Project MICHIGAN, conducted by the Institute of Science and Technology at the University of Michigan, focused on advancing the Army's combat-surveillance and target-acquisition capabilities through research in imaging radar, MTI radar, infrared, radio location, image processing, and special investigations. The report details the theory and experimental results of signal detection using complex spatial filtering. The key idea is to use a coherent optical system to perform optimal linear filtering, which maximizes the ratio of peak signal energy to mean square noise energy. The theory is validated through experiments showing that the method provides excellent two-dimensional filtering capabilities, crucial for tasks like shape recognition and signal detection. The mathematical model describes the problem of sensing, recording, and processing imagery. The scene is represented by a function of two space coordinates, and the processing involves a third transformation to estimate the signal present. The optimal filter is derived based on the signal and noise spectral densities, and it is shown to be proportional to the complex conjugate of the signal spectrum divided by the noise spectral density. Optical processing systems, both coherent and noncoherent, are described. Coherent systems use Fourier transforms to achieve the desired filtering, while noncoherent systems are limited by the requirement that noise is uniform across all frequencies. The report also discusses the realization of the optimal filter using photographic film and other techniques, including the use of liquid cells and Mach-Zehnder interferometers to determine the phase of the signal. Experimental results demonstrate the effectiveness of the method in detecting simple geometrical shapes, alphanumeric characters, and isolated signals in noise. The results show that the technique provides better noise rejection than conventional filters and can detect signals with proper shape and orientation. The report concludes that the method has significant potential for applications in signal detection and image processing.Project MICHIGAN, conducted by the Institute of Science and Technology at the University of Michigan, focused on advancing the Army's combat-surveillance and target-acquisition capabilities through research in imaging radar, MTI radar, infrared, radio location, image processing, and special investigations. The report details the theory and experimental results of signal detection using complex spatial filtering. The key idea is to use a coherent optical system to perform optimal linear filtering, which maximizes the ratio of peak signal energy to mean square noise energy. The theory is validated through experiments showing that the method provides excellent two-dimensional filtering capabilities, crucial for tasks like shape recognition and signal detection. The mathematical model describes the problem of sensing, recording, and processing imagery. The scene is represented by a function of two space coordinates, and the processing involves a third transformation to estimate the signal present. The optimal filter is derived based on the signal and noise spectral densities, and it is shown to be proportional to the complex conjugate of the signal spectrum divided by the noise spectral density. Optical processing systems, both coherent and noncoherent, are described. Coherent systems use Fourier transforms to achieve the desired filtering, while noncoherent systems are limited by the requirement that noise is uniform across all frequencies. The report also discusses the realization of the optimal filter using photographic film and other techniques, including the use of liquid cells and Mach-Zehnder interferometers to determine the phase of the signal. Experimental results demonstrate the effectiveness of the method in detecting simple geometrical shapes, alphanumeric characters, and isolated signals in noise. The results show that the technique provides better noise rejection than conventional filters and can detect signals with proper shape and orientation. The report concludes that the method has significant potential for applications in signal detection and image processing.