Abstract

An acoustooptic technique was used to design and construct a prototype of a processor capable of multiplying a 128 × 128 complex-element matrix by a 128 complex-element vector. The device was specified to execute 105 matrix–vector products per second with 8-bit resolution. The performance of each component of the prototype was evaluated, as was the impact of component performance on system performance.

© 1989 Optical Society of America

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References

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  1. P. Mengert et al., Patent3,525,856 (6Oct.1966).
  2. M. A. Monahan, R. P. Bocker, K. Bromley, A. C. H. Louie, R. D. Martin, R. G. Shepard, “The Use of Charge Coupled Devices in Electrooptical Processing,” in Proceedings, 1975 International Conference on the Applications of Charge-Coupled Devices (Naval Ocean Systems Center, San Diego, CA), pp. 217–227.
  3. J. W. Goodman, A. R. Dias, L. M. Woody, “Fully Parallel, High-Speed Incoherent Optical Method for Performing Discrete Fourier Transforms,” Opt. Lett. 2, 1–3 (1978).
    [CrossRef] [PubMed]
  4. A. R. Dias, “Incoherent Matrix–Vector Multiplication for High-Speed Data Processing,” Stanford University Doctoral Thesis, University Microfilms 8024641, Ann Arbor, MI (1980).
  5. Special Issue on Optical Computing, Proc. IEEE 72, No. 7, 755–979 (July1984).
  6. R. A. Athale, “Optical Matrix Algebraic Processors: A Survey,” in Tenth International Optical Computing Conference, 6–8 Apr. 1983, Cambridge, MA (IEEE Computer Society Press, 83CH1880-4, p. 24.
  7. R. A. Athale, J. N. Lee, “Optical Processing Using Outer-Product Concepts,” Proc. IEEE 72, 931–941 (1984).
    [CrossRef]
  8. H. J. Whitehouse, J. M. Speiser, Aspects of Signal Processing with Emphasis on Underwater Acoustics, Vol. 2, G. Tacconi, Ed. (Reidel, Hingham, MA, 1977).
  9. H. J. Caulfield, W. T. Rhodes, M. J. Foster, S. Horvitz, “Optical Implementation of Systolic Array Processing,” Opt. Commun. 40, 86–90 (1981).
    [CrossRef]
  10. M. A. Monahan, K. Bromley, R. P. Bocker, “Incoherent Optical Correlators,” Proc. IEEE 65, 121–129 (1977).
    [CrossRef]
  11. M. Carlotto, D. Casasent, “Microprocessor-Based Fiber-Optic Iterative Optical Processor,” Appl. Opt. 21, 147–152 (1982).
    [CrossRef] [PubMed]
  12. D. Casasent, S. Riedl, “Time and Space Integrating Optical Laboratory Matrix-Vector Array Processor,” Proc. Soc. Photo-Opt. Instrum. Eng. 698, 151–156 (Aug.1986).
  13. B. K. Taylor, D. P. Casasent, “Optical Laboratory Solution and Error Model Simulation of a Linear Time-Varying Finite Element Equation,” Proc. Soc. Photo-Opt. Instrum. Eng. 977, 253–270 (Aug.1988).
  14. R. Athale, H. Hoang, J. N. Lee, “High Accuracy Matrix Multiplication with a Magnetooptic Spatial Light Modulato,” Proc. Soc. Photo-Opt. Instrum. Eng. 431, 187–193 (1983).
  15. D. Casasent, J. Jackson, “Fabrication Considerations for Acousto-Optic Systolic Processors,” Proc. Soc. Photo-Opt. Instrum. Eng. 465, 104–112 (Jan.1984).
  16. Special Section on Acousto-Optic Signal Processing, Proc. IEEE 69, 48–118 (1981).
  17. E. P. Mosca, F. P. Pursel, R. D. Griffin, J. N. Lee, Acousto-Optical Vector Matrix Product Processor: Implementation Issues, NRL Memorandum Report 6372 (25Apr.1989).
  18. N. J. Berg, J. N. Lee, Acousto-Optic Signal Processing: Theory and Implementation (Marcel Dekker, New York, 1983).
  19. D. Casasent, J. Lambert, “General I and Q Data Processing on a Multichannel AO System,” Appl. Opt. 25, 3217–3224 (1986).
    [CrossRef] [PubMed]
  20. E. Pochapsky, D. Casasent, “Linear Acousto-Optic Heterodyning Processors for Complex-Valued Data Precessing,” Proc. Soc. Photo-Opt. Instrum. Eng. 752, 155–171 (1987).
  21. The price for our system is a loss in the dynamic range at the detector.
  22. A. Yariv, Quantum Electronics (Wiley, New York, 1975).
  23. W. C. Knight, R. G. Pridham, S. M. Kay, “Digital Signal Processing for Sonar,” Proc. IEEE 69, 1451–1506 (1981).
    [CrossRef]

