Researchers at Columbia University are working to produce a flexible sheet camera with stretchable lenses. The program aims to create very thin, high resolution cameras that can be wrapped around surfaces like car panels. Currently in concept form, the sheet lens array that such a camera might use has been developed to produce a seamless image on a flexible sensor when it is bent or wrapped around a physical object.

The focus of the research is in creating flexible lenses that are capable of changing shape (and hence the effective focal length) as they are stretched and compressed so that the imaging sensor can record a detailed image whatever the field of view.

With fixed lenses, gaps appear between the coverage of the lenses as the substrate is bent (left), but in the researcher's flexible lens example (right) the lenses bend with the substrate and offer continuous coverage of the subject.

In previous attempts at flexible lens arrays only the substrate has been flexible, and as the sheet of lenses has been bent gaps have appeared in the subject coverage as the angle between the lenses increased beyond their individual field of view. These gaps lead to aliasing artifacts in the final image that can't be corrected in post-processing software. In this new concept the lenses are also flexible and they stretch as the sheet bends, altering their focal length and providing better sampling of the subject.

So far the research has successfully produced a sheet of silicone with lenses molded on one side and a diffuser behind a sheet of apertures on the other. The apertures act as a low pass filter ensuring light from each molded lens reaches only one point on the viewing diffuser.

Images created with the substrate bend by different degrees, showing how the field of view changes

The system hasn’t actually been used with a sensor yet, but the study did use it to project images on to the diffuser screen to determine how effective it would be. Bending the sheet increased and decreased its field of view, or effective focal length, and the images were displayed without missing areas. All that is required now is a flexible sensor to go with it.

An array of lenses was formed by pouring silicone into a metal mold

The intention of the project is to work towards finding a way of making sheets of lenses to work with photosensitive materials that will record images when wrapped around real-world objects. The researchers want ultimately be able to produce these sheet cameras in roll format at a low cost so that the sheets can be cut to size to suit specific uses.

The released information suggests a sheet camera could be wrapped around the panels of a car to give the driver a view from all angles. Alternatively sheet cameras could be used by consumers to take normal pictures but with the user bending the sheet to alter the field of view, or zoom effect, of the system.

For more information see the project’s page on the University of Columbia website.

Press release:

Flexible Sheet Cameras With Elastic Optics

In this project, we pursue a radically different approach to imaging. Rather than seeking to capture the world from a single point in space, our goal is to explore the idea of imaging using a thin, large, flexible sheet. If such cameras can be made at a low cost (ideally, like a roll of plastic sheet), they can be used to image the world in ways that would be difficult to achieve using one or more conventional cameras. In the most general sense, such an imaging system would enable any surface in the real world to capture visual information. While there is significant ongoing work on the development of flexible image sensors, our interest here is in the design of the optics needed to form images on such sensors.

At first glance one might imagine that a simple lens array aligned with a flexible detector array would suffice - its field of view (FOV) can be varied by simply bending it. What is perhaps less apparent is the fact that, in a curved state, the FOV can end up being severely under-sampled. This under-sampling leads to a captured image that is not bandlimited. Thus, the Nyquist sampling criterion is violated and the image will suffer from aliasing artifacts when reconstructed. It is important to note that these artifacts cannot be removed via post-processing since scene information is lost during image formation.

To address the above aliasing problem over an entire range of sheet curvatures, we propose the design of a deformable (elastic) lens array. We show that, if designed carefully, the deformable lenses of the array will change shape (and hence focal length) under bending forces in a way that mitigates aliasing. A remarkable feature of our design is that the lens array can achieve aliasing compensation passively, without the use of any per-pixel actuation or control. Our optics can be combined with a flexible sensor array to obtain a complete sheet camera. This project was supported by the Office of Naval Research (ONR).