Exact design of complex amplitude holograms for producing arbitrary scalar fields.

Typical methods to holographically encode arbitrary wavefronts assume the hologram medium only applies either phase shifts or amplitude attenuation to the wavefront. In many cases, phase cannot be introduced to the wavefront without also affecting the amplitude. Here we show how to encode an arbitrary wavefront into an off-axis transmission hologram that returns the exact desired arbitrary wavefunction in a diffracted beam for phase-only, amplitude-only, or mixed phase and amplitude holograms with any periodic groove profile.