Fig. 1. Scattering imaging based on wave-front shaping^[15]. (a) Images of incoherent light source behind diffuser after optimizing the SLM phase pattern (scattering medium was 10×20° Newport light shaping diffuser); (b) image obtained by conventional imaging through diffuser with a color camera (inset: image of object before diffuser); (c) result of the same object through the diffuser using the optimized SLM phase pattern (scale bar: 3 mm)

Fig. 2. Scattering imaging based on PSF deconvolution^[30]. (a) Optical setup (a mask used as the target is placed behind a 120 grit Thorlabs ground glass diffuser, and the plane of the object is imaged onto a CMOS camera); (b) image of the object without scattering medium; (c) scrambled image recorded by camera through scattering medium; (d) PSF of overall setup recorded by replacing the object with an iris; (e) reconstructed object after deconvolution (scale bar: 200 μm)

Fig. 3. DiffuserCam setup and reconstruction principle^[35]. Lensless system consists of a sensor and a diffuser (a 0.5° off-the-shelf Luminit diffuser) placed in front of the sensor. The system encodes a 3D scene into a 2D image on the sensor. A one-time calibration consists of scanning a point source axially while capturing images through scattering media. Images are reconstructed computationally by solving a nonlinear inverse problem with a sparsity prior. The result is a 3D scene reconstructed from a single 2D image

Fig. 4. Imaging setup of scanning speckle correlation technique^[5]

Fig. 5. Single-shot speckle correlation technique^[41]. (a) Setup used for scattering imaging; (b) raw camera image of scattered light with 300-μm-thick chicken breast tissue as the scattering media; (c) corresponding autocorrelation of scattered image; (d) object reconstructed from autocorrelation of Fig. 5(c) by phase-retrieval algorithm; (e) object imaged directly without scattering medium (scale bar: 200 μm)

Fig. 6. Expanding the memory effect through ground glass via multiple PSF calibration^[51]. (a) Experimental setup; (b) spatial distribution of object plane; (c) superposed reconstruction image (scale bar: 1 mm)

Fig. 7. Dual-target large FOV prior-free scattering imaging^[56]. (a) Experimental setup; (b)(e) speckles and corresponding speckle autocorrelations through scattering media (220 grit frosted glass, Thorlabs); (c)(f) real dual-target masks “2F” and “FL”; (d)(g) final reconstructed objects from autocorrelation separation (scale bar: 96 μm)

Fig. 8. Multi-target large FOV prior-free scattering imaging^[57]. (a) Experimental setup; (b) multi-target mask as imaging target; (c) captured multi-target speckle (220 grit Thorlabs ground glass is used as scattering medium); (d) target locations obtained by using scaling vectors; (e) large FOV reconstruction result (scale bar: 240 mm)

Fig. 9. Approximate forward scattering coefficient q under different weather conditions^[61]

Fig. 10. Measuring device and F_APSF. (a) Apparatus for measuring internal scattering of milk to verify F_APSF[small bulb is placed in the center of a spherical container made of plastic. During the experiment, the container is filled with milk of different concentrations (corresponding to different optical thicknesses), and the camera takes pictures to verify the theoretical and practical accuracy of F_APSF under different conditions^[62]; (b) Legendre F_APSF normalized to 0--1 under different weather conditions^[61]; (c) form of generalized Gaussian distribution FAPSF[63]

Fig. 11. Use F_APSF for dehazing. (a) Electronic billboard with scattering; (b) electronic billboard after scattering removal using F_APSF estimated by Legendre polynomials [one of the bright spots is extracted from Fig. 11(a), and its F_APSF is fitted, which is deconvolved with Fig. 11(a) to obtain Fig. 11(b)^[61]]; (c) foggy image; (d) dehazed image obtained by using generalized Gaussian distribution FAPSF[63]

Fig. 12. Scattering imaging based on diffusion equation^[65]. (a) Diagram of acquisition device; (b) original target; (c) captured image; (d) reconstruction result

Fig. 13. Optical paths for measuring transmission matrix in spatial and frequency domains. (a) Optical path for measuring spatial transmission matrix (SLM is divided into reference field and signal field)^[67]; (b) optical path for measuring transmission matrix in frequency domain^[71]

Fig. 14. Reconstruction results obtained by using spatial and frequency domain transmission matrices. (a) Initial grayscale image; (b) reconstructed image using scattered input^[68]; (c) image of tiger pattern before inserting scattering medium (scale bar: 10 μm); (d) reconstructed image of tiger using scattered input^[71]

Fig. 15. Haze removal results obtained based on dark channel prior^[82]. (a) Input haze image; (b) estimated transmission map; (c) refined transmission map after soft matting; (d) final reconstructed image

