Abstract

Airborne synthetic-aperture radar (SAR) systems employ coherent techniques to generate images of terrain in the microwave region of the spectrum. The high degree of coherence required by radar system considerations results in the presence of radar speckle when diffuse scatterers are imaged. It is possible to introduce frequency and/or angle diversity in such a manner that multiple uncorrelated images of the terrain may be generated and then summed incoherently to reduce the speckle. When system bandwidth and/or viewing angle is severely constrained, then a compromise must be made between image resolution and speckle reduction. Visual examination of controlled samples of radar imagery shows that speckle is reduced noticeably when incoherent summation of uncorrelated images is provided via use of diversity. Some examples of radar images with varying degrees of diversity are presented in the paper and are compared qualitatively.

© 1976 Optical Society of America

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References

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  1. L. J. Cutrona, “Synthetic Aperture Radar,” in Radar Handbook, edited by M. I. Skolnik (McGraw-Hill, New York, 1970), Chap. 23.
  2. R. O. Harger, Synthetic Aperture Radar Systems: Theory and Design (Academic, New York, 1970).
  3. W. M. Brown and L. J. Porcello, “An Introduction to Synthetic Aperture Radar,” IEEE Spectrum 6, 52–62 (1969).
    [Crossref]
  4. E. N. Leith and A. L. Ingalls, “Synthetic Antenna Data Processing by Wavefront Reconstruction,” App. Opt. 7, 539–544 (1968).
    [Crossref]
  5. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).
  6. R. W. Lewis, “Redundancy in Coherent Imaging Systems,” Ph.D. Thesis (The University of Michigan, 1973) (unpublished) (University Microfilms, Ann Arbor, Mich., Order No. 73–24619).
  7. W. A. Penn, “Signal Fidelity in Radar Processing,” IRE Trans. Mil. Electron. MIL-6, 204–218 (1962).
    [Crossref]
  8. L. J. Cutrona and G. O. Hall, “A Comparison of Techniques for Achieving Fine Azimuth Resolution,” IRE Trans. Mil. Electron. MIL-6, 119–121 (1962).
    [Crossref]
  9. N. George and A. Jain, “Speckle in Microscopy,” Opt. Commun. 6, 253–257 (1972).
    [Crossref]
  10. E. N. Leith and J. Upatnieks, “Wavefront Reconstruction with Diffused Illumination and Three-Dimensional Objects,” J. Opt. Soc. Am. 54, 1295–1301 (1964).
    [Crossref]
  11. J. Upatnieks, “Improvement of Two-Dimensional Image Quality in Coherent Optical Systems,” Appl. Opt. 6, 1905–1910 (1967).
    [Crossref] [PubMed]
  12. L. J. Cutrona, E. N. Leith, L. J. Porcello, and W. E. Vivian, “On the Application of Coherent Optical Processing Techniques to Synthetic-Aperture Radar,” Proc. IEEE 54, 1026–1032 (1966).
    [Crossref]
  13. A. Kozma, E. N. Leith, and N. G. Massey, “Tilted-Plane Optical Processor,” Appl. Opt. 11, 1766–1777 (1972).
    [Crossref] [PubMed]
  14. J. S. Zelenka, “A Comparison of Continuous and Discrete Mixed-Integrator Processors,” J. Opt. Soc. Am. 66, 1303–1304 (1976) (this issue).
    [Crossref]
  15. C. J. Palermo, “Theory of Stochastic Delays,” Ph. D. Thesis, The University of Michigan (1963) (University Microfilms, Ann Arbor, Mich., Order No. 64-868).

1976 (1)

J. S. Zelenka, “A Comparison of Continuous and Discrete Mixed-Integrator Processors,” J. Opt. Soc. Am. 66, 1303–1304 (1976) (this issue).
[Crossref]

1972 (2)

1969 (1)

W. M. Brown and L. J. Porcello, “An Introduction to Synthetic Aperture Radar,” IEEE Spectrum 6, 52–62 (1969).
[Crossref]

1968 (1)

E. N. Leith and A. L. Ingalls, “Synthetic Antenna Data Processing by Wavefront Reconstruction,” App. Opt. 7, 539–544 (1968).
[Crossref]

1967 (1)

1966 (1)

L. J. Cutrona, E. N. Leith, L. J. Porcello, and W. E. Vivian, “On the Application of Coherent Optical Processing Techniques to Synthetic-Aperture Radar,” Proc. IEEE 54, 1026–1032 (1966).
[Crossref]

1964 (1)

1962 (2)

W. A. Penn, “Signal Fidelity in Radar Processing,” IRE Trans. Mil. Electron. MIL-6, 204–218 (1962).
[Crossref]

L. J. Cutrona and G. O. Hall, “A Comparison of Techniques for Achieving Fine Azimuth Resolution,” IRE Trans. Mil. Electron. MIL-6, 119–121 (1962).
[Crossref]

Brown, W. M.

W. M. Brown and L. J. Porcello, “An Introduction to Synthetic Aperture Radar,” IEEE Spectrum 6, 52–62 (1969).
[Crossref]

Cutrona, L. J.

