Understanding Light Beam Reflection with Coordinate Systems

1. Basic Technologies – Glass Bead

2. Reflectivity 101 Angles and Angle systems

3. z z P(R,θ,φ) P(x,y,z) R θ φ y y x x Point in Cartesian Coordinates: P(x,y,z) Point in Polar Coordinates: P(R,θ,φ) How to describe a lightbeam

4. z y x z Line l(θ,φ) θ φ y x 2 Independent Lines require 4 Angles to describe them For example l(θ,φ) and m(ρ,ζ) Require θ, φ, ρ and ζ) z Other Line m(ρ,ζ) ρ ζ y x

5. z Line l(θ,φ) θ φ y x μ Line l(σ,μ) σ Exactly the same line can be represented in different coordinate systems With different angles. Both coordinate systems are mathematically interchangable. Sometimes one coordinate system is “pleasant”, sometimes another …..

6. Example is Measuring Observation Angle () 2 independent light “lines” describe what the driver sees: • illuminating “line”: from the lightsource to the sign • reflected “lightline” that “hits the eye Both lines require 2 angles to describe them, so 4 angles in total are required in total

7. z θ φ y x μ σ Which 4 angles do we select? • Coordinate system can be choosen • Convenient system for the laboratory? • Goniometer system • Convenient system to understand what “happens on the road”? • Application system • Both systems describe exactly the same • Both systems are mathematically interchangeable and identical • Angles from one system can “easily” be converted into angles • of the other system

8. What happens on the road with Entrance Angle () Not the same situation for overhead sign and for sign next to the road

9. What happens on the road with Entrance Angle () – The Application System Datum axis Only a source is available No observer yet Entrance Angle β is defined Reflector axis β Illumination axis Source S

10. What happens on the road with Entrance Angle () – The Application System Datum axis With only β the illumination Is not uniquely determined. More information is required β Source S Precise orientation-rotation of prisms is Extremely important For the resulting reflection

11. What happens on the road with Entrance Angle () – The Application System Datum axis Datum axis The combination of β and ω Uniquely determines the illumination Situation. There is no Receiver so far involved Sometimes ωS is called ωSource or simply ω ωs β The circle plane and the sample plane are parallel. Define position of Source On the circle “Where is β?” Only in combination with ω Illumination is precisely defined Source S

12. What happens on the road with Observation Angle (α) – The Application System Datum axis • Now the • Observer, • Driver, • Receiver, is introduced • And Observation Angle α is defined • Observation angle α does not uniquely • Define the position of the receiver Observation axis Illumination axis α Receiver R Source S

13. What happens on the road with Observation Angle (α) – The Application System Datum axis Every Observer on the circle will Have exactly the same Observation Angle α ! Observation angle α does not uniquely Define the position of the receiver The position of the observer On the circle has to be precisely defined α The circle plane and the sample plane are parallel.

14. Observation angle α does not uniquelyDefine the position of the receiver Datum axis The Observers precise position on the circle Is defined by Rotation Angle ε. Epsilon is related to the Receiver (observer) and therefore sometimes called εReceiver or εR Datum axis The circle plane and the sample plane are parallel. α ε Receiver R Source S

15. Observation angle α does not uniquelyDefine the position of the receiver Datum axis Datum axis The angle ε can also be “seen on the sign” And is in fact “the rotation” of the signs datum axis Compared to the “observer – illumination” plane ε The circle plane and the sample plane are parallel. α ε Receiver R Source S

16. The Application System, the complete picture Datum axis Entrance Angle β Observation Angle α Orientation Angle ωS Rotation Angle ε ωS β The circle planes and the sample plane are parallel. α ε Receiver R Source S

17. Practice Orientation Angle ωS Car drivers INTO the slide shadow ωS β α ε ωS ωS shadow A wide variaty of ω values exists in practice Consequently prisms are illuminated from all kinds of angles

18. Practice Rotation Angle εR for the left headlamp ωS Car drivers INTO the slide β ε α ε ωS The Rotation Angle ε for the left headlamp

19. Practice Rotation Angle εR for the right headlamp ωS Car drivers INTO the slide β ε α ε ωS The Rotation Angle ε for the right headlamp

20. Observation Angle Alpha = 0.33°, Entrance Angle Beta = 40° Epsilon Omega Omni rotational performance of AD Prismatics Epsilon and Omega are rotation related angles Some existing prismatic materials are extremely rotational sensitive !!