Fast ray tracing on phase space

Transcription

1 Supervisor: Jan ten Thije Boonkkamp Philips supervisors: Wilbert IJzerman and Teus Tukker CASA-Day, 8 April 2015

2 Outline Introduction Physical background Monte Carlo ray tracing Phase space representation Results Conclusions

3 Introduction: Why ray tracing is important? Top: Vincent Thomas Bridge Bottom: Sistine Chapel Are illuminated by LED lamps

4 Physical background: Geometrical optics Reflection law t 2 = t 1 2(t 1, n)n Refraction law ( [ n s 2 = 1 n 2 )s 1 + n 1 ] ( ) 2 n 1 n 2 + (n, s1 ) 2 (n, s 1 )

5 Physical background: Geometrical optics Reflection law t 2 = t 1 2(t 1, n)n Refraction law ( [ n s 2 = 1 n 2 )s 1 + n 1 ] ( ) 2 n 1 n 2 + (n, s1 ) 2 (n, s 1 ) Luminous flux The luminous flux Φ is the measure of the perceived power of light by the human eye.

6 Photometric variables Intensity I = dφ dt [lm/rad] Luminance L = d2 Φ dx cos tdt [cd = lm/rad m] di = L(x, t) cos(t)dx I = L(x, t) cos(t)dx Luminance and intensity in two dimensions.

7 Ray tracing method Purpose: Given an optical system and the rays distribution at the source: Compute the propagation of rays from the light source to the target Calculate the photometric variables at the target. Figure: A two-dimensional optical system: the TIR-collimator

8 Ray tracing method Purpose: Given an optical system and the rays distribution at the source: Compute the propagation of rays from the light source to the target Calculate the photometric variables at the target. Figure: A two-dimensional optical system: the TIR-collimator

9 Ray tracing method Purpose: Given an optical system and the rays distribution at the source: Compute the propagation of rays from the light source to the target Calculate the photometric variables at the target. Figure: A two-dimensional optical system: the TIR-collimator

10 Ray tracing method Purpose: Given an optical system and the rays distribution at the source: Compute the propagation of rays from the light source to the target Calculate the photometric variables at the target. Figure: A two-dimensional optical system: the TIR-collimator

11 Ray tracing method Purpose: Given an optical system and the rays distribution at the source: Compute the propagation of rays from the light source to the target Calculate the photometric variables at the target. Figure: A two-dimensional optical system: the TIR-collimator

12 Ray tracing method Purpose: Given an optical system and the rays distribution at the source: Compute the propagation of rays from the light source to the target Calculate the photometric variables at the target. Figure: A two-dimensional optical system: the TIR-collimator

13 Ray tracing method Purpose: Given an optical system and the rays distribution at the source: Compute the propagation of rays from the light source to the target Calculate the photometric variables at the target. Figure: A two-dimensional optical system: the TIR-collimator

14 Ray tracing method Purpose: Given an optical system and the rays distribution at the source: Compute the propagation of rays from the light source to the target Calculate the photometric variables at the target. Figure: A two-dimensional optical system: the TIR-collimator

15 Ray tracing method Purpose: Given an optical system and the rays distribution at the source: Compute the propagation of rays from the light source to the target Calculate the photometric variables at the target. Figure: A two-dimensional optical system: the TIR-collimator

16 Monte Carlo ray tracing Calculate the distribution of rays at the target Divide the target T line into bins Consider the flux of rays that fall into each bin Take the average over a bin Problem: A large number of rays needs to be traced. Very slow and computationally expensive procedure.

17 Phase space representation Different approach: Consider the phase space representation of the source and the target. Every ray, with coordinates (x, t), is related to a unique point (x, τ) and (q, η) at source and target phase space. τ = n s sin(t), η = n t sin(θ), n s = n t = 1 Source phase space: P s = S [ 1, 1] Target phase space: P t = T [ 1, 1] A light ray with coordinates (x, t) on the source and (q, θ) on the target. L(x, t) = L(q, θ)

18 Edge ray principle A map that describes how the optical system changes the rays is defined as: M: P s P t (x, τ) (q, η). Rays that follow a similar path are located in the same region on phase space. R s,πi := {rays on the source that follow the path Π i } R t,πi := {rays on the target that follow the path Π i } M : R s,πi R t,πi Edge ray principle: Rays from the edge of the source strike the edge of the target. M : R s,πi R t,πi

19 Example: The two-faceted cup An example of a two faceted-cup - S = [ 2, 2] - T = [ 17, 17] - Reflectors: straight lines Boundaries of regions formed by rays that follow the same path

20 How to obtain the intensity? I (η) = T cos(η)l t (q, η)dq = cos(η) L t (q, η)dq T assuming L t (q, η) = const = L t if N is the number of intersection points I (η) = cos(η)l t N qi i=1 q i 1 dx = cos(η)l t N (q i q i 1 ) i=1

21 How to obtain the intensity? I (η) = T cos(η)l t (q, η)dq = cos(η) L t (q, η)dq T assuming L t (q, η) = const = L t if N is the number of intersection points I (η) = cos(η)l t N qi i=1 q i 1 dx = cos(η)l t N (q i q i 1 ) i=1

22 How to obtain the intensity? I (η) = T cos(η)l t (q, η)dq = cos(η) L t (q, η)dq T assuming L t (q, η) = const = L t if N is the number of intersection points I (η) = cos(η)l t N qi i=1 q i 1 dx = cos(η)l t N (q i q i 1 ) i=1

23 Results: Compare Intensity

24 Results: Compare Intensity The Monte Carlo method with 10 6 rays compared to the phase space method with rays Tracing far less rays the intensity calculated with the phase space method is a good approximation of the intensity calculated with the Monte Carlo method.

25 The TIR-collimator S = [ 2, 2] T = [ 9, 9] Optical system: lens, side wall and reflectors. Distribution of rays on target phase space.

26 The TIR-collimator S = [ 2, 2] T = [ 9, 9] Optical system: lens, side wall and reflectors. Distribution of rays on target phase space. I (η) = N i=1 q2i q 2i 1 dx = N (q 2i q 2i 1 ) i=1 with N the number of intersection points.

27 Compare Monte Carlo method and phase space method The Monte Carlo method with rays and the phase space method with rays. The difference between the two intensity is still too high for certain values of the angles.

28 Conclusions and future work Conclusions Provided a new ray tracing method for optical design. Compared to the Monte Carlo method it is faster and less rays need to be traced. It works well for simple optical systems. There are still some issues with the TIR-collimator.

29 Conclusions and future work Conclusions Provided a new ray tracing method for optical design. Compared to the Monte Carlo method it is faster and less rays need to be traced. It works well for simple optical systems. There are still some issues with the TIR-collimator. Future work Find the exact intensity for the TIR-collimator. Extend the method to more realistic optical systems considering Fresnel reflection. Translate the two-dimensional method to three dimensional optical systems.

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31 Enjoy your coffee!!