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Spectrum analysis is one of the most fundamental tools in science today. Its use in one form or another spans virtually every discipline. It was one of the first recognized applications of optical processing, and the usefulness of optical spectrum analysis has grown remarkably in the past decade. This is due to the fundamental simplicity, parallelism and intrinsic speed of optical spectrum analyzers, the maturity of the components now available, and the remarkable variety and versatility of the processing architectures that have been developed. This paper presents six selected topics on spectrum analysis using optics. The topics were selected because they represent practical techniques with broad applicability and illustrate different aspects of the technology. The topics are grouped by architecture as space integrating and time integrating. The space integrating sections cover radiometry for detecting low-level signals in wide-band noise, programmable filtering of electrical signals for interference rejection applications, and an optical technique that is equivalent to 105-106parallel filters for application where fast response, high resolution, and wide bandwidth of coverage are simultaneously required. The time integrating sections cover the versatile time integrating spectrum analyzer, and its extension to the calculation of ambiguity surfaces which have important application to radar processing problems requiring simultaneous measurement of a radar return's time of arrival and possible Doppler frequency shift. This process also illustrates the parallel nature of optical operations, and introduces a fundamental concept, the use of one-dimensional optical components configured for performing two-dimensional operations. The discussion of this concept continues into two-dimensional time integrating spectrum analyzers that use two time integrating spectrum analyzers, each capable of resolving N elements, and combines them to produce N2resolvable elements in real time.