Abstract

We discuss a technique whereby an optical–digital computer is trained to do particle-size analysis by sampling the light diffracted from a collection of particles in a coherent optical system. The computer learns the signatures of different particle classes by analyzing the light diffracted from mixed slides, i.e., slides containing more than one class of particles. Two alternative algorithms for particle-size estimation are given. Some important design considerations are discussed.

© 1977 Optical Society of America

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References

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  1. H. Stark, D. Lee, B. Dimitriadis, J. Opt. Soc. Am. 65, 1436 (1975).
    [CrossRef]
  2. H. Stark, D. Lee, B. W. Koo, Appl. Opt. 15, 2246 (1976).
    [CrossRef] [PubMed]
  3. W. L. Anderson, R. E. Beissner, Appl. Opt. 10, 1503 (1971).
    [CrossRef] [PubMed]

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1975 (1)

1971 (1)

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Figures (7)

Fig. 1
Fig. 1

Computer printout of a typical unsmoothed Fourier irradiance.

Fig. 2
Fig. 2

The Fourier irradiance of Fig. 1 after smoothing.

Fig. 3
Fig. 3

The suitable spatial-frequency sampling range is limited by the zero-order stop and the noise level in the system. The LSSF should be slightly to the right of the edge of the stop to avoid the edge-effect zone.

Fig. 4
Fig. 4

The computer-generated unnormalized smoothed spectrum for the large (700-μm) particles.

Fig. 5
Fig. 5

The computer-generated unnormalized smoothed spectrum fo the medium (500-μm) particles.

Fig. 6
Fig. 6

The computer-generated unnormalized smoothed spectrum for the small (300-μm) particles.

Fig. 7
Fig. 7

The measured spectrum for a slide containing seventy large, thirty medium, and fifty small particles.

Tables (2)

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Table I Results of Particle Count from Signature Learning Routine (Smoothing)

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Table II Results of Particle Count from Signature Learning Routine (No-Smoothing)

Equations (16)

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n ^ = [ SS T ] - 1 SU             S = [ S k j ] ,
W i j = k = 1 C N i k S k j             i = 1 , , R ; j = 1 , , D ,
W = NS .
S ^ = [ N T N ] - 1 N T W .
U j = k = 1 C S k j n k             j = 1 , , D ,
U = S T n .
n ^ = [ S ^ S T ] - 1 S ^ U ,
U j = i = 1 R W i j p i             j = 1 , , D .
U = W T p ,
p ^ = [ W W T ] - 1 WU .
n ^ = N T p ^ .
n ^ = AWU ,
A ( N T N ) [ ( N T W ) ( N T W ) T ] - 1 N T .
n ^ = BWU ,
B N T [ W W T ] - 1 .
= i = 1 R = 13 k = 1 C = 3 n k i - n ^ k i i = 1 13 k = 1 3 n k i

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