<title>High-resolution absolute position detection using a multiple grating</title>

Several new types of absolute optical encoders of both rotary and linear function are discussed. The means for encoding are complete departures from conventional optical encoders and offer advantages of reliability, compact form, immunity to damage-induced dropouts of position information, and about an order of magnitude higher sensitivity over what is commercially available. Rotary versions have sensitivity from 0.02 arcseconds down to 0.003 arcsecond while linear models have demonstrated sensitivity of 10 nm (0.01 micrometers ) with higher sensitivities possible.

The diffraction efficiency of gratings etched into fused silica was measured and modelled. 950, 2120 and 3710 nm period gratings were fabricated with the use of two-beam interferometric laser-induced backside wet etching (TWIN-LIBWE). The spatial distribution of the modulation depth (MD), determined from AFM measurements, followed the spatial intensity distribution of the laser beam throughout the grooved areas. The diffraction efficiency of the fabricated gratings was measured to all allowed diffraction orders at several wavelengths (266, 532 and 654.5 nm). Within the frame of Gsolver code, a model was developed that takes into account the spatial distribution of MD. The computed diffraction efficiencies showed good agreement with the results of measurements.

Machine learning-based method for linearization and error compensation of a novel absolute rotary encoder

We report on hard x-ray phase contrast imaging experiments using a grating interferometer of approximately 1/10th the grating period achieved in previous studies. We designed the gratings as a staircase array of multilayer stacks which are fabricated in a single thin film deposition process. We performed the experiments at 19 keV x-ray energy and 0.8 μm pixel resolution. The small grating period resulted in clear separation of different diffraction orders and multiple images on the detector. A slitted beam was used to remove overlap of the images from the different diffraction orders. The phase contrast images showed detailed features as small as 10 μm, and demonstrated the feasibility of high resolution x-ray phase contrast imaging with nanometer scale gratings.

The development of a multi-turn absolute encoder—a new concept in accordance with a design insensitive to accuracy

UV imprint fabrication of polymeric scales for optical rotary encoders

Dense wavelength division multiplexing (DWDM) is an important technology for expanding the capacity of optical network. The optical component based on the superimposed Bragg gratings shows that it can be used as one of advantageous multichannel components because of its excellent angle and wavelength selectivities. An optimized method for recording multiple Bragg gratings for wavelength demultiplexing in optical telecommunication band is proposed to achieve gratings with equal diffraction efficiency. A structure of three layers with twenty four gratings is demonstrated in a LiNbO(3):Fe crystal by employing the optimized recording method. Then an initial wavelength demultiplexing experiment based on the formed gratings is carried out in optical telecommunication C-band. The results obtained by measuring and analyzing the transmitted spectra of the fabricated gratings show that the diffraction efficiencies of the gratings are uniform. It is suggested that this kind of multiple gratings can be used for increasing the number of the demultiplexed wavelengths in recording medium with unit volume for WDM.

The low efficiency of conventional single layer gratings at the tender X-ray region (E=1~5 keV) significantly limits the photon flux of the beamline and the development of related imaging and spectroscopy experiments in this region. To overcome this issue, multilayer coated gratings have been proposed and developed. The diffraction behavior of a multilayer grating is more complex than a single layer grating. To understand the diffraction behavior and exert the maximum potential of this new optics, we have built an analytical theory based on coupled wave theory. A high efficiency single order diffraction regime was first identified which means only one diffraction order will be excited with a certain incidence angle and structure parameters. This is applicable to blazed multilayer gratings (BMGs). To achieve maximum efficiency, the optimum grating and multilayer structures were analyzed. The highest theoretical efficiency of a BMG can reach the same value of the coated multilayer reflectance. Moreover, blazed multilayer gratings exhibit the advantage of high harmonics suppression. For the BMG, the conventional condition of maximal diffraction efficiency, Dsinα = nd, where D and d is the grating period and multilayer period, respectively, α is blaze angle, n is diffraction order, has been proved invalid. This is due to the contribution of anti-blaze facets to diffraction and effect of strongly asymmetric diffraction. Based on these, a Cr/C BMG was fabricated in collaboration with the Department for Nanometer Optics and Technology in BESSY-II. Maximum efficiency of up to 60% was demonstrated at 3 keV which is close to the theoretical prediction.

Holographic polymer dispersed liquid crystal (HPDLC) based distributed feedback (DFB) lasers were prepared with poly (-methoxy-5-(2′-ethyl-hexyloxy)-1,4-phenylene-vinylene) (MEH-PPV) film as the active medium layer. The HPDLC grating film was fabricated via holographic induced photopolymerization. The pure film spectra of MEH-PPV and the amplified spontaneous emission (ASE) spectrum were investigated. The laser device was single-longitudinal mode operation. The tunability of the HPDLC DFB laser was achieved by selecting different grating periods. The lasing performances were also characterized and compared from different diffraction orders. The lasing threshold increased with the diffraction order and the third order laser possessed the largest conversion efficiency in this device. The experimental results were in good agreement with the theoretical calculations.

We present the theory of the diffraction of electromagnetic waves by generalized spacetime periodic diffraction gratings. It is shown that such gratings produce spatial and temporal diffraction orders, yielding a quite unique diffraction pattern, not seen in conventional spatially periodic diffraction gratings. We show that in contrast with conventional static gratings, spacetime periodic diffraction gratings generate both spatial and temporal diffraction orders, where each spatial diffraction order is formed by an infinite set of temporal diffraction orders. Such dynamic gratings offer enhanced functionalities and unique characteristics, e.g., an asymmetric diffraction pattern, nonreciprocal transmissive and reflective diffraction, and enhanced diffraction efficiency. In addition, the theoretical analysis of the structure is supported by time and frequency domain FDTD numerical simulation results.

