Approximating fully complex spatial modulation with pseudorandom phase-only modulation

Any desired diffraction pattern can be produced in the Fourier plane by the specification of a corresponding input-plane transparency. Complex-valued transmittance is generally required, but in practice phase-only transmittance is used. Many design procedures use numerically intensive, constrained optimization. We instead introduce a noniterative procedure that directly translates the desired but unavailable complex transparency into an appropriate phase transparency. At each pixel the value of phase is pseudorandomly selected from a random distribution whose standard deviation is specified by the desired amplitude. We also derive statistical expressions and use them to evaluate the approximation errors between the desired and achieved diffraction patterns.