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The sensitivity to path length changes is analyzed in coherent beam combining architectures based on Fourier plane spatial filtering. Unlike superposition architectures based on 3-dB couplers and Dammann gratings, the supermodes of a two-laser spatially filtered cavity exhibit two distinctly different types of behavior depending on the path length error. When the error is small, the two modes present different cavity loss values and can be differentiated by gain. However, cavities containing path length errors greater than a critical value produce modes with identical losses and different resonant frequencies. Cavities with more than two elements exhibit similar behavior. Alternative filtering techniques are also discussed and compared. It is found that complementary filtering, where absorption spots are placed in the nulls of the intensity pattern in the Fourier plane, results in reduced power loss while preserving the same degree of modal discrimination.