X-ray Compound Refractive Lenses Research Articles

Study on the focusing performance of the compound X-ray refractive lenses with fabrication errors

The compound X-ray refractive lens is a kind of optical components for X-rays focusing and imaging. This paper reports the authors’ research on focusing performance of the compound X-ray refractive lens with fabrication errors. Firstly SEM measurements of the semi-cylindrical PMMA compound X-ray refractive lens fabricated by means of deep X-ray lithography are performed, and accordingly the fabrication errors are measured. Then the theoretical analysis and simulations are done for the focusing performance of the compound X-ray refractive lens with the fabrication errors. Finally, X-ray microbeam experimental system is built on the 4W1A beamline of Beijing Synchrotron Radiation Facility (BSRF) for measuring the focusing performance of the semi-cylindrical PMMA X-ray refractive lenses we fabricated. And the focusing performances of the semi-cylindrical PMMA compound X-ray refractive lenses with and without distinct fabrication errors are measured and analyzed under 8 keV monochromatic X-rays.

X射线长组合折射透镜的理论和实验研究

X射线长组合折射透镜的理论和实验研究

Theoretical and experimental results of focusing performance for the parabolic compound X-ray refractive lenses

The parabolic compound X-ray refractive lenses are a kind of novel optical components, especially suitable for hard X-rays. Due to their parabolic profiles they are free of spherical aberration and are proper devices for sub-micrometer focusing and imaging. The focusing performance of the parabolic compound X-ray refractive lenses is studied theoretically and experimentally in this paper. Firstly, the derivation of the exact focal length formula using matrix optics method and a criterion of the thin lens approximation are described. And the intensity distribution near focus, limiting focal spot size, effective aperture and transmittance are deduced based on the diffraction theory. Several parabolic compound X-ray refractive lenses with PMMA material were fabricated by means of deep X-ray lithography. Then the X-ray microbeam experimental system was built on the 4W1A beamline of Beijing Synchrotron Radiation Facility （BSRF） based on the parabolic compound X-ray refractive lenses we fabricated. The focusing performances of three PMMA parabolic compound X-ray refractive lenses were measured and analyzed under 8 keV monochromatic X-rays. According to the experimental results, it is concluded that the PMMA parabolic compound X-ray refractive lenses promises good hard X-ray focusing performance.

Hourglass-shaped X-ray compound refractive lens made by back-mask exposure technology

Using back-mask exposure technology，the hourglass-shaped X-ray compound refractive lens （XCRL） was made. Firstly，the theory of the refractive focusing of the hourglass-shaped XCRL was analyzed. Then the hourglass-shaped XCRL was manufactured using back-mask exposure technology for the first time，which avoids two-time masking and reduces the transfer times of the figure. The refractive focusing performance of the lens was tested with 10?keV monochromatic X-ray. The experimental results indicated that it has good focusing performance in one dimension, which is in general coincident with the calculated results.

Fabrication and performance of 2-D compound X-ray refractive lenses

Due to the weak refraction of X-rays in matter, a focusing or deflection of X-ray using conventional refractive optics was not feasible. However, since compound X-ray refractive lens (CXRL) with consecutive holes array was proposed, it becomes currently a noticeable issue in X-ray optics. In this paper, we report on fabrication and performance test of two types of PMMA (polymethyl methacrylate) CXRLs. Firstly, one dimensional refractive X-ray lenses of parabolic and circular shape is fabricated by LIGA process. Based on the results, we conduct a fabrication of 2-D CXRLs. Here we suggest a LIGA-self align method which doesn’t need a special align equipment and is simpler method than conventional one. Through performance tests, we show experimentally that CXRLs are novel optical components for the hard X-ray range of about 8 keV and that they have possibilities to apply the X-ray optics for micro-focusing, imaging, and lithography.

Fabrication of PMMA X-ray Compound Refractive Lenses for the Pohang Light Source and Performance Tests

Fabrication of PMMA X-ray Compound Refractive Lenses for the Pohang Light Source and Performance Tests

Development, production, and investigation of PMMA-based X-ray compound refractive lenses

Equipment and technology for producing X-ray refractive lenses from polymethyl methacrylate are described. Each single lens has a spherical profile with a radius of 2.38 mm. A compound lens is composed of 235 single lenses. The focal length of the compound lens for 14-keV X-ray photons is 4.8 m. The lenses developed thereby have been tested on the synchrotron radiation source of the Scientific and Engineering Complex at the Kurchatov Centre of Synchrotron Radiation and Nanotechnologies. The advantages and the drawbacks of the parabolic and spherical lenses are discussed.

