Strong phase diffusers with the minimized standard deviation of roughness

Abstract

For a random phase diffuser (RPD), the probability-density function of the surface roughness is found that minimizes rms roughness under the condition that scattered radiation does not contain a specular component. This function is found to be discrete and is obeyed by binary diffusers that introduce to the incident radiation two phase shifts, π/2 and −π/2. For an RPD that is assumed to be fabricated by a photographic method and whose phase obeys the continuous density function, which closely approximates the above discrete distribution, a general form of the autocorrelation of amplitude transmittance is calculated. The present study shows that strong scattering can be performed by surfaces whose rms roughness equals only λ/4 when reflecting geometry is assumed and when λ is a wavelength of incident radiation.