Fig. 1. Design of STEP and principle of image reconstruction. (a) Sequence of patterns consisting of a bundle of sinusoidal time series with unique frequencies at each spatial location. (b) Grayscale pattern sequence used to image an object through scattering media. (c) The object is first illuminated by STEP. The intensity of the transmitted light I(t) is measured by a single-pixel photodetector, and then transformed to a spectral domain by FFT. For each target frequency fij, we find the nearest frequency f^ij in the spectrum using a binary search algorithm and save its amplitude. An image of the object can be reconstructed by filling an H×W matrix with the amplitudes.

Fig. 2. Experimental demonstration of STEP with ground glass diffusers. (a) Schematic of the setup. DMD, digital micromirror device; L1 and L2, lenses; I, iris; D1 and D2, diffusers; O, object; PD, photodetector. (b) Images captured by a CMOS camera under three conditions: without scattering media (ND), with stationary diffusers (SD), and with dynamic diffusers (DD). (c) Images reconstructed by STEP with β=8 (top) and β=64 (bottom). Bilinear interpolation is applied to remove the pixelation effect.

Fig. 3. Imaging through two slices of chicken breast (∼1.2  mm each slice) with STEP. (a) One of the chicken breast slices used in the experiment, which is sealed in plastic wraps. (b) Camera image of the object hidden between two chicken breast slices. (c) Image reconstructed by STEP with β=96 (top). Bilinear interpolation is applied to remove the pixelation effect (bottom).

Fig. 4. Comparison of different image reconstruction algorithms. (a) Fourier transform (FT): a segment of M data points in the time domain is transformed by FFT to frequency domain (spectrum). (b) Cross-spectrum (CS): a segment of M data points is divided into halves, and their CS is calculated. (c) Correlation: the correlation between a segment of M data points and the time series in the original pattern sequence is calculated. (d) Visibility of the reconstructed images using the three algorithms with different values of β for SD and DD. (e) Comparison of time complexity of the image reconstruction algorithms. Computing time is measured with varying sizes of images in total pixels.