Exploiting scattering media for exploring 3D objects

OPEN Light: Science & Applications (2017) 6, e16219; doi:10.1038/lsa.2016.219 Official journal of the CIOMP 2047-7538/17 www.nature.com/lsa ORIGINAL ARTICLE Exploiting scattering media for exploring 3D objects Alok Kumar Singh1, Dinesh N Naik1,2, Giancarlo Pedrini1, Mitsuo Takeda1,3 and Wolfgang Osten1 Scattering media, such as diffused glass and biological tissue, are usually treated as obstacles in imaging. To cope with the random phase introduced by a turbid medium, most existing imaging techniques recourse to either phase compensation by optical means or phase recovery using iterative algorithms, and their applications are often limited to two-dimensional imaging. In contrast, we utilize the scattering medium as an unconventional imaging lens and exploit its lens-like properties for lensless threedimensional (3D) imaging with diffraction-limited resolution. Our spatially incoherent lensless imaging technique is simple and capable of variable focusing with adjustable depths of focus that enables depth sensing of 3D objects that are concealed by the diffusing medium. Wide-field imaging with diffraction-limited resolution is verified experimentally by a single-shot recording of the 1951 USAF resolution test chart, and 3D imaging and depth sensing are demonstrated by shifting focus over axially separated objects. Light: Science & Applications (2017) 6, e16219; doi:10.1038/lsa.2016.219; published online 24 February 2017 Keywords: intensity correlation technique; lensless imaging; scattering media; 3D imaging INTRODUCTION Since the early work in the 1960s by Goodman et al.1, Leith and Upatnieks2 and Kogelnik and Pennington3, many methods have been proposed for imaging through diffusing media. These methods have a potentially wide range of applications from biomedical to astronomical imaging. Thus, imaging through an opaque diffusing medium with diffraction-limited resolution has become an important technical challenge because of these widely recognized needs. One straightforward strategy is imaging with ballistic photons selected either by coherence gating as in optical coherence tomography4, time gating as in femto-photography5, or holographic gating6–8. Because only a limited number of ballistic photons are used (with scattered photons being wasted) and also because the sequential scanning of the gate window is required, these methods are used mostly for imaging static objects through a weakly scattering medium. An alternative solution is to ‘descramble’ the phase of the scattered light2,3,9,10 by means of phase compensation with a spatial light modulator11–21 or a hologram22. The spatial light modulator-based phase compensation11–14 involves an iterative search for the unknown phase for compensation, and the holographic phase conjugation requires strict positional alignment of the hologram and the read-out beam2,3,10. Another way to make use of the diffused light is to implement unconventional imaging techniques that are insensitive to phase perturbation. Among these are photon correlation holography23, remote imaging digital holography24,25, coherence holography26,27 and Doppler-shift digital holography28,29 that can image through a dynamic diffusing media, but they are not lensless systems30. Freund proposed a lensless imaging technique based on speckle intensity correlation, in which he regarded a diffuser as a useful imaging device and made use of its memory effect31,32. This idea was further developed by other researchers. Bertolotti et al.33 reported an angular correlation technique that can exclude prior calibration with a reference source (which was necessary in Freund’s scheme) although the sequential scanning of the illumination angle may prevent imaging dynamic objects. Katz et al. proposed another reference-free method34 and showed that the intensity autocorrelation of the scattered light is identical to the autocorrelation of the object image itself and that the object can be reconstructed using a phase retrieval algorithm35. The intensity correlation techniques were demonstrated only for two-dimensional (2D) images because of their intrinsic property of infinite depth of focus31. Recently, Takasaki et al.36 and Liu et al.37 presented phase–space analysis methods for three-dimensional (3D) imaging behind the diffuser. However, these techniques require a sequential data acquisition to create a Wigner function and are limited to objects made of a sparse set of point sources. As described above, a majority of techniques regard a turbid medium as a nuisance in imaging and aim at coping with the random phase introduced by the turbid medium. An exception is the idea behind the speckle intensity correlation technique proposed by Freund for 2D imaging31,32. In his seminal papers, Freund proposed a lensless imaging technique in which he regarded a diffuser as a useful imaging device and named it wall lens31,32. Extending this idea, we make use of the turbid medium as a virtual imaging lens. We exploit the potential of the virtual imaging lens for 3D imaging; so that, it can form an image of 3D objects with variable focusing and controllable depth of focus. To avoid the computational burden of a 3D phase retrieval 1 Institut für Technische Optik (ITO) and Stuttgart Research Center of Photonic Engineering (SCoPE), University of Stuttgart, Pfaffenwaldring 9, 70569 Stuttgart, Germany; 2School of Physics, University of Hyderabad, Hyderabad 500 046, India and 3Center for Optical Research and Education (CORE), Utsunomiya University, Yoto 7-1-2, Utsunomiya, Tochigi, 321- 8585, Japan Correspondence: AK Singh, Email: Received 2 May 2016; revised 22 August 2016; accepted 4 September 2016; accepted article preview online 7 September 2016 Exploiting scattering media for 3D imaging AK Singh et al 2 algorithm and the restricted field of view incidental to image recovery from the autocorrelation, we modify the intensity correlation technique and introduce a reference point source near the object. The reference point source, which is incoherent with the object illumination, has the role of a guide star in a manner similar to Goodman’s interferometric imaging38. The use of a reference source may set a certain restriction in some applications but provides a much simpler practical solution than that based on the autocorrelation combined with an iterative phase retrieval algorithm. Our solution is free from iterative phase retrieval, gives a wider field of view, and permits direct 3D image reconstruction from the cross-correlation between the intensity distributions on a pair of planes axially separated in the scattered fields. By virtue of the variable plane of focus (which is selectable by the distance between the cross-correlation planes) and the finite depth of focus (which is controllable by the size of the aperture defined by the illuminated area on the diffuser), this technique can perform direct depth sensing of 3D objects hidden behind the diffusing medium without recourse (...truncated)