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Computational periscopy with an ordinary digital camera


Computing the amounts of light arriving from different directions enables a diffusely reflecting surface to play the part of a mirror in a periscope—that is, perform non-line-of-sight imaging around an obstruction. Because computational periscopy has so far depended on light-travel distances being proportional to the times of flight, it has mostly been performed with expensive, specialized ultrafast optical systems1,2,3,4,5,6,7,8,9,10,11,12. Here we introduce a two-dimensional computational periscopy technique that requires only a single photograph captured with an ordinary digital camera. Our technique recovers the position of an opaque object and the scene behind (but not completely obscured by) the object, when both the object and scene are outside the line of sight of the camera, without requiring controlled or time-varying illumination. Such recovery is based on the visible penumbra of the opaque object having a linear dependence on the hidden scene that can be modelled through ray optics. Non-line-of-sight imaging using inexpensive, ubiquitous equipment may have considerable value in monitoring hazardous environments, navigation and detecting hidden adversaries.

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Fig. 1: Experimental setup for computational periscopy.
Fig. 2: Reconstruction procedure.
Fig. 3: Computational field of view.
Fig. 4: Reconstructions of different hidden scenes.

Data availability

Raw data captured with our digital camera during the experiments presented here are available on GitHub at


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We thank F. Durand, W. T. Freeman, Y. Ma, J. Rapp, J. H. Shapiro, A. Torralba, F. N. C. Wong and G. W. Wornell for discussions. This work was supported by the Defense Advanced Research Projects Agency (DARPA) REVEAL Program contract number HR0011-16-C-0030.

Reviewer information

Nature thanks M. Laurenzis, M. O’Toole and A. Velten for their contribution to the peer review of this work.

Author information




V.K.G. conceptualized the project, obtained funding and supervised the research. C.S. and J.M.-B. developed the methodology, performed the experiments, wrote the software and validated the results. C.S. produced the visualizations. J.M.-B. wrote the original draft. C.S., J.M.-B. and V.K.G. reviewed and edited the paper.

Corresponding author

Correspondence to Vivek K Goyal.

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The authors declare no competing interests.

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Supplementary information

Supplementary Information

This file contains supplementary methods, supplementary text, supplementary references (36–45), figures S1-S19, tables S1 and S2 and a caption for the supplementary video.

Video 1

Supplementary Video describes the experimental setup, the computational field of view of the system, and each of the steps involved in the computational estimation of the non-line-of-sight occluder position and scene. Also shown is a moving scene measured at 1 frame per second and reconstructed frame-by-frame, without exploiting assumptions of temporal continuity of the scene.

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Saunders, C., Murray-Bruce, J. & Goyal, V.K. Computational periscopy with an ordinary digital camera. Nature 565, 472–475 (2019).

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