We have measured the intensity profile and transmission of x rays focused by a series of either spherical or parabolic lenses fabricated using Mylar® (C5H4O2) or Kapton® (polyimide). The use of plastics can extend the range of operation of compound refractive lenses, improving transmission and aperture size and reducing focal length. The number of unit lenses range from 193 to 600 for each compound refractive lens. Two-dimensional focusing was obtained for photon energies 8–14 keV with imaging distances of less than 1 m. For example, full-width-half-maximum linewidths down to 16 μm at a distance of only 47 cm from the lens were achieved at 9 keV. The effective apertures of the refractive lenses were measured between 250 and 364 μm with peak transmissions between 10% and 33%.

Images obtained with a high-magnification simple neutron microscope using a compound refractive lens are presented in this letter. The short focal length of the stack of Al biconcave lenses facilitated the setup of a simple neutron microscope at the D22 small angle scattering beam line at the Institut Laue Langevin, Grenoble, France that achieved a 35× magnification and a 214 μm resolution. Higher-resolution images could be obtained using improved neutron lens systems that enhance beam delivery from neutron sources and produce high-quality images in combination with higher resolution two-dimensional neutron detectors.

A compound refractive lens (CRL), consisting of a series of N closely spaced lens elements each of which contributes a small fraction of the total focusing, can be used to focus x rays or neutrons. The thickness of a CRL can be comparable to its focal length, whereupon a thick-lens analysis must be performed. In contrast with the conventional optical lens, where the ray inside the lens follows a straight line, the ray inside the CRL is continually changing direction because of the multiple refracting surfaces. Thus the matrix representation for the thick CRL is quite different from that for the thick optical lens. Principal planes can be defined such that the thick-lens matrix can be converted to that of a thin lens. For a thick lens the focal length is greater than for a thin lens with the same lens curvature, but this lengthening effect is less for the CRL than for the conventional optical lens.

We have measured the intensity profile and transmission of x rays focused by a series of biconcave spherical unit lenses fabricated from beryllium. The use of beryllium extends the range of operation of compound refractive lenses, improving transmission, aperture size, and gain. The compound refractive lens was composed of 160 biconcave unit lenses, each with a radius of curvature of 1.9 mm. Two-dimensional focusing with a gain of 1.5 was obtained at 6.5 keV with a focal length of 93 cm. The effective aperture of the compound refractive lens was measured as 600 mum , with 9% peak transmission.

The required alignment tolerances and surface roughness for unit lens elements in a compound refractive lens (CRL) for x rays are discussed. Contrary to what one might expect and what has been stated in the patent literature, alignment tolerances are large and for typical parameter values the effect of misalignment is minor. For a parabolic lens the focusing properties of the CRL are unaltered by misalignment and there is a small increase in absorption. For a lens with spherical aberration, there is a slight change in focal length, a minor translation of the image, and a small increase in absorption. This article also shows that lens gain is not appreciably reduced if the phase shift that is introduced by the roughness is limited to ±π/4 or if the transverse period of the roughness exceeds a specified value. The CRL can benefit from a managed misalignment of the elements to reduce the phase error introduced by surface imperfections of the lens.

We have measured the intensity profile and transmission of x rays focused by a series of biconcave parabolic unit lenses fabricated in lithium. For specified focal length and photon energy lithium compound refractive lenses ͑CRL͒ have a larger transmission, aperture size, and gain compared to aluminum, kapton, and beryllium CRLs. The lithium compound refractive lens was composed of 335 biconcave, parabolic unit lenses each with an on-axis radius of curvature of 0.95 mm. Two-dimensional focusing was obtained at 8.0 keV with a focal length of 95 cm. The effective aperture of the CRL was measured to be 1030 m with on-axis ͑peak͒ transmissions of 27% and an on-axis intensity gain of 18.9.

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.

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