1. Alignment Using a Beam Triangle
Opti 521
Phil Scott

2. Presentation Overview
Defining an Optical Axis
Optical Axis Woes
Defining a Mechanical Axis
Mechanical Axis Woes
Degrees of Freedom for an Iris
Setting up a Beam Triangle
Degrees of Freedom for a Mirror
Aligning the Axes
Inserting Elements
Why a Triangle??
Why Does this Work?

3. Defining an Optical Axis
Optical Axis is Defined by Surfaces
Plano Convex
Defined by Center of Curvature and surface normal
Spherical Surfaces
Defined by both Centers of Curvature
Center of Curvature
Center of Curvature 1
Center of Curvature 2

4. Optical Axis Woes We often design around an optical axis
Elements have imperfections
Optics can’t float
Mounts have non-zero tolerances
What Happens when a Lens is Decentered? s Δθ f
Δθ=s/f

5. Defining a Mechanical Axis
The Mechanical Axis is Defined by Mounts
Lens Barrel
Tube that contains all lenses in a single housing
Cage System
Rods that connect and align mounts
Iris Pair
Define two point in free space
Aitc-group.com
Thorlabs.com
Newport.com

6. Mechanical Axis Woes
Mechanical Errors Lead to Misalignment and Stresses
Metal Bends
Lens edges may not be well controlled
Lens decenter due to tolerances
Center of Curvature 1
Center of Curvature 2
Lens Center

7. Degrees of Freedom for an Iris
All objects have 6 degrees of freedom
X, Y, Z, roll, pitch, yaw
Relevant degrees for an iris
X, Y, sort of Z
Small rotations do very little
Iris Pair
2 X, 2 Y (4 Total Degrees)
ΔZ should be large enough so that the small angle approximation applies
Diracdelta.co.uk

8. Setting up a Beam Triangle
Use two irises to define a mechanical Axis
Use two mirrors to match the optical axis to the mechanical axis
Start by aligning the light on the first iris

9. Degrees of Freedom for a Mirror
All objects have 6 degrees of freedom
X, Y, Z, roll, pitch, yaw
Relevant degrees for a fold mirror
Tip, Tilt, sort of Z
Clocking and translation are irrelivant
Mirror Pair
2 Tip, 2 Tilt (4 Total Degrees)
These 4 degrees can accommodate the 4 degrees from the iris pair
Diracdelta.co.uk

10. Aligning the Axes
Rotating the first mirror will change the position where the light strikes the second mirror
Rotating the second mirror changes the direction of the light entering the system
Use mirror 1 to align the light on the front iris and mirror 2 to align the light onto the second iris. Iterate until the system is aligned*
*Since the mirrors are finite in size, you may need to translate them
if the beam walks off the edge of a mirror.

11. Inserting Elements
Now that there is a mechanical axis with a source that is aligned to it, we can insert optics into the system.
Recall: Decentered lenses lead to angular deviations (slide 4)
Insert the lens between the irises and adjust until the light is once more centered on the second iris. This shows that the optical axis of the lens is aligned to the mechanical axis of the system to some geometric tolerance
Wash, rinse, repeat for each optic

12. Why a Triangle?? Simple: It doesn’t have to be!!
Any two mirror arrangement can work
The beam triangle keeps the angles of reflection small so a larger beam footprint will fit on the mirror

13. Why Does This Work? The mechanical axis has four degrees of freedom
Using the four degrees of freedom from the mirrors we can accommodate any reasonable geometry.
Another way to think about it:
There are two ways to define a line (in other words: an axis)
Use both to define the same line so the axes overlap

14. Questions??*
*Insert applause here