Abstract

A general procedure is introduced for sidelobe and noise reduction in optical or digital signal processing. Specific examples of sidelobe reduction in imaging are presented. It is demonstrated that the new method provides superior spatial resolution to previously proposed sidelobe-reduction techniques.

© 1993 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. H. C. Andrews, B. R. Hunt, Digital Image Restoration (Prentice-Hall, Englewood Cliffs, N.J., 1977).
  2. M. I. Skolnik, ed., Radar Handbook, 2nd ed. (McGraw-Hill, New York, 1990).
  3. F. E. Nathanson, J. P. Kelley, M. N. Cohen, Radar Design Principles, 2nd ed. (McGraw-Hill, New York, 1991).
  4. T. T. Taylor, “Design of line source antennas for narrow beam width and low sidelobe level,” IRE Trans. Antennas Propag. AP-3, 16–28 (1955).
  5. A. VanderLugt, “Signal detection by complex spatial filtering,” IEEE Trans. Inf. Theory IT-10, 139–145 (1964).
    [Crossref]
  6. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).
  7. B. V. K. V. Kumar, Z. Bahri, L. Hassebrook, “Review of synthetic discriminant function algorithms,” in Real-Time Signal Processing for Industrial Applications, B. Javidi, ed., Proc. Soc. Photo-Opt. Instrum. Eng.,960, 18–28 (1988).
  8. U. Mahlab, J. Shamir, “Optical pattern recognition based on convex functions,” J. Opt. Soc. Am. A 8, 1233–1239 (1991).
    [Crossref]
  9. G. Zalman, J. Shamir, “Maximum discrimination filter,” J. Opt. Soc. Am. A 8, 814–821 (1991).
    [Crossref]
  10. U. Mahlab, J. Shamir, H. J. Caulfield, “Genetic algorithm for optical pattern recognition,” Opt. Lett. 16, 648–650 (1991).
    [Crossref] [PubMed]
  11. S. M. Watson, J. P. Mills, S. L. Gaiser, D. J. Diner, “Direct imaging of nonsolar planets with infrared telescopes using apodized coronagraphs,” Appl. Opt. 30, 3253–3262 (1991).
    [Crossref] [PubMed]

1991 (4)

1964 (1)

A. VanderLugt, “Signal detection by complex spatial filtering,” IEEE Trans. Inf. Theory IT-10, 139–145 (1964).
[Crossref]

1955 (1)

T. T. Taylor, “Design of line source antennas for narrow beam width and low sidelobe level,” IRE Trans. Antennas Propag. AP-3, 16–28 (1955).

Andrews, H. C.

H. C. Andrews, B. R. Hunt, Digital Image Restoration (Prentice-Hall, Englewood Cliffs, N.J., 1977).

Bahri, Z.

B. V. K. V. Kumar, Z. Bahri, L. Hassebrook, “Review of synthetic discriminant function algorithms,” in Real-Time Signal Processing for Industrial Applications, B. Javidi, ed., Proc. Soc. Photo-Opt. Instrum. Eng.,960, 18–28 (1988).

Caulfield, H. J.

Cohen, M. N.

F. E. Nathanson, J. P. Kelley, M. N. Cohen, Radar Design Principles, 2nd ed. (McGraw-Hill, New York, 1991).

Diner, D. J.

Gaiser, S. L.

Goodman, J. W.

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

Hassebrook, L.

B. V. K. V. Kumar, Z. Bahri, L. Hassebrook, “Review of synthetic discriminant function algorithms,” in Real-Time Signal Processing for Industrial Applications, B. Javidi, ed., Proc. Soc. Photo-Opt. Instrum. Eng.,960, 18–28 (1988).

Hunt, B. R.

H. C. Andrews, B. R. Hunt, Digital Image Restoration (Prentice-Hall, Englewood Cliffs, N.J., 1977).

Kelley, J. P.

F. E. Nathanson, J. P. Kelley, M. N. Cohen, Radar Design Principles, 2nd ed. (McGraw-Hill, New York, 1991).

Kumar, B. V. K. V.

B. V. K. V. Kumar, Z. Bahri, L. Hassebrook, “Review of synthetic discriminant function algorithms,” in Real-Time Signal Processing for Industrial Applications, B. Javidi, ed., Proc. Soc. Photo-Opt. Instrum. Eng.,960, 18–28 (1988).

