Error-source effects in a high-accuracy optical finite-element processor

Bradley K. Taylor; David P. Casasent

doi:10.1364/AO.25.000966

Applied Optics
Vol. 25,
Issue 6,
pp. 966-975
(1986)
•https://doi.org/10.1364/AO.25.000966

Error-source effects in a high-accuracy optical finite-element processor

Bradley K. Taylor and David P. Casasent

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Bradley K. Taylor and David P. Casasent, "Error-source effects in a high-accuracy optical finite-element processor," Appl. Opt. 25, 966-975 (1986)

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Abstract

High-accuracy optical linear algebra processors are addressed with attention to three new aspects. These include: their application to the solution of finite-element problems; the first error-source models for component errors in such processors; and the first analysis of error sources in such processors.

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PLANE	ERROR SOURCE	NOTATION/MODEL
P₁	Spatial Gain Variations (multiplicative)	1 + δ_i¹
P₂	Acoustic Attenuation	exp(-αx_i)
P₂	Crosstalk (adjacent and even-odd channels)	$s_{j \pm k}^{'} = {Ks}_{j} + s_{j \pm k}$
P₃	Spatial Response (multiplicative)	1 + δ_j³
	Time-varying Noise (additive)	n_j(t)
	Dark Current (additive)	d_j
	A/D Conversion	Triangular Probability
		if Within Central 0.5
		Between Levels

		RANDOM EQUAL NO. 1's AND 0's		LARGE NO. OK ADJACENT 1's		FEW 1's; LARGE NO. ADJACENT 0's

TEST NO.	ERROR TYPE	% ERRORS	NO.BIT ERROR	% ERRORS	NO.BIT ERROR	% ERROR	NO.BIT ERRORS	REMARKS

1	P₁	50%	0	40%	0	60%	0	Multiplicative Errors Affect 1's Only
2	SPATIAL	60%	15	60%	12	70%	1	Multiplicative Errors Affect 1's Only

3	P₃	75%	0	90%	3	500%	2	Effect is Larger When More l's in Data
4	SPATIAL	80%	1					Effect is Larger When More l's in Data

5	P₃ NOISE	30%	0	30%	0	30%	0	Additive Errors are Worse than Multiplicative Ones
6	TIME	40%	1	40%	1	40%	1	Additive Errors are Worse than Multiplicative Ones

7	P₃ DARK CURRENT	35%	0	30%	0	30%	0	Additive Errors Affect Both 1's and 0's
8	(FIXED)	40%	1	40%	1	40%	1	Additive Errors Affect Both 1's and 0's

9	ADJACENT CROSSTALK	5dB	33	5dB	1	5dB	0	More Errors if More 1's Dependent on Position of 1's

INPUT SPATIAL GAIN ERROR		DETECTOR SPATIAL RESPONSE ERROR

Maximum Percent Error Siimulated	Average Percent Solution Error	Maximum Percent Error Simulated	Average Percent Solution Error
30.00	0.00	50.00	0.00
40.00	0.00	55.00	0.00
45.00	9.39	60.00	2.71
50.00	26.61	62.00	2.69
		65.00	54.82

DETECTOR TIME-VARYING NOISE		DETECTOR DARK CURRENT

Maximum Percent Full-Scale Error Simulated	Average Percent Solution Error	Maximum Percent Full-Scale Error Simulated	Average Percent Solution Error
10.00	0.00	25.00	0.00
18.00	0.00	30.00	0.00
18.65	0.00	33.80	0.00
18.75	126.40	33.90	123.31
20.00	126.40	35.00	8097.36
30.00	>10⁶	40.00	>10⁸

ACOUSTIC ATTENUATION

Attenuation Factor in dB/mm	Average Percent Solution Error
0.06	0.00
0.07	<0.01
0.08	1.31
0.09	3.09
0.10	21.24

ADJACENT AND EVEN-ODD CHANNEL CROSSTALK

Isolation in dB	Average Percent Solution Error
30.0	0.00
20.0	0.00
15.0	0.00
10.0	0.00
7.5	3.65
5.0	69.06

Test Number	1	5	10	11	13	15	17	22
Input Spatial Gain MPE	45	15	5	5	5	5	5	10

Detector Spatial Response MPE	62	30	5	5	5	5	5	10

Detector Time-Varying Noise MPFSE			2	5	5	5		6

Detector Dark Current MPFSE			2	5	5	5		8

Acoustic Attenuation dB/mm			0.09	0.08		0.08	0.08	0.03

Crosstalk Isolation in dB	∞	∞	20	20	20	∞	20	18

Average Percent Solution Error	246.53	0.00	4.78	2.92	0.00	2.87	1.99	<0.01

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Applied Optics