Abstract

An array illuminator converts a uniformly wide beam losslessly into an array of bright spots. These spots provide the necessary illumination for microcomponents such as optical logic gates or bistable elements. Such elements may serve as devices in a 2-D discrete parallel processor. We propose an array illuminator with a phase grating on its front end. The phase grating is illuminated uniformly and then converted into an amplitude image by means of a phase contrast setup. The bright spots of the amplitude image are to be used for illuminating the array of microdevices of a digital optical computer.

© 1988 Optical Society of America

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References

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  1. H. Dammann, K. Gortler, “High Efficiency In-Line Multiple Imaging by Means of Multiple Phase Holograms,” Opt. Commun. 3, 312 (1971); U. Killat, G. Rabe, W. Ravex, “Binary Phase Gratings for Star Couplers with High Splitting Ratio,” Fiber Int. Opt. 4, 159 (1982).
    [CrossRef]
  2. M. E. Prise, N. Streibl, M. M. Downs, “Computational Properties of Nonlinear Optical Devices,” in Technical Digest of Topical Meeting on Photonic Switching (Optical Society of America, Washington, DC, 1987), paper FB4.
  3. A. W. Lohmann, “An Array Illuminator Based on the Talbot Effect,” Optik 79, 41 (1988).
  4. A. Papoulis, Systems and Transforms in Optics (McGraw-Hill, New York, 1968).
  5. M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1980).
  6. W. Smith, Modern Optical Engineering (McGraw-Hill, New York, 1966).
  7. D. Malacara, Optical Shop Testing (Wiley, New York, 1978).
  8. J. J. Snyder, “Algorithm for Fast Digital Analysis of Interference Fringes,” Appl. Opt. 19, 1223 (1980).
    [CrossRef] [PubMed]
  9. G. J. Swanson, J. R. Leger, M. Holz, “Aperture Filling of Phase-Locked Laser Arrays,” Opt. Lett. 12, 245 (1987).
    [CrossRef] [PubMed]

1988 (1)

A. W. Lohmann, “An Array Illuminator Based on the Talbot Effect,” Optik 79, 41 (1988).

1987 (1)

1980 (1)

1971 (1)

H. Dammann, K. Gortler, “High Efficiency In-Line Multiple Imaging by Means of Multiple Phase Holograms,” Opt. Commun. 3, 312 (1971); U. Killat, G. Rabe, W. Ravex, “Binary Phase Gratings for Star Couplers with High Splitting Ratio,” Fiber Int. Opt. 4, 159 (1982).
[CrossRef]

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1980).

Dammann, H.

H. Dammann, K. Gortler, “High Efficiency In-Line Multiple Imaging by Means of Multiple Phase Holograms,” Opt. Commun. 3, 312 (1971); U. Killat, G. Rabe, W. Ravex, “Binary Phase Gratings for Star Couplers with High Splitting Ratio,” Fiber Int. Opt. 4, 159 (1982).
[CrossRef]

Downs, M. M.

M. E. Prise, N. Streibl, M. M. Downs, “Computational Properties of Nonlinear Optical Devices,” in Technical Digest of Topical Meeting on Photonic Switching (Optical Society of America, Washington, DC, 1987), paper FB4.

Gortler, K.

H. Dammann, K. Gortler, “High Efficiency In-Line Multiple Imaging by Means of Multiple Phase Holograms,” Opt. Commun. 3, 312 (1971); U. Killat, G. Rabe, W. Ravex, “Binary Phase Gratings for Star Couplers with High Splitting Ratio,” Fiber Int. Opt. 4, 159 (1982).
[CrossRef]

Holz, M.

Leger, J. R.

Lohmann, A. W.

A. W. Lohmann, “An Array Illuminator Based on the Talbot Effect,” Optik 79, 41 (1988).

Malacara, D.

D. Malacara, Optical Shop Testing (Wiley, New York, 1978).

Papoulis, A.

A. Papoulis, Systems and Transforms in Optics (McGraw-Hill, New York, 1968).

Prise, M. E.

M. E. Prise, N. Streibl, M. M. Downs, “Computational Properties of Nonlinear Optical Devices,” in Technical Digest of Topical Meeting on Photonic Switching (Optical Society of America, Washington, DC, 1987), paper FB4.

Smith, W.

W. Smith, Modern Optical Engineering (McGraw-Hill, New York, 1966).

Snyder, J. J.

Streibl, N.

M. E. Prise, N. Streibl, M. M. Downs, “Computational Properties of Nonlinear Optical Devices,” in Technical Digest of Topical Meeting on Photonic Switching (Optical Society of America, Washington, DC, 1987), paper FB4.

Swanson, G. J.

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1980).

Appl. Opt. (1)

Opt. Commun. (1)

H. Dammann, K. Gortler, “High Efficiency In-Line Multiple Imaging by Means of Multiple Phase Holograms,” Opt. Commun. 3, 312 (1971); U. Killat, G. Rabe, W. Ravex, “Binary Phase Gratings for Star Couplers with High Splitting Ratio,” Fiber Int. Opt. 4, 159 (1982).
[CrossRef]

Opt. Lett. (1)

Optik (1)

A. W. Lohmann, “An Array Illuminator Based on the Talbot Effect,” Optik 79, 41 (1988).

Other (5)

A. Papoulis, Systems and Transforms in Optics (McGraw-Hill, New York, 1968).

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1980).

W. Smith, Modern Optical Engineering (McGraw-Hill, New York, 1966).

D. Malacara, Optical Shop Testing (Wiley, New York, 1978).

M. E. Prise, N. Streibl, M. M. Downs, “Computational Properties of Nonlinear Optical Devices,” in Technical Digest of Topical Meeting on Photonic Switching (Optical Society of America, Washington, DC, 1987), paper FB4.

