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Proceedings Paper

Generalized Falling-Raster/Folded-Spectrum Relationship
Author(s): David N. Sitter; William T. Rhodes
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Paper Abstract

The conventional falling-raster/folded-spectrum relationship is shown to be a special case of a more general mapping of a 1-D signal and its spectrum into two dimensions. The well-known falling-raster/folded-spectrum relationship [1,2] allows the full two-dimensional (2-D) parallel processing capabilities of a coherent optical spectrum analyzer to be applied to the spectrum analysis of time waveforms of extremely large (106) time-bandwidth product. The basic relationship has been exploited with considerable success in space-integrating, time-integrating, and hybrid space- and time-integrating optical processors. We show here that the conventional falling-raster/folded-spectrum relationship is a special case of a more general mapping of a 1-D signal and its spectrum into two dimensions. This generalized relationship can also be exploited for optical implementation. The conventional falling raster recording format is shown in Fig. 1. The numbers indicate the order in which the lines are recorded. The fall angle 0 is given by 0 = tan-1( NW ) , (1) where I NI is the number of raster lines and W and H are the raster width and height, identified in the figure. The generalized falling raster is obtained by allowing the fall angle to assume more general values given by = tan-1( NW where ' (2) where M and N are relatively prime nonzero integers. A total of 'MI + I NI - 1 raster lines is recorded in a raster of width W and height H. As illustrated in the example of Fig. 2, the raster record is laid down modulo-W in the horizontal direction and modulo-H in the vertical direction. Thus, if the raster line disappears at the right margin it reappears at the left; if it disappears at the bottom it reappears at the top. The conventional falling raster corresponds to the case where I MI = 1.

Paper Details

Date Published: 8 February 1988
PDF: 3 pages
Proc. SPIE 0963, Optical Computing '88, (8 February 1988); doi: 10.1117/12.947916
Show Author Affiliations
David N. Sitter, Georgia Institute of Technology (United States)
William T. Rhodes, Georgia Institute of Technology (United States)


Published in SPIE Proceedings Vol. 0963:
Optical Computing '88
Pierre H. Chavel; Joseph W. Goodman; Gerard Roblin, Editor(s)

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