1988 (1)

B. K. Taylor, D. P. Casasent, “Optical Laboratory Solution and Error Model Simulation of a Linear Time-Varying Finite Element Equation,” Proc. Soc. Photo-Opt. Instrum. Eng. 977, 253–270 (Aug.1988).

1987 (1)

E. Pochapsky, D. Casasent, “Linear Acousto-Optic Heterodyning Processors for Complex-Valued Data Precessing,” Proc. Soc. Photo-Opt. Instrum. Eng. 752, 155–171 (1987).

1986 (2)

D. Casasent, S. Riedl, “Time and Space Integrating Optical Laboratory Matrix-Vector Array Processor,” Proc. Soc. Photo-Opt. Instrum. Eng. 698, 151–156 (Aug.1986).

D. Casasent, J. Lambert, “General I and Q Data Processing on a Multichannel AO System,” Appl. Opt. 25, 3217–3224 (1986).
[CrossRef] [PubMed]

1984 (3)

D. Casasent, J. Jackson, “Fabrication Considerations for Acousto-Optic Systolic Processors,” Proc. Soc. Photo-Opt. Instrum. Eng. 465, 104–112 (Jan.1984).

Special Issue on Optical Computing, Proc. IEEE 72, No. 7, 755–979 (July1984).

R. A. Athale, J. N. Lee, “Optical Processing Using Outer-Product Concepts,” Proc. IEEE 72, 931–941 (1984).
[CrossRef]

1983 (1)

R. Athale, H. Hoang, J. N. Lee, “High Accuracy Matrix Multiplication with a Magnetooptic Spatial Light Modulato,” Proc. Soc. Photo-Opt. Instrum. Eng. 431, 187–193 (1983).

1982 (1)

M. Carlotto, D. Casasent, “Microprocessor-Based Fiber-Optic Iterative Optical Processor,” Appl. Opt. 21, 147–152 (1982).
[CrossRef] [PubMed]

1981 (3)

H. J. Caulfield, W. T. Rhodes, M. J. Foster, S. Horvitz, “Optical Implementation of Systolic Array Processing,” Opt. Commun. 40, 86–90 (1981).
[CrossRef]

Special Section on Acousto-Optic Signal Processing, Proc. IEEE 69, 48–118 (1981).

W. C. Knight, R. G. Pridham, S. M. Kay, “Digital Signal Processing for Sonar,” Proc. IEEE 69, 1451–1506 (1981).
[CrossRef]

1978 (1)

1977 (1)

M. A. Monahan, K. Bromley, R. P. Bocker, “Incoherent Optical Correlators,” Proc. IEEE 65, 121–129 (1977).
[CrossRef]

Athale, R.

R. Athale, H. Hoang, J. N. Lee, “High Accuracy Matrix Multiplication with a Magnetooptic Spatial Light Modulato,” Proc. Soc. Photo-Opt. Instrum. Eng. 431, 187–193 (1983).

Athale, R. A.

R. A. Athale, J. N. Lee, “Optical Processing Using Outer-Product Concepts,” Proc. IEEE 72, 931–941 (1984).
[CrossRef]

R. A. Athale, “Optical Matrix Algebraic Processors: A Survey,” in Tenth International Optical Computing Conference, 6–8 Apr. 1983, Cambridge, MA (IEEE Computer Society Press, 83CH1880-4, p. 24.

Berg, N. J.

N. J. Berg, J. N. Lee, Acousto-Optic Signal Processing: Theory and Implementation (Marcel Dekker, New York, 1983).

Bocker, R. P.