Design of large-deflection-angle high-diffraction-efficiency high-dispersion hybrid gratings

This work presents the development of a meso-scale machine tool with a nanometer resolution. The newly developed meso-scale machine tool consists of a pagoda structure for Z-axis, four HR8 ultrasonic motors, three linear encoders with a resolution of 2 nm, a coaxial counter-balance system, a XY coplanar positioning stage, a rotary stage, a Galil 4-axis motion control card, an industrial PC and a CCD camera system. The optimal geometrical dimensions of the pagoda structure have been determined by ANSYS software. The designed meso-scale machine tool is equipped with an X–Y coplanar positioning stage with nanometer resolution. The coplanar stage developed by National Taiwan University was integrated with two linear encoders, so that a two-axis closed-loop control was possible. A circular positioning test with the radius of 1 mm using the developed stage was tested, and the overall circular positioning error was about 83 nm based on the test results. The micro V-grooves and the micro pyramid cutting tests of the polished oxygen free copper using a single crystal diamond tool on the developed meso-scale machine tool have been performed. The cutting tests under various combination of the depth of cut and cutting speed have been carried out. It revealed that the cutting speed had no great influence on the cutting force. The measured cutting forces for the depth of cut of 5, 10, 15 μm were 1.2, 1.6 and 2.4 N, respectively. The results showed the meso-scale machining tool can be used in micro pyramid structures manufacturing.

We describe a wavelength multiplexer design that employs multiple transmission volume Bragg gratings written in the same region of a photosensitive glass having a through channel loss of < 0.5 dB. A two-channel multiplexer for wavelengths of lambda = 1310 and 1550 nm is demonstrated to test our design methods and assumptions. Agreement between simulation and experiment is within 0.2 dB at the peak diffraction efficiency. Grating apodization is used to reduce the interchannel cross talk from (13.5 +/- 0.5) to (41.5 +/- 8.5) dB, with an experimental through channel loss of (0.6 +/- 0.2) dB. Effects of angular dispersion on diffraction efficiency and grating spectral shape due to the finite diameter of the incident reading beam are also analyzed.

Here we report on the fabrication and analysis of two different types of laterally structured multilayers, which act as highly efficient x-ray optical elements for focusing or spectral dispersion of soft x-rays at (near) normal incidence. The microfocusing of soft x-rays at (near) normal incidence with plane reflection optics can be obtained by multilayer Bragg-Fresnel zone plates. A circular condensor zone plate structure (2.9 mm diameter, 417 zones, inner zone radius 50 micrometers , outer zone width 0.9 micrometers ) has been recorded by holographic lithography followed by ion beam etching into a Mo-Si multilayer mirror of 24 periods and a doublelayer thickness of 7.2 nm. The focusing properties analyzed by soft x-ray reflectometry at (lambda) equals 13.8 nm show a focal spot size smaller than 40 micrometers measured 160 mm behind the multilayer zone plate. Multilayer blazed gratings offer the opportunity for highly resolved spectral dispersion of soft x-rays due to the possible combination of high efficiency and high diffraction orders with almost the whole intensity diffracted in one diffraction order. The sawtooth profile of a blazed grating structure (1221 l/mm, blaze angle 1.5 degree(s)) has been ruled into a 200 nm thick Au-film which has been deposited onto a plane glass substrate. A Mo/Si multilayer of 15 periods and a doublelayer thickness of 7.2 nm has been deposited onto the grating substrate. In order to smooth the rough Au-surface and to prevent interdiffusion of the Au-film with the upper Mo-Si multilayer a carbon film has been evaporated onto the Au-grating surface before the deposition of the soft x-ray coating. This procedure results in a significant increase of diffraction efficiency. The multilayer grating has been matched working on blaze in the third diffraction order, where an absolute diffraction efficiency of 3.4% at (lambda) equals 14 nm has been measured, while only 1.1% has been achieved for a similar grating without a carbon interlayer.

High diffraction efficiency and large diffraction angle are two major concerns in designing a liquid crystal (LC) phase grating for its applications in beam diffractive devices. High-spatial-frequency grating is capable of providing a large diffraction angle. However, fringing-field effect becomes more severe when the grating pitch size decreases, which imposes a limitation on the phase modulation depth and the diffraction efficiency of the LC grating. In this paper, a novel LC grating with striped electrodes patterned on both the top and bottom sides was proposed and fabricated. By using a specified biasing configuration, vertical electric fields are generated and well confined between the facing electrodes. Meanwhile, horizontal electrical fields are created between adjacent electrodes which help reducing the undesirable deformation of the LC director axis resulting from the fringing filed. Computer simulations show, in our novel structure, a maximum phase modulation depth of 4.15 rad (for 1.55 μm) can be achieved, which is large enough to satisfy the 1.17 π phase-shift requirement for maximum first order diffraction in sinusoidal phase gratings. Both the conventional single-sided and the novel double-sided LC gratings were fabricated and tested. Measurements showed, there was an efficiency enhancement of 77 times achieved by the double-sided structure comparing the conventional structure. A first order diffraction with diffraction angle at 14.5o and diffraction efficiency of ~31% is experimentally achieved, of which the efficiency approaches the theoretical upper limit at 33.8% for a sinusoidal phase grating.