The Fukunaga-Koontz (F-K) transform is a linear transformation that performs image-feature extraction for a two-class image classification problem. It has the property that the most important basis functions for representing one class of image data (in a least-squares sense) are also the least important for representing a second image class. A new method is presented of calculating the F-K basis functions for large dimensional imagery by using a small digital computer, when the intraclass variation can be approximated by correlation matrices of low rank. Having calculated the F-K basis functions, a coherent optical processor is used to obtain the coefficients of the F-K transform in parallel. Finally, these coefficients are detected electronically, and a classification is performed by the small digital computer.