Abstract

The purpose of this investigation has been to study the systematic and random effects of unresolved (i.e., smaller than instrument IFOV) cloud and haze on the ability to discriminate, e.g., vegetated targets using digital recorded radiance in preselected bandpasses. Calculations have, for the sake of example, centered on the discrimination of wheat and of soybeans from targets consisting of soybeans at various levels of stress severity. Calculations have mainly centered on nadir values (the only value of view angle for which reflectance data are available for various levels of disease stress severity), but some calculations of target discriminability for various view angles have been made to serve as examples. While means may be found to determine and to correct for systematic dependence of recorded radiance on view angle, it will not be possible to correct for random variations. Thus, while studies of systematic variations of target radiance with scan angle will lead to data calibration (to improve target discriminability), studies of random variation will indicate the limits imposed by fluctuations in physical factors on target differentiation and quantification. It is suggested that a future aim must be to determine which bandpasses or combinations of bandpasses may best be used to minimize random variations in target radiance, so as to optimize the discrimination of selected targets, in this case stressed from unstressed vegetation.

© 1984 Optical Society of America

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References

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  1. L. F. Lautenshlager, C. R. Perry, “Comparison of Vegetation Indices Based on Satellite Acquired Spectral Data,” in Proceedings, Survey Research Methods Section of American Statistical Association, Washington, D.C. (1981).
  2. M. J. Duggin, “On the Natural Limitations of Target Differentiation Using Spectral Discrimination Techniques,” in Proceedings, Ninth International Symposium on Remote Sensing of the Environment (Environmental Research Institute of Michigan, Ann Arbor, 1974).
  3. M. J. Duggin, Int. J. Remote Sensing 4, 601 (1983).
    [CrossRef]
  4. G. Tappan, G. E. Miller, AgRISTARS Tech. Memo., NASA JSC-17437, EW-L1-04190 (1982).
  5. M. J. Duggin, D. Piwinski, V. Whitehead, G. Ryland, Appl. Opt. 21, 1873 (1982).
    [CrossRef] [PubMed]
  6. M. J. Duggin, L. Schoch, T. I. Gray, Appl. Opt. 21, 2649 (1982).
    [CrossRef] [PubMed]
  7. W. L. Wolfe, G. J. Zissis, Eds., The Infrared Handbook (Environmental Research Institute of Michigan, Ann Arbor, 1978, pp. 3–44.
  8. O. L. Davies, Ed., Statistical Methods in Research and Production (Oliver & Boyd, London, 1961), p. 41.
  9. M. E. Bauer, L. L. Biehl, C. S. T. Daughtry, B. F. Robinson, E. R. Stone, AgRISTARS Supporting Research Final Report, Vol. 1, NAS9-15466 (1979).
  10. L. L. Biehl, Purdue University; private communication (1980).
  11. B. M. Herman, S. R. Browning, J. Atmos. Sci. 32, 1430 (1975).
    [CrossRef]
  12. P. N. Slater, U. Arizona; private communications (1981).
  13. T. I. Gray, D. G. McCrary, in Extended Abstracts, Fifteenth Conference on Agriculture and Forest Meteorology and Fifth Conference on Biometeorology, 1–3 April 1981, Anaheim, Calif. (American Meteorological Society, Boston, 1981), pp. 205–207.

1983

M. J. Duggin, Int. J. Remote Sensing 4, 601 (1983).
[CrossRef]

1982

1975

B. M. Herman, S. R. Browning, J. Atmos. Sci. 32, 1430 (1975).
[CrossRef]

Bauer, M. E.

M. E. Bauer, L. L. Biehl, C. S. T. Daughtry, B. F. Robinson, E. R. Stone, AgRISTARS Supporting Research Final Report, Vol. 1, NAS9-15466 (1979).

Biehl, L. L.

M. E. Bauer, L. L. Biehl, C. S. T. Daughtry, B. F. Robinson, E. R. Stone, AgRISTARS Supporting Research Final Report, Vol. 1, NAS9-15466 (1979).

L. L. Biehl, Purdue University; private communication (1980).

Browning, S. R.

B. M. Herman, S. R. Browning, J. Atmos. Sci. 32, 1430 (1975).
[CrossRef]

Daughtry, C. S. T.

