Interpolating phase-space data via measured data

Measurement data consisting of a percentage depth dose (PDD) and off-axis ratios (OAR) at several depths (0.5 cm, 1.0 cm and 2.0 cm) with the phantom surface at 100 cm from the source was obtained.

The data is extended to a 3D array according to the formula, $\pi(x,y,z)=\mbox{PDD}(z).\mbox{OAR}(x).\mbox{OAR}(y)$, with 2 mm graduations in the x and y directions and 1 mm graduations in the z direction

Particle are taken from the phase space distribution and transported multiple times with a small randomly distributed perturbation to its phase space coordinates.

Parameter		Standard deviation
Energy	$\varepsilon$	$\varepsilon/20$
Trajectory	$\phi$	$9^{\circ}$
	$\theta$	$18^{\circ}$
Position	x,y	1 cm