azu_td_1349475_sip1_... - Arizona Campus Repository

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OPD=Jrl+f 2 3 3
The incident plane wave is thus converted into a converging wave with a
resulting phase retardation of
0=^[Vr2+/ 2 ./]
A
3.4
From the discussion in section 3.1, the zone theory of Fresnel states that the
phase difference from the center of the lens to the m ,h zone must be equal to a
multiple of n. Setting Equation 3.4 equal to 7im, and solving for r m, the radius of
the mth zone, gives,
r m = J( a^-) 2 + mX~f
V 2
3.5
The maximum number of zones for a given focal length and radius is calculated
by solving Equation 3.4 for m, the number of zones,
m=f 36
These equations describe the parameters needed to construct a phase Fresnel
zone plate or binary diffractive lens. The term binary lens arises from the two
level phase structure (zero and jt) of the lens as illustrated in Figure 3-5. It
consists of transparent circular zones with a square wave profile. The thickness
change between alternating zones induces the necessary n phase shift
between successive zones. Because of its symmetry, the binary lens directs
equal amounts of incident light into the +1 and -1 orders. The resulting
diffraction efficiency of a binary lens is 40.5%.