Fig. 1. (a) Beam passes through an ideal random phase mask with negligible thickness and speckles generated by two light beams with different incident angles. The two speckle patterns show high similarity, and the speckle grains in the circles indicate the same local features. (b) Conceptual demonstration of the optical memory effect. Placing a phase object causes a local tilt of the incident light wavefront, which results in a partial translation of the speckle.

Fig. 2. Experimental setup for speckle pattern acquisition. Phase objects are loaded by the spatial light modulator. The thin diffuser is placed at the back focal plane of the 4−f system. (a) Designated speckle acquisition window (white dotted line box). (b) Autocorrelation of speckle patterns at different diffraction distances d2 and the correlation width is ∼20  μm. (c) Cross-correlation coefficients between speckle patterns corresponding to different incoming wavefronts at distances d2 varying from 5 to 80 mm. POL, linear polarizer; SLM, spatial light modulator; BS, beam splitter; CAM, camera.

Fig. 3. Schematic diagram of the proposed method for phase imaging and the basic architecture of CNN. The input to the network is a single-shot low-bit pattern or raw intensity measurement.

Fig. 4. Experimental results of phase recovery on (a) random grayscale image datasets (i–iii) and (b) human face datasets (iv–vi) with different diffraction distances d2. The images in leftmost column of each graph block are the speckle patterns, and the phase maps in the blue and the orange solid line boxes are estimates implemented by SDVF and DNN, respectively.

Fig. 5. (a) Raw measurement and processed patterns with different bit depth; (b) SSIM of the reconstructions at each image bit depth.

Fig. 6. Experimental demonstration of phase imaging with low-bit speckle pattern. Results of reconstructing random smooth phase maps (left) and human face images (right) via DNN with patterns of different bit depths. The images in the middle column of each graph group are enlarged views of the areas selected by the yellow dotted box in the low-bit speckle patterns in the first column. The speckle patterns acquired at a distance of d2=60  mm show lower local similarity and correspondingly lower reconstruction accuracy than the case of d2=5  mm.

Fig. 7. Generalizability testing of the trained DNN in full-bit (10 bit measurement) and low-bit (1 bit binary pattern) imaging and comparison of the results of phase recovery under the three schemes: (i) imaging using diffraction patterns (without diffuser) via DNN; (ii) imaging using speckle patterns (with diffuser) via DNN; (iii) imaging using speckle patterns (with diffuser) via SDVF. All the data acquisitions adopt the same experimental configuration except for the diffuser settings. The distance between the diffuser and the camera sensor is fixed to 5 mm in both scheme (ii) and scheme (iii).

Fig. 8. (a) Gray statistics of captured speckle images. Inset: graph of imaging accuracy and pattern sparseness at various binarization thresholds. (b) Result of reconstructing objects from binary patterns with different sparseness.