A generalization for optimized phase retrieval algorithms

Optics Express (Impact Factor: 3.53). 10/2012; 20(22):24778-90. DOI: 10.1364/OE.20.024778
Source: PubMed

ABSTRACT In this work, we demonstrate an improved method for iterative phase retrieval with application to coherent diffractive imaging. By introducing additional operations inside the support term of existing iterated projection algorithms, we demonstrate improved convergence speed, higher success rate and, in some cases, improved reconstruction quality. New algorithms take a particularly simple form with the introduction of a generalized projection-based reflector. Numerical simulations verify that these new algorithms surpass the current standards without adding complexity to the reconstruction process. Thus the introduction of this new class of algorithms offers a new array of methods for efficiently deconvolving intricate data.

  • [Show abstract] [Hide abstract]
    ABSTRACT: Recent breakthroughs in high harmonic generation have extended the reach of bright tabletop coherent light sources from a previous limit of ≍100 eV in the extreme ultraviolet (EUV) all the way beyond 1 keV in the soft X-ray region. Due to its intrinsically short pulse duration and spatial coherence, this light source can be used to probe the fastest physical processes at the femtosecond timescale, with nanometer-scale spatial resolution using a technique called coherent diffractive imaging (CDI). CDI is an aberration-free technique that replaces image-forming optics with a computer phase retrieval algorithm, which recovers the phase of a measured diffraction amplitude. This technique typically requires the sample of interest to be isolated; however, it is possible to loosen this constraint by imposing isolation on the illumination. Here we extend previous tabletop results, in which we demonstrated the ability to image a test object with 22 nm resolution using 13 nm light [3], to imaging of more complex samples using the keyhole CDI technique adapted to our source. We have recently demonstrated the ability to image extended objects in a transmission geometry with ≍100 nm resolution. Finally, we have taken preliminary CDI measurements of extended nanosystems in reflection geometry. We expect that this capability will soon allow us to image dynamic processes in nanosystems at the femtosecond and nanometer scale.
    Proceedings of SPIE - The International Society for Optical Engineering 09/2013; DOI:10.1117/12.2026300 · 0.20 Impact Factor
  • [Show abstract] [Hide abstract]
    ABSTRACT: Many imaging techniques provide measurements proportional to Fourier magnitudes of an object, from which one attempts to form an image. One such technique is intensity interferometry which measures the squared Fourier modulus. Intensity interferometry is a synthetic aperture approach known to obtain high spatial resolution information, and is effectively insensitive to degradations from atmospheric turbulence. These benefits are offset by an intrinsically low signal-to-noise (SNR) ratio. Forward models have been theoretically shown to have best performance for many imaging approaches. On the other hand, phase retrieval is designed to reconstruct an image from Fourier-plane magnitudes and object-plane constraints. So it's natural to ask, "How well does phase retrieval perform compared to forward models in cases of interest?" Image reconstructions are presented for both techniques in the presence of significant noise. Preliminary conclusions are presented for attainable resolution vs. DC SNR.
    Proceedings of SPIE - The International Society for Optical Engineering 09/2013; DOI:10.1117/12.2026974 · 0.20 Impact Factor
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: Coherent X-ray diffraction imaging (CXDI) of the displacement field and strain distribution of nanostructures in kinematic far-field conditions requires solving a set of non-linear and non-local equations. One approach to solving these equations, which utilizes only the object's geometry and the intensity distribution in the vicinity of a Bragg peak as a priori knowledge, is the HIO+ER-algorithm. Despite its success for a number of applications, reconstruction in the case of highly strained nanostructures is likely to fail. To overcome the algorithm's current limitations, we propose the HIOO<sub>R</sub>M+ER<sup>M</sup>-algorithm which allows taking advantage of additional a priori knowledge of the local scattering magnitude and remedies HIO+ER's stagnation by incorporation of randomized overrelaxation at the same time. This approach achieves significant improvements in CXDI data analysis at high strains and greatly reduces sensitivity to the reconstruction's initial guess. These benefits are demonstrated in a systematic numerical study for a periodic array of strained silicon nanowires. Finally, appropriate treatment of reciprocal space points below noise level is investigated.
    Optics Express 11/2013; 21(23):27734-49. DOI:10.1364/OE.21.027734 · 3.53 Impact Factor