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Figures (13)

Fig. 1
Fig. 1

Scheme of the phase contrast illuminator: OBJ, phase mask due to the envisioned compression ratio; FILT, plane where the phase shifter is positioned so that the zero–zero order is retarded; IMG, output plane; bright spots are the locations of the optical switches; 01,02, Fourier transform lenses.

Fig. 2
Fig. 2

(a) Phase distribution in the input plane OBJ (b) intensity distribution in the output plane.

Fig. 3
Fig. 3

Working principle of the phase contrast illuminator.

Fig. 4
Fig. 4

Complex amplitudes ū,u1,u2 and their relative orientations. For an explanation see text.

Fig. 5
Fig. 5

One elementary cell of the OBJ plane mask.

Fig. 6
Fig. 6

Intensities I1,I2 in the output as a function of the compression ratio C. Note: to the left of C = 4 the Φ0 is due to Eq. (7) and to the right, Φ0 = π const. Here I1: intensity in the bright spots; I2 = intensity of the surrounding area; C = 1/p2 (or 1/pq) = compression ratio.

Fig. 7
Fig. 7

Shearing interferogram of the phase platelet used as a phase shifter. Fringe number adjusted by a suitable amount of defocus of the wave entering a Michelson shearing interferometer.

Fig. 8
Fig. 8

Similar to Fig. 7 but detected with a CCD camera and read into a buffer memory for further processing. The evaluation has been carried out in ten cross sections (only one is shown). The overlaid picture is the first derivative of the intensity along the indicated section.

Fig. 9
Fig. 9

Output plane of the phase contrast illuminator when the phase shifter is strongly maladjusted. The result is a normal bright-field picture of the input phase mask.

Fig. 10
Fig. 10

Direct photograph of the output plane of the PCI with the phase mask having compression ratios of C = 100/9 (left) and C 100/16 (right)

Fig. 11
Fig. 11

Same as Fig. 10 but scanned with a CCD camera: left, scan through the bright spots; right, scan through the dark surrounding. The bright bar to the left corresponds to the dynamic range of the CCD.

Fig. 12
Fig. 12

Experiment with a variable phase mask. Aspect ratio p2 varies between 4/100 and 81/100. Phases Φ0 = α = π have been used. Left: Scan through the bright patches of the output plane. Note: with decreasing p2 the brightness I1 of the patches increases as predicted (Fig. 8). Right: Scan through the surrounding showing with decreasing p2 an increase in the background intensity I2. For p2 > 25/100 the phases Φ0 and α show the mismatch by failure to concentrate the energy in the regions desired.

Fig. 13
Fig. 13

Output intensity distribution of the phase contrast illuminator with the phase shifter at the position of one first order (0,+1). Due to the mismatch in this case a fringe system appears in the image plane.

Equations (24)

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C = ( d / b ) 2 ,
complex object amplitude : u ( x ) = exp [ i Φ ( x ) ] = { 1 , exp ( i Φ 0 ) , object phase [ see Fig . 2 ( a ) ] : Φ ( x ) = 0 or Φ 0 , average object amplitude : u ¯ = p · 1 + ( 1 - p ) exp ( i Φ 0 ) ,
relative slit width [ see Fig . 2 ( a ) ] : p = b / d , object variation : Δ u ( x ) = u ( x ) - u ¯ = 1 - u ¯ = u 1 , u 2 = exp ( i Φ 0 ) - u ¯ phase factor of phase contrast platelet : exp ( i α ) .
v ( x ) 2 C = 1 / p 2 or 0.
u 1 = ( 1 - p ) [ 1 - exp ( i Φ 0 ) ] ,
u 2 = - p ( 1 - exp ( i Φ 0 ) ] .
u ¯ = p 2 + 2 p ( 1 - p ) cos Φ 0 + ( 1 - p ) 2 ,
arg u ¯ = arctan { ( 1 - p ) sin Φ 0 / [ p + 1 ( 1 - p ) cos Φ 0 ] } .
p 2 + 2 p ( 1 - p ) cos Φ 0 + ( 1 - p ) 2 = 2 p sin Φ 0 / 2.
cos Φ 0 = 1 - 1 2 p .
arg u ¯ + α = arg u 2 + π ,
arg u 2 = π - arctan { sin Φ 0 / ( 1 - cos Φ 0 ) } .
α = 2 π - Φ 0
v 1 = ( u ¯ exp i α + u 1 ) ,             v 2 = ( u ¯ exp i α + u 2 ) .
I 1 = 4 ( p 2 - p ) cos 2 Φ 0 + 4 ( 1 - p ) ( 2 p - 1 ) cos Φ 0 + 4 ( 1 - p ) 2 + 1 = 1 / p
I 1 = ( 3 - 4 p ) 2 , I 2 = ( 1 - 4 p ) 2 .
u ¯ = d e { p q + [ 1 - p q ] exp i Φ 0 } .
u = π q 2 + [ 1 - π q 2 ] exp i Φ 0 ,
Δ I V Δ Φ 0 2             ( or Δ α 2 ) ,
V = { 4 - 8 p q } / { 5 - 16 p q + 16 ( p q ) 2 } ,
α = 2 π - arctan { sin Φ 0 / ( 1 - cos Φ 0 ) } + arctan { ( 1 - p ) sin Φ 0 / [ p + ( 1 - p ) cos Φ 0 ] } ,
arctan A + arctan B = arctan ( A + B ) / ( 1 - A B )             for A B 1 ,
α = 2 π - arctan { sin Φ 0 / ( 1 - 2 p ) cos Φ 0 } .
α = 2 π - arctan ( 4 p - 1 ) / ( 1 - 2 p ) 2 .

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