Optimization of phase-only computer-generated holograms using

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Position x
Fig. 6 Phase profile of the wavefront through an aperture.
Figure 6 shows an example of a phase profile. A high
index difference (aperture center area) gives a large phase
shift. Because of the diffusion that takes place in all directions,
there is also a phase shift outside the aperture region.
This causes only small reductions in diffraction efficiency,
but is a major problem when making aperture holograms.
Fourier transforming the phase profile of Fig. 6 gives the
diffraction pattern, and therefore also the diffraction effi-
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1262 / OPTICAL ENGINEERING / June 1992 / Vol. 31 No. 6
(a)
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I I I I I Ji L I I I I
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Pos I t I on
(c)
BOLSTAD, YATAGAI, and SEKI
Fig. 7 Calculated diffraction patterns: (a) 0=182.1
(d) 0=240.3 deg.
ciency, as shown in Fig. 7. In this figure we can see the
result for four different phase profiles. It is drawn with the
maximum phase shift as a variable. We can see that at near
180 deg, there is still a considerable energy left in the zeroorder
(30%), whereas there is about 35% in the first orders.
Increasing the phase shift to about 220 deg gave the best
result for this particular profile with 13% left in the zero
order and about 37% in the first orders, compared to the
theoretical limit of 40% for a binary phase-only grating.
Other profiles had even higher efficiencies. Figure 8 shows
the best result with maximum of 38.5% in the first orders
at 210-deg phase shift, which is very close to theoretical
prediction of 0 — 220 deg. A corresponding low diffraction
efficiency of 5% is obtained at 250 deg for the zero order.
Because of the broadening of the phase profile in the ion
exchange there is a shift in the efficiency curve to a somewhat
higher phase shift compared to the theoretical result
for a rectangular grating.
6 Conclusion
We have proposed the use of an ion-exchange technique to
produce binary phase-only CGHs. The optimum ion-exchange
condition is discussed. For binary phase-only holograms,
the optimum amount of phase change is IT, whereas this
condition is shifted to 220 deg in the ion-exchange case
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deg, (b) 0 = 204.5 deg, (c) 0 = 226.9 deg, and