formed on the film rather than a sharp point. The impulse response is

a line, and the corresponding frequency response of the distorting

system is a sine function (sin u /u). To retrieve the European

photo collection, merely multiply the Fourier transform of the

pictures by u/sin u and re-image.

 In the physical implementation of this process, there are several

practical problems. To multiply the image transform by the inverse

function, a transparency with the appropriate response is produced.

In general, a transparency can only attenuate the light striking it.

That is, the transparency can only represent non-negative real values

less than one. Herein lies the problem. The inverse response

required to correct a specific distortion may, in fact, be complex.

In some cases, a combination of two transparencies can be combined to

provide complex values. One transparency is used for amplitude or

attenuation, and another phase transparency or phase plate is used to

provide the appropriate phase shift at each point. A phase

transparency can be produced by bleaching film with an appropriate

latent image induced in the emulsion. Chu, Fienup, and Goodman18

demonstrated a technique in color film which consists of three

emulsions. One emulsion was used as an amplitude transparency and

another emulsion was used as a phase plate. The appropriate patterns

were determined by a computer and the film was given the proper

exposure using colored filters.

 Even with a two-transparency system, not all distortions are

possible to remove. Note that in the linear blur case, the inverse

response is u/sin u. The denominator goes to zero for specific values

of u, and the response has a pole at those values. The filter cannot