Any desired diffraction pattern can be produced in the Fourier plane b
y the specification of a corresponding input-plane transparency. Compl
ex-valued transmittance is generally required, but in practice phase-o
nly transmittance is used. Many design procedures use numerically inte
nsive, constrained optimization. We instead introduce a noniterative p
rocedure 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 als
o derive statistical expressions and use them to evaluate the approxim
ation errors between the desired and achieved diffraction patterns.