Complex-Coherence Measurements for Lensless Object Positioning

Fast measurement of the transverse beam size (bunch-by-bunch) has always been a research hotspot in the field of beam diagnosis in accelerators. A bunch-by-bunch transverse beam size system is developing at the HLS-II storage ring. The system is based on an optical imaging system and linear array multi-anode Photomultiplier tubes. A high-band-width oscilloscope is utilized to process bunch-by-bunch signal from the photodetector. In this article, the synchrotron optical imaging system, the photodetector and the signal acquisition system are introduced. According to theoretical analysis and optical system design, it is shown that this system can simultaneously measure bunch-by-bunch transverse beam size and position.

Method of generating a vortex array embedded in a partially coherent beam is proposed and experimentally demonstrated. The vortex array exists in the complex coherence function of a random field arising due to interference of three independent coherence functions with appropriate phase profiles. Existence of the vortex array is confirmed by presenting amplitude and phase distributions of the complex coherence function. The phase structure of the complex coherence function, embedded with a vortex array, is obtained by interfering it with an independent fourth coherence function known as a reference and applying the Fourier fringe analysis technique to the cross-covariance of the intensity of the resultant random field.

The recent development of light-based 3D printing technologies has marked a turning point in additive manufacturing. Through photopolymerization, liquid resins can be solidified into complex objects. Usually, the polymerization is triggered by exciting a photoinitiator with ultraviolet (UV) or blue light. In two-photon printing (TPP), the excitation is done through the non-linear absorption of two photons; it enables printing 100-nm voxels but requires expensive femtosecond lasers which strongly limit their broad dissemination. Upconversion nanoparticles (UCNPs) have recently been proposed as an alternative to TPP for photopolymerization but using continuous-wave lasers. UCNPs convert near-infrared (NIR) into visible/UV light to initiate the polymerization locally as in TPP. Here we provide a study of this multi-photon mechanism and demonstrate how the non-linearity impacts the printing process. In particular, we report on the possibility of fine-tuning the size of the printed voxel by adjusting the NIR excitation intensity. Using gelatin-based hydrogel, we are able to vary the transverse voxel size from 1.3 to 2.8μm and the axial size from 7.7 to 59μm by adjusting the NIR power without changing the degree of polymerization. This work opens up new opportunities to construct 3D structures with micrometer feature size by direct laser writing with continuous wave inexpensive light sources.

In migrating fibroblasts with primary cilia, the primary cilium points in the direction of migration but why this is so is unknown. The objective of our work is to investigate whether directional signaling from the primary cilium (the ciliary vector) affects the direction of cell migration or vice versa and to determine what molecules and mechanisms are involved. Using a well defined cilium‐based RTK signaling pathway whose receptor (PDGFRα) specifically localizes and signals from the ciliary membrane, we use micropipettes to apply a variable concentration of directional stimulus to the cilium and phase shifted laser feedback interference microscopy to determine the transverse and axial position of the cilium in living fibroblasts. We have obtained data which demonstrate that we can correlate fluorescence imaging of GFP labeled cilia with our interference imaging. Although analogous to confocal imaging, our interferometer is a form of label free imaging that has high sensitivity to dense protein aggregations and can determine axial position with an accuracy and precision of better than 10nm in live cells. We have obtained data which indicates that we obtain a strong reflective signal from the primary cilium that we can use for localization. We plan to use this signal in a feedback loop so that we can introduce control perturbations to the direction of the cilium, with an AFM like probe, while simultaneously tracking signaling molecules. Assistence of Tabrez Alam is acknowledged.

Complex self-coherence function determination using geometric phase techniques

Coherence holography capable of real-time recording and reconstruction is proposed and experimentally demonstrated with a generic Leith-type coherence hologram. The coherence hologram is optically generated in real-time using a Mach-Zehnder interferometer and reconstructed using a Sagnac radial shearing interferometer. With this method one can create an optical field distribution with a desired spatial coherence function, and visualize the coherence function in real-time as the contrast and phase variations in an interference fringe pattern. The reconstructed image of the complex coherence function has been quantified with the Fourier transform method of fringe-pattern analysis.

We investigate the possibility of interferometric optical field sensor with DMD forming a series of sampling interferometers in the pupil of an optical system. Our preliminary experiment validates the feasibility of our approach for the field reconstruction in the case of coherent field. We believe that this approach can be extended to sensing of speckle patterns and even incoherent fields, by analyzing not only the intensity and phase, but also the amplitude and the visibility of the interference patterns. Such analysis would yield the complete complex amplitude and/or coherence function, making the approach directly applicable to a wide range of inverse source problems in optics.

The evolution of several structural characteristics during isothermal heat treatment of poly(p‐phenylene terephthalamide) was studied. In this work, heat treatment was interrupted after different treatment times, with the specimens immediately quenched to room temperature. These specimens were then characterized by tensile testing, wide‐ and small‐angle x‐ray scattering, and optical microscopy. Structural parameters obtained from these measurements relate to crystal perfection (via the paracrystalline axial distortion parameter), axial crystallite size, transverse crystallite size, degree of chain misorientation, and degree of pleating. Structural and mechanical parameters were then plotted against heat‐treatment time to obtain kinetic isotherms for each parameter. The kinetics of the removal of chain misorientation parallels that of tensile modulus increase under all conditions. Of the other structural parameters, only the kinetics of pleat removal mimics that of modulus change, indicating that pleat removal is the effective cause of increased chain alignment and thereby of increased axial stiffness. ©1995 John Wiley & Sons, Inc.

