# X-Ray Optics Calculator

 | Introduction | Lens Formula | Unit Conversion | Refractive Optics | Fresnel Optics | Transmission through matter | Transfocators | Table Data

## Main Formulae

### Optical properties versus material properties and wavelength

• Linear attenuation coefficient μ
μ = 4 π β / λ

• Length of 2π phase shift L
L = λ/ δ

• Transmission through length of 2π phase shift L
T = 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.