1. Basic Technologies – Glass Bead

2. Angles and Angle systems
Reflectivity 101
Angles and Angle systems

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

4. z x y 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. x y z
Line l(θ,φ) φ θ
Line l(σ,μ) 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. Which 4 angles do we select?x y z φ θ μ σ
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. β Datum axis Only a source is available No observer yet
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. β Datum axis With only β the illumination Is not uniquely determined.
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. ωs β Datum axis Datum axis The combination of β and ω
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. α Datum axis Now the Observer, Driver, Receiver, is introduced
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. α Datum axis Every Observer on the circle will Have exactly the same
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. α ε Datum axis The Observers precise position on the circle
Observation angle α does not uniquely Define 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. ε α ε Datum axis Datum The angle ε can also be “seen on the sign” axis
Observation angle α does not uniquely Define 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 ωS α ε 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
Car drivers INTO the slide ωS β ε α ε ωS
The Rotation Angle ε for the left headlamp

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

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