Bundles of the fibres could be fed through pipes and immersed in fluids, to image oil fields, aquifers, or plumbing, without risking damage to watertight housings.
Tight bundles of the fibres could yield endoscopes with narrower diameters, since they would require no additional electronics.
The fibres are connected to an array of photosensors at one end; the other ends can be left to wave free, so they could pass individually through micrometre-scale gaps in a porous membrane, to image whatever is on the other side.
The positions of the fibres' free ends do not need to correspond to the positions of the photodetectors in the array.
By measuring the differing times at which short bursts of light reach the photodetectors - a technique known as "time of flight" - the device can determine the fibres' relative locations.
In a commercial version of the device, the calibrating bursts of light would be delivered by the fibres themselves, but in experiments with their prototype system, the researchers used external lasers.
"Time of flight, which is a technique that is broadly used in our group, has never been used to do such things," said first author Barmak Heshmat, from Massachusetts Institute of Technology (MIT), who led the new work.
"Previous works have used time of flight to extract depth information. But in this work, I was proposing to use time of flight to enable a new interface for imaging," Heshmat said.
The researchers, including Ramesh Raskar, used a bundle of 1,100 fibres that were waving free at one end and positioned opposite a screen on which symbols were projected.
The other end of the bundle was attached to a beam splitter, which was in turn connected to both an ordinary camera and a high-speed camera that can distinguish optical pulses' times of arrival.
Perpendicular to the tips of the fibres at the bundle's loose end, and to each other, were two ultrafast lasers. The lasers fired short bursts of light, and the high-speed camera recorded their time of arrival along each fibber.
Since the bursts of light came from two different directions, software could use the differences in arrival time to produce a 2D map of the positions of the fibres' tips.
It then used that information to unscramble the jumbled image captured by the conventional camera.
The study was published in the journal Nature Scientific Reports.
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