Skip to main content
Log in

Uniformly Redundant Arrays

  • Published:
Experimental Astronomy Aims and scope Submit manuscript

Abstract

Uniformly Redundant Arrays (URA's) are two–dimensional binary arrays with constant sidelobes of their periodic autocorrelation function. They are widely agreed upon to be optimum mask patterns for coded aperture imaging, particularly in imaging systems with a cyclic coded mask. In this paper, a survey of all currently known construction methods for URA's is given and the sizes and open fractions of the arrays resulting from each construction method are pointed out. Alternatives to URA's for situations in which a URA does not exist, are discussed.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Antweiler, M., and Lüke, H.D.: 1994, 'Mismatched-Filterung periodischer Binärarrays', Frequenz 48, 58-65.

    Google Scholar 

  • Baumert, L.D.: 1971, Cyclic Difference Sets (Springer-Verlag, New York).

    Google Scholar 

  • Baumslag, B., and Chandler, B.: 1979, Theory and Problems of Group Theory (McGraw-Hill, New York, NY).

    Google Scholar 

  • Beth, T., Jungnickel, D., and Lenz, H.: 1985, Design Theory (Bibliographisches Institut, Mannheim).

    Google Scholar 

  • BÖmer, L., and Antweiler, M.: 1989, 'Two-dimensional binary arrays with constant sidelobes in their PACF', Proc. IEEE Int. Conf. Acoust., Speech, Signal Processing (Institute of Electrical and Electronics Engineers, Piscataway, NJ), pp. 2768-2771.

    Google Scholar 

  • BÖmer, L., and Antweiler, M.: 1990, 'Two-dimensional perfect binary arrays with 64 elements', IEEE Trans. Inf. Theory 36, 411-414.

    Google Scholar 

  • BÖmer, L., Antweiler, M., and Schotten, H.: 1993, 'Quadratic residue arrays', Frequenz 47, 190-196.

    Google Scholar 

  • BÖmer, L., and Antweiler, M.: 1993, 'Optimizing the aperiodic merit factor of binary arrays', Signal Processing 30, 1-13.

    Google Scholar 

  • Busboom, A., Elders-Boll, H., and Schotten, H.D.: 1997a, 'Combinatorial design of near-optimum masks for coded aperture imaging', Proc. IEEE Int. Conf. Acoust., Speech, Signal Processing (Institute of Electrical and Electronics Engineers, Piscataway, NJ), pp. 2817-2820.

    Google Scholar 

  • Busboom, A., Schotten, H.D., and Elders-Boll, H.: 1997b, 'Coded aperture imaging with multiple measurements', J. Opt. Soc. Am. A 14, 1058-1065.

    Google Scholar 

  • Calabro, D., and Wolf, J.K.: 1968, 'On the synthesis of two-dimensional binary arrays with desirable correlation properties', Inform. Contr. 11, 537-560.

    Google Scholar 

  • Chan, Y.K., Siu, M.K., and Tong, P.: 1979, 'Two-dimensional binary arrays with good autocorrelation', Inform. Contr. 42, 125-130.

    Google Scholar 

  • Cook, W.R., Finger, M., Prince, T.A., and Stone, E.C.: 1984, 'Gamma-ray imaging with a rotating hexagonal uniformly redundant array', IEEE Trans. Nucl. Sci. 31, 771-775.

    Google Scholar 

  • Dicke, R.H.: 1968, 'Scatter-hole cameras for x-rays and gamma rays', Astrophys. J. 153, L101-L106.

    Google Scholar 

  • Fenimore, E.E., and Cannon, T.M.: 1978, 'Coded aperture imaging with uniformly redundant arrays', Appl. Opt. 17, 337-347.

    Google Scholar 

  • Fenimore, E.E.: 1978, 'Coded aperture imaging: predicted performance of uniformly redundant arrays', Appl. Opt. 17, 3562-3570.

    Google Scholar 

  • Finger, M.H., and Prince, T.A.: 1985, 'Hexagonal uniformly redundant arrays for coded-aperture imaging', Proc. 19th Int. Cosmic Ray Conf. (Scientific and Technical Information Branch, NASA, Washington, DC), pp. 295-298.

