Modelling the effects of optical vibrations on photon beam parameters using ray-tracing software.

A method to simulate beam properties observed at the beamline sample-point in the presence of motion of optical components has been developed at Diamond Light Source. A series of stationary ray-tracing simulations are used to model the impact on the beam stability caused by dynamic motion of optical elements. Ray-tracing simulations using SHADOW3 in OASYS, completed over multiple iterations and stitched together, permit the modelling of a pseudo-dynamic beamline. As beamline detectors operating at higher frequencies become more common, beam stability is crucial. Synchrotron ring upgrades to low-emittance lattices require increased stability of beamlines in order to conserve beam brightness. By simulating the change in beam size and position, an estimate of the impact the motion of various components have on stability is possible. The results presented in this paper focus on modelling the physical vibration of optical elements. Multiple beam parameters can be analysed in succession without manual input. The simulation code is described and the initial results obtained are presented. This method can be applied during beamline design and operation for the identification of optical elements that may introduce large errors in the beam properties at the sample-point.

Development of a multi-lane X-ray mirror providing variable beam sizes.

Grazing incidence mirrors are used on most X-ray synchrotron beamlines to focus, collimate or suppress harmonics. Increasingly beamline users are demanding variable beam shapes and sizes at the sample position. We have now developed a new concept to rapidly vary the beam size and shape of a focused X-ray beam. The surface of an elliptically figured mirror is divided into a number of laterally separated lanes, each of which is given an additional longitudinal height profile calculated to shape the X-ray beam to a top-hat profile in the focal plane. We have now fabricated two prototype mirrors and present the results of metrology tests and measurements made with one of the mirrors focusing the X-rays on a synchrotron beamline. We envisage that such mirrors could be widely applied to rapid beam-size switching on many synchrotron beamlines.

Nanofocusing optics for synchrotron radiation made from polycrystalline diamond.

Diamond possesses many extreme properties that make it an ideal material for fabricating nanofocusing x-ray optics. Refractive lenses made from diamond are able to focus x-ray radiation with high efficiency but without compromising the brilliance of the beam. Electron-beam lithography and deep reactive-ion etching of silicon substrates have been used in a transfer-molding technique to fabricate diamond optics with vertical and smooth sidewalls. Latest generation compound refractive lenses have seen an improvement in the quality and uniformity of the optical structures, resulting in an increase in their focusing ability. Synchrotron beamline tests of two recent lens arrays, corresponding to two different diamond morphologies, are described. Focal line-widths down to 210 nm, using a nanocrystalline diamond lens array and a beam energy of E = 11 keV, and 230 nm, using a microcrystalline diamond lens at E = 15 keV, have been measured using the Diamond Light Source Ltd. B16 beamline. This focusing prowess is combined with relatively high transmission through the lenses compared with silicon refractive designs and other diffractive optics.

High efficiency nano-focusing kinoform optics for synchrotron radiation.

Modern synchrotron sources have provided for decades intense beams of photons over a large energy spectrum. The availability of improved optics and detectors has opened up new opportunities for the study of matter at the micrometre and nanometre scale in many disciplines. Whilst exploitation of micro-focused beams occurs almost daily in many beamlines, the production of beams of 100 nm is achieved on few instruments which use specialised optics. Refractive lenses, zone plates, curved mirrors, multilayers, and multilayer Laue lenses, can all focus x-rays to less than 50 nm under strict beam stability conditions. Focusing the synchrotron radiation to beam sizes smaller than 10 nm is considered the ultimate goal for the current decade. Silicon micro-technology has so far provided some of the most advanced x-ray refractive lenses; we report on design and characterisation of a novel silicon kinoform lens that is capable of delivering nano-beams with high efficiency.

Application of kinoform lens for X-ray reflectivity analysis.

