title: Reconstructing state mixtures from diffraction measurements.
abstract: Progress in imaging and metrology depends on exquisite control over and comprehensive characterization of wave fields. As reflected in its name, coherent diffractive imaging relies on high coherence when reconstructing highly resolved images from diffraction intensities alone without the need for image-forming lenses. Fully coherent light can be described adequately by a single pure state. Yet partial coherence and imperfect detection often need to be accounted for, requiring statistical optics or the superposition of states. Furthermore, the dynamics of samples are increasingly the very objectives of experiments. Here we provide a general analytic approach to the characterization of diffractive imaging systems that can be described as low-rank mixed states. We use experimental data and simulations to show how the reconstruction technique compensates for and characterizes various sources of decoherence quantitatively. Based on ptychography, the procedure is closely related to quantum state tomography and is equally applicable to high-resolution microscopy, wave sensing and fluctuation measurements. As a result, some of the most stringent experimental conditions in ptychography can be relaxed, and susceptibility to imaging artefacts is reduced. Furthermore, the method yields high-resolution images of mixed states within the sample, which may include quantum mixtures or fast stationary stochastic processes such as vibrations, switching or steady flows.
authors: Physics Department, Technische Universität München, 85748 Garching bei München, Germany. pierre.thibault@tum.de
authors: Pierre
authors: P
authors: Thibault
authors: Andreas
authors: A
authors: Menzel
references: Ultramicroscopy. 2009 Sep;109(10):1256-62
references: 19541420
references: J Opt Soc Am A Opt Image Sci Vis. 2003 Jan;20(1):40-55
references: 12542317
references: Opt Lett. 2011 Jun 1;36(11):1954-6
references: 21633413
references: Science. 2008 Jul 18;321(5887):379-82
references: 18635796
references: Appl Opt. 1982 Aug 1;21(15):2758-69
references: 20396114
references: Phys Rev Lett. 2012 Feb 17;108(7):073901
references: 22401205
references: Nature. 2004 Dec 16;432(7019):885-8
references: 15602557
references: Nature. 2010 Sep 23;467(7314):436-9
references: 20864997
references: Nanotechnology. 2010 Jul 23;21(29):295303
references: 20601756
references: Phys Rev Lett. 2009 Dec 11;103(24):243902
references: 20366201
references: Opt Lett. 2010 Aug 1;35(15):2585-7
references: 20680066
references: Phys Rev Lett. 2005 Apr 29;94(16):164801
references: 15904233
references: Opt Express. 2008 May 12;16(10):7264-78
references: 18545432