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Early 90s:

The “Collapsed cone” (CC) method, that speeds up the PSF-

convolution was proposed

In parallel, the

pencil beam

method - a 2D convolution approach

was developed for photons (PB) (Mohan

et al

.).

PB implemented in several commercial systems and much

faster than 3D convolution

Good agreement with measurement for irregular fields in flat-

surface water tank.

Poor agreement between measurement and calculations in

heterogeneous media (e.g. lung)

Analytical methods, photon beam calculation