Scaling law for computational imaging using spherical optics

Abstract

The resolution of a camera system determines the fidelity of visual features in captured images. Higher resolution implies greater fidelity, and thus greater accuracy when performing automated vision tasks such as object detection, recognition, and tracking. However, the resolution of any camera is fundamentally limited by geometric aberrations. In the past, it has generally been accepted that the resolution of lenses with geometric aberrations cannot be increased beyond a certain threshold. We derive an analytic scaling law showing that, for lenses with spherical aberrations, resolution can be increased beyond the aberration limit by applying a post-capture deblurring step. We then show that resolution can be further increased when image priors are introduced.Based on our analysis, we advocate for computational camera designs consisting of a spherical lens shared by several small planar sensors. We show example images captured with a proof-of-concept gigapixel camera, demonstrating that high resolution can be achieved with a compact form factor and low complexity. We conclude with an analysis on the trade-off between performance and complexity for computational imaging systems with spherical lenses.

Toward Wide-Angle Microvision Sensors

“…We may consider using other optical elements, such as adaptive templates [41], artificial insect eyes [28], [27], and multiplexed configurations [55], as and when they become widely available in small, low-power form factors. In particular, curved sensors [31], [33], [17] are increasingly becoming a reality. In Fig.…”

Image Processing and Cell Phone Microscopy to Analyze the Immunomagnetic Beads on Micro-Contact Printed Gratings

“…It was shown that the sapphire ball lens has a better imaging quality and higher refractive index [22], which could improve the lateral resolution and decrease the noise. Also by using spherical sensor arrays with a spherical ball lens, uniform spatial resolution [23] and gigapixel resolution can be reached [24].…”

Characterization of spatially varying aberrations for wide field-of-view microscopy

“…Knowledge of these different imaging platforms' aberrations allows users to predict the achievable resolution, and permits system designers to correct aberrations either actively through adaptive optics or passively with post-detection image deconvolution. Digital aberration removal techniques play an especially prominent role in computational imaging platforms aimed at achieving simple and compact optical arrangements [2]. A recent important class of such platforms is geared towards efficiently creating gigapixel images with high resolution over a wide fieldof-view (FOV) [2,3].…”

“…Digital aberration removal techniques play an especially prominent role in computational imaging platforms aimed at achieving simple and compact optical arrangements [2]. A recent important class of such platforms is geared towards efficiently creating gigapixel images with high resolution over a wide fieldof-view (FOV) [2,3]. Given the well-known linear scaling relationship between the influence of aberrations and imaging FOV [4], it is critical to characterize their effect before camera throughput can be successfully extended to the gigapixel scale.…”

“…The variability of off-axis aberrations must be considered in microscopy systems or advanced computational imaging platforms that are designed to provide a very wide FOV, as their aberrated PSFs will vary significantly in shape across the image plane. These systems geared, for example, towards gigapixel photography [2,3] and whole slide imaging [32], typically exhibit aberrations that increase as a function of distance from the image center. While prior work reports measurement of such spatially varying aberrations in lithography systems [33,34], they unfortunately require custom designed reticle masks and interferometry setups.…”