The complex coherence function describes information that is necessary to create maps from interferometric synthetic aperture radar (InSAR). This coherence function is complicated by building layover. This paper presents a mathematical model for this complex coherence in the presence of building layover and shows how it can describe intriguing phenomena observed in real interferometric SAR data.

We report a quantitative measurement of the full transverse coherence function of the 14.4 keV x-ray radiation produced by an undulator at the Swiss Light Source. An x-ray grating interferometer consisting of a beam splitter phase grating and an analyzer amplitude grating has been used to measure the degree of coherence as a function of the beam separation out to 30 microm. Importantly, the technique provides a model-free and spatially resolved measurement of the complex coherence function and is not restricted to high resolution detectors and small fields of view. The spatial characterization of the wave front has important applications in discovering localized defects in beam line optics.

The mutual coherence function (MCF) of the acoustic wavefunction from a point source is derived by the path-integral technique for transmission in the presence of a sound channel. Separations in time, transverse horizontal position, vertical position, and acoustic frequency are treated. Approximate coherence times, lengths, and bandwidths due to internal-wave fluctuations are derived. The MCF of frequency is explicitly evaluated for fluctuations due to internal waves. The shape of an ensemble-averaged pulse is derived from the MCF of frequency.

Foucault knife-edge method is an irreplaceable qualitative testing method in the early stage of optical processing, but it needs to accurately place the knife-edge at the focus of the mirror surface to be measured for testing. In view of the complex and difficult calibration process of the knife-edge instrument and the inability to perform quantitative testing efficiently, here the Foucault knife-edge testing method is improved by digitizing and automating it. The knife-edge instrument is first placed on the motorized precision translation stage for two programmed cutting movement perpendicular to the optical axis with controlled axial spacing. And the normal vector of each point on the mirror surface to be measured is solved through the knife-edge transverse position relationship for the bright and dark transition of the corresponding point on a series of knife-edge shadow grams obtained by two cuts. Then the automation and quantification of knife-edge method can be realized. The experimental results of this method are compared with the interferometer testing results, which have good consistency and high accuracy. This method does not require high calibration accuracy for the knife-edge instrument and can perform rapid and efficient testing. It provides a testing method with good performance for automatic and quantitative testing in the early stage of optical processing.

This paper presents an experimental analysis of matrix bead size distribution and voidage variations with axial height in an expanded bed adsorption system. Use of a specially constructed expanded bed with side ports has enabled sampling from within the expanded bed along the vertical axis. Particles removed from within the bed were measured for their size distributions. Residence time distribution studies were used to estimate bed voidage. Measurements of axial and radial particle size distributions and axial voidage distribution have been made at different flow rates. Particle size was found to be radially constant, indicating constant stratification in the column. The particle size was found to decrease with increasing axial height. Voidage increased with axial height from a settled bed value of 0.39 to approaching unity for high liquid velocities and increased at a constant axial position with increased flowrate. This information provides key insight into bed stability and data for the improved modeling of this important unit operation.

Progressive MS is typically heralded by a myelopathic pattern of asymmetric progressive motor weakness. Focal individual "critical" demyelinating spinal cord lesions anatomically associated with progressive motor impairment may be a compelling explanation for this clinical presentation as described in progressive solitary sclerosis (single CNS demyelinating lesion), progressive demyelination with highly restricted MR imaging lesion burden (2-5 total CNS demyelinating lesions; progressive paucisclerotic MS), and progressive, exclusively unilateral hemi- or monoparetic MS (>5 CNS demyelinating progressive unilateral hemi- or monoparetic MS [PUHMS] lesions). Critical demyelinating lesions appear strikingly similar across these cohorts, and we describe their specific spinal cord MR imaging characteristics. We performed a retrospective, observational MR imaging study comparing spinal cord critical demyelinating lesions anatomically associated with progressive motor impairment with any additional "noncritical" (not anatomically associated with progressive motor impairment) spinal cord demyelinating lesions. All spinal cord MR images (302 cervical and 91 thoracic) were reviewed by an experienced neuroradiologist with final radiologic assessment on the most recent MR imaging. Anatomic association with clinical progressive motor impairment was confirmed independently by MS subspecialists. Ninety-one individuals (PUHMS, 37 [41%], progressive paucisclerosis 35 [38%], progressive solitary sclerosis 19 [21%]) with 91 critical and 98 noncritical spinal cord MR imaging demyelinating lesions were evaluated. MR imaging characteristics that favored critical spinal cord demyelinating lesions over noncritical lesions included moderate-to-severe, focal, lesion-associated spinal cord atrophy: 41/91 (45%) versus 0/98 (0%) (OR, 161.91; 9.43 to >999.9); lateral column axial location (OR, 10.43; 3.88-28.07); central region (OR, 3.23; 1.78-5.88); ventral column (OR, 2.98; 1.55-5.72); and larger lesion size of the axial width (OR, 2.01;1.49-2.72), transverse axial size (OR, 1.66; 1.36-2.01), or lesion area (OR, 1.14; 1.08-1.2). Multiple regression analysis revealed focal atrophy and lateral axial location as having the strongest association with critical demyelinating lesions. Focal, lesion-associated atrophy, lateral column axial location, and larger lesion size are spinal cord MR imaging characteristics of critical demyelinating lesions. The presence of critical demyelinating lesions should be sought as these features may be associated with the development of progressive motor impairment in MS.

We demonstrate an optimized two-step procedure for measuring the full complex coherence function. The measurement relies on a wavefront shearing interferometer that permits characterizing nonstationary fields over an extended angular domain. The accuracy of the coherence measurement was demonstrated by excellent agreement with theoretical predictions.