Leveraging digital processing to minimize optical system costs

The majority of imaging systems rely on spherical lens surfaces because they are easy to manufacture and test. During the last century, optical system design involved optimizing the shape and materials of spherical lenses. The goal of this approach was to minimize inherent optical aberrations to achieve the highest-contrast image. Recently, joint analysis of both the optical subsystem and the algorithmic capabilities of digital processing have enabled new classes of digital-optical imaging systems.1 This joint design approach can reduce system cost, improve manufacturing yield, and even transcend historic performance limitations. The key challenge in this framework is to efficiently balance optical and imageprocessing parameters. We introduce a concept called spherical coding, in which the optical designer deliberately allows or even enhances the spherical aberration. Then, digital post-processing sharpens the blurry captured images, achieving high contrast. Such a framework provides several advantages. In particular, it improves light collection—providing higher signal-to-noise ratios (SNRs)—and boosts manufacturing yield. In addition, spherical coding offers simplicity: the relationship between optical parameters and spherical aberration is well understood, and the system is supported by modern lens design software. Our approach works by exploiting the unique properties of spherical aberration and its effect on the modulation transfer function (MTF). Optical aberrations in general reduce image contrast by creating blurry optical images. The system MTF characterizes the optical blur by quantifying the contrast preserved by the imaging system as a function of spatial frequency. Spherical aberration reduces contrast in a distinctive rotationally symmetric, field-independent fashion that requires only simple, space-invariant digital sharpening filters for compensation. The optical MTF, as traditionally defined, preserves contrast (dashed Figure 1. (left) The curves on the graph compare the transfer functions for a spherically aberrated optical system (dashed), a compensating digital filter (dotted), and the combined digital-optical transfer function (solid). A captured image (center) degraded by spherical aberration can be restored (right) after applying the filter.