Lensless coded-aperture imaging with separable Doubly-Toeplitz masks

Abstract

Abstract. In certain imaging applications, conventional lens technology is constrained by the lack of materials which can effectively focus the radiation within a reasonable weight and volume. One solution is to use coded apertures-opaque plates perforated with multiple pinhole-like openings. If the openings are arranged in an appropriate pattern, then the images can be decoded and a clear image computed. Recently, computational imaging and the search for a means of producing programmable software-defined optics have revived interest in coded apertures. The former state-of-the-art masks, modified uniformly redundant arrays (MURAs), are effective for compact objects against uniform backgrounds, but have substantial drawbacks for extended scenes: (1) MURAs present an inherently ill-posed inversion problem that is unmanageable for large images, and (2) they are susceptible to diffraction: a diffracted MURA is no longer a MURA. We present a new class of coded apertures, separable Doubly-Toeplitz masks, which are efficiently decodable even for very large images-orders of magnitude faster than MURAs, and which remain decodable when diffracted. We implemented the masks using programmable spatial-light-modulators. Imaging experiments confirmed the effectiveness of separable Doubly-Toeplitz masks-images collected in natural light of extended outdoor scenes are rendered clearly. © The Authors. Published by SPIE under a Creative Commons Attribution 3.0 Unported License. Distribution or reproduction of this work in whole or in part requires full attribution of the original publication, including its DOI.

FlatCam: Replacing Lenses with Masks and Computation

“…For a megapixel scene and a megapixel sensor, Φ L and Φ R have only 10 6 elements each, as opposed to 10 12 elements in Φ. Similar idea has been recently proposed in [8] with the design of doubly toeplitz mask. In our implementation, we also estimate the system matrices using a separate calibration procedure, which also becomes significantly simpler for a separable system.…”

“…Existing coded aperture-based lensless systems have two main limitations: First, a majority of coded aperture systems place the mask significantly far away from the sensor (e.g., 65mm distance in [8]). In contrast, our FlatCam design offers a thin form factor.…”

“…In recent years, coded aperture-based systems using compressive sensing principles [5,10,2] have been studied for image super-resolution [17], spectral imaging [20], and video capture [16]. Maskbased lens-free designs have also been proposed for flexible field-of-view selection in [21], compressive single-pixel imaging using a transmissive LCD panel [15], and for separable coded masks [8].…”

“…As a consequence, the light throughput of our designs are many orders of magnitude larger as compared to previous designs. Furthermore, the lensless cameras proposed in [15,8] use programmable spatial light modulators (SLM) and capture multiple images while changing the mask patterns. In contrast, we use a static mask in our design, which can potentially be fixed on the sensor during fabrication or the assembly process.…”

Lensless image scanner using multilayered aperture array for noncontact imaging

“…Recently, application of coded aperture to photos in visible light has been reported. 4 Variable coded aperture using a liquid crystal device has also been reported. 5 A lensless miniature CMOS imager has been proposed, which uses a unique angle-sensitive pixel sensor and a spiral pattern grating.…”