X-ray tube spectrum

The continuous spectrum

When fast electrons strike the tungsten anode, most lose energy gradually and radiate a continuous band of X-rays — bremsstrahlung, or "braking radiation". The highest photon energy equals the tube voltage: a 100 kVp tube can make a 100 keV photon and no more. Raise the voltage and the whole curve extends to the right and grows; the mean energy climbs with it.

This view shows the raw spectrum leaving the anode, before any filter. It is soft and low-energy: in practice the tube housing and an added aluminium or copper filter remove the lowest energies first, and those filters are outside what this calculator draws.

Reading the chart

The horizontal axis is photon energy in keV, from zero to the chosen tube voltage, so the right-hand edge of the chart is always the endpoint. The vertical axis is relative photon fluence per keV, scaled so that the tallest point of the current spectrum is 1. The chart therefore compares shapes, not output: it does not say how many more photons a higher voltage produces, only where along the energy axis they fall.

The log-scale option spreads the vertical axis over several decades. Use it to see the high-energy tail near the endpoint, which on a linear axis is squeezed against the baseline, and to check that the curve reaches zero exactly at the tube voltage.

The narrow peak just below 10 keV, and the sharp fall after it, are part of the model, not a drawing error. Photons made inside the anode must cross some tungsten to escape, and tungsten absorbs much more strongly just above its L-shell edges at about 10.2, 11.5 and 12.1 keV. The smaller step near 2–3 keV comes from the M-shell edges in the same way. The glass or metal envelope of a diagnostic tube, and any added filter, absorb almost all of this region, which is why measured spectra from such tubes do not show it.

Why the raw spectrum is soft

In a thick target, the number of photons produced per keV rises steadily towards low energies — the simple form of this is Kramers' rule. On their way out of the anode, however, the lowest-energy photons are absorbed by the tungsten itself, so the curve turns over and falls away below about 10 keV instead of rising without limit. What remains is a broad hump near the low end with a long, thinning tail out to the endpoint.

The model behind this calculator gives these figures for the unfiltered tungsten beam:

Across this range the mean energy of the raw beam stays close to 30% of the tube voltage. A large share of the photons sit below 20 keV; in a patient almost all of these are absorbed in the first few centimetres of tissue, adding to skin dose without reaching the image receptor. That is the reason every diagnostic tube carries filtration — general radiography typically requires a total of at least 2.5 mm of aluminium equivalent.

Using it

Move the voltage slider and watch the endpoint and the mean energy move together. Going from 60 to 120 kVp roughly doubles the mean energy, while the low-energy hump hardly moves: most of the change happens in the tail. This is a quick way to show why a higher voltage penetrates further, and why the voltage alone does not fix beam quality once a filter is added.

What this view leaves out

Characteristic lines (the sharp spikes near 58–69 keV that appear once the tube voltage passes tungsten's K-edge at 69.5 kV) and filtration are not part of this calculator, so it gives no half-value layer or air kerma. The source is treated as a point on the central axis, so there is no heel effect here. For a filtered beam, use a full spectrum model such as SpekPy, which this calculator's table is drawn from.

Worked examples

Raising the tube voltage from 70 to 90 kVp

A radiographer raises an exposure from 70 kVp to 90 kVp to get through a thicker patient. Set the slider to each value and read the mean energy under the chart. The two fractions in the table are summed from the same spectrum the chart draws.

The mean energy rises by about a quarter, but the share of photons at 50 keV or more more than doubles, and those are the photons that reach the image receptor through tissue. The low-energy share falls too, yet it remains large in the raw beam. In a real tube most of it is removed by the inherent and added filtration before it reaches the patient, which is exactly the part this view does not model, so read the table as a comparison of shapes rather than of patient dose.

A dental unit next to a CT scanner

The same calculator can show why survey work around different X-ray units needs different care. Compare 60 kVp, typical of an intraoral dental unit, with 120 kVp, typical of CT.

Doubling the voltage nearly doubles the mean energy and multiplies the share above 40 keV by more than four, while the most common photon energy in the raw beam stays at the same place, just below tungsten's L-shell edges. Scattered radiation around both units is softer still. A survey meter calibrated with Cs-137 at 662 keV can read well off at these energies, so check its energy response for the range shown here, or use an ionisation chamber with a flat response down to the energies that matter.

FAQ

What is the difference between kVp and keV?

kVp is the peak voltage across the X-ray tube; keV is the energy of a single photon. An electron accelerated through 100 kV arrives with 100 keV, so the highest photon energy in the beam, in keV, equals the tube voltage in kV. Most photons have far less than that.

What is the mean energy of an X-ray beam?

For the unfiltered tungsten spectrum shown here it stays close to 30% of the tube voltage: 18.5 keV at 60 kVp and 35.5 keV at 120 kVp. Filtration removes the soft end of the spectrum and raises the mean, so a clinical beam has a higher mean energy than the raw figure.

Where does the spectrum come from?

It is a precomputed SpekPy table for a tungsten anode at a 20° angle, tabulated in 1 keV steps at tube voltages from 20 to 300 kVp in 10 kV steps. Voltages between the grid points are interpolated linearly, and the curve is scaled so its tallest point is 1.

Why are the tungsten K lines missing?

The table contains the continuous bremsstrahlung spectrum only. The tungsten K lines at about 58 to 69 keV appear once the tube voltage passes the K-edge at 69.5 kV; when they matter, for example for detector response near those energies, use a full spectrum model such as SpekPy.

Can this calculator give the half-value layer or air kerma of a beam?

No. Both depend on the filtration, which this view does not include, and air kerma also needs the tube output. Model the filtered beam in SpekPy, or measure the half-value layer directly with aluminium filters and a calibrated dosemeter.