Advanced Imaging, Volume. 2, Issue 6, 061003(2025)

Single-shot scattering-assisted computational optical synthetic aperture imaging

Wei Li, Zichao Liu, Yi Sun, Yijun Zhou, and Feihu Xu*
Figures & Tables(8)
Imaging setup and flowchart of the scattering-assisted OSA imaging. (a) The experimental schematic. A divergent laser beam propagates a distance z1 to the object plane, interacts with the object, and travels a distance z2 to the diffuser screen. The resulting scattered field is then captured by a camera. (b) Experimental corridor (40 m) with the diffraction area (orange dashed box). (c) Unified computational phase retrieval algorithm using FrFTs (Fp, F−p) spanning the Fraunhofer to Fresnel regimes. (d) Comparison of detection methods. Direct detection: In a conventional setup, the object’s Fourier spectrum is captured at a focal plane (typically 1 m in front of the lens), with its range being limited by the lens aperture. Scattering-assisted detection: In contrast, by positioning a scattering medium as a virtual lens at this focal plane, the entire diffraction field is encoded and captured in a single shot.
Fractional Fourier transform modeling of diffraction from near to far field. (a) Mapping of the fractional order, target size, and propagation distance (N=400). Blue dashed lines delineate the Fraunhofer (below) and Fresnel (above) regimes. Stars indicate experimental measurements from Figs. 3 and 4 (four-point stars) and Fig. 5 (five-point star). (b) and (c) Profiles along gray solid/dashed lines in (a) for various fractional orders. (d1)–(d5) Simulated amplitude diffraction patterns for orders in (b) (p=0.9 is not shown). (e1)–(e5) Corresponding reconstruction results of (d1)–(d5). (f) and (g) Diffraction patterns and reconstructions corresponding to (c) (p=0.1 is not shown). Note that the source plane scaling factor s1=1 is fixed in all simulations. All diffraction amplitude patterns are shown in lg scale and normalized.
Main experimental results. Experimental results for imaging at a fixed distance of z1=40 m. (a1) and (a2) Single-shot diffraction patterns recorded from two-inch targets (highlighted within the orange circles). (b1) and (b2) The corresponding ground truth targets. (c1) and (c2) Phase retrieval reconstruction results. (d) Direct imaging result of the resolution target (e) at a 40 m distance. The inset is the photograph of the target. (e) The 3D printed resolution target used in the experiment. (f) Diffraction pattern of the three-spiral target shown in the first column of (g). (g) 1 in. target images and their corresponding reconstructions. (h) A magnified region from (c2) and its corresponding intensity profiles along the colored lines. (i) Resolution measurement from the target showing that 1.15 mm corresponds to two line pairs, indicating a spatial resolution of 1.74 line pairs/mm. All diffraction patterns are displayed on a normalized lg scale. Scale bars in (a1), (a2), and (f) are 1 cm; in (b1)–(c2) and (e) are 5 mm; in (d) is 5 cm.
Imaging results at varying propagation distances. Diffraction patterns and reconstructions for a 1 in. target (within blue circles) at z1=40, 30, and 20 m. (a1)–(a3) Diffraction amplitude patterns (lg scale). (b1)–(b3) Corresponding reconstruction results. Scale bars represent 1 cm in (a) and 5 mm in (b).
Fraunhofer diffraction imaging and reconstruction. Imaging results at z1=40 m for target size of approximately 2.8 mm×3.5 mm. (a1)–(a4) Diffraction amplitude patterns for different targets (lg scale). (b) Ground truth targets. (c) Corresponding reconstruction results. Scale bars represent 1 cm in (a) and 1 mm in (b) and (c).
Comparison of convergence speed and reconstruction quality with varying fractional orders p. (a) Experimental PSNR and MSE curves for 10 reconstructions with random initialization at p=0.46 [Fig. 3(a1)] and p=0.79 [Fig. 3(f)]. Blue and orange lines show mean values with standard deviation error bars. (b) Similar curves for p=1 [Fig. 5(a4)]. Red arrows in (a) and (b) mark the MSE oscillation onset, indicating algorithm convergence after several iterations. (c1) and (c2) Simulated PSNR and MSE versus p under mixed noise conditions (Poisson noise followed by 1%, 5%, and 10% Gaussian noise) using the target from Fig. 2(g).
Imaging results with different scattering masks. (a1)–(a3) Photography of the three scattering media: Xuan paper, A3 paper, and an acrylic scatterer. The target [Fig. 3(e)] was positioned 5 mm beneath the scattering medium. (b1)–(b3) Corresponding raw diffraction patterns with the imaging distance of 40 m. (c1)–(c3) Reconstructed images from the diffraction patterns in (b1)–(b3). Scale bars represent 1 cm in (b) and 5 mm in (c).
  • Table 1. Unified phase retrieval algorithm.

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    Table 1. Unified phase retrieval algorithm.

    Input: initial guess O(0), initial support S0, initial standard deviation of the Gaussian kernel σ(0), iteration times N, start iteration counter i=1, support region update symbol m.
    Output: recovered object O^, estimated support S^, recovered Fourier phase {Fp(O^)}
    1:  whileiNdo
    2:   ifmod(i,m)=0then
    3:   σ(i)=max(0.99σ(i1),0.5σ(0))
    4:   else
    5:   σ(i)=σ(i1)
    6:   end if
    7:   Si=Si1*exp(r22(σ(i))2)
    8:  SiSi×(Simax(0.15Si))
    9:   O^(i)=Fp{PS(PM(Fp{O^(i1)}))}
    10:   O^(i)max(0,real(O^(i)))
    11:   O^(i+1)PSparse(O^(i))
    12:   ii+1
    13:  end while
    14:  returnO^=O^(N), S^=SN, {Fp(O^)}={Fp(O^(N))}.
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Wei Li, Zichao Liu, Yi Sun, Yijun Zhou, Feihu Xu, "Single-shot scattering-assisted computational optical synthetic aperture imaging," Adv. Imaging 2, 061003 (2025)

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Paper Information

Category: Research Article

Received: Jun. 22, 2025

Accepted: Aug. 29, 2025

Published Online: Sep. 26, 2025

The Author Email: Feihu Xu (feihuxu@ustc.edu.cn)

DOI:10.3788/AI.2025.10016

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