Noise-Like Structure in the Image of Diffusely Reflecting Objects in Coherent Illumination

Holographic and other imaging systems utilizing coherent light introduce a speckled or noise-like pattern in the image of a diffuse object which severely degrades image quality. It is desirable to understand this effect quantitatively. Intelligent design in many cases requires knowledge of the mean-square value, spatial power spectral density, and autocorrelation junction of the noise-like fluctuations. These quantities have been determined for the image of a uniform diffuse object. Major results are: (i) The mean-square value of the fluctuation in the image intensity is equal to the square of the mean intensity. (ii) One can decrease the relative magnitude of the noise-like fluctuations at the cost of a corresponding increase in the aperture required of the optical system (or hologram) over that required to resolve the desired image in a spatial frequency sense. In a holographic facsimile or TV system, this calls for a corresponding increase in electrical bandwidth. (Hi) The improvement in (ii) is not possible for direct viewing with the human eye, since the resolution of a healthy eye is known to be limited by diffraction at the iris. I. INTRODUCTION' Holographic and other imaging systems using coherent light have been receiving considerable attention lately. 1 , 2 , 3 , 4 Most analyses on this subject assume that the object reflects specularly, or transmits specularly if the object is a transparency, i.e., the reflectivity or transmissivity of the object varies smoothly. Most objects, however, are more nearly diffuse reflectors.