IMG-32

X-ray tube output

K ∝ kVp² mAs / d². Air kerma from a diagnostic tube.

Reading speed

RadiographyX-ray output

Governing equation

K\propto kVp^{2}\,\mathrm{mAs}/d^{2}

$kVp \in \left[40, 140\right]$

where

kVp: Tube voltage (kV)
mAs: mAs (mAs)
d: Distance (cm)
k: Output at 80 kV, 100 cm (µGy/mAs)
K: Air kerma (µGy)

The figure, part by part

Each numbered marker wears the color of its card. Hover a card to light the marker. Tap a marker to jump to that card. The slider walks a red point along the curve; Animate drawing traces it like a pen.

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①

Governing law — red

K\propto kVp^{2}\,\mathrm{mAs}/d^{2}

$kVp \in \left[40, 140\right]$

$kVp = 40$ $K = 100$

Along the curve

②

Domain of the variable — blue

kVp_{\min} = 40,\quad kVp_{\max} = 140

$kVp \in \left[40, 140\right]$

$kVp = 40$ $kVp = 40$

Along the curve

③

Response curve — green

K\propto kVp^{2}\,\mathrm{mAs}/d^{2}

$kVp \in \left[40, 140\right]$

$kVp = 40$ $K = 100$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}K}{\mathrm{d}kVp}

$kVp \in \left[40, 140\right]$

$kVp = 40.63$ $K^{\prime} = 5.079$

Along the curve

Lecture brief

Historical brief

Larmor precession, CT Beer projections, SNR and Nyquist sampling are why MRI and CT images exist as numbers. The lab computes frequency, dose and resolution limits. This sheet (IMG-32 — X-ray tube output) is the form associated with X-ray output. Working symbols: $kVp$ , $mAs$ , $d$ , $k$ $\rightarrow$ $K$ . Bremsstrahlung yield grows ~Z V². The inverse square is the geometric dilution from the focus.

Purpose

Purpose: compute

K

from

kVp

mAs

d

k

in Medical imaging via

K\propto kVp^{2}\,\mathrm{mAs}/d^{2}

K ∝ kVp² mAs / d². Air kerma from a diagnostic tube. Use it when a real medical imaging question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

kVp = 80.000\,\mathrm{kV}

mAs = 10.000\,\mathrm{mAs}

d = 100.000\,\mathrm{cm}

k = 40.000\,\mathrm{\mu Gy/mAs}

, the governing relation

K\propto kVp^{2}\,\mathrm{mAs}/d^{2}

yields

K = 400.0\,\mathrm{\mu Gy}

. A focus, a kV, an mAs, a falling kerma. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Tube voltage kVp80 kVmAs mAs10 mAsDistance d100 cmOutput at 80 kV, 100 cm k40 µGy/mAs

Outputs

Air kerma K400.0 µGy

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Narration of this film

A focus, a kV, an mAs, a falling kerma.

Bremsstrahlung yield grows ~Z V². The inverse square is the geometric dilution from the focus.

Reading speed

Watch on YouTube