Abstract

New techniques in nonlinear optical processing are explored, based on the operation of intensity level selection as performed by a Fabry-Perot interferometer containing a phase object. The image being processed is recorded on a medium between the mirrors as a spatially varying phase shift less than π. The interferometer only transmits light through those portions of the object that correspond to a single value of the phase and hence to a single intensity level in the input. More complicated operations such as thresholding and analog-to-digital conversion are performed by modulating the light source as the different levels are selected. Photoresist and lithium niobate have been used as phase objects, and experimental data for both are presented. Three kinds of Fabry-Perot interferometers have been used to demonstrate nonlinear processing using coherent and incoherent light. Color images have been produced with black and white inputs and white light illumination.

© 1980 Optical Society of America

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References

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  1. D. P. Jablonowski, S. H. Lee, Appl. Phys., 8, 51 (1975).
    [Crossref]
  2. P. N. Tamura, J. C. Wyant, Proc. SPIE 74, 57 (1976).
    [Crossref]
  3. S. H. Lee, B. J. Bartholomew, J. Cederquist, Proc. SPIE 83, 78 (1976).
    [Crossref]
  4. R. A. Bartolini, Appl. Opt. 11, 1275 (1972).
    [Crossref] [PubMed]
  5. J. Cederquist, S. H. Lee, in Proceedings, Electro-Optics/Laser Conference, Anaheim, Calif. (Industrial & Scientific Conference Management, Chicago, 1977), pp. 221–225. The properties of the confocal interferometer as they pertain to optical processing will be discussed in detail by Cederquist, Ph.D. thesis UCSD, (1980).
  6. The maximum phase shift that can be obtained in LiNbO3 is determined by crystal parameters such as iron-doping levels and the Fe+2:Fe+3 ratio and the crystal thickness. W. Burke at RCA Laboratories had suggested that a heavily doped, lightly reduced crystal would work best in this experiment, but he had no data on the specific sample that he gave us. It may be possible to increase the refractive-index change by optimizing the crystal parameters, and it is always possible to increase the phase shift by using a thicker crystal.
  7. D. Post, J. Opt. Soc. Am. 44, 243 (1954). This equation is not identical to the one in Post’s paper because the effect of the beam that suffers no reflections has been included. See B. J. Bartholomew, “Nonlinear Optical Processing with Fabry-Perot Interferometers,” Ph.D. thesis, UCSD, (1979).
    [Crossref]
  8. The three-mirror interferometer in this configuration can be used as a very sensitive tool for measuring dispersion. The difference in the index of refraction at two wavelengths λ1 and λ2 is given by n(λ2) − n(λ1) = (d1 − d2)/te, where d1 and d2 are the distances between the plate and the solid étalon when fringes at λ1 and λ2 appear, and te is the étalon thickness. By increasing te, very small index changes can be observed.

1976 (2)

P. N. Tamura, J. C. Wyant, Proc. SPIE 74, 57 (1976).
[Crossref]

S. H. Lee, B. J. Bartholomew, J. Cederquist, Proc. SPIE 83, 78 (1976).
[Crossref]

1975 (1)

D. P. Jablonowski, S. H. Lee, Appl. Phys., 8, 51 (1975).
[Crossref]

1972 (1)

1954 (1)

Bartholomew, B. J.

S. H. Lee, B. J. Bartholomew, J. Cederquist, Proc. SPIE 83, 78 (1976).
[Crossref]

Bartolini, R. A.

Cederquist, J.

S. H. Lee, B. J. Bartholomew, J. Cederquist, Proc. SPIE 83, 78 (1976).
[Crossref]

J. Cederquist, S. H. Lee, in Proceedings, Electro-Optics/Laser Conference, Anaheim, Calif. (Industrial & Scientific Conference Management, Chicago, 1977), pp. 221–225. The properties of the confocal interferometer as they pertain to optical processing will be discussed in detail by Cederquist, Ph.D. thesis UCSD, (1980).

Jablonowski, D. P.

D. P. Jablonowski, S. H. Lee, Appl. Phys., 8, 51 (1975).
[Crossref]

Lee, S. H.

S. H. Lee, B. J. Bartholomew, J. Cederquist, Proc. SPIE 83, 78 (1976).
[Crossref]

D. P. Jablonowski, S. H. Lee, Appl. Phys., 8, 51 (1975).
[Crossref]

J. Cederquist, S. H. Lee, in Proceedings, Electro-Optics/Laser Conference, Anaheim, Calif. (Industrial & Scientific Conference Management, Chicago, 1977), pp. 221–225. The properties of the confocal interferometer as they pertain to optical processing will be discussed in detail by Cederquist, Ph.D. thesis UCSD, (1980).

Post, D.

Tamura, P. N.

P. N. Tamura, J. C. Wyant, Proc. SPIE 74, 57 (1976).
[Crossref]

Wyant, J. C.

