Coherent diffraction imaging (CDI) for visualizing objects at atomic resolution has been realized as a promising tool for imaging single molecules. Drawbacks of CDI are associated with the difficulty of the numerical phase retrieval from experimental diffraction patterns; a fact which stimulated search for better numerical methods and alternative experimental techniques. Common phase retrieval methods are based on iterative procedures which propagate the complex-valued wave between object and detector plane. Constraints in both, the object and the detector plane are applied. While the constraint in the detector plane employed in most phase retrieval methods requires the amplitude of the complex wave to be equal to the squared root of the measured intensity, we propose a novel Fourier-domain constraint, based on an analogy to holography. Our method allows achieving a low-resolution reconstruction already in the first step followed by a high-resolution reconstruction after further steps. In comparison to conventional schemes this Fourier-domain constraint results in a fast and reliable convergence of the iterative reconstruction process.
In conventional diffraction theory, a subwavelength period is considered a prerequisite to achieve interesting resonance-assisted physical phenomena, such as bound states in the continuum and diverse zero-order spectral responses with $100\%$ diffraction efficiency. Here, we present modified diffraction equations that provide mechanisms to control light diffraction beyond the subwavelength limit. We show that resonant diffraction phenomena are governed by the superposition of scattering processes, owing to higher Fourier harmonic components. By appropriately engineering the Fourier harmonic co…
We experimentally demonstrate how to solve the phase problem of diffraction using multi-wave interference with standard diffraction experimental setups without the need for taking any auxiliary data. In particular, we show that the phases of the Fourier components of a periodic structure can be fully recovered by deliberately choosing a probe wavelength of the diffracting radiation much smaller than the lattice constant. In the course of the demonstration, we accurately determine the refractive index profile of nanocomposite phase gratings by light and neutron diffraction measurements.
A forward model is presented to an inverse scattering problem that arises in the application of reflective Fourier ptychographic microscopy. The model allows us to determine the 3D distributions of refractive index for weakly scattering semi-transparent objects using Fourier ptychographic tomography. The derivation results show that both transmission types reported previously and reflective type present in this article are corresponding to a specific application in Wolf's work (Emil Wolf, Opt. Commun. 1969 1(4) pp. 153-156). The transmission type measures the forward scattering field while the…
Recently introduced speckle-correlations based techniques enable noninvasive imaging of objects hidden behind scattering layers. In these techniques the hidden object Fourier amplitude is retrieved from the scattered light autocorrelation, and the lost Fourier phase is recovered via iterative phase-retrieval algorithms, which suffer from convergence to wrong local-minima solutions and cannot solve ambiguities in object-orientation. Here, inspired by notions used in astronomy, we experimentally demonstrate that in addition to Fourier amplitude, the object phase information is naturally and inhe…
Fourier optics is a powerful and efficient tool for solving many diffraction problems, but relies on the assumption of scalar diffraction theory and ignores the three-dimensional structure and material properties of the diffracting element. Recent experiments of sub-scale starshade external occulters revealed that the inclusion of these physical properties is necessary to explain the observed diffraction at 1e-10 of the incident light intensity. Here, we present a methodology for implementing non-scalar diffraction while maintaining the efficiency and ease of standard Fourier optics techniques…
We report the reconstruction of a transparency image in Ghost diffraction scheme using a statistical optics approach. This is implemented by using a static diffuser rather than a pseudo thermal light source with a rotating diffuser. The experimental implementation makes use of spatial ergodicity and spatial stationarity for spatially distributed random fields. A strategy to realize the Ghost diffraction scheme through spatial intensity correlation with a phase retrieval algorithm permits reconstruction of the transparency.
Coherent diffraction imaging (CDI) is a promising imaging technique revealing most of the information from diffraction measurements. An ideal CDI should reconstruct complex-valued object from a single-shot far-field diffraction without any priori information about the target. To realize the ideal CDI, we propose a class of parameter-robust illumination pattern. A direct phase optimizing algorithm is also raised here to improve the performance of phase retrieval in strong noise. Experimental result demonstrates the efficiency of our scheme in practical noisy measurement for complex-valued targe…
Ubiquitous to most molecular scattering methods is the challenge to retrieve bond distance and angle from the scattering signals since this requires convergence of pattern matching algorithms or fitting methods. This problem is typically exacerbated when imaging larger molecules or for dynamic systems with little a priori knowledge. Here, we employ laser-induced electron diffraction (LIED) which is a powerful means to determine the precise atomic configuration of an isolated gas-phase molecule with picometre spatial and attosecond temporal precision. We introduce a simple molecular retrieval m…
In this manuscript we demonstrate a method to reconstruct the wavefront of focused beams from a measured diffraction pattern behind a diffracting mask in real-time. The phase problem is solved by means of a neural network, which is trained with simulated data and verified with experimental data. The neural network allows live reconstructions within a few milliseconds, which previously with iterative phase retrieval took several seconds, thus allowing the adjustment of complex systems and correction by adaptive optics in real time. The neural network additionally outperforms iterative phase ret…
In optical diffraction tomography (ODT), the three-dimensional scattering potential of a microscopic object rotating around its center is recovered by a series of illuminations with coherent light. Reconstruction algorithms such as the filtered backpropagation require knowledge of the complex-valued wave at the measurement plane, whereas often only intensities, i.e., phaseless measurements, are available in practice. We propose a new reconstruction approach for ODT with unknown phase information based on three key ingredients. First, the light propagation is modeled using Born's approximation …
Experimental robustness of Fourier Ptychography phase retrieval algorithms
University of California, Berkeley（加州大学伯克利分校）；École Normale Supérieure（巴黎高等师范学院）；Colorado School of Mines（科罗拉多矿业学院）；University of Southern California（南加州大学）
We propose and demonstrate a new phase retrieval method for imaging through random media. Although methods to recover the Fourier amplitude through random distortions are well established, recovery of the Fourier phase has been a more difficult problem and is still a very active research area. Here, we show that by simply ensemble averaging shift-corrected images, the Fourier phase of an object obscured by random distortions can be accurately retrieved up to the diffraction limit. The method is simple, fast, does not have any optimization parameters, and does not require prior knowledge or ass…
