image. -Many points are required to represent a transform with a large

dynamic range accurately.

 Lee9 proposed a method in 1970 which helped relieve some of

the phase granularity. The Brown-Lohmann technique represented each

cell with an amplitude and phase component. The complex value for

each cell may be represented by a magnitude and phase or by the sum of

in-phase and out-of-phase terms. The Lee method represents each cell

with such a quadrature representation. For each cell the magnitude

and phase are converted to real and imaginary components. As in the

Brown-Lohmann method, the tilted wave is set to provide a wavelength

of delay across the cell. The cell is divided into four components

which represent the positive and negative real and imaginary axes.

Lee defined the functions as


IF(u,v)lexp[j 0(u,v)] = F1(u,v)-F2(u,v)+jF3(u,v)-jF4(u,v) (3.7)


where


 F1(u,v)= IF(u,v) cos+(u,v) if cos((u,v) > 0
 = 0 otherwise,


 F2(u,v)= IF(u,v) sinp(u,v) if sini(u,v) > 0
 = 0 otherwise,


 F3(u,v)= IF(u,v)Icos4(u,v) if cost(u,v) > 0
 = 0 otherwise,


 F4(u,v)= IF(u,v) sin(u,v) if sinq(u,v) > 0
 = 0 otherwise.


For any given complex value, two of the four components are zero.

Each of the components Fn(u,v) is real and non-negative and can be

recorded on film. The Lee hologram uses four apertures for each cell