Fig. 1. Experiment result of optical memory effect^[41]

Fig. 2. Three different types of spatial correlations in disordered media. (a) The optical “tilt” memory effect; (b) The anisotropic “shift” memory effect; (c) Generalized optical memory effect^[45]

Fig. 3. Experiment results of spectral memory effect. (a) Examples of the speckle patterns at the output of a sample for three totally uncorrelated wavelengths; (b) Normalized spectral correlation functions of different strongly scattering media^[47]

Fig. 4. Experimental results of scattering imaging based on optical memory effect. (a) Speckle; (b) Autocorrelation of speckle; (c) Original object; (d) Reconstructed object^[25]

Fig. 5. Schematic of single-frame imaging based on speckle autocorrelation. (a) Schematic of imaging model； (b) Speckle; (c) Speckle autocorrelation; (d) Reconstructed objects^[26]

Fig. 6. Experimental results of scattering imaging based on shower-curtain effect. (a) Original object; (b) Object is far away from thin scatter; (c) Object is close to thin scatter; (d) Principle of scattering imaging system based on shower-curtain effect; (e) Process of object reconstruction^[30]

Fig. 7. (a) Experimental results of reflective configuration based on Fourier-domain shower-curtain effect; (b) and (c) correspond to the objects "π" and "Z", respectively^[51]

Fig. 8. Imaging results of dynamic scattering media. (a)-(d) Random intensities recorded by the CCD camera for the digit 6 for the angular velocity of the rotating ground glass of 4 r/min, 6 r/min, 8 r/min, 22 r/min, respectively; (e)-(h) Autocorrelation of speckle patterns; (i)-(l) Reconstruction image^[52]

Fig. 9. Principle behind non-invasive imaging of obscured moving objects. (a) Experimental light path; (b) Speckle images are acquired by the camera sensor at different times; (c) Process of object reconstruction^[53]

Fig. 10. Schematic diagram of the optical structure and experiment results^[55]

Fig. 11. Schematic and numerical simulation results of tracking a moving objec in the lateral direction (a) and axis direction (b)^[56]

Fig. 12. Procedure of color image reconstruction^[60]

Fig. 13. Flowchart of the proposed two-step deep learning correlation strategy^[61]

Fig. 14. (a) Object; (b) Reconstruction results of the HIO algorithm (c) Reconstruction results of the CHIO algorithm^[67]

Fig. 15. Reconstruction results of imaging through an opaque ground diffuser. (a) Speckle images; (b) The estimated Fourier amplitude; (c) The estimated Fourier phase; (d) Reconstruction objects (display in intensity); (e) The objects^[39]

Fig. 16. Experimental imaging through a standard scattering medium. (a) Reference speckle pattern (PSF) of a single pixel on projector, the white dash circle denotes the exit pupil; (b) Speckle pattern of unknown object on projector; (c) Retrieved image from (a) and (b) by a deconvolution algorithm; (d) Large view imaging of a resolution target (signed as optics worldwide) to confirm the FOV size. The insert dash rectangle shows the first three letters at the edge of the FOV; (e) Measurement of the FOV by shifting a point target along x axis, the measured FOV is 6.0 mm (75.0 mrad); (f) The defocus-like properties of retrieved images. Scale bars: 200 pixel^[74]

Fig. 17. (a) Experimental setup; (b) Spatial distribution of the objects on the object plane, red circles indicate the spatial positions of point sources for measuring the various spatial PSFs; (c) Superposed reconstruction image, dashed red circle indicates the enlarged FOV^[75]

Fig. 18. (a) Schematic of deconvolution 3D imaging beyond DOF limit through a scattering medium, virtual PSFs from virtual point (green) can be calculated with PSF from a real pinhole (red); (b) Reconstruction of objects with different DOFs^[76]

Fig. 19. Experimental set-up and PSF calibration. (a) Schematic of experimental setup; (b) The calibrated PSFs in the measurement range and the stacked PSF by superimposing these calibrated PSFs^[78]

Fig. 20. Imaging two objects at different positions along the optical axis. (a) Schematic of experimental setup; (b) Images obtained with a conventional imaging system without and with diffuser; (c) The recorded PSFs and the reconstructed images; (d) The reconstructed results in 3D coordinates^[78]

Fig. 21. Schematic of experimental setup of imaging through scattering layers exceeding OME range (a) and experimental results of imaging extended object through scattering layers (b)^[82]

Fig. 22. Flow chart of multi-object antialiasing imaging technology based on independent component analysis^[83]

Fig. 23. Experiment results of multi-targets' imaging beyond 3D OME range through a scattering layer. (a) Raw captured speckles; (b) Extracted independent speckles from (a) using ICA; (c) Equivalent model of the ground truth object; (d) Autocorrelations of (a) and their corresponding retrieved objects directly using the speckle correlation method; (e) Experiment results of imaging through a scattering layer using ICA. Scale bars in (a) and (b) are 1 mm^[83]

Fig. 24. Schematic diagram of imaging system^[84]

Fig. 25. Schematic of the experimental setup and reconstruction principle. (a) Schematic view of experimental setup. A coherent light source illuminates a rotating diffuser in order to excite the fluorescent object through a scattering medium with a random modulated speckle pattern. Once excited, the emitted signal from the fluorescent objects is recorded with a camera. I_fluo is a series of fluorescent speckles corresponding to different random speckle illuminations. The fingerprints can be recovered from I_fluo by using NMF. Fingerprint-based reconstruction; (b) Pairwise deconvolution between all the possible pairs of emitter fingerprints is performed; (c) The result of each deconvolution provides the relative position between one emitter and its neighbors; (d) By adding the resulting images for each emitter, it is possible to recover a partial image of the object centered at that emitter; (e) All the partial images can be merged into the final reconstruction according to the relative position between neighboring emitters. Dashed circle indicates the optical memory range. Scale bar sizes are 10 μm. RD: rotating diffuser, DM: dichroic mirror, OB: objective, Scat. : scattering medium, Fluo. Obj. : fluorescent object, SF: spectral filter, TL: tube lens^[85]

Fig. 26. Structure of the proposed PDSNet^[86]

Fig. 27. (a) Experiment setup uses an DMD as the object; (b) Test PDSNet’s ability to reconstruct targets through several scattering media^[86]

Fig. 28. (a) Schematic of the physics-informed learning method for scalable scattering imaging; (b) Generalization results of imaging exceeding OME range with different complexity objects^[62]