report TE 77-11, U.S. Army Missile and Research Development Command Redstone Arsenal, Ala. (1977).
  3. R. N. Bracewell, The Fourier Transform and its Applications (McGraw-Hill, New York, 1965).
  4. A. T. Maksymowicz et al., “Phenomenology of Thermal Infrared Background Scenes,” Proc. Soc. Photo-Opt. Instrum. Eng. 366, 23 (1981).
  5. A. LaRocca et al., “Handbook of the Statistics of Various Terrain and Water (Ice) Backgrounds From Selected U.S. Locations,” Report 139900-1-X, Environmental Research Institute of Michigan, Ann Arbor (1980).

1981

A. T. Maksymowicz et al., “Phenomenology of Thermal Infrared Background Scenes,” Proc. Soc. Photo-Opt. Instrum. Eng. 366, 23 (1981).

1974

Y. Ikatura et al., Infrared Phys. 14, 17 (1974).
[CrossRef]

Bracewell, R. N.

R. N. Bracewell, The Fourier Transform and its Applications (McGraw-Hill, New York, 1965).

Hester, C.

C. Hester, “Wiener Spectra Data Analysis for Infrared Background Modeling,” Report TE 77-11, U.S. Army Missile and Research Development Command Redstone Arsenal, Ala. (1977).

Ikatura, Y.

Y. Ikatura et al., Infrared Phys. 14, 17 (1974).
[CrossRef]

LaRocca, A.

A. LaRocca et al., “Handbook of the Statistics of Various Terrain and Water (Ice) Backgrounds From Selected U.S. Locations,” Report 139900-1-X, Environmental Research Institute of Michigan, Ann Arbor (1980).

Maksymowicz, A. T.

A. T. Maksymowicz et al., “Phenomenology of Thermal Infrared Background Scenes,” Proc. Soc. Photo-Opt. Instrum. Eng. 366, 23 (1981).

Infrared Phys.

Y. Ikatura et al., Infrared Phys. 14, 17 (1974).
[CrossRef]

Proc. Soc. Photo-Opt. Instrum. Eng.

A. T. Maksymowicz et al., “Phenomenology of Thermal Infrared Background Scenes,” Proc. Soc. Photo-Opt. Instrum. Eng. 366, 23 (1981).

Other

A. LaRocca et al., “Handbook of the Statistics of Various Terrain and Water (Ice) Backgrounds From Selected U.S. Locations,” Report 139900-1-X, Environmental Research Institute of Michigan, Ann Arbor (1980).

C. Hester, “Wiener Spectra Data Analysis for Infrared Background Modeling,” Report TE 77-11, U.S. Army Missile and Research Development Command Redstone Arsenal, Ala. (1977).

R. N. Bracewell, The Fourier Transform and its Applications (McGraw-Hill, New York, 1965).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (3)

Fig. 1
Fig. 1

Variance reduction factor.

Fig. 2
Fig. 2

Inner and outer solutions for C(X).

Fig. 3
Fig. 3

Clutter leakage results.

Tables (1)

Tables Icon

Table I Typical Parameters for Backgrounds

Equations (22)

Equations on this page are rendered with MathJax. Learn more.

D ( X ) = [ N ( X ) N ( 0 ) ] 2 ¯ ,
D ( X ) = 2 [ var N data C ( X ) ] .
C ( X ) = var N bkg [ exp ( | X | / d ) ] ,
N ( X ) = 1 L N B ( X ) * rect X X L ,
PSD A ( k ) = ( sin π L k π L k ) 2 = sinc 2 L k .
PSD B ( k ) = a var N bkg π ( a 2 + k 2 ) , a = 1 2 π d .
C ( X ) = 2 a var N bkg π 0 1 ( a 2 + k 2 ) ( sin π L k π L k ) 2 ( cos 2 π k X ) d k .
C ( X ) = var N bkg exp ( X / d ) * 1 L rect X X L * 1 L × rect X X L
C ( X ) = [ 2 ( d / L ) 2 exp ( L / d ) cos h X d 2 ( d / L ) 2 exp ( X / d ) ( 2 d / L 2 ) ( X L ) ] var N bkg ;
C ( X ) = [ 2 ( d / L ) 2 ( cos h L d 1 ) exp ( X / d ) ] var N bkg .
C ( X ) = var N bkg exp ( | X | / d ) ,
C ( 0 ) = { 2 ( d / L ) 2 ( d / L ) 2 [ 1 exp ( L / d ) ] } var N bkg
C ( 0 ) C ¯ ( 0 ) var N bkg .
( var N ) data = ( var N ) bkg C ¯ ( 0 ) ,
D ( X ) = 2 var N bkg C ¯ ( 0 ) [ 1 C ( X ) var N bkg C ¯ ( 0 ) ] .
d = 0 C ( X ) d X .
C ( X ) = 2 [ ( d / L ) 2 exp ( L / d ) cos h X d 2 ( d / L ) 2 exp ( X / d ) ( 2 d / L 2 ) ( X L ) ] var N bkg .
C ( X ) C ¯ ( 0 ) + ( exp L / d 1 ) ( X / L ) 2 var bkg .
D ( X ) 2 var N bkg [ 1 exp ( L / d ) ] ( X / L ) 2 ,
[ D ( X ) / var N bkg ] 1 / 2
2 [ 1 exp ( L / d ) .
2 [ 1 exp ( 1 ) ] X L = 1.12 X L .

Metrics