Unfortunately, this parallel technique is somewhat cumbersome to

implement due to alignment of the multiple lenses and filters.

 To avoid the need for multiple lenses and filters, it is possible

to combine several reference images into one filter. The use of

multiple lenses and filters superimposes the outputs of the individual

correlators. Because the Fourier transform and correlation are

linear, the superposition at the output is equivalent to superimposing

the individual filter functions into one filter. Likewise, this is

equivalent to superimposing the reference images in the creation of

the filter. Rather than create separate filters from many images, a

single filter is created from a sum of the images. This simplifies

the optical hardware. Caulfield et a155 defines a "composite matched

filter" CMF as a single filter which is a linear sum of ordinary

matched filters, MF.


 CMF = E wk MFk (5.1)
 k


These filters can be implemented by either multiple exposure optical

holography or computer holography. In the optical hologram, the

weights in the linear combination are obtained by varying the exposure

time. The latter approach is to use computers to generate the CMF

off-line. In this way, the long-drawn-out creation of the CMF is

performed on a digital computer where time is not critical. This

takes advantage of the control, dynamic range, and flexibility of

digital processors.

 Once the CMF function is determined, an optical filter is

 produced, tested, and optimized. It is then inserted in an optical

 correlator to take advantage of its real-time processing. To