R 50 as a beam quality specifier for selecting stopping‐power ratios and reference depths for electron dosimetry

For electron beam reference dosimetry in radiotherapy, it is shown that by choosing the reference depth as d ref =0.6 R 50 −0.1 cm, where R 50 is the half‐value depth in centimeters, the Spencer–Attix water‐to‐air stopping‐power ratio at d ref is given by( L ̄ / ρ ) air w =1.2534−0.1487 ( R 50 ) 0.2144 . This is derived from data for( L ̄ / ρ ) air wobtained from realistic Monte Carlo simulations for 24 clinical beams. The rms deviation of this expression from the Monte Carlo calculations is 0.16%, with a maximum deviation of 0.26%. This approach fully takes into account the spectral differences between real electron beams of the same R 50 and allows an absorbed‐dose calibration at a standards laboratory to be easily and accurately transferred to a reference clinical beam. Using a single paraeter to specify( L ̄ / ρ ) air w , rather than the two parameters ( R 50 and depth) needed when the reference depth is chosen as the depth of dose maximum, has the potential to greatly simplify electron beam dosimetry protocols and allows the use of a similar formalism for photon and electron beam dosimetry. For use in converting a depth–ionization curve into a depth–dose curve, a somewhat less accurate but general expression for( L ̄ / ρ ) air was a function of R 50 and depth is presented.