Minimum mean-square error linear optical filter

A method of forming a minimum mean-square error linear optical filter having the following mathematical amplitude frequency response;

• ##EQU9## where:
• S.sub.ss (.omega.) is the power spectral density of the signal to be enhanced by the minimum mean-square error linear optical filter;
• and,
• S.sub.nn (.omega.) is the power spectral density of the signal to be suppressed by the minimum mean-square error linear optical filter, said method comprising the steps of:
• directing a beam of coherent monochromatic light toward a monolayer of particles having a high percentage of particles having the power spectral density S.sub.ss (.omega.);
• collecting the light scattered by said particles with a transforming lens;
• making a first photographic negative of the scattered light collected by said transforming lens at the focal plane of said transforming lens;
• developing said first photographic negative for a gamma of one;
• obtaining a photographic positive from said first photographic negative;
• directing a beam of coherent monochromatic light toward a monolayer of particles having the power spectral density S.sub.ss (.omega.) + S.sub.nn (.omega.);
• collecting the light scattered by said monolayer with a transforming lens;
• making a second photographic negative of the light collected by said transforming lens at the focal plane of said transforming lens;
• developing said second photographic negative for a gamma of two;
• and,
• sandwiching said photographic positive and said second photographic negative together.

A minimum mean-square error linear optical filter having the amplitude frequency transfer function:

• ##EQU10## where:
• S.sub.ss (.omega.) is the power spectral density of a desired optical signal;
• and,
• S.sub.nn (.omega.) is the power spectral density of the remainder of the optical signal, said minimum mean-square linear optical filter formed in a photographic plate prepared in accordance with a process comprising the steps of:
• directing a beam of coherent monochromatic light toward a monolayer of particles having a high percentage of particles having the power spectral density S.sub.ss (.omega.);
• collecting the light scattered by said particles with a transforming lens;
• making a first photographic negative of the scattered light collected by said transforming lens at the focal plane of said transforming lens;
• developing said first photographic negative for a gamma of one;
• directing a beam of coherent monochromatic light toward a monolayer of particles having the power spectral density S.sub.ss (.omega.) + S.sub.nn (.omega.);
• collecting the light scattered by said monolayer with a transforming lens;
• making a second photographic negative of the light collected by said transforming lens at the focal plane of said transforming lens using said first photographic negative as a filter;
• and,
• developing said second photographic negative for a gamma of two.

A minimum mean-square error linear optical filter having the amplitude frequency transfer function:

• ##EQU11## where:
• S.sub.ss (.omega.) is the power spectral density of a desired optical signal;
• and,
• S.sub.nn (.omega.) is the power spectral density of the remainder of the optical signal, said minimum mean-square linear optical filter contained in a photographic plate formed of a sandwich of a photographic positive having the transfer function S.sub.ss (.omega.) and a photographic negative having the transfer function S.sub.ss (.omega.) + S.sub.nn (.omega.) prepared in accordance with a process comprising the steps of:
• directing a beam of coherent monochromatic light toward a monolayer of particles having a high percentage of particles having the power spectral density S.sub.ss (.omega.);
• collecting the light scattered by said particles with a transforming lens;
• developing said first photographic negative for a gamma of one;
• obtaining a photographic positive from said first photographic negative;
• directing a beam of coherent monochromatic light toward a monolayer of particles having the power spectral density S.sub.ss (.omega.)+ S.sub.nn (.omega.);
• collecting the light scattered by said monolayer with a transforming lens;
• making a second photographic negative of the light collected by said transforming lens at the focal plane of said transforming lens;
• developing said second photographic negative for a gamma of two;
• and,
• sandwiching said photographic positive and said second photographic negative together.