Abstract
A new method to compute the target photometric variables of non-imaging optical systems is presented. The method is based on the phase space representation of each surface that forms the optical system. All surfaces can be modeled as detectors of the incident light and emitters of the reflected light. Moreover, we assume that the source can only emit light and the target can only receive light. Therefore, one phase space is taken into account for the source and one for the target. For the other surfaces both the source and target phase spaces are considered. The output intensity is computed from the rays that leave the source and hit the target. We implement the method for two-dimensional optical systems, and we compare the new method with Monte Carlo (MC) ray tracing. This paper is a proof of principle. Therefore, we present the results for systems formed by straight lines which are all located in the same medium. Numerical results show that the intensity found with the ray mapping method equals the exact intensity. Accuracy and speed advantages of several orders are observed with the new method.
Highlights
The goal in non-imaging optics is to compute the light distribution at the target of the system
In the following we describe the geometry of this system, we introduce the notion of phase space for all the lines that constitute the system
We indicate the phase space (PS) with S = Q × P, where Q is the set of the position coordinates q and P is the set of the direction coordinates p = n sin τ with n the index of refraction of the medium in which the line is located and τ the angle between the ray segment inside the cup and the normal ν of the line which we choose directed inwards of the optical system
Summary
The goal in non-imaging optics is to compute the light distribution at the target of the system. Since not all the rays whose corresponding coordinates are located inside the segment [qtm,jin, qtm,jax] with direction p = pt,j follow the same path, the intersection segment [vmj,iin, vmj,iax] = [qtm,jin, qtm,jax] ∩ [umj,iin, umj,iax] needs to be calculated. If no intersection points are found, the rays traced are not emitted by the source, no contribution to the intensity needs to be added To compute the intensity along another direction pk ∈ [–1, 1] on T4, the procedure explained for p = –0.2 is repeated for p = pk In this way we find all the possible paths and the regions R( ) with positive luminance on T4.
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