oo
ders cu eO exp Dian Ng o ns0761, 12, (4)
no
where the Fourier coefficients are given by
— * I/Po — n
Ca = po f, gt Xo) e ??*^Po*oQ xo (5)
-
The amplitude transmittance of the grating and PSF transparency
in contact is
h'»' (xo, yg ) 7 h(Xo. Yo) * g(Xg)
its Fourier transform is
H'® (Sf. m= 2 C..H(£-np,.m
n . )
Similarly, the Fourier transform of the transmittance of the
blurred picture in contact with the.grating is
B'»'(&. n= 2 CnF(&- nP,. N) + HCE- n p,. M (73
where we have applied the convolution theorem to Eg.(2). Cor-
responding to the various diffraction orders of the modulating
grating, the spectra of the PSF and blurred picture ‘appears in
a series of equally spaced islands in the filter plane, the am-
plitude distributions across each islands vary in ‘proportional
to the Fourier transform H and B respectively. The amplitudes
of various islands, if compared at points corresponding to the
same spatial frequency, are proportional to the Fourier coeffi-
cients of the amplitude transmittance of the grating.
In the following, we will assume that the functions h(x,y)
and f(x.y) are band-limited in the x, direction, as expressed
by
(8)
Hocm 9
: } foreclbiz p.42
Fei. n=10
It is equivalent to requiring that various islands of the spec-
trum do not overlap.
B. The attenuating mask
Two parts are involved in the filter-generating step. The
first is to get an absorptive mask with the amplitude trans-
parency in proportional to |H'"(&.m|^", by recording the inten-
sity distribucion "cs q-[^-. And^ Chen, Co ‚make the filter‘by
recordina a. hologram in .the- back “of ‘the absorptive mask
|H *"«t. p ^, with the interference between a weak reference
beam and the Fourier spectrum of h'" (x,y).
In the object plane, the collimated beam transilluminates
a transparency representing the function h(x,y) which is in
contact with the transmission grating, the distribution of the
Fourier spectrum plane is
A s Cn * HCE- NP,» M (95
jAf RETO
Hr: 2. m=
where H is a normalized function, A, is the peak value of “its
Zero order and i is the optical wavelength. As a consequence of
the band-limited condition (8), the terms in Eq(9) do not over-
39
