Clarification of Horner efficiency

Joseph L. Horner The author is with the Solid State Sciences Directorate, Hanscom Air Force Base, Massachusetts 01731-5000. Received 23 December 1991.

Several different definitions of the metric Horner efficiency seem to have come into use. This note is an attempt to clarify and standardize the definition.

Judging by several papers and oral presentations I have seen and heard in the past year there seems to be some confusion on this metric. In a paper published in 19841I suggested a performance measure for assessing how much of the energy in an optical correlator ends up doing useful work. With a frequency plane correlator in mind, I defined an efficiency

where C(x) is the correlation signal and represents the total energy in the correlation plane. The denominator is the energy in the input plane, and η M is a materials parameter such as the effective diffraction efficiency in the case of a holographically implemented spatial filter (which was all there was in those days). We assume that the input image sin is on a noise-free, zero-filled background. In that same

10 July 1992 / Vol. 31, No. 20 / APPLIED OPTICS 4629

issue of Applied Optics, Caulfield2 suggested defining the "Horner efficiency" as

where C(0) is the correlation peak energy, and the denomina­tor, as in Eq. (1), is the total input energy to the system. It seems that both quantities have been taken to be the Horner efficiency. I would like to recommend that only the one suggested by Caulfield2 be used to designate Horner efficiency. I think it is a more useful measure because it determines how much of the input energy actually does useful information processing, and that sets the lower limit on the size of the laser that is required to power the system. At the same time this measure also says something about the sharpness of the correlation peak. This is also impor­tant because a sharp peak is more desirable than a broad one, especially if there are multiple targets in the field of view. I would also like to refer the reader to Refs. 3 and 4. These papers discuss some metrics that are useful for pat­tern recognition and the various relationships among them.

References 1. J. L. Horner, "Light efficiency in optical correlators," Appl. Opt.

21,4511-4514(1984). 2. H. J. Caulfield, "Role of the Horner efficiency in the optimiza­

tion of spatial filters for optical pattern recognition," Appl. Opt. 21, 4391-4392 (1984).

3. J. L. Horner, "Metrics for assessing pattern recognition performance," Appl. Opt. 31, 165-166 (1992).

4. B. V. K. V. Kumar and L. Hassebrook, "Performance measures for correlation filters," Appl. Opt. 29, 2997-3006 (1990).

4630 APPLIED OPTICS / Vol. 31, No. 0 0 / 1 0 Month 1992

Image logic algebra and its optical implementations: errata Masaki Fukui and Ken-ichi Kitayama

The authors are with NTT Transmission Systems Labo­ratories, 1-2356 Take, Yokosuka-shi, Kanagawa 238-03, Japan. Received 27 January 1992. 0003-6935/92/234630-01$05.00/0. © 1992 Optical Society of America.

The following corrections should be made to Ref. 1: Equa­tion (9) should read as

In Eq. (12), x(0) and x(1) should be interchanged to this

corrected form:

In Eq.(20),xklm(0)and xklm

(1) should also be interchanged:

New Tables VI and VII replace the tables with the same numbers in the original paper.1

Reference 1. M. Fukui and K. Kitayama, "Image logic algebra and its optical

implementations," Appl. Opt. 31, 581-591 (1992).

Table VI. Relation between the Operation Kernel of OAL and NCP

Table VII. Symbols of Operation Kernels of OALα