Research ArticleAPPLIED OPTICS

SAVI: Synthetic apertures for long-range, subdiffraction-limited visible imaging using Fourier ptychography

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Science Advances  14 Apr 2017:
Vol. 3, no. 4, e1602564
DOI: 10.1126/sciadv.1602564
  • Fig. 1 Creating synthetic apertures to improve image resolution.

    Objects illuminated with a coherent wave reflect a signal back toward the detector that diffracts to an area larger than the aperture of the receiver. (A) SAR is a technique to increase the resolution of mobile radar imaging systems by scanning the antennae over the synthetic aperture. (B) We extend the principles of SAR to create SAVI. A coherent source (for example, a laser) illuminates a distant target, and the reflected signal is captured by a camera. The camera system is translated to capture all of the light that would enter the desired synthetic aperture. Unlike SAR, phase information cannot be recorded for visible light. Therefore, high-resolution image reconstruction necessitates postcapture computational phase recovery. (C) Experimental implementation of SAVI in three steps. (1) A diffuse object is illuminated with a coherent source, and overlapping images are captured. Each image has low resolution and suffers from speckle. (2) Missing phase information is recovered computationally, which requires redundancy between captured intensity images. (3) A high-resolution image is reconstructed using the recovered phase. Additional examples of captured data and reconstructions are shown in Figs. 3 and 4.

  • Fig. 2 Differences when recovering optically rough objects.

    Previous FP methods, particularly transmissive geometries, have assumed that the scene consists of smooth objects with a flat phase. Left: Simulation of recovering a smooth resolution target in a transmissive geometry, adapted from Holloway et al. (32). The recovered Fourier magnitude (shown on a log scale) follows a nicely structured pattern with a peak at the dc component and decaying magnitudes for high spatial frequencies. Right: Simulation of recovering a rough resolution target in a reflective geometry. Diffuse objects spread Fourier information more uniformly, and the Fourier magnitude does not exhibit any meaningful structure. The difference in Fourier patterns is evident in the captured images taken from the same locations in both modalities. The diffuse reflectance results in captured and reconstructed images that contain speckle.

  • Fig. 3 Experimental setup for reflection mode FP and results of common objects.

    (A) A simplified rendering of the experiment and (B) the experimental setup for reflection mode FP. An object is placed 1 m away from the illumination source and camera. To satisfy the Fraunhofer approximation for a short optical path, a lens is used to focus coherent light onto the aperture of the camera lens. Multiple images are acquired to create a large synthetic aperture by translating the camera and lens using a translation stage. In the bottom row, examples are shown using SAVI to improve spatial resolution in long-range imaging for everyday diffuse objects. Images captured with a small aperture are unrecognizable because of diffraction blur and speckle. Following reconstruction, fine details are visible, permitting scene identification. (C) Fingerprint deposited on glass. The fingerprint is coated in diffuse powder to provide contrast against the glass. (D) Reverse side of a U.S. $2 bill. Scale bars, 1 mm.

  • Fig. 4 FP for improving spatial resolution in diffuse objects.

    A USAF resolution target is used to characterize the performance of the proposed method to create SAVI. (A) Resolution of a USAF target under coherent light under various imaging modalities. First row: Captured images exhibit large diffraction blur and speckle. Second row: Averaging short-exposure frames of a vibrating target reduces speckle. Third row: A rotating diffuser removes temporal coherence to approximate an incoherent source at the expense of light efficiency. Fourth row: SAVI without the denoising step described in the “Suppressing speckle” section in Materials and Methods. Fifth row: SAVI using denoising improves the contrast of the fourth row. (B) Magnified regions of various bar groups recovered by the five techniques. The pink line demarcates resolvable features. Scale bars at the bottom of each column show the size of a single bar in that column. (C) Contrast of the bars as a function of feature size. Features above the pink dashed line are resolvable. Resolution in the captured image deteriorates rapidly (purple). Mimicking an incoherent source via averaging (yellow) or rotating diffuser (gray) increases spatial resolution. SAVI without (blue) and with (orange) a regularizer markedly increases resolution. Use of the regularizer improves image contrast. See the main text for a complete explanation of the contrast metric. (D) Speckle size and resolution loss are inversely proportional to the size of the imaging aperture. By increasing the synthetic aperture to just over six times the size of the camera’s aperture, we observe a sixfold increase in resolution (blue lines and circles) accompanied by a corresponding decrease in speckle size (orange lines and diamonds). The measured and predicted values are shown in dashed and solid lines, respectively. Speckle size computed without the use of the denoising regularizer. Note that the slight deviation of measured improvement is a consequence of discretization of the resolution chart. See fig. S4 discussed in part D of the Supplementary Materials for further details.

  • Fig. 5 Simulated reconstructions for varying background/foreground contrast ratios.

    Objects with strong contrast between the foreground and background amplitude values have a higher fidelity reconstruction than those where the background and foreground amplitudes are similar. The high-resolution complex object used for testing is shown in the top row. Simulation parameters are chosen to match the experimental parameters used in Fig. 4. The bottom three rows represent reconstructions where the amplitude in the high-resolution object is varied to different intensity ranges. Reconstruction quality falls as the contrast in the amplitude decreases. This suggests that a more robust signal model is necessary to suppress speckle for objects with low contrast.

  • Fig. 6 Recovering high-resolution images with FP and phase retrieval.

    The complete recovery algorithm for SAVI is presented on the left side of the figure. A high-resolution estimate of Ψ(u) is recovered by iteratively enforcing intensity measurement constraints in the spatial domain and updating estimates of the spectrum in the Fourier domain. Image denoising is applied every s iterations to suppress the influence of speckle noise in the final reconstruction. Left branch (blue): Traditional FP recovery algorithm used by Ou et al. (18) and Tian et al. (25). Right branch (brown): Image denoising to reduce speckle noise in the estimate of Ψ(u). To illustrate how image recovery improves resolution, a simulation is shown on the right. (A and B) A complex object with an amplitude shown in (A) and having uniformly distributed phase in the range [−π, π] is recorded by a diffraction-limited imaging system (B). (C) FP reduces diffraction blur and speckle size, leading to increased resolution, but still suffers from the presence of speckle and reconstruction artifacts. (D) Incorporating a denoising regularizer in the FP recovery algorithm reduces variation in speckle intensity and reduces the effect of reconstruction artifacts. Brightness in the outsets has been increased to highlight the artifacts. View digitally to see the fine details.

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/3/4/e1602564/DC1

    Supplementary Materials

    fig. S1. Cost and weight increase rapidly when improving lens resolution.

    fig. S2. Comparison with incoherent superresolution methods for diffuse surfaces.

    fig. S3. A simplified depiction of the imaging geometry.

    fig. S4. Discretization in the USAF resolution chart.

    fig. S5. Convergence of proposed phase retrieval algorithm.

    fig. S6. Example of recovered phase map.

    References (5364)

  • Supplementary Materials

    This PDF file includes:

    • Supplementary Materials
    • fig. S1. Cost and weight increase rapidly when improving lens resolution.
    • fig. S2. Comparison with incoherent superresolution methods for diffuse surfaces.
    • fig. S3. A simplified depiction of the imaging geometry.
    • fig. S4. Discretization in the USAF resolution chart.
    • fig. S5. Convergence of proposed phase retrieval algorithm.
    • fig. S6. Example of recovered phase map.
    • References (53–64)

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