M. E. Bauer, L. L. Biehl, C. S. T. Daughtry, B. F. Robinson, E. R. Stone, AgRISTARS Supporting Research Final Report, Vol. 1, NAS9-15466 (1979).

Duggin, M. J.

M. J. Duggin, Int. J. Remote Sensing 4, 601 (1983).
[CrossRef]

M. J. Duggin, D. Piwinski, V. Whitehead, G. Ryland, Appl. Opt. 21, 1873 (1982).
[CrossRef] [PubMed]

M. J. Duggin, L. Schoch, T. I. Gray, Appl. Opt. 21, 2649 (1982).
[CrossRef] [PubMed]

M. J. Duggin, “On the Natural Limitations of Target Differentiation Using Spectral Discrimination Techniques,” in Proceedings, Ninth International Symposium on Remote Sensing of the Environment (Environmental Research Institute of Michigan, Ann Arbor, 1974).

Gray, T. I.

M. J. Duggin, L. Schoch, T. I. Gray, Appl. Opt. 21, 2649 (1982).
[CrossRef] [PubMed]

T. I. Gray, D. G. McCrary, in Extended Abstracts, Fifteenth Conference on Agriculture and Forest Meteorology and Fifth Conference on Biometeorology, 1–3 April 1981, Anaheim, Calif. (American Meteorological Society, Boston, 1981), pp. 205–207.

Herman, B. M.

B. M. Herman, S. R. Browning, J. Atmos. Sci. 32, 1430 (1975).
[CrossRef]

Lautenshlager, L. F.

L. F. Lautenshlager, C. R. Perry, “Comparison of Vegetation Indices Based on Satellite Acquired Spectral Data,” in Proceedings, Survey Research Methods Section of American Statistical Association, Washington, D.C. (1981).

McCrary, D. G.

T. I. Gray, D. G. McCrary, in Extended Abstracts, Fifteenth Conference on Agriculture and Forest Meteorology and Fifth Conference on Biometeorology, 1–3 April 1981, Anaheim, Calif. (American Meteorological Society, Boston, 1981), pp. 205–207.

Miller, G. E.

G. Tappan, G. E. Miller, AgRISTARS Tech. Memo., NASA JSC-17437, EW-L1-04190 (1982).

Perry, C. R.

L. F. Lautenshlager, C. R. Perry, “Comparison of Vegetation Indices Based on Satellite Acquired Spectral Data,” in Proceedings, Survey Research Methods Section of American Statistical Association, Washington, D.C. (1981).

Piwinski, D.

Robinson, B. F.

M. E. Bauer, L. L. Biehl, C. S. T. Daughtry, B. F. Robinson, E. R. Stone, AgRISTARS Supporting Research Final Report, Vol. 1, NAS9-15466 (1979).

Ryland, G.

Schoch, L.

Slater, P. N.

P. N. Slater, U. Arizona; private communications (1981).

Stone, E. R.

M. E. Bauer, L. L. Biehl, C. S. T. Daughtry, B. F. Robinson, E. R. Stone, AgRISTARS Supporting Research Final Report, Vol. 1, NAS9-15466 (1979).

Tappan, G.

G. Tappan, G. E. Miller, AgRISTARS Tech. Memo., NASA JSC-17437, EW-L1-04190 (1982).

Whitehead, V.

Appl. Opt.

Int. J. Remote Sensing

M. J. Duggin, Int. J. Remote Sensing 4, 601 (1983).
[CrossRef]

J. Atmos. Sci.

B. M. Herman, S. R. Browning, J. Atmos. Sci. 32, 1430 (1975).
[CrossRef]

Other

P. N. Slater, U. Arizona; private communications (1981).

T. I. Gray, D. G. McCrary, in Extended Abstracts, Fifteenth Conference on Agriculture and Forest Meteorology and Fifth Conference on Biometeorology, 1–3 April 1981, Anaheim, Calif. (American Meteorological Society, Boston, 1981), pp. 205–207.

G. Tappan, G. E. Miller, AgRISTARS Tech. Memo., NASA JSC-17437, EW-L1-04190 (1982).

L. F. Lautenshlager, C. R. Perry, “Comparison of Vegetation Indices Based on Satellite Acquired Spectral Data,” in Proceedings, Survey Research Methods Section of American Statistical Association, Washington, D.C. (1981).

