Using photon mapping for multispectral modeling of scenes within the THz range

A method for simulating the appearance of a large, geometrically modeled environment in the THz range is presented. A photon mapping technique is used with Monte Carlo photon sampling. The propagation of radiation within the scene is simulated for multiple discrete radiation frequencies, various materials are being modeled with emissivity, reflectivity and attenuation characteristics. The results are used to predict the answer of a passive, multispectral terahertz detector matrix. The recent development of a passive spectroscopic detector working in the THz range [1] opens up possibilities for remote identification of certain materials which have spectral features within this range. Because of the passive nature of a measured signal such identification requires special processing techniques to distinguish between a subject and the background. The described method was developed to allow testing of various approaches for multispectral, passive image processing in the THz range, particularly for testing the efficiency of remote material recognition algorithms in various geometric configurations. The second important goal is allowing to optimize the set of discrete sensitivity frequencies for the sensor, taking into account a certain set of materials to be recognized as well as the influence of the atmosphere (because of contamination of water vapour air has a strongly nonlinear spectral attenuation characteristics in the THz range with significant radiation blocking and passing areas). In order to realize above goals the following assumptions and simplifications are taken into consideration:  Simulation for multiple narrowband ranges (to mimic the sensor)  Energy conservation is obeyed for each frequency independently (no phosphorescence or fluorescence)  Plank’s Law – the amount of radiation emitted by a certain body is dependent on its temperature, area, radiation frequency and emissivity characteristics  Other material features are spectral characteristics of reflectivity and transmissivity (modelled as a linear attenuation coefficient)  Lambertian emission and reflection models are used (ideally diffusive) * E-mail: w.golebiowski@ska-polska.pl  Definable atmosphere attenuation characteristics, atmosphere itself doesn’t emit radiation  Phenomena like refraction, diffraction, interference are not modelled (radiation propagates along straight lines) The described method is a global illumination algorithm based on a photon mapping method [2]. The simulated scene is modelled as a set of objects (Fig. 1). There are two types of objects: solid and shell with a defined thickness (to simulate the propagation of radiation through relatively thin covers). Objects are approximated as a set of triangles which may form an open or closed surface. Each of the objects has its assigned type (solid or shell), temperature, thickness and material. The materials are defined with an emissivity, reflectivity and linear attenuation coefficient for each of the declared frequencies. A set of frequencies to be simulated is declared together with a relative spectral thickness (assuming the Gaussian distribution within a frequency domain). Fig. 1. Definition of the scene with GUI. As a starting point for calculation a so-called rendering equation [3] is used. In terms of the above assumptions, the radiation leaving an elementary surface for each of the frequencies may be described as: (1) where the indices denote respectively: outgoing radiation, radiation emitted by the surface, radiation reflected from the surface and radiation transmitted through the surface. These terms may be expressed as following (for a given outgoing direction): (2)