We report the impact on imaging quality of mirror suspensions, referred to as spider legs, used to support the reference mirror in a Mirau micro-interferometer that requires the vertical alignment of lens, mirror, and beamsplitter. Because the light goes from the microlens to the beamsplitter through the mirror plane, the spider legs are a source of diffraction. This impact is studied as a function of different parameters of the spider legs design. Imaging criteria, such as the resolution as well as the symmetry of the imaging system, are determined using the point spread function and the modulation transfer function of the pupil. These imaging criteria are used to determine the optimum radius of curvature, thickness, and number of legs of the spider structure. We show that 3 curved legs give performances, with specific radius of curvature and thickness, similar to a suspension-free mirror.