The relative dose distributions of small circular fields for 6 MV photons may be calculated using a simple mathematical model. This model has been developed for stereotactic collimators with cylindrical cross section and diameters between 5 mm and 30 mm. The model consists of the description of depth dose curves and off-axis dose distributions. The function for off-axis dose distributions is calculated by convolution of a simple profile function with a constant function. The width of the constant function is defined by beam geometry. In the result of integration only the width of the profile function is unknown, but it can be iteratively calculated. The agreement between measured and calculated dose distributions was tested at 5 cm and 20 cm depth in water and 100 cm source-to-surface distance using thermoluminescent dosimetry (TLD) and films, giving a resolution of 1 mm. The depth dose curve is described using the inverse square law and two exponential functions. The first of these functions contains the effective attenuation coefficient in the argument, the second describes the build-up. The increase of irradiated volume with increase of field diameter is accounted for using scatter-air ratios. The calculations were compared with TLD and ion-chamber measurements.
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