Optically efficient free-space folded perfect shuffle network

Michael W. Haney; James J. Levy

doi:10.1364/AO.30.002833

Applied Optics
Vol. 30,
Issue 20,
pp. 2833-2840
(1991)
•https://doi.org/10.1364/AO.30.002833

Optically efficient free-space folded perfect shuffle network

Michael W. Haney and James J. Levy

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Michael W. Haney and James J. Levy, "Optically efficient free-space folded perfect shuffle network," Appl. Opt. 30, 2833-2840 (1991)

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Abstract

A light-efficient folded perfect shuffle network is described. Two-dimensional (2-D) raster encoding of the processing element nodes is used to accommodate large arrays with simple imaging optics. The network uses 2-D arrays of lenslets and prisms to correct for magnification and replication losses. Simulation results show the required prism arrays to be of low complexity and suggest that the network is tolerant to imperfections in the prism parameters.

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Input Half-Arrays

Stage m	Stage m + 1	ΔSlope × 9f/2d
Upper	Upper	0
Upper	Lower	−N + 1
Lower	Upper	N − 1
Lower	Lower	0

Input Quadrants		ΔSlope × 9f/2d

Stage m	Stage m + 1	Horizontal	Vertical
I	I	−N^1/2 + 1	−N^1/2 + 1
	II	−N^1/2	1
	III	1	−N^1/2
	IV	0	0
II	I	−N^1/2	1
	II	−N^1/2 − 1	N^1/2 + 1
	III	0	0
	IV	−1	N^1/2
III	I	1	−N^1/2
	II	0	0
	III	N^1/2 + 1	−N^1/2 − 1
	IV	N^1/2	−1
IV	I	0	0
	II	−1	N^1/2
	III	N^1/2	−1
	IV	N^1/2 − 1	N^1/2 − 1

	Behavior

f (mm)	0% Fill Factor (Central Ray)	40% Fill Factor	75% Fill Factor
12.5	Lossless through 25 stages	n = 8 loses 4% in stage 7	Total internal reflection occurs at n = 8
15	Lossless through 25 stages	Lossless through 25 stages	n = 8 loses 12% in stage 1
20	Lossless through 25 stages	Lossless through 25 stages	n = 7 loses 3.2% in stage 9
25	Lossless through 25 stages	Lossless through 25 stages	Lossless through 25 stages

Input Half-Arrays

Stage m	Stage m + 1	ΔSlope × 9f/2d
Upper	Upper	0
Upper	Lower	−N + 1
Lower	Upper	N − 1
Lower	Lower	0

Input Quadrants		ΔSlope × 9f/2d

Stage m	Stage m + 1	Horizontal	Vertical
I	I	−N^1/2 + 1	−N^1/2 + 1
	II	−N^1/2	1
	III	1	−N^1/2
	IV	0	0
II	I	−N^1/2	1
	II	−N^1/2 − 1	N^1/2 + 1
	III	0	0
	IV	−1	N^1/2
III	I	1	−N^1/2
	II	0	0
	III	N^1/2 + 1	−N^1/2 − 1
	IV	N^1/2	−1
IV	I	0	0
	II	−1	N^1/2
	III	N^1/2	−1
	IV	N^1/2 − 1	N^1/2 − 1

Abstract

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Figures (11)

Tables (3)

Equations (11)

Applied Optics