Lenses

Choosing the lens material

Our refractive x-ray lenses can be used in a very wide range of photon energies, roughly from 2 to 150 keV. Roughly speaking, beryllium is the material of choice up to about 40 keV, while aluminium is usually employed for about 40 to 80 keV. Beyond these energies, nickel is typically recommended (on request).

In Figure 1 is shown the attenuation of x-rays in these materials, more precisely, the mass attenuation coefficients μ/ρ as a function of the photon energy. The power-law behavior due to photo absorption is limited by Compton scattering that becomes dominant at higher energies.

For a fixed focal length, the effective aperture of a CRL is a decreasing function of μ/ρ × ε², where ε is the photon energy. Hence, from the purely optical point of view, beryllium is the best material for the whole energy range. However, the number of individual lenses needed is roughly proportional to ε²/ρ, where ρ is the mass density of the respective material. As a consequence, aluminium and nickel with their larger mass densities are usually employed for higher energies in order to limit the number of individual lenses.

A comparison of beryllium, aluminium, and nickel with other lens materials such as the resist SU-8 and diamond can be found in our section on frequently asked questions.

Types of refractive x-ray lenses

Our refractive x-ray lenses are available as paraboloids of revolution (2D lenses) and as parabolic cylinders (1D lenses), focusing in both directions or only in one direction, and within a wide range of focal lengths. The 2D lenses have circular frames with a diameter of 12 mm, while the 1D lenses have quadratic frames of 20×20 mm².

In Figure 2, the following notation is used: F frame thickness, D lens thickness, L lens length, d web thickness, R radius of curvature at the apex of the paraboloid, 2R₀ geometric aperture. A typical value for the frame thickness F is 2 mm. The lens length L of the 1D lenses usually is 2 mm. The figure shows the typical relative dimensions of x-ray lenses with R = 0.5 mm.

Available refractive x-ray lenses

The following lenses are available from RXOPTICS. Please contact us for more detailed information on available materials (beryllium grades, nickel) and on geometric parameters such as lens thicknesses and geometric apertures. All lenses are UHV compatible.

Radius of curvature R (mm)	Beryllium 2D lenses	Aluminium 2D lenses	Beryllium 1D lenses	Aluminium 1D lenses
0.05	⨯	⨯
0.1	⨯	⨯		⨯
0.2	⨯	⨯	⨯	⨯
0.3	⨯	⨯	⨯	⨯
0.5	⨯	⨯	⨯	⨯
1.0	⨯	⨯	⨯
1.5	⨯
2.0	⨯
2.5	⨯
3.0	⨯
4.0	⨯
5.0	⨯