Theory and verification of moiréfringes for x-ray three-phase grating interferometer

Dual-phase and three-phase grating x-ray interference is a promising new technique for grating-based x-ray differential phase contrast imaging.Dual-phase grating interferometers have been relatively completely studied and discussed.In this paper,the corresponding imaging fringe formula of the three-phase grating interferometer is provided.At the same time,the similarities and differences between the three-phase grating interferometer and the dual-phase grating interferometer are investigated and verified,and that the three-phase grating interferometer can produce large-period moiréfringes without using the analyzing grating is demonstrated experimentally.Finally,a simple method of designing three-phase grating and multi-grating imaging systems from geometric optics based on the thin-lens theory of gratings is presented.These theoretical formulas and experimental results provide optimization tools for designing three-phase grating interferometer systems.

Laser Doppler Vibrometer Without Directional Ambiguity Using Rectangular Phase Grating

The two-phase detection method for directional discrimination in laser Doppler measurements is discussed.The diffraction efficiency of a sin- gle period rectangular phase grating is analysed and a kind of back-scattered laser Doppler vibrometer without directional ambiguity using the single peri- od rectangular phase grating as the beam-combiner described.The principles of this kind of vibrometer are explained in detail,and some experimental re- sults are given.In this kind of vibrometer,the rectangular phase grating, without the zero diffracted order and even orders,is used to eliminate use- less stray light and to combine the useful signal light.Differential electronics is employed to reject signal noise.Therefore,the signal-to-noise ratio of Doppler signals and the measurement accuracy of the instrument are im- proved and the range of application is expanded.

Fast generation of controllable equal-intensity four beams based on isosceles triangle multilevel phase grating realized by liquid crystal spatial light modulator

Liquid crystal spatial light modulator （LCSLM） realizing equal-intensity multiple beams often has some features, i.e., phase valley between two adjacent pixels, flybaek region when phase decreases immediately from 2~r to 0, and inevitable backplane curvature, which are different from those of most conventional diffractive optical elements （DOEs）, such as static DOEs. For optimal intensity uniformity, equal-intensity multi-beam generation must be considered for these artifacts. We present a tunable-grating method in which the intensity uniformity can be improved by considering the LCSLM artifacts. For instance, tuning phase modulation depth of the grating, called isosceles triangle multilevel phase grating （ITMPG）, can be used not only to improve the intensity uniformity, but also to fast steer four beams with narrow beamwidths, determined by the same effective aperture of ITMPG. Improved intensity uniformity and high relative diffraction efficiency are demonstrated through experiments with phase-only LCSLM.

COMPACT PHASE GRATING INTERFERENCE SENSOR FOR MICRO-DISPLACEMENT

On the basis of existing techniques, a compact micro-displacement sensor of phase grating interference （PGI） is described, which adopts cylindrical hologram diffraction grating as the calibration standard. The optical principle of the sensor is explained, and the relation between the grating motion displacement and the phase shift of interference stripes is deduced. The improvement of the integral structure and the method of photoelectric signal processing are described in detail. With the software system based on the virtual instrument development platform Labwindows/CVI and other hardwares such as the precision displacement worktable, the surfaces of typical parts are measured and the characterization results are given. The sensor has wide measuring range and high resolution, its sensitivity and resolution being independent of the wavelength of the incident light. The vertical measuring range is 0-6 mm, and the vertical resolution is 0.005μm. The experimental results show that the sensor can be used to measure and characterize the surface topography parameters of the plane and curved surface.

Phase grating in a doubly degenerate four-level system

In this paper, we suggest a doubly degenerate four-level system, in which the transition takes place between the hyperfine energy 52S1/2 F = 1 and 52P3/2 F = 2 in rubidium 87 D2 line, for studying atomic phase grating based on the cross-Kerr and phase conjugation effects. The phase grating with high efficiency can be obtained by tuning phase shift Ф between the coupling and probe field, when the coupling intensity is much stronger than the strength of probe field. Under different coupling intensities, a high diffraction efficiency can be maintained. A new and simple way of implementing phase grating is presented. However, in such an atomic system, two main limitations must be taken into account. First, the independence between steady state probe susceptibility and the coupling intensity, when the population decay rate is larger than the Rabi frequency of the coupling field, cannot result in diffraction grating; second, the sample to be prepared should not be too long.

