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In an interferometer-based fluorescence microscope, a beam splitter is often used to combine two emission wavefronts interferometrically. There are two perpendicular paths along which the interference fringes can propagate and normally only one is used for imaging. However, the other path also contains useful information. Here we introduced a second camera to our interferometer-based three-dimensional structured-illumination microscope (I(5)S) to capture the fringes along the normally unused path, which are out of phase by π relative to the fringes along the other path. Based on this complementary phase relationship and the well-defined phase interrelationships among the I(5)S data components, we can deduce and then computationally eliminate the path length errors within the interferometer loop using the simultaneously recorded fringes along the two imaging paths. This self-correction capability can greatly relax the requirement for eliminating the path length differences before and maintaining that status during each imaging session, which are practically challenging tasks. Experimental data is shown to support the theory.