Abstract
The classic Monte-Carlo ray tracing is a powerful method which allows to simulate virtually all effects in ray optics, but it may be inadmissibly slow for many cases, such as calculation of images seen by a lens or pin-hole camera. In this cases another stochastic method is more efficient such as the bi-directional ray Monte-Carlo tracing with photon maps (BDPM). The level of noise i.e. the r.m.s. (root mean square) of pixel luminance calculated in one iteration of the method, depends on various parameters of the method, such as the number of light and camera paths, radius of integration sphere etc. so it is desirable to be able to predict this dependence to choose optimal parameters of the method. It was shown that this r.m.s is a sum of 3 functions scaled by reverse number of camera and light rays. These functions themselves are independent of the number of rays, so knowing them one can predict the noise for any number of rays and thus find the optimal one. These functions are a sort of correlations and their calculation from ray tracing is not a trivial problem. In this paper we describe a practical method of calculation and demonstrate the usage of its results for the choice of ray number.
Highlights
Simulation of light propagation is widely used in optical engineering and in design of new materials
The classic Monte-Carlo ray tracing is a powerful method which allows to simulate virtually all effects in ray optics, but it may be inadmissibly slow for many cases, such as calculation of images seen by a lens or pin-hole camera
In this cases another stochastic method is more efficient such as the bi-directional ray Monte-Carlo tracing with photon maps (BDPM)
Summary
Simulation of light propagation is widely used in optical engineering and in design of new materials. Most publications are devoted to the first two means, for example, [9], [7], [10] or [8], while less attention had been paid to the number of rays It is an important factor and frequently it happens that e.g. the number of forward rays is already superfluous, so increasing it further does not decrease noise but only increases the run time. In [6] the general law which determines the noise in BDPM had been derived It states that the variance of pixel luminance is a sum of three components scaled by inverse number of rays. In other words, had we knew these 3 components (which usually depend on pixel) we would be able to predict the noise level for any number of rays Their mathematical definition is trivial, these three values are not that easy to calculate numerically by ray tracing. In this paper we describe a method of their efficient calculation and demonstrate their usage to choose the optimal number of rays
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