Exclude Data Points ............................................................................................................ 66 4.4.3
Interpreting Results ............................................................................................................ 66 4.4.4
Divergence ..................................................................................................................... 67 4.4.4.1
Chapter 5 M
2
Tutorial and Theory ....................................................................................................... 68
Introduction to M
2
.................................................................................................................... 68 5.1
M
2
< 1 ..................................................................................................................................... 68 5.2
Laser Beam Parameters ............................................................................................................ 69 5.3
An M
2
Tutorial .......................................................................................................................... 70 5.4
The Transforming Lens ....................................................................................................... 71 5.4.1
Beam Width Measurement Criteria ....................................................................................... 72 5.4.2
Spot Size and Resolution .................................................................................................... 73 5.4.3
Attenuation and Distortions ................................................................................................. 76 5.4.4
M
2
Theory of Operation ............................................................................................................. 76 5.5
Operation Limitations ................................................................................................................ 77 5.6
Electro-Mechanical Operation ..................................................................................................... 77 5.7
Data Collection ......................................................................................................................... 78 5.8
Chapter 6 M
2
Computations ................................................................................................................ 79
Curve Fitting ............................................................................................................................ 79 6.1
M
2
, K Factor, and BPP ......................................................................................................... 79 6.1.1
Translation Equations ......................................................................................................... 79
6.1.2
Full Divergence Angle ...................................................................................................... 79 6.1.2.1
Waist Width ................................................................................................................... 80 6.1.2.2
Waist Location ................................................................................................................ 81 6.1.2.3
Waist Location Relative to Principal Plane .................................................................... 81 6.1.2.3.1
Waist Location Relative to Laser Aperture .................................................................... 82 6.1.2.3.2
Rayleigh Range .................................................................................................................. 82 6.1.3
Astigmatism and Asymmetry ............................................................................................... 83 6.1.4
Focal Length Calculation ..................................................................................................... 83 6.1.5
Path Length Calibration Values ............................................................................................ 84 6.1.6
Z Lens ........................................................................................................................... 85 6.1.6.1
Z Fixture ........................................................................................................................ 85 6.1.6.2
Z Camera ....................................................................................................................... 85 6.1.6.3
BeamSquared Distance ....................................................................................................... 86 6.1.7
Chapter 7 Troubleshooting ................................................................................................................. 88