Shot noise perturbations in digital holographic microscopy phase images Florian Charrière a , Frederic Montfort a , Etienne Cuche b and Christian D. Depeursinge a a Ecole Polytechnique Fédérale de Lausanne (EPFL), Imaging and Applied Optics Institute, CH- 1015 Lausanne, Switzerland; florian.charriere@epfl.ch; phone +41 21 693 51 82 b Lyncée Tec SA, rue du Bugnon 7, CH-1005 Lausanne, Switzerland, www.lynceetec.com ABSTRACT In digital holographic microscopy, shot noise is an intrinsic part of the recording process with a digital camera. We present a study based on simulations describing how shot noise influences the quality of the reconstructed phase images under different beams intensities configurations. A model for image quality estimation based on the decision statistical theory proposed by Wagner and Brown (R.F. Wagner and D.G. Brown, “Unified SNR Analysis of Medical Imaging- Systems,” Phys. Med. Biol. 30, 489-518 (1985)) will be presented. A simulation will depict the variations of the reconstructed phase images SNR for different distributions of the total intensity between the reference and the object beam. Keywords: holography, shot noise, signal-to-noise ratio 1. INTRODUCTION Digital holographic microscopy (DHM) is nowadays subject to important developments, so its popularity grows continually up. Its success is due to its capacity to extract both amplitude and phase signal of the wavefront diffracted by an object from a hologram recorded through a digital camera and to provide three-dimensional (3D) quantitative phase images. The principle of digital holography (DH) was first proposed by Goodman and Lawrence 1 and by Kronrod et al. 30 years ago 2 . At the beginning, holograms were registered on photographic plates but digital camera quickly became more convenient tools. In DH the intensity distribution of the Fresnel hologram is multiplied by a digitally computed reference wave. The amplitude and phase distributions in the image plane are computed by propagating the diffracted field with the Fresnel-Kirschof integral. The quantitative phase information is easily achievable with DH and can be extracted from a single hologram 3-5 . DH is really competitive with other optical imaging system. The transverse resolution is diffraction limited, as with classical microscope, but axial resolution of half a degree, have already been reached in a reflection geometry with the phase information DH provides. This corresponds to an axial resolution of approximately 1 nanometer at a wavelength of 633 nm. Despite the large number of applications and reconstruction methods, no systematic theory has been developed to quantify the quality of the reconstructed phase images. We propose here a model for image quality estimation based on the decision statistical theory proposed by Wagner and Brown 6 . In order to understand the influence of shot noise on the reconstructed phase images, we propose a study based on simulations. We will establish the influence of the repartition of the total intensity between the reference and the object beams. 2. THEORY 1.1. A. Simulations Simulated holograms have been used to investigate the behavior of the reconstructed phase images SNR. The main object used for simulations is a virtual object representing a neuronal cell, the shape of which was derived from an actual neuron imaged with DHM (Fig. 1a) 7 . This choice has been made in order to have a broad distribution of spatial frequencies representative of common imaged object. It is considered as a phase object, imaged in transmission, for which the measured signal represents the phase shift induced by the specimen, which is proportional to the optical path length, resulting from the product of the refractive index by the thickness of the sample. The characteristics of this virtual object are summarized in Fig. 1b) and 1c). The shape was schematized in order to suppress the noise due to the preparation containing the neuron, but the broad distribution of spatial frequencies was preserved.