L. J. Cutrona, E. N. Leith, L. J. Porcello, and W. E. Vivian, “On the Application of Coherent Optical Processing Techniques to Synthetic-Aperture Radar,” Proc. IEEE 54, 1026–1032 (1966).
[Crossref]

L. J. Cutrona and G. O. Hall, “A Comparison of Techniques for Achieving Fine Azimuth Resolution,” IRE Trans. Mil. Electron. MIL-6, 119–121 (1962).
[Crossref]

L. J. Cutrona, “Synthetic Aperture Radar,” in Radar Handbook, edited by M. I. Skolnik (McGraw-Hill, New York, 1970), Chap. 23.

George, N.

N. George and A. Jain, “Speckle in Microscopy,” Opt. Commun. 6, 253–257 (1972).
[Crossref]

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).

Hall, G. O.

L. J. Cutrona and G. O. Hall, “A Comparison of Techniques for Achieving Fine Azimuth Resolution,” IRE Trans. Mil. Electron. MIL-6, 119–121 (1962).
[Crossref]

Harger, R. O.

R. O. Harger, Synthetic Aperture Radar Systems: Theory and Design (Academic, New York, 1970).

Ingalls, A. L.

E. N. Leith and A. L. Ingalls, “Synthetic Antenna Data Processing by Wavefront Reconstruction,” App. Opt. 7, 539–544 (1968).
[Crossref]

Jain, A.

N. George and A. Jain, “Speckle in Microscopy,” Opt. Commun. 6, 253–257 (1972).
[Crossref]

Kozma, A.

Leith, E. N.

A. Kozma, E. N. Leith, and N. G. Massey, “Tilted-Plane Optical Processor,” Appl. Opt. 11, 1766–1777 (1972).
[Crossref] [PubMed]

E. N. Leith and A. L. Ingalls, “Synthetic Antenna Data Processing by Wavefront Reconstruction,” App. Opt. 7, 539–544 (1968).
[Crossref]

L. J. Cutrona, E. N. Leith, L. J. Porcello, and W. E. Vivian, “On the Application of Coherent Optical Processing Techniques to Synthetic-Aperture Radar,” Proc. IEEE 54, 1026–1032 (1966).
[Crossref]

E. N. Leith and J. Upatnieks, “Wavefront Reconstruction with Diffused Illumination and Three-Dimensional Objects,” J. Opt. Soc. Am. 54, 1295–1301 (1964).
[Crossref]

Lewis, R. W.

R. W. Lewis, “Redundancy in Coherent Imaging Systems,” Ph.D. Thesis (The University of Michigan, 1973) (unpublished) (University Microfilms, Ann Arbor, Mich., Order No. 73–24619).

Massey, N. G.

Palermo, C. J.

C. J. Palermo, “Theory of Stochastic Delays,” Ph. D. Thesis, The University of Michigan (1963) (University Microfilms, Ann Arbor, Mich., Order No. 64-868).

Penn, W. A.

W. A. Penn, “Signal Fidelity in Radar Processing,” IRE Trans. Mil. Electron. MIL-6, 204–218 (1962).
[Crossref]

Porcello, L. J.

W. M. Brown and L. J. Porcello, “An Introduction to Synthetic Aperture Radar,” IEEE Spectrum 6, 52–62 (1969).
[Crossref]

L. J. Cutrona, E. N. Leith, L. J. Porcello, and W. E. Vivian, “On the Application of Coherent Optical Processing Techniques to Synthetic-Aperture Radar,” Proc. IEEE 54, 1026–1032 (1966).
[Crossref]

Upatnieks, J.

Vivian, W. E.

L. J. Cutrona, E. N. Leith, L. J. Porcello, and W. E. Vivian, “On the Application of Coherent Optical Processing Techniques to Synthetic-Aperture Radar,” Proc. IEEE 54, 1026–1032 (1966).
[Crossref]

Zelenka, J. S.

J. S. Zelenka, “A Comparison of Continuous and Discrete Mixed-Integrator Processors,” J. Opt. Soc. Am. 66, 1303–1304 (1976) (this issue).
[Crossref]

App. Opt. (1)

E. N. Leith and A. L. Ingalls, “Synthetic Antenna Data Processing by Wavefront Reconstruction,” App. Opt. 7, 539–544 (1968).
[Crossref]

Appl. Opt. (2)

IEEE Spectrum (1)

W. M. Brown and L. J. Porcello, “An Introduction to Synthetic Aperture Radar,” IEEE Spectrum 6, 52–62 (1969).
[Crossref]

IRE Trans. Mil. Electron. (2)

W. A. Penn, “Signal Fidelity in Radar Processing,” IRE Trans. Mil. Electron. MIL-6, 204–218 (1962).
[Crossref]

L. J. Cutrona and G. O. Hall, “A Comparison of Techniques for Achieving Fine Azimuth Resolution,” IRE Trans. Mil. Electron. MIL-6, 119–121 (1962).
[Crossref]

J. Opt. Soc. Am. (2)

E. N. Leith and J. Upatnieks, “Wavefront Reconstruction with Diffused Illumination and Three-Dimensional Objects,” J. Opt. Soc. Am. 54, 1295–1301 (1964).
[Crossref]