Mahlab, U.

Mills, J. P.

Nathanson, F. E.

F. E. Nathanson, J. P. Kelley, M. N. Cohen, Radar Design Principles, 2nd ed. (McGraw-Hill, New York, 1991).

Shamir, J.

Taylor, T. T.

T. T. Taylor, “Design of line source antennas for narrow beam width and low sidelobe level,” IRE Trans. Antennas Propag. AP-3, 16–28 (1955).

VanderLugt, A.

A. VanderLugt, “Signal detection by complex spatial filtering,” IEEE Trans. Inf. Theory IT-10, 139–145 (1964).
[Crossref]

Watson, S. M.

Zalman, G.

Appl. Opt. (1)

IEEE Trans. Inf. Theory (1)

A. VanderLugt, “Signal detection by complex spatial filtering,” IEEE Trans. Inf. Theory IT-10, 139–145 (1964).
[Crossref]

IRE Trans. Antennas Propag. (1)

T. T. Taylor, “Design of line source antennas for narrow beam width and low sidelobe level,” IRE Trans. Antennas Propag. AP-3, 16–28 (1955).

J. Opt. Soc. Am. A (2)

Opt. Lett. (1)

Other (5)

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

B. V. K. V. Kumar, Z. Bahri, L. Hassebrook, “Review of synthetic discriminant function algorithms,” in Real-Time Signal Processing for Industrial Applications, B. Javidi, ed., Proc. Soc. Photo-Opt. Instrum. Eng.,960, 18–28 (1988).

H. C. Andrews, B. R. Hunt, Digital Image Restoration (Prentice-Hall, Englewood Cliffs, N.J., 1977).

M. I. Skolnik, ed., Radar Handbook, 2nd ed. (McGraw-Hill, New York, 1990).

F. E. Nathanson, J. P. Kelley, M. N. Cohen, Radar Design Principles, 2nd ed. (McGraw-Hill, New York, 1991).

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 (8)

Fig. 1
Fig. 1

4-f optical processor that may contain linear or nonlinear devices at each plane noted.

Fig. 2
Fig. 2

Output-plane distributions when the system shown in Fig. 1 is used as a conventional linear imaging of a point source: (a) imaging with a square aperture aligned with the axes, (b) square processing aperture rotated by 45°.

Fig. 3
Fig. 3

PSF p for (a) p = 1, (b) p = 4, (c) p = 0.3.

Fig. 4
Fig. 4

Square-aperture image synthesis with two equal-amplitude point sources. The two conventional images through the corresponding apertures are shown at the top, and processed images, with p as a parameter, are shown in the middle and at the bottom.

Fig. 5
Fig. 5

Square-aperture image synthesis with two closely spaced point sources differing in amplitude by a factor of 16.

Fig. 6
Fig. 6

Along-axis 3-dB width versus peak-to-sidelobe ratio for various sidelobe reduction algorithms. On the Rota-Lobe curve, p equals 1 around the bend and increases toward the left.

Fig. 7
Fig. 7

Along-axis first-zero location versus peak-to-sidelobe ratio. The shaded area corresponds to various weighting parameters used in the Taylor method.

Fig. 8
Fig. 8

Image synthesis comparing uniform aperture weighting to Rota-Lobe and to 35-dB Taylor weighting for extended objects.

Equations (7)

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

s i ( x , y ) = f ( x , y ) * h i ( x , y ) ,
c ( x , y ) = O { s 1 , s 2 , s n } ,
c p ( x , y ) = O p { s 1 , s 2 } = ½ s 1 + s 2 p - s 1 - s 2 p 1 / p ,
PSF p = ½ | | sinc ( a x ) sinc ( a y ) + sinc ( a x - y 2 ) sinc ( a x + y 2 ) | p - | sinc ( a x ) sinc ( a y ) - sinc ( a x - y 2 ) sinc ( a x + y 2 ) | p | 1 / p .
PSF p = ½ [ ( m + s ) + ( m r + s r ) p - ( m + s ) - ( m r + s r ) p ] 1 / p .
PSF p m + ½ [ s + s r p - s - s r p ] 1 / p .
PSF p m + ( s s r ) 1 / 2 .

Metrics