#### Highly curved image sensors: a practical approach for improved optical performance

##### Brian Guenter, Neel Joshi, Richard Stoakley, Andrew Keefe, Kevin Geary, Ryan Freeman, Jake Hundley, Pamela Patterson, David Hammon, Guillermo Herrera, Elena Sherman, Andrew Nowak, Randall Schubert, Peter Brewer, Louis Yang, Russell Mott, Geoff McKnight

The significant optical and size benefits of using a curved focal surface for imaging systems have been well studied yet never brought to market for lack of a high-quality, mass-producible, curved image sensor. In this work we demonstrate that commercial silicon CMOS image sensors can be thinned and formed into accurate, highly curved optical surfaces with undiminished functionality. Our key development is a pneumatic forming process that avoids rigid mechanical constraints and suppresses wrinkling instabilities. A combination of forming-mold design, pressure membrane elastic properties, and controlled friction forces enables us to gradually contact the die at the corners and smoothly press the sensor into a spherical shape. Allowing the die to slide into the concave target shape enables a threefold increase in the spherical curvature over prior approaches having mechanical constraints that resist deformation, and create a high-stress, stretch-dominated state. Our process creates a bridge between the high precision and low-cost but planar CMOS process, and ideal non-planar component shapes such as spherical imagers for improved optical systems. We demonstrate these curved sensors in prototype cameras with custom lenses, measuring exceptional resolution of 3220 line-widths per picture height at an aperture of f/1.2 and nearly 100% relative illumination across the field. Though we use a 1/2.3" format image sensor in this report, we also show this process is generally compatible with many state of the art imaging sensor formats. By example, we report photogrammetry test data for an APS-C sized silicon die formed to a 30$^\circ$ subtended spherical angle. These gains in sharpness and relative illumination enable a new generation of ultra-high performance, manufacturable, digital imaging systems for scientific, industrial, and artistic use.

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