Generalized Falling-Raster/Folded-Spectrum Relationship

David N. Sitter Jr.; William T. Rhodes

doi:10.1117/12.947916

8 February 1988 Generalized Falling-Raster/Folded-Spectrum Relationship

David N. Sitter Jr., William T. Rhodes

Proceedings Volume 0963, Optical Computing '88; (1988) https://doi.org/10.1117/12.947916
Event: Optical Computing '88, 1988, Toulon, France

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.

Citation Download Citation

David N. Sitter Jr. and William T. Rhodes "Generalized Falling-Raster/Folded-Spectrum Relationship", Proc. SPIE 0963, Optical Computing '88, (8 February 1988); https://doi.org/10.1117/12.947916

ACCESS THE FULL ARTICLE

INSTITUTIONAL
Select your institution to access the SPIE Digital Library.

SELECT YOUR INSTITUTION

PERSONAL
Sign in with your SPIE account to access your personal subscriptions or to use specific features such as save to my library, sign up for alerts, save searches, etc.

PERSONAL SIGN IN

No SPIE Account? Create one

PURCHASE THIS CONTENT

SUBSCRIBE TO DIGITAL LIBRARY

50 downloads per 1-year subscription

Members: $195

Non-members: $335 ADD TO CART

25 downloads per 1 - year subscription

Members: $145

Non-members: $250 ADD TO CART

PURCHASE SINGLE ARTICLE

Includes PDF, HTML & Video, when available

Members: $17.00

Non-members: $21.00 ADD TO CART

PROCEEDINGS
3 PAGES

DOWNLOAD PAPER SAVE TO MY LIBRARY

GET CITATION

RIGHTS & PERMISSIONS

Get copyright permission Get copyright permission on Copyright Marketplace

KEYWORDS

Raster graphics

Spectrum analysis

Parallel processing

Analog electronics

Convolution

Electrical engineering

Fourier transforms

Show All Keywords

Keywords/Phrases

Search In:

Publication Years