The effect of unit lens alignment and surface roughness on x-ray compound lens performance

Abstract

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.

A planar parabolic refractive nickel lens for high-energy X-rays

“…The same parameters should remain for the present lens. However, it is most probable that the imperfections in the lens cause broadening of the source image and reduce the intensity (Pantell et al, 2001).…”

Large area x-ray and neutron imaging using three-dimensional arrays of microlenses

“…15. The finite length, ᐉ, and the small aperture, 2r a , of the CRL forms a lens system that restricts the area of the object that can be imaged.…”

“…IV, adjacent CRLs must be spaced apart (in the y and z directions) by approximately the same distance, b, which must be approximately equal to the FOV of the combined CRLs (i.e., b Ϸ FOV). To achieve uniform FOV the spacing between adjacent lenses of array #1 must be roughly given by (15), b 1 Ϸ FOV. From (14) the spacing between the second array must be approximately given by: b 2 Ϸ ⌬b 1 Ϸ ⌬FOV.…”

Compound Refractive Lenses for Thermal Neutron Applications

“…As shown in Adelphi's patent for Fresnel CRLs [17], ignoring losses to the walls, each zone must be about twice the median misalignment to preserve the transmitted intensity and resolution is not significantly affected by misalignment. Essentially, the effective aperture is reduced when there is random variation of the unit lenses off the average optical axis of the lenses, but that there is no other degradation to image quality or efficiency [14]. If those neutrons that do pass through the region of the walls are not scattered, then alignment will be no more critical than for the parabolic case.…”