X-Ray Optics Calculator
Main Formulae
Optical properties versus material properties and wavelength
- Linear attenuation coefficient μ
μ = 4 π β / λ
- Length of 2π phase shift L2π
L2π = λ/ δ
- Transmission through length of 2π phase shift L2π
T2π = exp(- λ μ / δ)
= exp(- 4 π β / δ)
- Length of π phase shift Lπ
Lπ = λ/ 2δ
- Transmission through length of π phase shift Lπ
Tπ = exp(- λ μ / 2δ)
= exp(- 2 π β / δ)
- Length of π/2 phase shift Lπ/2
Lπ/2 = λ/ 4δ
- Transmission through length of π/2 phase shift Lπ/2
Tπ/2 = exp(- λ μ / 4δ)
= exp(- π β / δ)
- Effective aperture Aeff
Aeff = (f λ δ / β)½
= (4 π f δ / μ)½
- Diffraction-limited resolution for plane wave σ
σ = 0.664 (f λ β / δ)½
= 0.664 [f λ2 μ / (4 π δ)]½
- Minimal radius of curvature at parabola apex RC
RC = 2 f δ
- Tolerance on radius of curvature at parabola apex ΔRC/RC
ΔRC/RC =
(6.4/π) (β / δ) =
(1.6/π2) λ(μ / δ)
- Transmission TA through full aperture
TA = [√(fλδ/(2β)) / A]
erf[A / (2√(fλδ/(2πβ))]
- Transmission T through effective aperture Aeff
T = (1/√2) erf(√(π/2))
≈ 0.65314 = 65.314%
- Maximum possible gain G
G = T Aeff / σ
≈ δ/β
= 4 π δ / (λ μ)
Serguei Kuznetsov , IMT RAS, Chernogolovka, Russia. |