X-Ray Emission

The vertical axis is the photon flux per unit wavelength, N(λ), in arbitrary units per Ångström: the number of photons, not the energy they carry. The X-Ray Filters page uses the same quantity, so the two pages show the same continuum shape.

The energy flux would be N(λ)·hc/λ. The continuum is then proportional to (λ/λ_min − 1)/λ³ and peaks at 1.5 λ_min; as a photon flux it falls as 1/λ² and peaks at 2 λ_min.

Kramers' law gives the energy per unit frequency, ∝ Z(ν_max − ν). Dividing by hν gives photons per unit frequency, and dν = c dλ/λ² converts to wavelength.

Photons are absorbed in the anode on their way out (depth from the Kanaya–Okayama range, take-off angle 20°) and in a 0.25 mm beryllium window. This removes the long-wavelength part of the continuum and puts a step at the anode's own K edge. Without it, the photon number would diverge logarithmically at long wavelength.

• Intensities are relative. The K-line scale is fixed so that, for Cu at 40 kV and before absorption, the energy in the K lines is 35 % of the energy in the continuum.
• The anode attenuation uses the Bragg–Pierce form with a K-edge jump (no L or M edges): do not read absolute values from it. The Be coefficient is fitted to NIST (about 10 % from 1 to 10 keV).
• Only Kα_1,2, Kβ and Lα/Lβ lines are modelled. Detector resolution is not applied, so the natural line widths are shown.
• The X-Ray Filters page uses the same photon-flux units but a simpler source: no anode or window absorption, and a line intensity ∝ (V − V_K)^1.5. Peak-to-continuum ratios therefore differ between the two pages.