Abstract

We use information-theory to analyze two simple incoherent imaging systems [1,2]: (1) a conventional single-lens imager and (2) an extended depth-of-field imager employing a cubic phase mask in the aperture stop of the first system [3]. Consider a scene comprising relatively few monochromatic point sources (1 to 5) located in a source volume whose axial and lateral extents are both L as shown in Fig. 1(a). The conventional imager comprises a single lens with aperture D and focal length f. The ideal object plane is located at distance S_o and the ideal image plane is located at a distance S_i. System parameters used in this paper are: L=1cm, f=10cm, S_o=40cm. A two-dimensional analysis of this volumetric imaging system is used for computational simplicity. The optical power collected by a detector (I_rn) serves as measurement of the scene and is assumed to be corrupted by additive white Gaussian noise. Imagers with two detectors are also considered here. Due to the constraints placed on the source space, any scene can be completely described by the axial and lateral position of each point source in the volume. Therefore, if the information content of the measured image data I_rn and scene S are quantified in terms of their respective Shannon entropies h(I_rn) and h(S), the mutual information (MI) I(I_rn;S) between the scene and the image data can be used as a objective measure of the imaging system performance. For the purpose of computing MI the scene volume is quantized into a 128 × 128 square grid of allowed point source positions. Thus the total scene information is given by h(s)=log₂ (¹⁶³⁸⁴ CM), where M is the number of point sources in the scene (e.g. M=1, h(s)=14bits).

© 2003 Optical Society of America