X-ray analysis apparatus with a graded multilayer mirror

A curved multilayer Bragg reflector for an X-ray analysis apparatus having a source emitting X-ray radiation, a sample to be analyzed, a detector sensitive to X-ray radiation, and at least one of beam-shaping and beam-limiting means, the Bragg reflector disposed in an optical path between the source and the sample, the Bragg reflector comprising:

• a periodically repeating sequence of layers, wherein a period comprises at least two individual layers A, B having different index of refraction decrements δA≠δB and having thicknesses dA and dB,
• wherein a period thickness, a sum d=dA+dB+dC+ . . . of individual layers A, B, C, . . . of a period, changes constantly along an x direction and
• wherein said reflector is curved in such a fashion that it forms a partial surface of a paraboloid at one of a focal line and a focal point of which, said source or an image of said source is disposed so that a parallel beam is produced subsequent to reflection and,
• wherein said layers of said reflector are directly disposed on a concave curved surface of a paraboloid-shaped hollow substrate through one of evaporation, sputtering and growth, wherein a curvature of said concave substrate surface, in an xy plane, is given by
• y2=2px
• with one of 0.02 mm<p<0.5 mm, and p≈0.1 mm, and wherein a concave substrate surface facing said reflector has a maximum allowable shape deviation of
• Δp={square root over (2px+L )}·ΔθR,
• wherein ΔθR is a full width half maximum of Bragg reflection of said reflector and assumes values of one of
• 0.01°<ΔθR<0.5°,
• and
• 0.02°<ΔθR<0.20°,
• and said concave substrate surface facing said reflector having a maximum allowable waviness of Δ ⁢ ⁢ y Δ ⁢ ⁢ x = 1 2 ⁢ ⁢ Δ ⁢ ⁢ θ R ,
• and said concave substrate surface facing said reflector having a maximum allowable roughness of one of Δ ⁢ ⁢ y = d 2 ⁢ ⁢ π , ⁢ and ⁢ ⁢ Δ ⁢ ⁢ y ≤ 0.3 ⁢ ⁢ nm ,
• and said X-ray radiation being incident on a curved surface of said reflector at a n angle of incidence 0°<θ≦5°, wherein
• said period thickness d changes along an x direction in such a fashion that said X-radiation of a particular wavelength λ from a point or line X-ray source always experiences Bragg reflection independent of a point of incidence (x, y) on said reflector, wherein said period thickness d increases towards a paraboloid opening in said x direction in accordance with d = λ 2 ⁢ ⁢ 1 ( 1 - δ _ / sin 2 ⁢ θ ) ⁢ sin ⁢ ⁢ θ with ⁢ ⁢ θ = arccot ⁢ 2 ⁢ x p
• wherein {overscore (δ)} is a decrement of an average index of refraction of said multilayer Bragg reflector and
• a deviation Δd/Δx of said period thickness d at each point of said multilayer Bragg reflector along said x direction is smaller than Δ ⁢ ⁢ d Δ ⁢ ⁢ x = 1 2 ⁢ ⁢ d x , ⁢ and 1 nm≦d≦20 nm,
• and wherein one of the following conditions obtain for the number N of periods:
• 10<N<500, and 50≦N≦100 with N being a a number of periods and wherein
• 0.1 keV<E<0.1 MeV with E being an energy of quanta of the X-radiation.