The future of adaptive optics relies heavily on the development of membranous optical lenses. Large, deformable mirrors offer clear advantages over their glass counterparts: flexibility, low density, and minimal actuation for optical aberration correction. This paper develops a novel set of polynomials to describe incoming wavefront aberrations that is amiable to a membrane mirror’s mode shapes. The novel basis, named the clamped Zernike radial polynomials, conveniently delineates the image correction into four distinct actuation categories feasible with membrane optics.

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