Orthonormalization of phase-only basis functions

Orthonormal bases serve as a powerful mathematical tool in theoretical and experimental optics. However, producing arbitrary optical fields in real-world experiments is limited by the hardware, which in many cases involves a phase-only spatial light modulator. Since most basis functions also have a varying amplitude component, they cannot be represented truthfully. We present a general method to construct an orthonormal phase-only basis, optionally possessing desirable properties like smoothness and symmetry. We demonstrate the practical benefit of our approach in a wavefront shaping experiment, achieving a factor 1.5 increase in performance over a non-orthonormal phase only basis.