M. A. Monahan, K. Bromley, R. P. Bocker, “Incoherent Optical Correlators,” Proc. IEEE 65, 121–129 (1977).
[CrossRef]

M. A. Monahan, R. P. Bocker, K. Bromley, A. C. H. Louie, R. D. Martin, R. G. Shepard, “The Use of Charge Coupled Devices in Electrooptical Processing,” in Proceedings, 1975 International Conference on the Applications of Charge-Coupled Devices (Naval Ocean Systems Center, San Diego, CA), pp. 217–227.

Bromley, K.

M. A. Monahan, K. Bromley, R. P. Bocker, “Incoherent Optical Correlators,” Proc. IEEE 65, 121–129 (1977).
[CrossRef]

M. A. Monahan, R. P. Bocker, K. Bromley, A. C. H. Louie, R. D. Martin, R. G. Shepard, “The Use of Charge Coupled Devices in Electrooptical Processing,” in Proceedings, 1975 International Conference on the Applications of Charge-Coupled Devices (Naval Ocean Systems Center, San Diego, CA), pp. 217–227.

Carlotto, M.

M. Carlotto, D. Casasent, “Microprocessor-Based Fiber-Optic Iterative Optical Processor,” Appl. Opt. 21, 147–152 (1982).
[CrossRef] [PubMed]

Casasent, D.

E. Pochapsky, D. Casasent, “Linear Acousto-Optic Heterodyning Processors for Complex-Valued Data Precessing,” Proc. Soc. Photo-Opt. Instrum. Eng. 752, 155–171 (1987).

D. Casasent, J. Lambert, “General I and Q Data Processing on a Multichannel AO System,” Appl. Opt. 25, 3217–3224 (1986).
[CrossRef] [PubMed]

D. Casasent, S. Riedl, “Time and Space Integrating Optical Laboratory Matrix-Vector Array Processor,” Proc. Soc. Photo-Opt. Instrum. Eng. 698, 151–156 (Aug.1986).

D. Casasent, J. Jackson, “Fabrication Considerations for Acousto-Optic Systolic Processors,” Proc. Soc. Photo-Opt. Instrum. Eng. 465, 104–112 (Jan.1984).

M. Carlotto, D. Casasent, “Microprocessor-Based Fiber-Optic Iterative Optical Processor,” Appl. Opt. 21, 147–152 (1982).
[CrossRef] [PubMed]

Casasent, D. P.

B. K. Taylor, D. P. Casasent, “Optical Laboratory Solution and Error Model Simulation of a Linear Time-Varying Finite Element Equation,” Proc. Soc. Photo-Opt. Instrum. Eng. 977, 253–270 (Aug.1988).

Caulfield, H. J.

H. J. Caulfield, W. T. Rhodes, M. J. Foster, S. Horvitz, “Optical Implementation of Systolic Array Processing,” Opt. Commun. 40, 86–90 (1981).
[CrossRef]

Dias, A. R.

J. W. Goodman, A. R. Dias, L. M. Woody, “Fully Parallel, High-Speed Incoherent Optical Method for Performing Discrete Fourier Transforms,” Opt. Lett. 2, 1–3 (1978).
[CrossRef] [PubMed]

A. R. Dias, “Incoherent Matrix–Vector Multiplication for High-Speed Data Processing,” Stanford University Doctoral Thesis, University Microfilms 8024641, Ann Arbor, MI (1980).

Foster, M. J.

H. J. Caulfield, W. T. Rhodes, M. J. Foster, S. Horvitz, “Optical Implementation of Systolic Array Processing,” Opt. Commun. 40, 86–90 (1981).
[CrossRef]

Goodman, J. W.

Griffin, R. D.

E. P. Mosca, F. P. Pursel, R. D. Griffin, J. N. Lee, Acousto-Optical Vector Matrix Product Processor: Implementation Issues, NRL Memorandum Report 6372 (25Apr.1989).

Hoang, H.

R. Athale, H. Hoang, J. N. Lee, “High Accuracy Matrix Multiplication with a Magnetooptic Spatial Light Modulato,” Proc. Soc. Photo-Opt. Instrum. Eng. 431, 187–193 (1983).

Horvitz, S.

H. J. Caulfield, W. T. Rhodes, M. J. Foster, S. Horvitz, “Optical Implementation of Systolic Array Processing,” Opt. Commun. 40, 86–90 (1981).
[CrossRef]

Jackson, J.

D. Casasent, J. Jackson, “Fabrication Considerations for Acousto-Optic Systolic Processors,” Proc. Soc. Photo-Opt. Instrum. Eng. 465, 104–112 (Jan.1984).