In this paper the first practical application of kinoform lenses for the X-ray reflectivity characterization of thin layered materials is demonstrated. The focused X-ray beam generated from a kinoform lens, a line of nominal size approximately 50 microm x 2 microm, provides a unique possibility to measure the X-ray reflectivities of thin layered materials in sample scanning mode. Moreover, the small footprint of the X-ray beam, generated on the sample surface at grazing incidence angles, enables one to measure the absolute X-ray reflectivities. This approach has been tested by analyzing a few thin multilayer structures. The advantages achieved over the conventional X-ray reflectivity technique are discussed and demonstrated by measurements.

Characterization of germanium linear kinoform lenses at Diamond Light Source.

The unprecedented brilliance achieved by third-generation synchrotron sources and the availability of improved optics have opened up new opportunities for the study of materials at the micrometre and nanometre scale. Focusing the synchrotron radiation to smaller and smaller beams is having a huge impact on a wide research area at synchrotrons. The key to the exploitation of the improved sources is the development of novel optics that deliver narrow beams without loss of brilliance and coherence. Several types of synchrotron focusing optics are successfully fabricated using advanced miniaturization techniques. Kinoform refractive lenses are being developed for hard X-ray beamlines, and the first test results at Diamond are discussed in this paper.

Accuracy of the diffusion equation to describe photon migration through an infinite medium: numerical and experimental investigation.

The accuracy of results obtained from the diffusion equation (DE) has been investigated for the case of an isotropic point source in a homogeneous, weakly absorbing, infinite medium. The results from the DE have been compared both with numerical solutions of the radiative transfer equation obtained with Monte Carlo (MC) simulations and with cw experimental results. Comparisons showed that for the cw fluence rate, discrepancies are of the same order as statistical fluctuations on MC results (within 1%) when the distance r from the source is > 2/mu(s)', (mu(s)' is the reduced scattering coefficient). For these values of r, discrepancies for the time-resolved fluence rate are of the same order of statistical fluctuations (within 5%) when the time of flight is t > 4t0 with to time of flight for unscattered photons. For shorter times the DE overestimates the fluence discrepancies are larger for larger values of the asymmetry factor. As to the specific intensity, for small values of r the MC results are more forward peaked than expected from the DE, and the forward peak is stronger for photons arriving at short times. We assumed r > 2/mu(s)' and t > 4t0 for the domain of validity of the DE and we determined the requirements for which the simplifying assumptions necessary to obtain the DE, expressed by two inequalities, are fulfilled. Comparisons with cw experimental results showed a good agreement with MC results both at high and at small values of r mu(s)', while the comparison with the DE showed significant discrepancies for small values of r mu(s)'. Using MC results we also investigated the error made on the optical properties of the medium when they are retrieved using the solution of the DE. To obtain accuracy better than 1% from fitting procedures on time-resolved fluence rate data it is necessary to disregard photons with time of flight < 4t0. Also from cw data it is possible to retrieve the optical properties with good accuracy: by using the added absorber technique discrepancies are < 1%, both on mu(s)' and on mu(a), if the absorption coefficient is small (mu(a)/mu(s)' < 0.005).

Method for measuring the mean time of flight spent by photons inside a volume element of a highly diffusing medium.

A method of measuring the mean time of flight, ?t(i)? , spent by photons inside a generic volume element of a highly diffusing medium is presented. The method comes from a general property of the radiative transfer equation and is based on relative measurements of cw attenuation that correspond to small variations of the absorption coefficient inside the volume element. By use of a liquid phantom and small gels with known optical properties it was possible to measure ?t(i)? with good accuracy, even when it was only a few picoseconds long. The results were in good agreement with Monte Carlo results.

Monte carlo procedure for investigating light propagation and imaging of highly scattering media.

A Monte Carlo procedure has been developed to study photon migration through highly scattering nonhomogeneous media. When two scaling relationships are used, the temporal response when scattering or absorbing inhomogeneities are introduced can be evaluated in a short time from the results of only one simulation carried out for the homogeneous medium. Examples of applications to the imaging of defects embedded into a diffusing slab, a model usually used for optical mammography, are given. Comparisons with experimental results show the correctness of the results obtained.