Minimum mean-square error linear optical filter

• US 4,067,645 A
• Filed: 12/29/1975
• Issued: 01/10/1978
• Est. Priority Date: 05/13/1974
• Status: Expired due to Term

• Current Assignee: Board of Regents of The University of Washington (University of Washington)
• Original Assignee: Board of Regents of The University of Washington (University of Washington)
• Inventors: Carlson, F. Paul, Ward, Joseph E. III
• Primary Examiner(s): Stern, Ronald J.
• Application Number:
  US05/644,894
• Time in Patent Office: 743 Days
• Field of Search: 350/162 SF, 350/3.5, 356/71
• US Class Current: 359/564
• CPC Class Codes: G01N 15/1433 using image recognition
• CPC Class Codes: G01N 15/1434 Optical arrangements
• CPC Class Codes: G01N 15/1459 the analysis being performed on a sample stream
• CPC Class Codes: G01N 2015/1486 Counting the particles
• CPC Class Codes: G02B 27/46 Systems using spatial filters
• CPC Class Codes: G06V 10/893 characterised by the kind of filter
• CPC Class Codes: Y10S 359/90 Methods

Abstract

A method of forming a minimum mean-square error linear filter photographically is disclosed.

The optimum filter may be obtained photographically. In one form, a first photographic negative of a monolayer of cells having a high percentage of cells of the given type is made at the focal plane of a transforming lens mounted so as to collect the light scattered by the monolayer; and, developed for a gamma of unity. Thereafter, a second photographic negative is made at the same focal plane of a monolayer of cells containing a normal percentage of cells of the given type using the first negative as a filter. The second negative is developed for a gamma of two. The resulting photographic plate is a realization of the desired optimum (minimum mean-square error linear) filter. Alternatively, a sandwich of two photographic plates, one positive and obtained from a monolayer of cells having a high percentage of cells of the given type and the other negative obtained from a monolayer of cells having a normal percentage of cells of the given type, is constructed to provide a physical realization of the desired optimum filter.

Claims

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

##EQU8##where;

S_ss (ω

) is the power spectral density of the signal to be enhanced by the minimum mean-square linear optical filter; and

,

S_nn (ω

) is the power spectral density of the signal to be suppressed by the minimum mean-square 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_ss (ω

);

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_ss (ω

) + S_nn (ω

);

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.

2. A minimum mean-square error linear optical filter formed in accordance with the process recited in claim 1.

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

##EQU9##where;

S_ss (ω

) is the power spectral density of the signal to be enhanced by the minimum mean-square error linear optical filter; and

,

S_nn (ω

) 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_ss (ω

);

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_ss (ω

) + S_nn (ω

);

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.

4. A minimum mean-square error linear optical filter formed in accordance with the process recited in claim 3.

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

##EQU10##where;

S_ss (ω

) is the power spectral density of a desired optical signal; and

,

S_nn (ω

) 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_ss (ω

);

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_ss (ω

) + S_nn (ω

);

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.

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

##EQU11##where;

S_ss (ω

) is the power spectral density of a desired optical signal; and

,

S_nn (ω

) 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_ss (ω

) and a photographic negative having the transfer function S_ss (ω

) + S_nn (ω

) 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_ss (ω

);

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_ss (ω

)+ S_nn (ω

);

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.