Effects of sampling on the phase transfer function of incoherent imaging systems

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.

Applications of the phase transfer function of digital incoherent imaging systems

“…(4) Based on an analysis of Eq. (4) for various sampling phases and aliasing conditions, the following key insights are obtained [4]:…”

“…When a digital sensor is included in the imaging chain, the effects of sampling and any possible aliasing must also be included when evaluating the overall PTF of the imager. A synopsis of these effects on the measured PTF is elucidated in [4] and briefly reviewed next.…”

“…In a recent work [4], it was advocated that the former argument made in [2] does not necessarily apply to the new breed of imaging systems that take advantage of computational imaging techniques. These systems routinely defy the traditional philosophy pertaining to PTF characteristics of a well-designed imaging system.…”

“…Meanwhile, their PTFs could exhibit parametric variations and magnitudes much larger than π∕4, and would hence need to be taken into account if optimal imaging performance is to be achieved [9]. Furthermore, scenarios where the PTF exceeds π∕4 even when the MTF is greater than 0.2 are no longer infeasible, as illustrated by an example in [4]. The advent of computational imaging architectures has frequently seen optical subsystems wherein a substantial PTF presence is often the norm and therefore, it becomes important to account for this PTF so that system performance may be optimized.…”

“…Furthermore, in modern-day digital imaging systems, sampling and aliasing are important considerations while evaluating the PTF of these systems. Given this need, the effects of sampling and aliasing on the PTF of digital incoherent imaging systems were studied and reported in [4].…”