Kay, S. M.

W. C. Knight, R. G. Pridham, S. M. Kay, “Digital Signal Processing for Sonar,” Proc. IEEE 69, 1451–1506 (1981).
[CrossRef]

Knight, W. C.

W. C. Knight, R. G. Pridham, S. M. Kay, “Digital Signal Processing for Sonar,” Proc. IEEE 69, 1451–1506 (1981).
[CrossRef]

Lambert, J.

Lee, J. N.

R. A. Athale, J. N. Lee, “Optical Processing Using Outer-Product Concepts,” Proc. IEEE 72, 931–941 (1984).
[CrossRef]

R. Athale, H. Hoang, J. N. Lee, “High Accuracy Matrix Multiplication with a Magnetooptic Spatial Light Modulato,” Proc. Soc. Photo-Opt. Instrum. Eng. 431, 187–193 (1983).

E. P. Mosca, F. P. Pursel, R. D. Griffin, J. N. Lee, Acousto-Optical Vector Matrix Product Processor: Implementation Issues, NRL Memorandum Report 6372 (25Apr.1989).

N. J. Berg, J. N. Lee, Acousto-Optic Signal Processing: Theory and Implementation (Marcel Dekker, New York, 1983).

Louie, A. C. H.

M. A. Monahan, R. P. Bocker, K. Bromley, A. C. H. Louie, R. D. Martin, R. G. Shepard, “The Use of Charge Coupled Devices in Electrooptical Processing,” in Proceedings, 1975 International Conference on the Applications of Charge-Coupled Devices (Naval Ocean Systems Center, San Diego, CA), pp. 217–227.

Martin, R. D.

M. A. Monahan, R. P. Bocker, K. Bromley, A. C. H. Louie, R. D. Martin, R. G. Shepard, “The Use of Charge Coupled Devices in Electrooptical Processing,” in Proceedings, 1975 International Conference on the Applications of Charge-Coupled Devices (Naval Ocean Systems Center, San Diego, CA), pp. 217–227.

Mengert, P.

P. Mengert et al., Patent3,525,856 (6Oct.1966).

Monahan, M. A.

M. A. Monahan, K. Bromley, R. P. Bocker, “Incoherent Optical Correlators,” Proc. IEEE 65, 121–129 (1977).
[CrossRef]

M. A. Monahan, R. P. Bocker, K. Bromley, A. C. H. Louie, R. D. Martin, R. G. Shepard, “The Use of Charge Coupled Devices in Electrooptical Processing,” in Proceedings, 1975 International Conference on the Applications of Charge-Coupled Devices (Naval Ocean Systems Center, San Diego, CA), pp. 217–227.

Mosca, E. P.

E. P. Mosca, F. P. Pursel, R. D. Griffin, J. N. Lee, Acousto-Optical Vector Matrix Product Processor: Implementation Issues, NRL Memorandum Report 6372 (25Apr.1989).

Pochapsky, E.

E. Pochapsky, D. Casasent, “Linear Acousto-Optic Heterodyning Processors for Complex-Valued Data Precessing,” Proc. Soc. Photo-Opt. Instrum. Eng. 752, 155–171 (1987).

Pridham, R. G.

W. C. Knight, R. G. Pridham, S. M. Kay, “Digital Signal Processing for Sonar,” Proc. IEEE 69, 1451–1506 (1981).
[CrossRef]

Pursel, F. P.

E. P. Mosca, F. P. Pursel, R. D. Griffin, J. N. Lee, Acousto-Optical Vector Matrix Product Processor: Implementation Issues, NRL Memorandum Report 6372 (25Apr.1989).

Rhodes, W. T.

H. J. Caulfield, W. T. Rhodes, M. J. Foster, S. Horvitz, “Optical Implementation of Systolic Array Processing,” Opt. Commun. 40, 86–90 (1981).
[CrossRef]

Riedl, S.

D. Casasent, S. Riedl, “Time and Space Integrating Optical Laboratory Matrix-Vector Array Processor,” Proc. Soc. Photo-Opt. Instrum. Eng. 698, 151–156 (Aug.1986).

Shepard, R. G.

M. A. Monahan, R. P. Bocker, K. Bromley, A. C. H. Louie, R. D. Martin, R. G. Shepard, “The Use of Charge Coupled Devices in Electrooptical Processing,” in Proceedings, 1975 International Conference on the Applications of Charge-Coupled Devices (Naval Ocean Systems Center, San Diego, CA), pp. 217–227.