M. J. Duggin, “On the Natural Limitations of Target Differentiation Using Spectral Discrimination Techniques,” in Proceedings, Ninth International Symposium on Remote Sensing of the Environment (Environmental Research Institute of Michigan, Ann Arbor, 1974).

W. L. Wolfe, G. J. Zissis, Eds., The Infrared Handbook (Environmental Research Institute of Michigan, Ann Arbor, 1978, pp. 3–44.

O. L. Davies, Ed., Statistical Methods in Research and Production (Oliver & Boyd, London, 1961), p. 41.

M. E. Bauer, L. L. Biehl, C. S. T. Daughtry, B. F. Robinson, E. R. Stone, AgRISTARS Supporting Research Final Report, Vol. 1, NAS9-15466 (1979).

L. L. Biehl, Purdue University; private communication (1980).

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Figures (23)

Fig. 1
Fig. 1

Example of the systematic scan-angle dependence of radiance in channel 1 of the NOAA-6 AVHRR. The 7300 sampled pixels were selected from an apparently cloud-free section of 10 July 1980 imagery over the north central U.S.A. Plotted are the mean and plus or minus two standard deviations at each scan angle.

Fig. 2
Fig. 2

Example of the systematic scan-angle dependence of radiance in channel 2 of the NOAA-6 AVHRR. The data set is the same as for Fig. 1.

Fig. 3
Fig. 3

Example of the systematic scan-angle dependence of the vegetative index, AVHRR 2 − AVHRR 1. The data set is the same as for Figs. 1 and 2. A quadratic regression line has been included to show the trend.

Fig. 4
Fig. 4

Geometric nomenclature for reflectance factor description.

Fig. 5
Fig. 5

Spectral reflectance of soybeans for various levels of disease stress.

Fig. 6
Fig. 6

Spectral reflectance of the healthy wheat and soybean targets used in contrast to the stressed soybean targets.

Fig. 7
Fig. 7

Discriminability function of wheat at the growth stage 3.5 on the modified Feeks scale from soybeans at various stress severity levels. Data are shown as a function of wavelength. Stress is the percentage of the leaf area affected by rust. The relative proportions of target and cloud in each pixel and the variance levels are shown in Table I and in Figs. 714, respectively.

Fig. 15
Fig. 15

Discriminability function at the shown wavelength for the separation of healthy soybeans from soybeans at the same growth stage at various levels of stress. Each set of four diagrams (i.e., for each of the two wavelengths) relates to each of the cases considered in Table I. The variance levels for the relative proportions of each pixel occupied by target and by cloud (as shown in Table I) are shown in Figs. 1522.

Fig. 23
Fig. 23

Discriminability function dependence on scan angle at 800 nm for the separation of wheat at the growth stage 3.5 on the modified Feeks scale from a target consisting of (70% wheat + 30% soil).

Tables (1)

Tables Icon

Table I Four Cases Analyzed Showing the Proportions of Cloud Present over Target A (ac) and over Target B ( a C )

Equations (10)

