Abstract

A technique is presented that enables the particle-size analysis of quasicircular particles to be made. A coherent optical system is used to generate the diffraction pattern of the particle population to be analyzed, and a digital computer is used to process the information in the pattern. A similar technique has been used earlier, with success, to count circular particles of varying diameters. A scene containing three classes of particles is analyzed, and results are furnished.

© 1976 Optical Society of America

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References

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  1. W. L. Anderson, R. E. Beissner, Appl. Opt. 10, 1503 (1971).
    [CrossRef] [PubMed]
  2. H. Stark, D. Lee, B. Dimitriadis, J. Opt. Soc. Am. 65, No. 120000 (1975).
  3. G. M. Jenkins, D. B. Watts, Spectral Analysis and Its Applications (Holden-Day, San Francisco, 1969), p. 211.

1975

H. Stark, D. Lee, B. Dimitriadis, J. Opt. Soc. Am. 65, No. 120000 (1975).

1971

Anderson, W. L.

Beissner, R. E.

Dimitriadis, B.

H. Stark, D. Lee, B. Dimitriadis, J. Opt. Soc. Am. 65, No. 120000 (1975).

Jenkins, G. M.

G. M. Jenkins, D. B. Watts, Spectral Analysis and Its Applications (Holden-Day, San Francisco, 1969), p. 211.

Lee, D.

H. Stark, D. Lee, B. Dimitriadis, J. Opt. Soc. Am. 65, No. 120000 (1975).

Stark, H.

H. Stark, D. Lee, B. Dimitriadis, J. Opt. Soc. Am. 65, No. 120000 (1975).

Watts, D. B.

G. M. Jenkins, D. B. Watts, Spectral Analysis and Its Applications (Holden-Day, San Francisco, 1969), p. 211.

Appl. Opt.

J. Opt. Soc. Am.

H. Stark, D. Lee, B. Dimitriadis, J. Opt. Soc. Am. 65, No. 120000 (1975).

Other

G. M. Jenkins, D. B. Watts, Spectral Analysis and Its Applications (Holden-Day, San Francisco, 1969), p. 211.

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Figures (3)

Fig. 1
Fig. 1

Optical-digital computer (ODC). Coherent light is filtered and expanded by a spatial filter (a) and collimated by the lens (b). The sample is held in a phase-matching liquid (c) and placed against the Fourier-transforming lens (d). The spectrum is observed in the back-focal plane xfyf. A TV camera (e) scans the spectrum and transmits the information to the computer (g) which furnishes the least-squares estimate N ^.

Fig. 2
Fig. 2

A scene consisting of three classes of noncircular particles. The class index is determined by particle area.

Fig. 3
Fig. 3

The Fourier irradiance generated by the scene in Fig. 2.

Tables (1)

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Table I Experimental Results

Equations (21)

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y ( r , θ ) = m = - y m ( r ) exp ( j m θ ) ,
Y ( ω , ϕ ) = m = - Y m ( ω ) exp { j [ m ( ϕ - π / 2 ) ] }
Y m ( ω ) = 2 π 0 y m ( r ) J m ( r ω ) r d r ,
Y ( ω , ϕ - α k ) exp [ - j r k ω cos ( θ k - ϕ ) ] .
I N ( ω , ϕ ) = | k = 1 N Y ( ω , ϕ - α k ) exp [ - j r k ω cos ( θ k - ϕ ) ] | 2 = N - Y ( ω ) m 2 .
G ( ω ) = I N ( ω , ϕ ) N = - Y m ( ω ) 2 .
I N ( ω , ϕ ) = N - Y m ( ω ) 2 + n N ( ω , ϕ ) ,
G ( ω , ϕ ) = G ( ω ) + n ( ω , ϕ ) , where n ( ω , ϕ ) = n N ( ω , ϕ ) / N .
N = i = 1 L N i .
R N ( ω , ϕ ) = i = 1 L m = - Y i m ( ω ) k = 1 N i exp { j [ ( m ϕ - α k - π / 2 ) - ω r k cos ( θ k - ϕ ) ] } ,
H ( ω , ϕ ) = R N ( ω , ϕ ) 2 = i = 1 L N i G i ( ω ) + n ( ω , ϕ ) ,
G i ( ω ) m = - Y i m ( ω ) 2 ,
H = GN + n ,
N ^ = N = [ G T G ] - 1 G T H .
G W = W G = WG + Wn WG ,
H W = W H = W G N + Wn .
N ^ = [ ( WG ) T WG ] - 1 ( WG ) T ( WGN + Wn )
N ,
H W ( l , n ) = i k H ( i , k ) W ( l - i , n - k ) ,
W ( i , k ) = K 1 [ 1 - K 2 ( i 2 + k 2 ) ] , i 2 + k 2 < q 2 = 0 , i 2 + k 2 q 2 ,
j = 1 3 N j

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