The Compound Refractive Lens for Hard X-ray Focusing

The compound refractive X-ray lens (CRL) for focusing hard X-rays is investigated to determine the parameters such as the focal length, the focal spot size, and spatial distribution at the focal spot using a simple theoretical calculations and CRLs fabricated by the self-assembly method. The number of individual compound lenses are defined for the given focal length of 1 m. The X-ray energy of 1 to 40 keV is used in the calculations. The CRL for focusing hard X-rays which generated from the X-ray tube is fabricated by nanoparticle-polymer composite in the form of circular concaves. The self-assembly method is applied to form the nanoaluminum-poly (methly meth-acrylate) composite and carbon-polymer composite CRL lenses. Aluminum nanoparticles of 100 nm and carbon microparticles are diffused in the polymer solution then the high gravity up to 6000G is applied in it to form the concave lens shape. X-ray energy at 8 keV is used for characterization of the composite CRLs. The FWHM of intensity for the fabricated nanoaluminium composite CRL system, N=10 is measured as 1.8 mm, which would give about $70{\mu}m$ in FWHM at 1 m of the focal length.

Ray-tracing simulation of parabolic compound refractive lenses

X-ray compound refractive lenses (CRL) are becoming a widespread tool for the generation of microfocus spot sizes at synchrotron beamlines. The calculation of their performance by means of ray-tracing is useful for a rapid estimation of flux, resolution and focusing properties achievable in a beamline, when other optics are present, or simply to study the lens acceptance and focusing in the presence of a particular bending magnet, wiggler or undulator X-ray source. The ray-tracing method presented in this paper has been used to calculate the efficiency of beryllium CRL's using, for the instrument layout, realistic source size and divergence, and usual optics like perfect crystal monochromators. It is shown that the intensity transmitted by the lens, the effective aperture and the gain are in good agreement with analytical formulas. Additional information provided when running the program are the precise shape of beam at the focus, and at any position along the optical axis. For instance the intensity distribution at the CRL entrance and exit planes allows a comparison between the effective and the geometrical apertures. Finally, the method provides a precise value for the lens focal distance, which depends on the CRL length.

Study of SR beam focusing with X-ray compound refractive lenses at the VEPP-3 storage ring

X-ray compound refractive lenses (CRLs) are successfully applied in many experiments with synchrotron radiation, especially, at the third generation SR sources. At the same time, advantages of CRL employment at SR sources of previous generations with larger source sizes are not so obvious, and it seems to be useful to reveal the conditions and the experiments in which application of CRLs could be effective. With this purpose, first study of SR beam focusing by plastic planar lenses with a parabolic profile in the photon energy range from 10.4 to 14 keV was carried out at the VEPP-3 storage ring. Three different experimental techniques were applied to measure intensity distribution in the focal line. The measured focused beam line was 17–18 μm and the real gain in intensity was about 7. The obtained values differ from the expected calculated ones by a factor of about 2. The possible reasons of this discrepancy and potential employment of CRLs in real SR experiments at the VEPP-3 are discussed.

A formulation for the performance of compound x-ray refractive lenses

A theoretical method for describing the focusing of x-rays by compound x-ray refractive lenses is presented in this paper. The first moment, the second moment, and the standard deviation in the theory of probability are used to clarify the roles of the parameters of the compound lenses in the optical performances. As an example, the structural parameters for a compound x-ray refractive lens made of Si are designed. Also the focusing performance and transmission efficiency are calculated numerically, and the results given for 4.95, 14.99, and 29.78 keV x-rays.

