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Theoretical description of phase discretization and quantization is provided for coaputer generated optical
eleients (CGOK). Suitable estiiations of seanaquared and iaxiaui aberrations, Strehl nuaber and aean wavefront
deviation are derived in dependence of discretization and quantization paraieters. A diffractive aberration corrector
for thin len5 and also phase diffractive coipensator for aspheric wavefront foriation are investigated as
exasples,
1 . PROBLEM OF CGOE D ISCRETI ZAT ION AND QUANTI ZAT ION.
Wide-range possibilities of coaputer generated holograis and optical eleients1' are soietiies liiited by
discretization of their phase transfer function. The known aethods for studying phase nonlinearities treat
quantization as a superposition of iany diffraction orders but do not take discretization into account.
In this paper coibined studying of discretization and quantization is perforied for siooth phase functions such as
of zoned phase plates, coipensators, Fresnel lenses and siiilar type CGOK.
Digital holography applications provide us coiputer generated optical elesents including kinoforis' with purely
phase-type t'ransfer function
r (t) exp{L.treod25rrrt (p(a)] (1)
where • : (u,v) are 2-D Cartesian coordinates in the CGOI's plane, 'f (ii) is the phase shift perforied in point IT,
iod2,,,tf ) is the value of 'p the aodulo (2ira), 1:1 or another positive nuiber. Coiputer-aided design of CGOK
includes calculation of digital saiples for 'P function brought to [O,2%a) interval, driving suitable nak generator
to access grey-level or binary iasks. Grey-level iasks used in bleaching or photopolyaer technology yield a CGO with
variable iicrorelief thickness. Optical lithography with a set of binary aasks or iulti-stepped electron-beaw
lithography yields aulti-level COOK described by quantization of 'P . Raster scanning iask generator set up all saska
iI the field G fros so called resolution cells G7that are centered in i;point, enuierated by double index
1 : (i,,i) froi J set and obey the equations
Q=,U G; , &!;flp=O if T (2)
Mask's spatial resolution is fully deteriined by the size of cell. This is the way that discretization of takes
place and results in piecewise approxiiation of 1'.
Thus discretization and quantization are specific for CGOK and cannot be resoved. It should be noted that
quantization take place also in holographic optical elesents lithographically fabricated fro. physical holograss used as
aasks. Next parts of this paper are placed in the following sequence. For the first, zoie iatheaatical iodel is
presented for phase discretization and quantization in CGOK. For the second, phase fluctuations are evaluated only on
the CGOK's plane. For the third CGOK's light field is transforied to the plane at a soie distance fros CGOK's plane,
soae characteristic are evaluated in general case and for such applications as iiage foriation and aspheric wavefront
foraing.
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