PHOTOINDUCED HOLOGRAPHIC PHASE GRATINGS BURIED IN AZOBENZENE SIDE-CHAIN POLYMER FILMS WITH A CHIRAL GROUP

An optically active polymer (PM1) containing azobenzene moieties with a chiral group (s-2-methyl-butyl) wassynthesized by homopolymerization of monomer, 4-[2-(methacryloyloxy)ethyloxy-4'-(s-2-methyl-1-butyl oxycarbonyl)azobenzene, using the free radical polymerization method. The polymer dissolved in tetrahydrofuran (THF) could be easilyprocessed into high optical quality films. The optical anisotropy of the polymer films was investigated by polarizing opticalmicroscopy (POM). The experimental results showed that irradiation with a circularly polarized beam could align theorientation of the molecules in the polymer films. Moreover, the holographic phase gratings of photo-induced polymer filmswere detected by atomic force microscopy (AFM) and POM. In comparison with polymer containing no chiral group, it wasfound from the preliminary measurement of the photo-induced holographic phase gratings that PM1 containing a chiralgroup could form holographic phase gratings buried in the films.

A Fast Algorithm for Phase Grating Preparation by Real Space Method

Making use of this expression to calculate the phase grating in high resolution image simulation can greatly reduce the calculating time. In this paper, the derivation of the expression is introduced, and then the computer routine is explained in details. Finally the potential projection map of Mg44Rh7 along [001] direction is shown as an illustration. All operations are carried out in real space, so we call the calculation method as the real space method.

Electrically tunable holographic polymer templated blue phase liquid crystal grating

In this paper, we demonstrate an alternative approach to fabricating an electrically tunable holographic polymer tem- plated blue phase liquid crystal grating. This grating is obtained by preforming a polymer template comprised of periodic fringes, and then refilling it with a blue phase liquid crystal. Compared with conventional holographic polymer dispersed liquid crystal gratings, our grating can remarkably reduce its switching voltage from 200 V to 43 V while maintaining a sub-millisecond response time. The holographic polymer templated blue phase liquid crystal （HPTBPLC） grating is free from electrode patterning, thus leading to a lower cost and more flexible applications.

Dynamic Gain Equalizer Based on the H-PDLC Volume Phase Grating

The structure and Bragg diffraction characteristics of volume phase gratings based on H-PDLC technology are presented, and the principles and simulation aided design of dynamic gain equalizers with the gratings are discussed.

Asymmetric dynamic phase holographic grating in nematic liquid crystal

A new scheme for recording a dynamic phase grating with an asymmetric profile in C60-doped homeotropically aligned nematic liquid crystal（NLC） was presented.An oblique incidence beam was used to record the thin asymmetric dynamic phase holographic grating.The diffraction efficiency we achieved is more than 40%,exceeding the theoretical limit for symmetric profile gratings.Both facts can be explained by assuming that a grating with an asymmetric saw-tooth profile is formed in the NLC.Finally,physical mechanism and mathematical model for characterizing the asymmetric phase holographic grating were presented,based on the photo-refractive-like（PR-like） effect.

Fiber Bragg Grating Sensor Array System Based on Digital Phase Generated Carrier Demodulation and Reference Compensation Method

A novel fiber Bragg grating （FBG） sensor array system based on digital phase generated carrier （PGC） demodulation and reference compensation method is proposed and set up. Experimental results confirm that the digital PGC demodulation can be used for wavelength-division-multiplexed FBG sensor array and the reference compensation method can reduce the environmental interference by approximately 40 dB in the frequency range from 20 Hz to 2 kHz. The minimum detectable wavelength-shift of the sensor system is 1 × 10^-3 pm/Hz^1/2.