Specific properties of X-ray compound refractive lens. Theoretical analysis

We present the diffraction theory for the x-ray compound refractive lens (XCRL) operation as an imaging device in the paraxial approximation. We obtain the analytical expression for the image propagator in the case of parabolic XCRL that allows us to explain the peculiarities of imaging and focusing with the XCRL observed previously in the experiments. We propose the enhanced thin lens formula for the relatively long XCRL with the longitudinal size L taking into account the linear corrections in L/F where F is the focal length in the thin lens approximation. A relatively small aperture of XCRL due to absorption of x rays limits the resolution and, in addition, leads to phase effects visualizing the local phase gradient of the radiation wave field produced by transparent objects. This opens novel technique of imaging for purely phase objects, which is different from the in-line phase contrast imaging techniques. Since the first demonstration (1) of the x-ray compound refractive lens (XCRL) for focusing a synchrotron radiation beam, the x-ray refractive optics is under extensive development. There are successful attempts to develop the refractive optics by means of various approaches. The XCRL with a parabolic profile of surfaces is more promising (2-5). Unlike visible optics, collecting XCRL has a concave shape and the material of the lens is always absorbing. The latter leads to a significant limitation of the effective aperture aγ which is smaller than the physical transverse size a of the XCRL. This property influences the XCRL operation as an imaging device. The XCRL has a rather large longitudinal size L, therefore the thin lens approximation must be verified. In most practical cases XCRL satisfies the condition L/F << 1, where F is the focal length in the thin lens approximation, so that the linear corrections in L/F are sufficient. In this work we present the diffraction theory for the parabolic planar (1D) XCRL in paraxial approximation. We solve the parabolic wave equation in terms of propagators. We calculate analytically the intermediate convolutions and obtain the image propagator which connects straightforwardly the wave field Ao(x) at the plane just after the object and the wave field Ai(x) at the image (detector) plane . Due to a relatively small effective aperture of the XCRL the image propagator stays the gauss function of finite width instead of the delta-function. This leads to developing phase or edge enhanced imaging effects, which make visible transparent objects at the image plane. We found out that these edge-enhanced images are associated with the local phase gradient of the wave field Ao(x). Moreover, these images are sensitive to the sign of the phase gradient. This opens quite a new technique of microimaging for purely phase objects, which is different from the traditional phase contrast microimaging techniques.

Diffraction theory of imaging with X-ray compound refractive lens

Specific features of X-ray compound refractive lens (XCRL) with parabolic profile of concave surfaces for hard Xray focusing and micro-imaging are analyzed theoretically. Large longitudinal size L of the XCRL requires a verification of the thin lens approximation widely used in the literature. We show that the parabolic XCRL can be treated as a thin lens placed in the middle of the XCRL with the focal length Fl ¼ F þ L=6, where F is the XCRL focal distance in the thin lens approximation. The relatively small aperture of XCRL due to the absorption of X-rays leads to finite resolution and phase effects (or artifacts) of the images. This feature reveals itself as a visibility of transparent objects. It is shown that XCRL allows one to visualize the local phase gradient of the radiation wave field produced by the object. This opens quite a new technique of micro-imaging for purely phase objects which is different from the traditional phase contrast micro-imaging techniques. Optical properties of XCRL as a Fourier transformer are considered as well. 2002 Elsevier Science B.V. All rights reserved.

Refractive X-ray lens for high pressure experiments at SPring-8

A stacked compound refractive X-ray lens was designed to produce an efficiently focused ( ϕ<0.1 mm) beam for high-pressure experiments at SPring-8. High-pressure X-ray diffraction requires an intense, high-energy and monochromatic X-ray beam in order to penetrate the absorptive window of a diamond anvil cell (DAC). Our lens, producing a focal spot of 120×275 μm 2 and a peak gain of 12, is well matched to these requirements. It is composed of many plastic chips made by molding, which allows many identical chips to be made precisely. Other advantages of this lens include high throughput, simple energy tunability and easy installation.

Glass capillary X-ray lens: fabrication technique and ray tracing calculations

A new method for producing a compound refractive X-ray lens is described. The lens is designed as glass capillary filled by a set of concave individual lenses. The method is appropriate for the preparation of 10–1000 spherical lenses in a glass capillary with a diameter of 0.1–1 mm. Lens aberrations are considered and simple formulas for spot size are derived. Ray-tracing simulations on the focusing experiments using 18 keV X-rays are reported.

Cylindrical compound refractive x-ray lenses using plastic substrates

We have measured the intensity profile of x rays focused by compound refractive lenses (CRLs) fabricated using acrylic (Lucite) and polyethylene plastics. A linear array of closely spaced holes acts as multiple cylindrical lenses. The important parameters for this type of focusing are the focal length and absorption, and, for wavelengths shorter than 3 Å, low atomic number plastics are suitable. We have experimentally demonstrated that we can achieve one-dimensional focusing for photon energies between 9 and 19.5 keV with focal lengths between 20 and 100 cm. For example, using 12 keV x rays we have achieved focal full width at half maximum linewidths down to 21 μm at a distance of only 20 cm from the CRL. The x-ray source was a synchrotron emitter whose source size in the vertical dimension was 445 μm.