Partial Spatial Coherence Research Articles

Multi-focus TIE algorithm including partial spatial coherence and overlapping filters.

The transport of intensity equation (TIE) relates the variation of intensity of a wave-front along its mean direction of propagation with its phase. In experimental application, characteristic artefacts may affect the retrieved phase. These originate from inadequacies in estimating the axial derivative and the amplification of noise in the inversion of the TIE. To tackle these issues, images recorded at multiple planes of focus can be integrated into a multi-focus TIE (MFTIE) solution. This methodology relies on the efficient sampling of phase information in the spatial-frequency domain, typically by the definition of band pass filters implemented as a progression of sharp spatial frequency cut-offs. We present a convenient MFTIE implementation which avoids the need for recording images at very specific planes of focus and applies overlapping cut-offs, greatly simplifying the experimental application. This new approach additionally also accounts for partial spatial coherence in a flux-preserving framework. Using simulated data as well as experimental data from optical microscopy and electron microscopy we show that the frequency response of this MFTIE algorithm recovers efficiently a wide range of spatial frequencies of the phase that can be further extended by simple iterative refinement.

Non-iterative method for phase retrieval and coherence characterization by focus variation using a fixed star-shaped mask

A novel non-iterative phase retrieval method is proposed and demonstrated with a proof-of-principle experiment. The method uses a fixed specially designed mask and through-focus intensity measurements. It is demonstrated that this method is robust to spatial partial coherence in the illumination, making it suitable for coherent diffractive imaging using spatially partially coherent light, as well as for coherence characterization.

Partially coherent isodiffracting pulsed beams

We investigate a class of isodiffracting pulsed beams, which are superpositions of transverse modes supported by spherical-mirror laser resonators. By employing modal weights that, for stationary light, produce a Gaussian Schell-model beam, we extend this standard model to pulsed beams. We first construct the two-frequency cross-spectral density function that characterizes the spatial coherence in the space-frequency domain. By assuming a power-exponential spectral profile, we then employ the generalized Wiener-Khintchine theorem for nonstationary light to derive the two-time mutual coherence function that describes the space-time coherence of the ensuing beams. The isodiffracting nature of the laser resonator modes permits all (paraxial-domain) calculations at any propagation distance to be performed analytically. Significant spatiotemporal coupling is revealed in subcycle, single-cycle, and few-cycle domains, where the partial spatial coherence also leads to reduced temporal coherence even though full spectral coherence is assumed.

Ultra high-speed x-ray imaging of laser-driven shock compression using synchrotron light

A high-power, nanosecond pulsed laser impacting the surface of a material can generate an ablation plasma that drives a shock wave into it; while in situ x-ray imaging can provide a time-resolved probe of the shock-induced material behaviour on macroscopic length scales. Here, we report on an investigation into laser-driven shock compression of a polyurethane foam and a graphite rod by means of single-pulse synchrotron x-ray phase-contrast imaging with MHz frame rate. A 6 J, 10 ns pulsed laser was used to generate shock compression. Physical processes governing the laser-induced dynamic response such as elastic compression, compaction, pore collapse, fracture, and fragmentation have been imaged; and the advantage of exploiting the partial spatial coherence of a synchrotron source for studying low-density, carbon-based materials is emphasized. The successful combination of a high-energy laser and ultra high-speed x-ray imaging using synchrotron light demonstrates the potentiality of accessing complementary information from scientific studies of laser-driven shock compression.

