Micro-electro-mechanical system-based digitally controlled optical beam profiler

An optical beam profiler is introduced that uses a two-dimensional (2-D) small-tilt micromirror device. Its key features include fast speed, digital control, low polarization sensitivity, and wavelength independence. The use of this 2-D multipixel device opens up the important possibility of realizing several beam profile measurement concepts, such as a moving knife edge, a scanning slit, a moving pinhole, a variable aperture, and a 2-D photodiode array. The experimental proof of the optical beam profiler concept using a 2-D digital micromirror device to simulate the 2-D moving knife edge indicates a small measurement error of 0.19% compared with the expected number based on a Gaussian beam-propagation analysis. Other 2-D pixel arrays such as a liquid-crystal-based 90 degrees polarization rotator sandwiched between crossed polarizers can also be exploited for the optical beam whose polarization direction is known.     

Fast, micrometer scale characterization of group-III nitrides with laboratory X-ray diffraction

We have designed a convergent beam, concurrent detection X-ray diffractometer. The instrument was built by Bruker AXS and is equipped with a rotating anode generator, a Johannson monochromator crystal for beam focusing, and a Soller slit arrangement in combination with a knife edge in front of the sample which defines the illuminated area on the sample. Samples up to 12 in. can be mounted on the sample stage of a D8 Eulerian cradle. A large area detector enables rapid simultaneous detection of the diffracted intensity. The instruments allow for a fast evaluation of large samples at high lateral resolution. In favourable cases lateral resolution down to 1 μm is possible. Furthermore a grazing incidence diffractometer has been developed which allows for depth-dependent measurements at high intensity.     

Propagation properties of a hard-edged diffracted beam generated by a Gaussian mirror resonator

Based on the scalar diffraction theory, the propagation and focusing properties of a hard-edged diffracted beam generated by a Gaussian mirror resonator were investigated. Explicit expressions for the field distribution of the truncated beam that propagates through a paraxial optical ABCD system were derived in detail. Numerical examples are given to illustrate our analytical results.     

Three-dimensional electromagnetic diffraction of a Gaussian beam by a perfectly conducting half-plane

Formulas are derived for the diffraction of a three-dimensional electromagnetic Gaussian beam by a perfectly conducting half-plane. The beam can be incident from any direction, and the main component of the electric field can point in any direction on the plane of the beam waist. The center of the beam waist is on the edge of the half-plane. The incident beam is constructed as a superposition of plane waves, and the total diffracted field is obtained from a superposition of the diffracted fields that are due to each plane wave. Physical constraints that limit the size and direction of the beam relative to the half-plane are described and incorporated into the theory. The scattered field in the far zone is obtained by asymptotic evaluation of the general formulas. Graphical results for the near-field as well as far-field patterns are presented and discussed.     

High resolution X-ray diffraction using a high brilliance source, with rapid data analysis by auto-fitting

In a production environment in particular, fast data collection and analysis, which are also highly reliable, are desirable. Measurement can be speeded up by increasing the diffracted intensity, thus reducing the time required to measure it reliably. Increased intensity with a smaller beam footprint at the sample have been achieved in a double-crystal diffractometer by the use of a novel ellipsoidal mirror working by total external reflection, positioned before the reference crystal. To optimise the performance of the mirror and provide high brightnesses, an X-ray source with a very small focal spot is required. Such a high brightness source has been made that uses electromagnetic focusing of the electron beam onto the target. Rapid data analysis is achieved by the use of an auto-fitting program that employs a genetic algorithm and the full dynamical theory of X-ray diffraction. Choice of an appropriate error function produces a deep global minimum while the genetic algorithm avoids convergence on local minima. From the model that produces the best fit, samples parameters such as layer thickness and alloy composition are extracted with quantified goodness of fit.     

Wave optical theory of in-focus Lorentz microscopy

The purpose of this paper is to evaluate the significance of Foucault-type electron micrographs of thin ferromagnetic films, taking wave optical effects into account. The film is considered as a pure phase object and the diffraction pattern is determined exactly for an extremely collimated incident beam. The illumination on the photographic plate is then evaluated when the diffraction pattern is cut by a knife edge, as a function of the position of the knife edge.     

