This report, authored by A. B. Vander Lugt and published in July 1963, discusses the problem of signal detection using complex spatial filtering. The report is part of Project MICHIGAN, a long-term research and development program aimed at advancing the Army's combat-surveillance and target-acquisition capabilities. The key findings include: 1. **Problem Statement**: The report formulates the problem of signal detection, emphasizing the importance of maximizing the ratio of peak signal energy to mean square noise energy. 2. **Optimum Filtering**: It derives the optimal filter that maximizes this ratio, which is proportional to the complex conjugate of the signal spectrum divided by the noise spectral density. 3. **Optical Processing Systems**: The report describes two types of optical systems for implementing the optimal filter: - **Coherent Optical Systems**: These systems use Fourier transform principles and can handle complex filters by arranging lenses to form successive Fourier transform planes. - **Noncoherent Optical Systems**: These systems are limited to real filters and require a reference function to realize the filter. 4. **Realization of Complex Filters**: The report details methods for realizing complex filters, including techniques for handling nonnegative and real filter functions, and a method using a Mach-Zehnder interferometer to determine the phase of a signal's Fourier transform. 5. **Performance Evaluation**: The report evaluates the performance of matched filters under different conditions, such as changes in signal scale and orientation, and demonstrates the effectiveness of the techniques through experimental results. 6. **Experimental Results**: The report presents several examples of signal detection, including the detection of simple geometric shapes, alphanumerics, and isolated signals in random noise, showcasing the potential of the proposed techniques. The report concludes by highlighting the advantages of the proposed methods, particularly the superior noise rejection capability of complex filters compared to conventional filters.This report, authored by A. B. Vander Lugt and published in July 1963, discusses the problem of signal detection using complex spatial filtering. The report is part of Project MICHIGAN, a long-term research and development program aimed at advancing the Army's combat-surveillance and target-acquisition capabilities. The key findings include: 1. **Problem Statement**: The report formulates the problem of signal detection, emphasizing the importance of maximizing the ratio of peak signal energy to mean square noise energy. 2. **Optimum Filtering**: It derives the optimal filter that maximizes this ratio, which is proportional to the complex conjugate of the signal spectrum divided by the noise spectral density. 3. **Optical Processing Systems**: The report describes two types of optical systems for implementing the optimal filter: - **Coherent Optical Systems**: These systems use Fourier transform principles and can handle complex filters by arranging lenses to form successive Fourier transform planes. - **Noncoherent Optical Systems**: These systems are limited to real filters and require a reference function to realize the filter. 4. **Realization of Complex Filters**: The report details methods for realizing complex filters, including techniques for handling nonnegative and real filter functions, and a method using a Mach-Zehnder interferometer to determine the phase of a signal's Fourier transform. 5. **Performance Evaluation**: The report evaluates the performance of matched filters under different conditions, such as changes in signal scale and orientation, and demonstrates the effectiveness of the techniques through experimental results. 6. **Experimental Results**: The report presents several examples of signal detection, including the detection of simple geometric shapes, alphanumerics, and isolated signals in random noise, showcasing the potential of the proposed techniques. The report concludes by highlighting the advantages of the proposed methods, particularly the superior noise rejection capability of complex filters compared to conventional filters.