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.
Similar content being viewed by others
References
Antweiler, M., and Lüke, H.D.: 1994, 'Mismatched-Filterung periodischer Binärarrays', Frequenz 48, 58-65.
Baumert, L.D.: 1971, Cyclic Difference Sets (Springer-Verlag, New York).
Baumslag, B., and Chandler, B.: 1979, Theory and Problems of Group Theory (McGraw-Hill, New York, NY).
Beth, T., Jungnickel, D., and Lenz, H.: 1985, Design Theory (Bibliographisches Institut, Mannheim).
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.
BÖmer, L., and Antweiler, M.: 1990, 'Two-dimensional perfect binary arrays with 64 elements', IEEE Trans. Inf. Theory 36, 411-414.
BÖmer, L., Antweiler, M., and Schotten, H.: 1993, 'Quadratic residue arrays', Frequenz 47, 190-196.
BÖmer, L., and Antweiler, M.: 1993, 'Optimizing the aperiodic merit factor of binary arrays', Signal Processing 30, 1-13.
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.
Busboom, A., Schotten, H.D., and Elders-Boll, H.: 1997b, 'Coded aperture imaging with multiple measurements', J. Opt. Soc. Am. A 14, 1058-1065.
Calabro, D., and Wolf, J.K.: 1968, 'On the synthesis of two-dimensional binary arrays with desirable correlation properties', Inform. Contr. 11, 537-560.
Chan, Y.K., Siu, M.K., and Tong, P.: 1979, 'Two-dimensional binary arrays with good autocorrelation', Inform. Contr. 42, 125-130.
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.
Dicke, R.H.: 1968, 'Scatter-hole cameras for x-rays and gamma rays', Astrophys. J. 153, L101-L106.
Fenimore, E.E., and Cannon, T.M.: 1978, 'Coded aperture imaging with uniformly redundant arrays', Appl. Opt. 17, 337-347.
Fenimore, E.E.: 1978, 'Coded aperture imaging: predicted performance of uniformly redundant arrays', Appl. Opt. 17, 3562-3570.
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.
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.
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.
In't Zand, J.J.M., Heise, J., and Jager, R.: 1994, 'The optimum open fraction of coded apertures', Astron. Astrophys. 288, 665-674.
Jedwab, J., and Mitchell C.: 1988, 'Constructing new perfect binary arrays', Electron. Lett. 24, 650-652.
Jedwab, J., and Mitchell, C.: 1990, 'Infinite families of quasiperfect and doubly quasiperfect binary arrays', Electron. Lett. 26, 294-295.
Kopilovich, L.E.: 1989, 'Difference sets in noncyclic abelian groups', Cybernetics 25, 153-157.
Lander, E.S.: 1981, 'Symmetric designs and self-dual codes', Journal of the London Mathematical Society 24, 193-204.
Lidl, R., and Niederreiter, H.: 1983, Finite Fields (Addison-Wesley, Reading, MA).
Lüke, H.D.: 1987, 'Zweidimensionale Folgen mit perfekten periodischen Korrelationsfunktionen', Frequenz 41, 131-137.
Lüke, H.D.: 1992, Korrelationssignale (Springer-Verlag, New York).
Lüke, H.D., and Busboom, A.: 1997, 'Binary arrays with perfect odd-periodic autocorrelation', Appl. Opt. 36, 6612-6619.
Lüke, H.D., and Busboom, A.: 1998, 'Mismatched filtering of periodic and odd-periodic binary arrays', Appl. Opt., 37, 856-864.
MacWilliams, F., and Sloane, N.J.A.: 1976, 'Pseodo-random sequences and arrays', Proc. IEEE 64, 1715-1729.
McFarland, R.L.: 1973, 'A family of difference sets in non-cyclic groups', J. Comb. T. (A) 15, 1-10.
Mertz, L., and Young, N.O.: 1961, 'Fresnel transformations of images', Proc. Int. Conf. Optical Instruments and Techniques (Chapman and Hall, London), p. 305.
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.
Skinner, G.K.: 1984, 'Imaging with coded-aperture masks', Nucl. Instr. and Meth. 221, 33-40.
Skinner, G.K., and Ponman, T.J.: 1995, 'Inverse problems in x-ray and gamma-ray astronomical imaging', Inverse Problems 10, 655-676.
Spann, R.: 1965, 'A two-dimensional correlation property of pseudorandom maximal length sequences', Proc. IEEE 53, 2137.
Spence, E.: 1977, 'A family of difference sets', J. Comb. Th. (A) 22, 103-106.
Wild, P.: 1988, 'Infinite families of perfect binary arrays', Electron. Lett. 24, 845-847.
Author information
Authors and Affiliations
Rights 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
Issue Date:
DOI: https://doi.org/10.1023/A:1007966830741