X-Ray Optics and Instrumentation

Review Article

Diffractive X-Ray Telescopes

Table 3

Achromatic correction of PFLs. Parameters are given for systems with the same overall length, 𝑓 , at the nominal design energy, 𝐸 0 , and for the case when 𝑡 2 𝜋 is proportional to energy, 𝐸 . In the table Δ 𝐸 is specified relative to 𝐸 0 , and 𝑑 is the diameter of the refractive component.
Simple PFL Doublet Separated pair
Diffractive focal length 𝑓 𝑓 / 2 𝑓 / 3
Separation —0 𝑓 / 9
Refractive focal length — − 𝑓 − 8 / 2 7 𝑓
Image plane distance 𝑓 ( 1 + Δ 𝐸 ) 𝑓 ( 1 + Δ 𝐸 2 + ⋯ ) 𝑓 ( 1 + 1 . 3 5 Δ 𝐸 3 + ⋯ )
Image scale 𝑓 𝑓 4 3 𝑓 ( 1 − ( 1 / 2 ) Δ 𝐸 + ⋯ )
Diffraction-limited bandwidth (fractional) 4 ( ( 𝑓 / 𝑑 2 ) ( ℎ 𝑐 / 𝐸 ) ) 4 ( ( 𝑓 / 𝑑 2 ) ( ℎ 𝑐 / 𝐸 ) ) 1 / 2 ( ( 1 6 / 3 ) ( 𝑓 / 𝑑 2 ) ( ℎ 𝑐 / 𝐸 ) ) 1 / 3