Fig. 16. Haze-line demonstration (take the artificial haze image as the example) ^[112]. (a) Pixels of haze free color image are clustered using K-means according to color (pixels belonging to four colors are marked); (b) four color clusters in haze free image depicted in RGB space; (c) image after adding artificial fog into scene; (d) hazy pixels of the same color in hazy image depicted in RGB color space are distributed along lines (haze-lines pass through corresponding points of atmospheric light, marked in black)

Fig. 17. Comparison of several de-scattering results based on single frame image (fog as the scattering medium). (a) Input hazed image; (b) experimental result obtained by Tarel et al.^[88]; (c) experimental result obtained by Fattal et al.^[93]; (d) experimental result obtained by He et al.^[82]; (e) experimental result obtained by Galdran et al.^[116]; (f) experimental result obtained by Berman et al.^[112]

Fig. 18. Comparison of several de-scattering results obtained based on single frame image (turbid water is used as the scattering medium). (a) Input scattered images (the 1^st row images are significantly more blurred than the 2^nd row images); (b)--(d) experimental results of running UDCP^[102], Robust Retinex^[117], and Multi-scale Fusion^[105],after debugging

Fig. 19. Scattering imaging based on photon counting via light field data^[166]

Fig. 20. Comparison of de-scattering removal results based on light field data (turbid water is used as the scattering medium). (a) Experimental setup of Tian et al.^[160]; (b)(c) input scattered image and corresponding de-scattering result of Dansereau et al.^[171]; (d)(e) experimental results of Cho et al.^[166]; (f)(g) experimental results of Tian et al.^[160]; (h)(i) experimental results of Cho et al.^[164]

Fig. 21. Difference of arrival time between scattered photons and ballistic photons^[173] (time-of-flight curve of point source passing through scattering medium with 200 μm diameter

Fig. 22. Schematic of optical coherence tomography technique^[174-175]

Fig. 23. Classification of reflected waves passing through scattering medium. E^S(τ): electric field of a wave scattered once by a target where τ is the time of flight from the surface. E^M(τ): multiple-scattered waves with the same time of flight as the single-scattered waves, coherent with the reference beam. E^M(τ'≠τ): multiple-scattered waves with a time of flight that is different from τ, incoherent with the reference beam^[176]

Fig. 24. CLASS algorithm was applied to in vivo imaging through intact mouse skull with thickness of 125--150 μm^[182]. (a) Experimental setup; (b) intensity image of myelinated fibers at a 200-μm depth from the upper surface of the skull obtained by optical coherence microscopy; (c) CLASS intensity image (upper) and the corresponding aberration map (lower) for a 30 μm×30 μm area marked by the dotted box in Fig. 24(b); (d)(e) CLASS intensity images with their representative aberration maps for one of the 2×2 and 4 ×4 subregions, respectively

Fig. 25. Setups for distinguishing arrival time of photons. (a) Setup based on Kerr gate^[173]; (b) setup based on SPAD^[185]; (c) setup based on terahertz camera^[188]

Fig. 26. Imaging results obtained by distinguishing arrival time of photons. (a)--(c) Reference image, gating reconstruction results without delay, and reconstruction results with delay when Wang et al.^[173] reconstructed fringe image under thin biological tissue; (d)--(f) reconstructed results at depths in foggy days obtained by Laurenzis et al.^[184]; (g) reference images and (h)reconstruction results used by Redo-Sanchez et al.^[185] for text on overlapping paper; (i)--(k) reference image, reconstruction result, and reconstructed depth map used by Satat et al.^[188] in dynamic scattering scenes

Fig. 27. Imaging principle for modeling ballistic photon flight paths^[194]. (a) Transient imaging system; (b) transient image; (c) 3D reconstruction result

Fig. 28. Phase of received signal is delayed compared to reference signal due to different time-of-flight paths under modulated light source irradiation^[203]

Fig. 29. Scattering imaging and depth reconstruction based on amplitude modulated light. (a)(b) Experimental scene (scattering medium is turbid water) and reconstruction result for experiment conducted by Heide et al.^[201]; (c)(d) experimental scene and deep reconstruction result in outdoor foggy days for experiment conducted by Muraji et al.^[203]

Fig. 30. Scattering imaging based on quadrature lock-in discrimination^[204]. (a) Schematic diagram of acquisition device (the scattering medium equals the fog, the object moves on the conveyor belt, and the acquisition frame rate is 100 frame/s); (b) captured image ; (c) reconstruction 1; (d) reconstruction 2

Fig. 31. Comparison of various scattering imaging techniques