The infrared imaging video bolometer (IRVB) as a foil bolometry technique can be an alternative solution to the conventional resistive bolometer due to its electro-magnetic immunity and 2D plasma profiles. The plasma profile of the IRVB cannot be directly derived from the foil images due to the difference between the foil pixel number and the plasma pixel number and the line integrated nature of the incident rays on the foil. So, it needs tomography such as the Phillips-Thikhonov algorithm. The projection matrix constructing the foil image from the plasma very directly influences the tomography. So, the projection matrix needs to be constructed precisely. For the technique calculating the precise projection matrix, a forward Monte-Carlo ray-tracing method is proposed here, and this technique can provide the detailed descriptions of the foil image. And it can give enhanced performance in the reconstructions of the plasmas with spatially localized power. Published by AIP Publishing.