P. N. Tamura, J. C. Wyant, Proc. SPIE 74, 57 (1976).
[Crossref]

Appl. Opt. (1)

Appl. Phys. (1)

D. P. Jablonowski, S. H. Lee, Appl. Phys., 8, 51 (1975).
[Crossref]

J. Opt. Soc. Am. (1)

Proc. SPIE (2)

P. N. Tamura, J. C. Wyant, Proc. SPIE 74, 57 (1976).
[Crossref]

S. H. Lee, B. J. Bartholomew, J. Cederquist, Proc. SPIE 83, 78 (1976).
[Crossref]

Other (3)

J. Cederquist, S. H. Lee, in Proceedings, Electro-Optics/Laser Conference, Anaheim, Calif. (Industrial & Scientific Conference Management, Chicago, 1977), pp. 221–225. The properties of the confocal interferometer as they pertain to optical processing will be discussed in detail by Cederquist, Ph.D. thesis UCSD, (1980).

The maximum phase shift that can be obtained in LiNbO3 is determined by crystal parameters such as iron-doping levels and the Fe+2:Fe+3 ratio and the crystal thickness. W. Burke at RCA Laboratories had suggested that a heavily doped, lightly reduced crystal would work best in this experiment, but he had no data on the specific sample that he gave us. It may be possible to increase the refractive-index change by optimizing the crystal parameters, and it is always possible to increase the phase shift by using a thicker crystal.

The three-mirror interferometer in this configuration can be used as a very sensitive tool for measuring dispersion. The difference in the index of refraction at two wavelengths λ1 and λ2 is given by n(λ2) − n(λ1) = (d1 − d2)/te, where d1 and d2 are the distances between the plate and the solid étalon when fringes at λ1 and λ2 appear, and te is the étalon thickness. By increasing te, very small index changes can be observed.

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Figures (11)

Fig. 1
Fig. 1

Plane–parallel Fabry-Perot phase object processing system. The input image is recorded as a phase object exp[(x,y)] mounted between two mirrors. The system is illuminated with a collimated beam from a single-mode laser. The output lens forms a magnified image of the interference pattern on the output plane where the individual intensity levels may be viewed.

Fig. 2
Fig. 2

Intensity transmittance function of the Fabry-Perot with phase object. TPO is plotted as a function of kd for different δs. The vertical dashed line illustrates intensity level selection. For that value of kd, those areas in the image where the intensity produced a phase shift δ = π/3 will transmit light, and the other areas are dark. Changing kd selects a new intensity level.

Fig. 3
Fig. 3

Plane mirror–photoresist system. The collimator, iris, beam steering mirrors, interferometer, and output lens are set up exactly as shown in Fig. 1. The output plane is located off the edge of the table to the left.

Fig. 4
Fig. 4

Intensity level selection with the plane–parallel system. The central image is gray tone input. Eight dots around the outside were given different exposures to make a gray scale. The dot in (h) had the highest exposure equal to the exposure of the funnel. The dot in (a) had zero exposure. Eight intensity levels are selected with intensity increasing from (a) through (h).

Fig. 5
Fig. 5

Analog-to-digital conversion of the gray tone image in Fig. 4. The most significant bit plane is on the left. The least significant bit plane is on the right. The intensity level for any point in the original can be found from these three binary images (see text).

Fig. 6
Fig. 6

Confocal Fabry-Perot processing system. Input object is a LiNbO3 crystal with recorded phase image. The object is imaged back onto itself by two spherical mirrors, and diffraction does not degrade image quality.

Fig. 7
Fig. 7

Output of the confocal system. The input image consisted of a step tablet with linear exposure steps increasing in intensity from left to right. The step tablet was perpendicular to the c axis, and on the crystal the image was 0.06 mm × 0.9 mm. The image was limited to the region in the center of the crystal where the phase shift was uniform. The interferometer clearly separates five levels.

Fig. 8
Fig. 8

Series interferometer. Using three mirrors light with a short coherence length will produce high-contrast, narrow fringes. If d1 = d2, rays (2) and (3) and rays (4), (5), (6), and (7) all have the same optical path length and will interfere in the output. Adding up the contributions from all interfering terms yields T3M in Eq. (6).

Fig. 9
Fig. 9

Transmittance of series interferometer. Plot of transmittance of series interferometer vs 2k∊ for two values of mirror reflectance. Calculation assumed R + T = 1.

Fig. 10
Fig. 10

Possible configurations for series interferometer. (a) Three-plate system where the thickness of plates 2 and 3 is equal so that dispersion in the cavity between M1 and M2 is same as dispersion in the cavity between M2 and M3. (b) System with one plate and solid étalon is easier to stabilize and align, but the achromatic fringes will be dispersed.

Fig. 11
Fig. 11

Intensity selection with series interferometer. The gray tone image is in the upper left-hand corner. The output with one mirror tilted slightly to show sharpened fringes is in the upper right-hand corner. Remaining pictures show four different levels selected. R = 80% and λ = 5461 Å using a 20-Å bandpass interference filter.

Equations (6)

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T P O ( x , y ) = T 2 ( 1 - R 2 ) + 4 R sin 2 [ k d + δ ( x , y ) ] ,
k d + δ ( x , y ) = l π ,
N = π R 3 ( 1 - R ) 1 1 - R ,
N = F R / 3 ,
T C P O ( x , y ) = T 2 ( 1 - R 2 ) 2 + 4 R 2 sin 2 ( 2 k d + δ / 2 ) ,
T 3 M = T 3 [ 1 + R 2 1 - cos 2 k ( 1 1 - R 2 + R 2 cos 2 k - cos 4 k 1 + R 4 - 2 R cos 2 k ) ] ,

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