Beam blocking method for optical characterization of surfaces

A new method for measuring local topography of optical surfaces gives excellent lateral resolution. To obtain one‐dimensional image information, the surface is mechanically scanned at a slow rate and vibrated sinusoidally in the direction of the scan. The motion lies in a plane perpendicular to an incident, focused, probing laser beam. The reflected laser beam, angularly modulated by the moving variations in the vibrating surface, is gathered by a lens and directed toward a knife‐edge and photodiode combination. One half of the beam is blocked by the knife‐edge, the orientation of which is at a right angle with respect to the angular motion of the beam. The detected signal from the photodiode is proportional to the derivative of the local slope convolved with a spread function stemming from the surface vibration and the beam profile. The operational characteristics of the proposed method are superior compared with available methods. © 2001 John Wiley & Sons, Inc. Int J Imaging Syst Technol 11, 164–169, 2000     

Comment on ‘Two-state Description of Total Polarization by Means of Singular Eigenvalue Problems’

We derive a formulation that can be used to determine the electromagnetic field distribution in the focal region of a wide-angle spherical mirror illuminated by an obliquely incident and linearly polarized plane monochromatic wave. The integrals representing the diffracted fields derived in part 1 [1] for the two cases of polarization of the incident field are first suitably expanded in series form. The integrals with respect to the azimuth 0 are then evaluated analytically with the help of some new integration formulae developed in this paper. The diffracted field components for the two cases of incident polarization are finally expressed in forms suitable for numerical computation. Our formulae can be used to determine the three-dimensional field distribution in the caustic region of the mirror for any obliquity of the incident beam. Simpler expressions for the field components for a few special cases of interest are also derived. In particular, it is shown that the series solution obtained for the case of oblique incidence reduces to the simpler results found by previous authors for the case of normal incidence.     

Integration of grating couplers in two-story waveguides for rotary displacement sensing

An integrated-optic device, constructed by stacking two types of grating coupler in a two-story structure of waveguides, is proposed for sensing angular displacement of spindle rotation. In the first story a guided wave is diffracted by a grating coupler and becomes a sensing beam. The sensing beam is reflected by a mirror with a quarter-wave plate attached to a spindle head and is coupled back into the second story by another grating coupler. We measured the rotary displacement of the spindle by detecting variation of polarization direction of the reflected beam. A prototype device has been designed and fabricated, and the operation principle is experimentally confirmed.     

Visualization of internal energy flows in optical fields carrying a pair of fractional vortices

The internal energy flows resulting from the azimuthal component of optical currents in beams carrying a pair of fractional vortices during propagation have been experimentally detected in a knife edge test. Two optical vortices of fractional charge in a beam pair up by means of a connecting dark intensity line between intensity zeros of the vortices. Independent of the polarity of the fractional vortices, this pairing up process occurs. This is in contrast to the isolated intensity null points of vortices of integer charges and thus calls for a study on the internal energy flows in such beams.     

Mutual coherence function for a double-passage retroreflected optical wave in atmospheric turbulence

The mutual coherence function in the source-receiver plane of a reflected Gaussian beam wave from a retroreflector is calculated and analyzed for two refractive-index spectral models and compared with similar results for the case of a plane mirror. Specific expressions are calculated for the mean irradiance and spatial coherence radius based on a Gaussian model for the finite reflector. Results that we obtained here using a modified spectrum with a high wave-number rise and inner scale generally show greater amplitude enhancements in the reflected wave than predicted by the pure power-law spectrum of Kolmogorov. In contrast, a finite outer scale in the spectral model leads to a reduction in the amount of beam spreading caused by turbulence and, in the case of a retroreflector, also leads to a reduction in the peak amplitude enhancement on the optical axis. This last result is in contrast with a plane mirror reflector, in which outer scale effects tend to increase the peak amplitude enhancement on the optical axis. The theory also predicts that, except for small reflectors, the coherence radius associated with a retroreflector can be as much as 1.4 times larger than that associated with a plane mirror, and 1.2 times that of a bistatic configuration for a plane mirror. All calculations are based on weak fluctuation theory and generalized spectral representations that use complex ABCD ray matrices.     

Focusing waveguide mirror with a tapered edge

We propose a focusing waveguide mirror with a shallow tapered edge in a slab waveguide and demonstrate it by planar processes and wet etching. A light beam 2 mm wide is focused to 6.5 μm full width at half-maximum at a wavelength of 0.6328 μm. A reflectivity of higher than 90% at the tapered edge is obtained. The inclination ratio of the tapered mirror edge is 1:90. Fairly good correspondence between measured and calculated focused spot sizes is obtained.     

Mathematical formulations for the schlieren detection method applied to the measurement of photodeformation

In a schlieren detection scheme for photodeformation measurements, the divergence of the probe beam that is induced by the axisymmetric but radially inhomogeneous periodic photothermal displacement of the surface of a sample is transformed into an intensity variation by insertion of an iris in front of the detection photodiode. We present three expressions for the intensity profile of a Gaussian laser beam that is reflected by the inhomogeneous photodeformation of a solid. The first expression proceeds from geometrical optics (or photometry), whereas the second one derives from the use of the well-known ABCD law and the third one from diffraction principles. Comparing these formulations of the schlieren signal with their behavior as a function of different geometrical parameters, we obtain the domain of validity of each expression, and we deduce the advantages of the different formalisms.     