Speiser, J. M.

H. J. Whitehouse, J. M. Speiser, Aspects of Signal Processing with Emphasis on Underwater Acoustics, Vol. 2, G. Tacconi, Ed. (Reidel, Hingham, MA, 1977).

Taylor, B. K.

B. K. Taylor, D. P. Casasent, “Optical Laboratory Solution and Error Model Simulation of a Linear Time-Varying Finite Element Equation,” Proc. Soc. Photo-Opt. Instrum. Eng. 977, 253–270 (Aug.1988).

Whitehouse, H. J.

H. J. Whitehouse, J. M. Speiser, Aspects of Signal Processing with Emphasis on Underwater Acoustics, Vol. 2, G. Tacconi, Ed. (Reidel, Hingham, MA, 1977).

Woody, L. M.

Yariv, A.

A. Yariv, Quantum Electronics (Wiley, New York, 1975).

Acousto-Optic Signal Processing, Proc. IEEE (1)

Special Section on Acousto-Optic Signal Processing, Proc. IEEE 69, 48–118 (1981).

Appl. Opt. (1)

M. Carlotto, D. Casasent, “Microprocessor-Based Fiber-Optic Iterative Optical Processor,” Appl. Opt. 21, 147–152 (1982).
[CrossRef] [PubMed]

Appl. Opt. (1)

Opt. Commun. (1)

H. J. Caulfield, W. T. Rhodes, M. J. Foster, S. Horvitz, “Optical Implementation of Systolic Array Processing,” Opt. Commun. 40, 86–90 (1981).
[CrossRef]

Opt. Lett. (1)

Optical Computing, Proc. IEEE (1)

Special Issue on Optical Computing, Proc. IEEE 72, No. 7, 755–979 (July1984).

Proc. Soc. Photo-Opt. Instrum. Eng. (1)

D. Casasent, J. Jackson, “Fabrication Considerations for Acousto-Optic Systolic Processors,” Proc. Soc. Photo-Opt. Instrum. Eng. 465, 104–112 (Jan.1984).

Proc. IEEE (3)

R. A. Athale, J. N. Lee, “Optical Processing Using Outer-Product Concepts,” Proc. IEEE 72, 931–941 (1984).
[CrossRef]

M. A. Monahan, K. Bromley, R. P. Bocker, “Incoherent Optical Correlators,” Proc. IEEE 65, 121–129 (1977).
[CrossRef]

W. C. Knight, R. G. Pridham, S. M. Kay, “Digital Signal Processing for Sonar,” Proc. IEEE 69, 1451–1506 (1981).
[CrossRef]

Proc. Soc. Photo-Opt. Instrum. Eng. (1)

B. K. Taylor, D. P. Casasent, “Optical Laboratory Solution and Error Model Simulation of a Linear Time-Varying Finite Element Equation,” Proc. Soc. Photo-Opt. Instrum. Eng. 977, 253–270 (Aug.1988).

Proc. Soc. Photo-Opt. Instrum. Eng. (3)

R. Athale, H. Hoang, J. N. Lee, “High Accuracy Matrix Multiplication with a Magnetooptic Spatial Light Modulato,” Proc. Soc. Photo-Opt. Instrum. Eng. 431, 187–193 (1983).

E. Pochapsky, D. Casasent, “Linear Acousto-Optic Heterodyning Processors for Complex-Valued Data Precessing,” Proc. Soc. Photo-Opt. Instrum. Eng. 752, 155–171 (1987).

D. Casasent, S. Riedl, “Time and Space Integrating Optical Laboratory Matrix-Vector Array Processor,” Proc. Soc. Photo-Opt. Instrum. Eng. 698, 151–156 (Aug.1986).

Other (9)

H. J. Whitehouse, J. M. Speiser, Aspects of Signal Processing with Emphasis on Underwater Acoustics, Vol. 2, G. Tacconi, Ed. (Reidel, Hingham, MA, 1977).

R. A. Athale, “Optical Matrix Algebraic Processors: A Survey,” in Tenth International Optical Computing Conference, 6–8 Apr. 1983, Cambridge, MA (IEEE Computer Society Press, 83CH1880-4, p. 24.

The price for our system is a loss in the dynamic range at the detector.