Ptychographic imaging with partially coherent plasma EUV sources

Abstract We report on high-resolution lens-less imaging experiments based on ptychographic scanning coherent diffractive imaging (CDI) method employing compact plasma sources developed for extreme ultraviolet (EUV) lithography applications. Two kinds of discharge sources were used in our experiments: a hollow-cathode-triggered pinch plasma source operated with oxygen and for the first time a laser-assisted discharge EUV source with a liquid tin target. Ptychographic reconstructions of different samples were achieved by applying constraint relaxation to the algorithm. Our ptychography algorithms can handle low spatial coherence and broadband illumination as well as compensate for the residual background due to plasma radiation in the visible spectral range. Image resolution down to 100 nm is demonstrated even for sparse objects, and it is limited presently by the sample structure contrast and the available coherent photon flux. We could extract material properties by the reconstruction of the complex exit-wave field, gaining additional information compared to electron microscopy or CDI with longer-wavelength high harmonic laser sources. Our results show that compact plasma-based EUV light sources of only partial spatial and temporal coherence can be effectively used for lens-less imaging applications. The reported methods may be applied in combination with reflectometry and scatterometry for high-resolution EUV metrology.

Combining Coherent Hard X-Ray Tomographies with Phase Retrieval to Generate Three-Dimensional Models of Forming Bone

Holotomography, a phase sensitive synchrotron-based μCT modality, is a quantitative 3D imaging method. By exploiting partial spatial X-ray coherence, bones can be imaged volumetrically with high resolution coupled with impressive density sensitivity. This tomographic method reveals the main characteristics of the important tissue compartments in forming bones, including the rapidly-changing soft tissue and the partially or fully mineralized bone regions, while revealing subtle density differences in 3D. Here we show typical results observed within the growing femur bone midshafts of healthy mice that are 1, 3, 7, 10 and 14 days old (postpartum). Our results make use of partially-coherent synchrotron radiation employing inline Fresnel-propagation in multiple tomographic datasets obtained in the imaging beamline ID19 of the ESRF. The exquisite detail creates maps of the juxtaposed soft, partially mineralized and highly mineralized bone revealing the environment in which bone cells create and shape the matrix. This high resolution 3D data is a step towards creating realistic computational models that may be used to study the dynamic processes involved in bone tissue formation and adaptation. Such data will enhance our understanding of the important biomechanical interactions directing maturation and shaping of the bone micro- and macro-geometries.

Experimental evidence for partial spatial coherence in imaging Mueller polarimetry.

We demonstrate experimentally the validity of the partial spatial coherence formalism in Mueller polarimetry and show that, in a finite spatial resolution experiment, the measured response is obtained through convolving the theoretical one with the instrument function. The reported results are of primary importance for Mueller imaging systems.

Precise method for measuring spatial coherence in TEM beams using Airy diffraction patterns.

We have developed a method to precisely measure spatial coherence in electron beams. The method does not require an electron biprism and can be implemented in existing analytical transmission electron microscopes equipped with a post-column energy filter. By fitting the Airy diffraction pattern of the selector aperture, various parameters such as geometric aberrations of the lens system and the point-spread function of the diffraction blurring are precisely determined. From the measurements of various beam diameters, components that are attributed to the partial spatial coherence are successfully separated from the point-spread functions. A linear relationship between the spatial coherence length and beam diameter is revealed, thus indicating that a wide range of coherence lengths can be determined by our proposed method as long as the coherence length remains >80% of the aperture diameter. A remarkable feature of this method is its ability to simultaneously determine diffraction blurring and lens aberrations. Possible applications of this method are also discussed.

Spatial coherence measurements of the EUV emission from laser-plasma source based on xenon/helium gas puff target

In this paper, we present the first measurements of the partial spatial coherence of the EUV emission from xenon plasma in laser-plasma source, based on a double stream gas puff target. The Young double slit approach was employed to measure complex coherence factor of the EUV Xe emission at 13.5-nm wavelength in two orthogonal directions. The radius of coherence of ~60 μm was estimated at the distance of 2.1 m from the source. The number of coherently emitted photons was sufficient to demonstrate coherent imaging. Using partially coherent radiation from such source Gabor EUV holography was successfully demonstrated.

