Computational methods for aberration correction in simple lens imaging

The complexity of camera optics has greatly increased in recent decades. The lenses of modern single-lens reflex (SLR) cameras may contain a dozen or more individual lens elements, which are used to optimize the light efficiency of optical systems while minimizing the imperfections inherent in them. Geometric distortions, chromatic aberrations, and spherical aberrations are prevalent in simple lens systems and cause blurring and loss of detail. Unfortunately, complex optical designs come at a significant cost and weight. Instead of developing ever more complex optics, we propose1 an alternative approach using much simpler optics of the type used for hundreds of years,2 while correcting for the ensuing aberrations computationally. Although using computational methods for aberration correction has a long history,3–7 these methods are most effective in the removal of residual aberrations found in already well-corrected optical systems. A combination of large-aperture simple lens optics with modern high-resolution image sensors can result in very large wavelength-dependent blur kernels (i.e., point spread functions or PSFs: the response of an imaging system to a point source), with disk-shaped supports of 50–100 pixels diameter (see Figure 1). Such large PSFs destroy high-frequency image information, which cannot be recovered using existing methods. The fundamental insight of our work is that the chromatic part of the lens aberration (which occurs when colors are not focused to the same convergence point) can be used to our advantage, since the wavelength dependence of the blur means that different spatial frequencies are preserved in different color channels. Moreover, combining information from different color channels and enforcing consistency of edges (and similar image features) Figure 1. Calibrated point spread functions (PSFs) for two simple lenses, for different regions on the image sensor. (a) PSF of a 100mm biconvex lens at f/2.0. (b) PSF of a 130mm plano-convex lens at f/4.5.