The theoretical performance of a Mach-Zehnder interferometer used as a spectral analyzer for wind-speed measurement by direct-detection Doppler lidar is presented. The interferometer is optimized for the measurement of wind velocity from the signal that is backscattered by the molecules. In the proposed fringe-imaging Mach-Zehnder (FIMZ) interferometer, a pattern of equally spaced linear fringes is formed and detected by two conventional detector linear arrays. Assuming a pure molecular signal with Gaussian spectral profile, an analytic expression for the standard deviation of the measurement error is obtained and compared with the Cramer-Rao lower bound given by an ideal spectral analyzer (ISA) in the case of shot-noise-limited signal. The FIMZ measurement error is shown to be 2.3 times that of the ISA and is comparable with the error given by previously developed multichannel spectral analyzers that are based on Fabry-Perot interferometers that, in contrast, have the disadvantages of producing unequally spaced circular fringes and requiring dedicated detectors. The optimal path difference for a FIMZ operating at 355 nm is approximately 3 cm. The interferometer is shown to match important lidar beam étendues without significant performance reduction.
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