Effect of Phase Modulation on Electromagnetically Induced Grating in a Five-Level M-Type Atomic System

We theoretically investigate the phenomena of electromagnetically induced grating in an M-type five-level atomic system. It is found that a weak field can be effectively diffracted into high-order directions using a standing wave coupling field, and different depths of the phase modulation can disperse the diffraction light into different orders. When the phase modulation depth is approximated to the orders of π, 2π and 3π, the first-, second- and third-order diffraction intensity reach the maximum, respectively. Thus we can take advantage of the phase modulation to control the probe light dispersing into the required high orders.

Visibility in differential phase-contrast imaging with partial coherence source

This paper gives theoretical analysis of visibility of fringes, which is influenced by distances, temporal and spatial coherence of source, in hard x-ray differential phase-contrast imaging with microfocus x-ray source. According to the character of longitudinal periodicity of the interferogram, the setup is insensitive to mechanical drift and vibrations. The effect of temporal coherence of x-ray source is investigated and its related bandwidth is derived. Based on the theory of partially coherent light, it shows that the requirement for the spatial coherence of x-ray source is not strict and can be met by the general microfocus x-ray tube for x-ray differential phase-contrast imaging.

Wavefront sensing based on phase contrast theory and coherent optical processing

A novel wavefront sensing method based on phase contrast theory and coherent optical processing is proposed. The wavefront gradient field in the object plane is modulated into intensity distribution in a gang of patterns, making highdensity detection available. By applying the method, we have also designed a wavefront sensor. It consists of a classical coherent optical processing system, a CCD detector array, two pieces of orthogonal composite sinusoidal gratings, and a mechanical structure that can perform real-time linear positioning. The simulation results prove and demonstrate the validity of the method and the sensor in high-precision measurement of the wavefront gradient field.

An Optical Fiber Hydrophone Using Equivalent Phase Shift Fiber Bragg Grating for Underwater Acoustic Measurement

An optical fiber hydrophone based on equivalent phase shift fiber Bragg grating （EPS-FBG） with temperature compensation package provides an improvement of sensitivity in underwater acoustic measurement at wide frequency range, from 2.SkHz to 12kHz. The acoustic pressure is transduced into elastic vibration of a circle metal disk, resulting in an intensity modulation of the reflected light wave back from fiber Bragg grating （FBG）. Experiment shows that the 500 EPS-FBG hydrophone has a minimum detectable acoustic pressure of about at 5 kHz and achieves about 18-dB improvement of acoustic pressure sensitivity compared with a regular apodized FBG hydrophone.

An interferometric phase shift fiber Bragg grating sensing system with greatly reduced background phase noise

We presented an interferometric phase shift fiber Bragg grating （FBG） sensor, which inherited the advantages of FBG sensors, and, at the same time, the greatly reduced full-width-at-half-maximum bandwidth brought longer coherent length, higher sensitivity, and lower phase noise. Experiments show that at least a 7 dB reduction of phase noise can be achieved compared to FBG sensors interrogated by interferometer with the same optical path difference.

Optical true time-delay for two-dimensional phased array antennas using compact fiber grating prism

A two-dimensional(2D) optical true-time delay(TTD) beam-forming system using a compact fiber grating prism(FGP) for a planar phased array antenna(PAA) is proposed. The optical beam-forming system mainly consists of a TTD unit based on the same compact FGP, one tunable laser for elevation beam steering, and a controlled wavelength converter for azimuth beam steering. A planar PAA using such 2D optical TTD unit has advantages such as compactness, low bandwidth requirement for tunable laser sources, and potential for large-scale system implementations. The proof-of-concept experiment results demonstrate the feasibility of the proposed scheme.

The Transplant of Technology of Capacitive Displacement Transducer to Phase Modulation Grating-the Research of the Grating with nm Measuring Resolution

The method rising measuring resolution through reducing pitch of the transducer has brought forward from the basic structure, principle and the corresponding relationship among pitches of capacitive electrodes, period T and phase shift of vv(x,t). But if the traditional technique of PCB made of the transducer is still used, it will meet with difficulties in lead wire. And so the technology transplant from the transducer to grating is presented, the basic principle of the phase modulation grating similar...

Writing Fiber Grating of Different Wavelength Using the Same Phase Mask

Chirped fiber grating was used in dispersion compensator. We tried to use the same phase mask to write fiber grating of different wavelength with two methods to reduce the price of the fiber grating.