荧光测钙装置中单色激发光源的设计和应用

为了满足胞内荧光测钙实验的需要,设计了一种新型的单色激发光源。其中,短弧氙灯发出的光经椭球反射镜聚焦后采用抛物面反射镜准直成平行光,通过光栅的衍射分光后又经过会聚物镜把光能量会聚到光纤端面,光纤的另一端面输出单色光。采用光路偏折的方法,有效地克服了灯源的噪声。结果显示,波长为340nm和380nm的光能量分别可达到30mW和120mW,能很好地满足荧光测钙实验的要求。     

Decreasing the total divergence of polycapillary X-ray microbeams

The divergence characteristics of intense quasi-parallel X-ray microbeams have been studied at the output of the “microfocus X-ray generator-cylindrical polycapillary structure” system by scanning the beam with a knife edge. It us established that the total microbeam divergence decreases in the region near the output edge of the polycapillary structure (divergence quasi-decrease effect).     

Beam separator for high-order harmonic radiation in the 3-10 nm spectral region

We present the scheme of a beam separator for ultrashort high-order harmonic radiation below 10 nm. The system consists of a collimating mirror and two plane grazing-incidence gratings in compensated configuration. The first grating acts as the beam separator: it diffracts the extreme ultraviolet (XUV) light into the first order while reflecting the fundamental laser beam into the zero order. The diffracted light goes to a second grating that compensates both for the spectral dispersion and for the temporal broadening of the XUV ultrashort pulse caused by the diffraction at the first grating. The system can be designed for any wavelength in the 3-40 nm region. Since the gratings are operated at extreme grazing incidence, the area of the optical surface illuminated by the fundamental laser pulse is large, and therefore there is no risk of damage of the optical surfaces. The effects on the phase of the ultrashort pulse for narrowband applications are discussed.     

Calibration standard for laser beam profilers: method for absolute accuracy measurement with a Fresnel diffraction test pattern

The absolute accuracy of a clip-level laser beam profiler is measured to the 0.3% level, by comparison of the profiler's reading to the known width of a Fresnel diffraction test pattern. A pair of opposed knife edges, illuminated by a quasi-uniform and quasi-plane wave, generates the pattern whose width is determined by the 50% cut points in translating the edge pair across a tightly focused beam. The convolution of the scanning aperture with the diffraction fringe pattern is modeled to remove the effect of the aperture size from the accuracy test and to give a means of measuring the aperture width. Discussions of the experimental aspects of this test method show it to be an acceptable calibration standard for optical profilers, of use to those working on the International Standards Organization draft standard for laser beam parameter measurements.     

Two-dimensional Raman-Nath acousto-optic bistability by use of frequency feedback

From the frequency dependence of the optical transmission characteristics of Raman-Nath acoustic-optic diffraction, the dynamic equations and steady-state solutions of a two-dimensional Raman-Nath acousto-optic bistable system are derived. In this system, feedback is realized by use of a diffracted light beam to control the frequency of the acoustic-optic driver. The curves of light output versus input corresponding to several orders of the diffracted beams are obtained by theoretical analysis. They can all lead to bistability. The amount of hysteresis is a function of the order of the diffracted beam, the bias frequency, and the feedback coefficient. Experimental results are presented and compared with theoretical analyses.     

Propagation characteristics of a diffracted M2 beam

The propagation characteristics of a beam diffracted by a circular aperture are investigated. The beam-quality factor M2 defined by an 86.5% power-content radius is given theoretically and experimentally as a function of the truncation ratio. It is found that the theoretical limit of M2 is 2.37 times as great as that of an incident beam as the truncation ratio approaches 0. For a weakly diffracted beam a simple formula giving M2 is derived. Although M2 does not increase much with diffraction, the influence of diffraction should be taken into account in beam brightness.     

Phase-shifting schlieren: high-resolution quantitative schlieren that uses the phase-shifting technique principle

A quantitative autocalibrated high-resolution schlieren technique for quantitative measurement of reflective surface shape is proposed. It combines the schlieren principle with the phase-shifting technique that is generally used in interferometry. With an appropriate schlieren filter and appropriately tailored setup, some schlieren fringes are generated. After application of the phase-shift technique, the schlieren phase is calculated and converted into beam deviation values. Theoretical and experimental demonstrations are given. The technique is validated on a reference target, and then its application in a fluid physics experiment is demonstrated. These two examples show the potential of the phase-shifting schlieren technique that in some situations can become competitive with interferometry but with a much better dynamic range and with variable sensitivity. The technique can also be used to measure refractive-index gradients in transparent media.