Propagation-based Phase-Contrast X-ray Imaging at a Compact Light Source

We demonstrate the applicability of propagation-based X-ray phase-contrast imaging at a laser-assisted compact light source with known phantoms and the lungs and airways of a mouse. The Munich Compact Light Source provides a quasi-monochromatic beam with partial spatial coherence, and high flux relative to other non-synchrotron sources (up to 1010 ph/s). In our study we observe significant edge-enhancement and quantitative phase-retrieval is successfully performed on the known phantom. Furthermore the images of a small animal show the potential for live bio-imaging research studies that capture biological function using short exposures.

Reconstructing mode mixtures in the optical near-field.

We propose a reconstruction scheme for hard x-ray inline holography, a variant of propagation imaging, which is compatible with imaging conditions of partial (spatial) coherence. This is a relevant extension of current full-field phase contrast imaging, which requires full coherence. By the ability to reconstruct the coherent modes of the illumination (probe), as demonstrated here, the requirements of coherence filtering could be relaxed in many experimentally relevant settings. The proposed scheme is built on the mixed-state approach introduced in [Nature494, 68 (2013)], combined with multi-plane detection of extended wavefields [Opt. Commun.199, 65 (2001), Opt. Express22, 16571 (2014)]. Notably, the diversity necessary for the reconstruction is generated by acquiring measurements at different defocus positions of the detector. We show that we can recover the coherent mode structure and occupancy numbers of the partial coherent probe. Practically relevant quantities as the transversal coherence length can be computed from the reconstruction in a straightforward way.

MHz frame rate hard X-ray phase-contrast imaging using synchrotron radiation.

Third generation synchrotron light sources offer high photon flux, partial spatial coherence, and ~10-10 s pulse widths. These enable hard X-ray phase-contrast imaging (XPCI) with single-bunch temporal resolutions. In this work, we exploited the MHz repetition rates of synchrotron X-ray pulses combined with indirect X-ray detection to demonstrate the potential of XPCI with millions of frames per second multiple-frame recording. This allows for the visualization of aperiodic or stochastic transient processes which are impossible to be realized using single-shot or stroboscopic XPCI. We present observations of various phenomena, such as crack tip propagation in glass, shock wave propagation in water and explosion during electric arc ignition, which evolve in the order of km/s (µm/ns).

Halo-free Phase Contrast Microscopy

We present a new approach for retrieving halo-free phase contrast microscopy (hfPC) images by upgrading the conventional PC microscope with an external interferometric module, which generates sufficient data for reversing the halo artifact. Acquiring four independent intensity images, our approach first measures haloed phase maps of the sample. We solve for the halo-free sample transmission function by using a physical model of the image formation under partial spatial coherence. Using this halo-free sample transmission, we can numerically generate artifact-free PC images. Furthermore, this transmission can be further used to obtain quantitative information about the sample, e.g., the thickness with known refractive indices, dry mass of live cells during their cycles. We tested our hfPC method on various control samples, e.g., beads, pillars and validated its potential for biological investigation by imaging live HeLa cells, red blood cells, and neurons.

Synthesizing time-evolving partially-coherent Schell-model sources

Time-evolving simulation of sources with partial spatial and temporal coherence is sometimes instructive or necessary to explain optical coherence effects. Yet, existing time-evolving synthesis techniques often require prohibitive amounts of computer memory. This paper discusses three methods for the synthesis of continuous or pulsed time-evolving sources with nearly arbitrary spatial and temporal coherence. One method greatly reduces computer memory requirements, making this type of synthesis more practical. The utility of all three methods is demonstrated via a modified form of Young's experiment. Numerical simulation and laboratory results for time-averaged irradiance are presented and compared with theory to validate the synthesis techniques.

General formalism for partial spatial coherence in reflection Mueller matrix polarimetry.

Starting from the first principles, we derive the expressions governing partially coherent Mueller matrix reflection polarimetry on spatially inhomogeneous samples. These are reported both in their general form and in the practically important specific form for two juxtaposed media.

Predicting visibility of interference fringes in X-ray grating interferometry.