J. S. Zelenka, “A Comparison of Continuous and Discrete Mixed-Integrator Processors,” J. Opt. Soc. Am. 66, 1303–1304 (1976) (this issue).
[Crossref]

Opt. Commun. (1)

N. George and A. Jain, “Speckle in Microscopy,” Opt. Commun. 6, 253–257 (1972).
[Crossref]

Proc. IEEE (1)

L. J. Cutrona, E. N. Leith, L. J. Porcello, and W. E. Vivian, “On the Application of Coherent Optical Processing Techniques to Synthetic-Aperture Radar,” Proc. IEEE 54, 1026–1032 (1966).
[Crossref]

Other (5)

C. J. Palermo, “Theory of Stochastic Delays,” Ph. D. Thesis, The University of Michigan (1963) (University Microfilms, Ann Arbor, Mich., Order No. 64-868).

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).

R. W. Lewis, “Redundancy in Coherent Imaging Systems,” Ph.D. Thesis (The University of Michigan, 1973) (unpublished) (University Microfilms, Ann Arbor, Mich., Order No. 73–24619).

L. J. Cutrona, “Synthetic Aperture Radar,” in Radar Handbook, edited by M. I. Skolnik (McGraw-Hill, New York, 1970), Chap. 23.

R. O. Harger, Synthetic Aperture Radar Systems: Theory and Design (Academic, New York, 1970).

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Figures (7)

FIG. 1
FIG. 1

Typical SLAR system geometry.

FIG. 2
FIG. 2

Two-dimensional spectrum diagram for a SAR system operating with N = 1. The vertical coordinate represents radar operating frequency and the horizontal coordinate represents Doppler frequency.

FIG. 3
FIG. 3

Two-dimensional spectrum diagram for a SAR system operating with N = NRND where NR > 1 and ND > 1.

FIG. 4
FIG. 4

Radar images, N = 1, of terrain region including fields and orchards. In this sequence, the resolution is degraded as one progresses from (a) through (c), and no diversity is introduced to compensate for the loss of resolution. (a) Case I result, 1.5 × 2.6 m resolution. (b) Case II result, 3 × 3 m resolution. (c) Case III result, 6 × 6 m resolution.

FIG. 5
FIG. 5

Radar images of same region as shown in Fig. 4, showing effect of increasing the diversity parameter N. The resolutions in (a) through (c) are identical, but N increases as one progresses through the sequence. Note that case I and case V use essentially identical spectral regions, but that case I uses the data in a fully coherent mode, while case V employs “mixed integration.” Image (d) is simply the fully coherent reference image shown in the previous figure. (a) Case III result, 6 × 6 m resolution, N = 1. (b) Case IV result, 6 × 6 m resolution, N = 4. (c) Case V result, 6 × 6 m resolution, N = 16. (d) Case I result, N = 1, 1.5 × 2.6 m.

FIG. 6
FIG. 6

Radar images, N = 1, of terrain region with assorted features. This sequence parallels that of Fig. 4 and shows the effect of degrading resolution when N = 1. (a) Case I result, 1.5 × 2.6 m resolution. (b) Case II result, 3 × 3 m resolution. (c) Case III result, 6 × 6 m resolution.

FIG. 7
FIG. 7

Radar images of same region as shown in Fig. 6, showing effect of increasing N. This sequence parallels that of Fig. 5 in which the resolutions in (a) through (c) are identical, but N increases as one progresses through the sequence. Image (d) is the fully coherent (N = 1) reference image of this scene, also shown in Fig. 6. (a) Case III result, 6 × 6 m resolution, N = 1. (b) Case IV result, 6 × 6 m resolution, N = 4. (c) Case V result, 6 × 6 m resolution, N = 16. (d) Case I result, N = 1, 1.5 × 2.6 m

Tables (1)

Tables Icon

TABLE I Parameter combinations used in sample imagery.

Equations (19)

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σ ¯ σ 0 ρ x ρ R sec ψ ,
p I ( μ ) = ( 1 / σ 0 ) exp ( - μ / σ 0 )             0 μ < .
p I ( μ ) = 1 ( σ 0 / N ) ( N - 1 ) ! ( μ σ 0 / N ) N - 1 exp ( - μ σ 0 / N )             0 μ < .
ρ x ( λ R / 2 D ) ,
R 0 = c t / 2 ,
ρ r = ( c / 2 ) ρ t ,
ρ t 1 / W ,
ρ r = c / 2 W
ρ y = ρ r sec ψ .
ρ x = v / Δ f D ,
Δ f D = ( 2 v / λ ) Δ ( sin θ ) .
Δ f D ( 2 v / λ ) Δ θ ,
ρ x λ / 2 Δ θ .
ρ x D / 2
W = N r ( c / 2 ρ r ) ,
Δ θ = N D ( λ / 2 ρ x ) ,
Δ f D = N D ( v / ρ x ) .
ρ r = N R ( ρ r ) coherent = N R ( c / 2 W )
ρ x = N D ( ρ x ) coherent = N D ( v / Δ f D )