A. Yariv, Quantum Electronics (Wiley, New York, 1975).

E. P. Mosca, F. P. Pursel, R. D. Griffin, J. N. Lee, Acousto-Optical Vector Matrix Product Processor: Implementation Issues, NRL Memorandum Report 6372 (25Apr.1989).

N. J. Berg, J. N. Lee, Acousto-Optic Signal Processing: Theory and Implementation (Marcel Dekker, New York, 1983).

A. R. Dias, “Incoherent Matrix–Vector Multiplication for High-Speed Data Processing,” Stanford University Doctoral Thesis, University Microfilms 8024641, Ann Arbor, MI (1980).

P. Mengert et al., Patent3,525,856 (6Oct.1966).

M. A. Monahan, R. P. Bocker, K. Bromley, A. C. H. Louie, R. D. Martin, R. G. Shepard, “The Use of Charge Coupled Devices in Electrooptical Processing,” in Proceedings, 1975 International Conference on the Applications of Charge-Coupled Devices (Naval Ocean Systems Center, San Diego, CA), pp. 217–227.

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Figures (9)

Fig. 1
Fig. 1

Schematic of system including the host computer, laser, Bragg cell, aperture array mask, detector, rf power supply, rf attenuator network, digital control board, and the digital I/O and A–D converter board.

Fig. 2
Fig. 2

Intensity of the laser pulse vs time. The FWHM of the pulse is ∼10 ns.

Fig. 3
Fig. 3

In the Bragg cell the acoustic power is spatially distributed in 256 features. When the laser is strobed, the acoustic power in each feature represents either the real or the imaginary part of a complex valued vector component.

Fig. 4
Fig. 4

Schematic of the Bragg cell, the rf attenuator network, and the digital control board.

Fig. 5
Fig. 5

Radio frequency attenuator network consists of eight branches, each successive branch with 6-dB of additional attenuation. Each branch also contains a two-state (on/off) digitally controlled switch and an adjustable phase shifter (not shown).

Fig. 6
Fig. 6

Aperture array mask consists of a rectangular array of 256 × (256 + 1) apertures, each 50 μm high with widths up to 82 μm. The center-to-center spacings are 100 μm vertically and 164 μm horizontally.

Fig. 7
Fig. 7

Overview of the optical layout. Spherical lenses are denoted L and the cylindrical lenses C. The lenses all have focal lengths of 200 mm, which is the distance between the vertical lines on the grid to the right of C1. For compactness the beam is multiply folded by front-surface mirrors located at the broken lines. Each mirror deflects the beam by 90°.

Fig. 8
Fig. 8

Intensity profile of the radiation from a single uniformly illuminated aperture incident on a detector pixel pair is the square of a sinc function. The length L of a pixel pair is 2500 μm.

Fig. 9
Fig. 9

Readout of the array displayed on an oscilloscope screen shows that the registration of aperture row images with every other detector pair was inadequate. If the registration were adequate, the two curves would not cross.

Tables (2)

Tables Icon

Table I Bragg Cell Specifications

Tables Icon

Table II Correction for the Attenuation of Acoustic Power as a Function of Vector Component at Instant of Strobing

Equations (16)

Equations on this page are rendered with MathJax. Learn more.

I d I 0 = sin 2 0.736 P ,
κ [ I ] = 255 × 10 0.05 β c I / f
A = a R + i a I ,
X = x R + i x I .
P = A X = ( a R x R a I x I ) + i ( a R x I + a I x R ) = p R + i p I ,
| p R p I | = | a R a I a I a R | | x R x I | .
y i = j a i j x j ,
a i j = a i j + a 0 , x j = x j + x 0 , y i = j ( a i j + a 0 ) ( x j + x 0 ) .
V i = j A i j I j ,
A i j = α ( a i j + a 0 ) , I j = β i j ( x j + x 0 ) ,
y i = V i α β i x 0 j ( a i j + a 0 ) a 0 j x j
β i = V i 0 [ α x 0 j ( a i j + a 0 ) ] 1 .
relative intensity ( x ) = sinc 2 ( x / x ) ,
P n = n P 0 / 255 = 1250 μ m + 1250 μ m sinc 2 ( x x n ) d x , x n = f / w n .
P > saturation energy η 1 η 2 η 3 τ ,
Deviation ( P A 2 < P A 2 > )

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