    Google Scholar 

  • Goldwurm, A., and Byard, K., and Dean, A.J., and Hall, C.J., and Harding, J.S.J.: 'Laboratory images with HURA coded apertures', Astron. Astrophys. 227, 640-648.

  • Gottesman, S.R., and Fenimore, E.E.: 1989, 'New family of binary arrays for coded aperture imaging', Appl. Opt. 28, 4344-4352.

    Google Scholar 

  • Gunson, J., and Polychronopulos, B.: 1976, 'Optimum design of a coded mask X-ray telescope for rocket applications', Mon. Not. R. astr. Soc. 177, 485-497.

    Google Scholar 

  • In't Zand, J.J.M., Heise, J., and Jager, R.: 1994, 'The optimum open fraction of coded apertures', Astron. Astrophys. 288, 665-674.

    Google Scholar 

  • Jedwab, J., and Mitchell C.: 1988, 'Constructing new perfect binary arrays', Electron. Lett. 24, 650-652.

    Google Scholar 

  • Jedwab, J., and Mitchell, C.: 1990, 'Infinite families of quasiperfect and doubly quasiperfect binary arrays', Electron. Lett. 26, 294-295.

    Google Scholar 

  • Kopilovich, L.E.: 1989, 'Difference sets in noncyclic abelian groups', Cybernetics 25, 153-157.

    Google Scholar 

  • Lander, E.S.: 1981, 'Symmetric designs and self-dual codes', Journal of the London Mathematical Society 24, 193-204.

    Google Scholar 

  • Lidl, R., and Niederreiter, H.: 1983, Finite Fields (Addison-Wesley, Reading, MA).

    Google Scholar 

  • Lüke, H.D.: 1987, 'Zweidimensionale Folgen mit perfekten periodischen Korrelationsfunktionen', Frequenz 41, 131-137.

    Google Scholar 

  • Lüke, H.D.: 1992, Korrelationssignale (Springer-Verlag, New York).

    Google Scholar 

  • Lüke, H.D., and Busboom, A.: 1997, 'Binary arrays with perfect odd-periodic autocorrelation', Appl. Opt. 36, 6612-6619.

    Google Scholar 

  • Lüke, H.D., and Busboom, A.: 1998, 'Mismatched filtering of periodic and odd-periodic binary arrays', Appl. Opt., 37, 856-864.

    Google Scholar 

  • MacWilliams, F., and Sloane, N.J.A.: 1976, 'Pseodo-random sequences and arrays', Proc. IEEE 64, 1715-1729.

    Google Scholar 

  • McFarland, R.L.: 1973, 'A family of difference sets in non-cyclic groups', J. Comb. T. (A) 15, 1-10.

    Google Scholar 

  • Mertz, L., and Young, N.O.: 1961, 'Fresnel transformations of images', Proc. Int. Conf. Optical Instruments and Techniques (Chapman and Hall, London), p. 305.

    Google Scholar 

  • Rideout, M.R.: 1995, Coded Imaging Systems for X-ray Astronomy (PhD thesis, University of Birmingham).

  • Singer, J.: 1938, 'A theorem in finite projective geometry and some applications to number theory', Trans. Amer. Math. Soc. 43, 377-385.

    Google Scholar 

  • Skinner, G.K.: 1984, 'Imaging with coded-aperture masks', Nucl. Instr. and Meth. 221, 33-40.

    Google Scholar 

  • Skinner, G.K., and Ponman, T.J.: 1995, 'Inverse problems in x-ray and gamma-ray astronomical imaging', Inverse Problems 10, 655-676.

    Google Scholar 

  • Spann, R.: 1965, 'A two-dimensional correlation property of pseudorandom maximal length sequences', Proc. IEEE 53, 2137.

    Google Scholar 

  • Spence, E.: 1977, 'A family of difference sets', J. Comb. Th. (A) 22, 103-106.

    Google Scholar 

  • Wild, P.: 1988, 'Infinite families of perfect binary arrays', Electron. Lett. 24, 845-847.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Busboom, A., Elders–Boll, H. & Schotten, H.D. Uniformly Redundant Arrays. Experimental Astronomy 8, 97–123 (1998). https://doi.org/10.1023/A:1007966830741

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1007966830741

Navigation