splited by the beam spliter BS is collimated by lens Le and 
illuminates the object plane OP, the other beam splited is col- 
limated by Ls and illuminates the filter plane FP at the angle 
© as the reference beam. The intensity of the reference beam is 
controlled. by a pair of polarizers g, and g,. The cameras L: 
and Lz with focal length equal to 600mm are used as the Fourier 
transform lenses. The front focal plane of Li ds: ithe object 
(input) plane OP, the back focal plane is the filter plane FP. 
which is also the front focal plane of the lens La. 
In the image processing step, the reference beam is blocked. 
The deblurred aerial image is formed in the image plane IP (the 
back focal plane of Lz). The frequency of the grating used in 
this system is 40 lps/mm.The recording material is the Tianjing 
holographic: 1 plate, its sensitivityds 30105 ;/ cmt. 
111... Theory 
The theoretical background . of optical. filtering. is: well 
known. However, for the sake of completeness,a brief outline of 
the mathematics involved is given as follows. 
The formation of a blurred photograph (for that matter any 
photographs, blurred or sharp) can be described in general by 
the superposition integral 
^ 4- wv * 
boy» | | f(x!',yt'ohGuuy:; x !uy' )dx dy" (1) 
where f(x,y) and b(x,y) are the image and object intensity dis- 
tribution respectively, and h(x,y) is the impulse response of 
the optical system. For certain types of blurs. which include 
linear motion of the camera under the assumption that the pic- 
ture occupies only a limited region of the field. Eq.(1) can be 
simplified to a convolution integral 
> Prt 
boy) [ [7 fO iy hex! y-y 0dxtdy' (2) 
In the Fourier plane, Eq.(2) can be written as 
B(t,m])-FCt£, 94) -H(5, m) (3) 
where &£,"n are spatial frequencies in the x, and y, directions, 
and the B, F and H are the Fourier transforms of b, f and h 
respectively. By passing  Eq.(3) througir a filter |with  trans- 
mittance proportional .;to H "I(t. nN), we can recover, F(£,n) com 
pletely, provided H never goes to zero within the region where 
F(:, 1)=0. The operations of multi-channel inverse ,filtering 
system are as follows. 
A. The basic relations 
in the filter-generating and image-processing steps, a 
grating, with spatial frequency p,, is superposed on the trans- 
parency representing the PSF (point spread function) and on the 
transparency representing the blurred picture. The amplitude 
transmittance of the grating with lines running parallel to the 
y, axis (perpendicular to the blurring direction) is described 
by a periodic function: g(x), which ircan- be expressed as a 
Fourier series 
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