lap, hence can be squared individually and summed to yield
|A‘P (it m|? .The exposure for the mask JHE Mean thus be written
as
N
E.6b n om 0€ En lmnpe m
n=—N\
where N is the highest order used in this system. The exposure
of the n-th islands is
sp AU * Aj
Ei np mE 4 IC. [2^ | HCE = np,’ ny]? (19)
The amplitude transmittance of the n-th island of the mask, for
the case of the ideal recording medium with a Gamma of 1 can be
expressed
k.Af 1
AAT. Cn +s H(&$- npo n C1íi)
where Kn is à constant which is related to the photographic
techniques. Now we have got the attenuating mask |H'^]^,
Ta =
C. The holographic inverse filter
As mentioned in section B, to make the filter, it is neces-
sary to replace the attenuating mask |H'"|4!. into its recording
position,. and it is, illuminated. bv the fields :A ‘?'££ + V. çand ,, the
reference beam-ReXp {-Jant. =x: 3 , Be is the. spatial frequency. of
the reference beam. The mask attenuates the A'" and reference
beam equally,the ratios between the two beams remain unchanged.
Now we record the hologram in the back of the mask,the exposure
to which the holographic plate in the plane(x;,y;) is subjected
is
E, CE. m = [HH (5 mReexpl - 2xtox 0 ct, m] (12)
E; can be arranged and seperated into two terms
B, zE- E = SE. + SE.)
En 1 + 1470 R/ M32. IC, [2+ {HE - AB. 1 |? (13a)
n = — si(2mTb.nue + Ya 8, 3
[CH | f H ) (13b)
where Ë is ‘the d-c part of, Eq. (12). E dsdts d-c part, m and
6, are defined as the phases of H(&-np,,n)> and C, respectively.
R/Ao is the ratio of the reference beam to object beam. Eg.(13b)
is the term of interest for the inverse filter. If the hologram
with a perfectly linear recording medium (amplitude transmit-
tance proportional to exposure), the ideal amplitude transmit-
tance corresponding to this term is
T¢ AMORIS {-j2mt
Sian Aij) DIS (14)
D. The deblurring processing
During the image processing step, the blurred image and the
grating are placed in contact, which yields an amplitude
I N
BCE Mn »—— Y C,:F(5- np, m* Hc& - np, m
j^f n=—N (15)
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