1. Date of download: 7/5/2016 Copyright © 2016 SPIE. All rights reserved. (a) Simulated measurement system scanning a surface element at position P(r→). (b) The observed phase value is constant for different observation directions, particularly the phase value in both observation directions φ(s→r1)=φ(s→r2). Figure Legend: From: Monte Carlo simulation of three-dimensional measurements of translucent objects Opt. Eng. 2015;54(8):084111. doi:10.1117/1.OE.54.8.084111

2. Date of download: 7/5/2016 Copyright © 2016 SPIE. All rights reserved. (a) The setup from Fig. 1 is extended with a second surface element at P(r→′), the light is partially interreflected between both elements. (b) The observed phase value from P(r→) depends on the observation direction s→r and deviates from the one observed without interreflections (see Fig. 1). Figure Legend: From: Monte Carlo simulation of three-dimensional measurements of translucent objects Opt. Eng. 2015;54(8):084111. doi:10.1117/1.OE.54.8.084111

3. Date of download: 7/5/2016 Copyright © 2016 SPIE. All rights reserved. Flow chart of the Monte Carlo simulation. The photon packets are tracked in the complete simulation space. The process is repeated for each photon packet many times until it is detected by the cameras, absorbed, or has left the simulation space. For each of the 7.5 billion photon packets, the three-dimensional simulation required the calculation of a few hundred individual steps. Figure Legend: From: Monte Carlo simulation of three-dimensional measurements of translucent objects Opt. Eng. 2015;54(8):084111. doi:10.1117/1.OE.54.8.084111

4. Date of download: 7/5/2016 Copyright © 2016 SPIE. All rights reserved. Polar plots of the Henyey-Greenstein phase equation for different anisotropy factors g from backscattering (g 0). Figure Legend: From: Monte Carlo simulation of three-dimensional measurements of translucent objects Opt. Eng. 2015;54(8):084111. doi:10.1117/1.OE.54.8.084111

5. Date of download: 7/5/2016 Copyright © 2016 SPIE. All rights reserved. Simulated camera images of (a) an opaque object and (b) a translucent object. The same square-shaped pattern was projected in both cases. Figure Legend: From: Monte Carlo simulation of three-dimensional measurements of translucent objects Opt. Eng. 2015;54(8):084111. doi:10.1117/1.OE.54.8.084111

6. Date of download: 7/5/2016 Copyright © 2016 SPIE. All rights reserved. Side view of the simulation setup. A translucent object is illuminated by a projector and observed by two cameras with a base length of 80 mm. The simulated materials have a small total interaction coefficient μt to activate high deviations of the simulated measurements and for a better visualization of the simulation results. Figure Legend: From: Monte Carlo simulation of three-dimensional measurements of translucent objects Opt. Eng. 2015;54(8):084111. doi:10.1117/1.OE.54.8.084111

7. Date of download: 7/5/2016 Copyright © 2016 SPIE. All rights reserved. Phase values for (a) camera 1 and (b) camera 2 observing the translucent object from different directions. φ=0 is marked by the horizontal planes. Two corresponding epipolar lines are marked by the vertical planes. In both cameras, the phase value φ=0 is observed to be slightly shifted from the expected pixel. Figure Legend: From: Monte Carlo simulation of three-dimensional measurements of translucent objects Opt. Eng. 2015;54(8):084111. doi:10.1117/1.OE.54.8.084111

8. Date of download: 7/5/2016 Copyright © 2016 SPIE. All rights reserved. Results of the Monte Carlo simulation for different scattering parameters g and surface roughness parameters σ at the same angle of 30 deg between the surface normal and measurement direction. A deep light penetration is observed if a high anisotropy factor g is chosen. The volume-scattered light is superimposed by the surface-reflected light with a sharp specular lobe if the surface roughness σ is small. Figure Legend: From: Monte Carlo simulation of three-dimensional measurements of translucent objects Opt. Eng. 2015;54(8):084111. doi:10.1117/1.OE.54.8.084111

9. Date of download: 7/5/2016 Copyright © 2016 SPIE. All rights reserved. Monte Carlo simulation of a tilted translucent object (g=0.9 and σ=0.05). For the purpose of illustration, the object is observed by a single camera only. The specular lobe points to different directions, as the orientation of the object is changed. Figure Legend: From: Monte Carlo simulation of three-dimensional measurements of translucent objects Opt. Eng. 2015;54(8):084111. doi:10.1117/1.OE.54.8.084111

10. Date of download: 7/5/2016 Copyright © 2016 SPIE. All rights reserved. Plot of the camera signal for the three different orientations of the translucent object in Fig. 9. The specular lobe causes a high- intensity peak and dominates the signal for the orientations of −10 and 0 deg. All photon packets detected for the 10 deg orientation were scattered in the object’s volume. Figure Legend: From: Monte Carlo simulation of three-dimensional measurements of translucent objects Opt. Eng. 2015;54(8):084111. doi:10.1117/1.OE.54.8.084111

11. Date of download: 7/5/2016 Copyright © 2016 SPIE. All rights reserved. Measurement deviation of the Monte Carlo simulation for the material parameters chosen in Fig. 8. For each material, the projection direction was varied in steps of 10 deg. Figure Legend: From: Monte Carlo simulation of three-dimensional measurements of translucent objects Opt. Eng. 2015;54(8):084111. doi:10.1117/1.OE.54.8.084111

12. Date of download: 7/5/2016 Copyright © 2016 SPIE. All rights reserved. Experimental results of the measurement deviation on translucent acrylic glass. Different surface roughnesses were generated by polishing the surface with different abrasive grains. The measurement deviation is dependent on the measurement direction and has the same shape as the results from the Monte Carlo simulations. Figure Legend: From: Monte Carlo simulation of three-dimensional measurements of translucent objects Opt. Eng. 2015;54(8):084111. doi:10.1117/1.OE.54.8.084111

13. Date of download: 7/5/2016 Copyright © 2016 SPIE. All rights reserved. Only the photon packets connecting the point illuminated from direction s→i and the point observed by the camera in direction s→r are shown. The most probable path connecting both points is determined by an A* path-finding algorithm and shown by the white line. The cost function of the path-finding algorithm is given by the path length in the object’s volume and the average traveling direction of the photon packets illustrated by the vector field. Figure Legend: From: Monte Carlo simulation of three-dimensional measurements of translucent objects Opt. Eng. 2015;54(8):084111. doi:10.1117/1.OE.54.8.084111