The interference fringe visibility is a common figure of merit in designs of x-ray grating-based interferometers. Presently one has to resort to laborious computer simulations to predict fringe visibility values of interferometers with polychromatic x-ray sources. Expanding the authors' previous work on Fourier expansion of the intensity fringe pattern, in this work the authors developed a general quantitative theory to predict the intensity fringe pattern in closed-form formulas, which incorporates the effects of partial spatial coherence, spectral average and detector pixel re-binning. These formulas can be used to predict the fringe visibility of a Talbot-Lau interferometer with any geometry configuration and any source spectrum.

Propagation of an optical vortex carried by a partially coherent Laguerre-Gaussian beam in turbulent ocean.

The analytical formulas for the orbital angular momentum (OAM) mode probability density, signal OAM mode detection probability, and spiral spectrum of partially coherent Laguerre-Gaussian (LG) beams with optical vortices propagation in weak horizontal oceanic turbulent channels were developed, based on the Rytov approximation theory. The effect of oceanic turbulence and beam source parameters on the propagation behavior of the optical vortices carried by partially coherent LG beams was investigated in detail. Our results indicated that optical turbulence in an ocean environment produced a much stronger effect on the optical vortex than that in an atmosphere environment; the effective range of the signal OAM mode of LG beams with a smaller ratio of the mode crosstalk was limited to only several tens of meters in turbulent ocean. The existence of oceanic turbulence evidently induced OAM mode crosstalk and spiral spectrum spread. The effects of oceanic turbulence on the OAM mode detection probability increased with the increase of radial and azimuthal mode orders, oceanic turbulent equivalent temperature structure parameter, and temperature-salinity balance parameter. The spatial partial coherence of the beam source would enhance the effect of turbulent aberrations on the signal OAM mode detection probability, and fully coherent vortex beams provided better performance than partially coherent ones. Increasing wavelength of the vortex beams would help improve the performance of this quantum optical communication system. These results might be of interest for the potential application of optical vortices in practical underwater quantum optical communication among divers, submarines, and sensors in the ocean environment.

Quantitative assessment of noise reduction with partial spatial coherence illumination in digital holographic microscopy.

Improving image quality in digital holographic microscopy is achievable by using partial spatial coherence (PSC) illumination instead of fully coherent illumination. This Letter presents simple theoretical models to quantitatively assess the reduction of noise as a function of both the spatial coherence of the illumination and the defocus distance of the noise source. The first developed model states that the effect of the PSC can be studied by discretizing the field of view in the plane of the noise source. The second model, following a continuous approach, corroborates the discrete model and extends it. Experimental results confirm theoretical expectations.

Partial coherence and polarization of a two-mode surface-plasmon polariton field at a metallic nanoslab.

Rigorous electromagnetic theory is utilized to characterize the partial spatial coherence and partial polarization of a two-mode field consisting of the long-range and the short-range surface-plasmon polariton at a metallic nanofilm. By employing appropriate formulations for the spectral degrees of coherence and polarization, we examine the fundamental limits for these quantities associated with such a superposition field and explore how the degrees are influenced when the media, frequency, and slab thickness are varied. It is in particular shown that coherence lengths extending from subwavelength scales up to thousands of wavelengths are possible and their physical origins are elucidated. In addition, we demonstrate that for ultra-thin films the generally highly polarized two-mode field can be partially polarized in close vicinity of the polariton excitation region. The results could benefit cross-disciplinary electro-optical applications in which near-field interactions between plasmons and nanoparticles are exploited.

Three-wave electron vortex lattices for measuring nanofields.

It is demonstrated how an electron-optical arrangement consisting of two electron biprisms can be used to generate three-wave vortex lattices with effective lattice spacings between 0.1 and 1 nm. The presence of vortices in these lattices was verified by using a third biprism to perform direct phase measurements via off-axis electron holography. The use of three-wave lattices for nanoscale electromagnetic field measurements via vortex interferometry is discussed, including the accuracy of vortex position measurements and the interpretation of three-wave vortex lattices in the presence of partial spatial coherence.