<title>Error diffusion concept in digital holography</title>

Abstract

ABSTRACT The calculation of high quality digital holograms with the error diffusion concept is presented. The cont'nts ofthis paper is based on reference 1. 1. INTRODUCTION In that part of diffractive optics which is called digital holography, the optical function of the diffractive element(DE) is usually defined by its Fresnel or Fourier diffraction pattern. Thus, the distribution F(il) to be stored in theelement results from the inverse transform of the diffraction pattern. In general F(il) is complex valued and notquantized. Hence, the fabrication procedure has to specify the phase and amplitude transmission of the element. As the control of phase and magnitude of the transmission of an element is difficult to realize in practice in a continous manner a restriction to either a phase or an amplitude transmission is the usual procedure. Especiallynonabsorbing elements, i.e. diffractive phase elements (DPE), are of interest. Moreover, the amplitude (or thephase) transmission is usually controlled in discrete steps, i.e. quantized diffractive phase elements (DAE) aredesired. In conclusion one has to restrict the set of values of the inverse transform of the desired diffraction patternbefore the fabrication step can be performed. In most cases this restriction is a nonlinear operation, e.g. quanti-zation (of a real valued function or of a phase) and restriction to complex valued functions with magnitude one(coding of a DPE).The nonlinearity in the calculation process of a DE causes noise in the corresponding Fourier plane. This resultsin a low signal to noise ratio (SNR) which can be increased by implementing an intelligent scheme to correct theeffects due to the nonlinearity (NL). The methods of controlling the noise in the Fourier plane can be devided intodirect and iterative ones2. We concentrate on one direct correction scheme, i.e. the error diffusion algorithm (ED)which is a powerful and easy implementable mean to handle nonlinearities concerning the calculation of DE.