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N S r = λ 1 λ 2 I ( λ ) · [ E ( θ , λ ) · , R ( θ , ϕ ; θ , ϕ , λ ) · τ ( θ , λ ) + L path ( θ 1 , ϕ 1 ; θ 1 , ϕ 1 , λ ) ] · d λ λ 1 λ 2 I ( λ ) · d λ ,
R ( θ , ϕ ; θ , ϕ , λ ) = [ a A · R A ( θ , ϕ ; θ , ϕ , λ ) + a c · R ( λ ) cloud ] .
L ( λ ) A = E ( θ , λ ) [ a A · R A ( θ , ϕ ; θ , ϕ , λ ) + a C · R ( λ ) cloud ] · τ ( θ , λ ) + L path ( θ 1 , ϕ 1 ; θ 1 , ϕ 1 , λ ) ,
L ( λ ) A = E · a A · R A · τ + E · a C · R C · τ + L p ,
( σ L L ) A = ( a A · R A · τ + a C · R C · τ ) 2 · σ E E + E 2 · R A 2 · τ 2 · σ a A a A + E 2 · R C 2 · τ 2 · σ a C a C + E 2 · a A 2 · τ 2 · σ R A R A + E 2 · a C 2 · τ 2 · σ R C R C + ( E · a A · R A + E · a C · R C ) 2 · σ τ τ + 2 E 2 · R A · R C · τ 2 · σ a A a C + σ L p L p .
H W [ ( L ¯ ) A - ( L ¯ ) B ] = t 0.5 , m - 1 m [ ( σ L L ) A + ( σ L L ) B ] 1 / 2 ,
[ ( L ¯ r ) A - ( L ¯ r ) B ] ,
H W [ ( L ¯ ) A - ( L ¯ ) B ] = t 0.5 , m - 1 m [ ( a A · R A · τ + a c · R c · τ ) 2 · σ E E + E 2 · R A 2 · τ 2 · σ a A a A + E 2 · R c 2 · τ 2 · σ a C a C + E 2 · a A 2 · τ 2 · σ R A R A + E 2 · a c 2 · τ 2 · σ R c R c + ( E · a A · R A + E · a c · R c ) 2 · σ τ τ + ( a B · R B · τ + a c · R c · τ ) 2 · σ E E + E 2 · R B 2 · τ 2 · σ a B a B + E 2 · R c 2 · τ 2 σ a C a C + E 2 · a B 2 · τ 2 · σ R B R B + E 2 · a c 2 · τ 2 · σ R c R c + ( E · a B · R B + E · a c · R c ) 2 · σ τ τ + 2 σ L p L p + 2 E 2 · R c · τ 2 · ( R A · σ a A a C + R B · σ a B a C ) ] 1 / 2 .
H W [ ( L ) A - ( L ) B ] = t 0.5 , m - 1 m { [ a A · R A ( z 1 , ϕ 1 ; θ 1 , ϕ 1 , λ ) · τ ( θ 1 , λ ) + a C · R C ( λ ) · τ ( θ 1 , λ ) ] 2 · σ E E + E 2 ( z 1 , λ ) · R A 2 ( z 1 , ϕ 1 ; θ 1 , ϕ 1 , λ ) · τ 2 ( θ 1 , λ ) · σ a A a A + E 2 ( z 1 , λ ) · R C 2 ( λ ) · τ 2 ( θ 1 , λ ) · σ a C a C + E 2 ( z 1 , λ ) · a A 2 · τ 2 ( θ 1 , λ ) · σ R A R A + E 2 ( z 1 , λ ) · a C 2 · τ 2 ( θ , λ ) · σ R C R C + E 2 ( z 1 , λ ) · [ a A · R A ( z 1 , ϕ 1 ; θ 1 , ϕ 1 , λ ) + a C · R C ( λ ) ] 2 · σ τ τ + E 2 ( z 2 , λ ) · R B 2 ( z 2 , ϕ 2 ; θ 2 , ϕ 2 , λ ) · τ 2 ( θ 2 , λ ) · σ a B a B + [ a B · R B ( z 2 , ϕ 2 ; θ 2 , ϕ 2 , λ ) · τ ( θ 2 , λ ) + a C · R C ( λ ) · τ ( θ 2 , λ ) ] 2 · σ E E + E 2 ( z 2 , λ ) · R C 2 ( λ ) · τ 2 ( θ 2 , λ ) · σ a C a C + E 2 ( z 2 , λ ) · a B 2 · τ 2 ( θ 2 , λ ) · σ R B R B + E 2 ( z 2 , λ ) · a C 2 · τ 2 ( θ 2 , λ ) · σ R C R C + E 2 ( z 2 , λ ) [ a B · R B ( z 2 , ϕ 2 ; θ 2 , ϕ 2 , λ ) + a C · R C ( λ ) ] 2 · σ τ τ + 2 σ L p L p + 2 E 2 ( z 1 , λ ) · R C ( λ ) · R A ( z 1 , ϕ 1 ; θ 1 , ϕ 1 , λ ) · τ 2 ( θ 1 , λ ) · σ a A a C + 2 E 2 ( z 2 , λ ) · R C ( λ ) · R B ( z 2 , ϕ 2 ; θ 2 , ϕ 2 , λ ) · τ 2 ( θ 2 , λ ) · σ a B a C } 1 / 2 ,
D F = H W ( L ¯ A - L ¯ B ) λ L ¯ A - L ¯ B λ ,

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