No abstract

With the advent of modern-day computational imagers, the phase of the optical transfer function may no longer be summarily ignored. This study discusses some important properties of the phase transfer function (PTF) of digital incoherent imaging systems and their implications on the performance and characterization of these systems. The effects of aliasing and sub-pixel image shifts on the phase of the complex frequency response of these sampled systems are described, including an examination of the specific case of moderate aliasing. Key properties of this function in aliased imaging systems are derived and their potential treatment to a range of diverse applications encompassing traditional and computational imaging systems is discussed.

The bulky form factor of traditional optical sensors limits their utility for certain applications. Flat multiplex imaging-sensor architectures face the light-gathering challenges inherent with small collection apertures. We examine a wavefront-coding approach wherein a cubic phase mask is used to increase the aperture sizes of multiplex imaging systems while maintaining the distance from the lens to the detector array. The proposed approach exploits the ability of cubic-phase-mask systems to operate over a large range of misfocus values. An exact expression for the optical transfer function of cubic-phase-mask systems is presented, and its misfocus-dependent spatial-filtering properties are described. Criteria for form-factor enhancement are assessed and trade-offs encountered in the design process are evaluated.

A mathematical analysis of the frequency response of the wavefront-coding odd-symmetric quadratic phase mask is presented. An exact solution for the optical transfer function of a wavefront-coding imager using this type of mask is derived from first principles, whose result applies over all misfocus values. The misfocus-dependent spatial filtering property of this imager is described. The available spatial frequency bandwidth for a given misfocus condition is quantified. A special imaging condition that yields an increased dynamic range is identified.

The optical transfer function of a cubic phase mask wavefront coding imaging system is experimentally measured across the entire range of defocus values encompassing the system's functional limits. The results are compared against mathematical expressions describing the spatial frequency response of these computational imagers. Experimental data shows that the observed modulation and phase transfer functions, available spatial frequency bandwidth and design range of this imaging system strongly agree with previously published mathematical analyses. An imaging system characterization application is also presented wherein it is shown that the phase transfer function is more robust than the modulation transfer function in estimating the strength of the cubic phase mask.