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Spie Press Book

Laser Beam Quality Metrics
Author(s): T. Sean Ross
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Book Description

Laser beam quality is more complicated and subtle than is usually assumed, a fact that has caused no end of frustration and misunderstanding between laser manufacturers, users, and acquirers. Laser Beam Quality Metrics guides the reader through the subtleties of laser beam quality analysis and requirements synthesis, arming the reader with the tools to understand beam quality specifications and to write custom specifications that are traceable to the intended application.

The book is geared toward engineers and laser physicists involved in the development of laser-based systems, especially laser systems for directed energy applications. It begins with a review of basic laser properties and moves to definitions and implications of the various standard beam quality metrics such as M2, power in the bucket, brightness, beam parameter product, and Strehl ratio. The practical aspects of beam metrology, which have not been sufficiently addressed in the literature, are amply covered here.

For those who are only interested in measuring Gaussian beams from commercial lasers, a reading of Chapter 1, Chapter 2 “What Your Laser Beam Analyzer Manual Didn’t Tell You,” and the first three sections of Chapter 6 “Cautionary Tales” will be sufficient. For those working in more off-the-map fields such as unique lasers, unstable resonators, multikilowatt lasers, MOPAs, or requirements generation and development, a reading of the entire text is recommended.


Book Details

Date Published: 25 March 2013
Pages: 204
ISBN: 9780819492975
Volume: TT96

Table of Contents
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Preface
Acknowledgment
List of Acronyms, Symbols, and Notation

1 Introduction
1.1 First Rule of Laser Beam Quality Metrics
1.2 History, Resources, and State of Laser Beam Quality
1.3 Anatomy of a Laser
      1.3.1 Generic laser resonator
      1.3.2 Stable resonator
      1.3.3 Unstable resonator
      1.3.4 Master oscillator power amplifier (MOPA)
      1.3.5 Temporal behavior of lasers
      1.3.6 Types of lasers
1.4 Basic Properties of Laser Radiation
      1.4.1 Near field versus far field
      1.4.2 Special shapes
1.5 Laser Modes and Modal Analysis
      1.5.1 Hermite–Gaussian modes
      1.5.2 Laguerre–Gaussian modes
      1.5.3 Unstable resonator modes
      1.5.4 Fiber laser modes
1.6 Common Measures of Beam Centroid
      1.6.1 First moment
      1.6.2 Peak irradiance
      1.6.3 Transmission maximization
      1.6.4 Geometrical center/cutoff
1.7 Common Measures of Beam Radius and Divergence Angle
      1.7.1 Second moment
      1.7.2 Best fit to Gaussian
      1.7.3 First null
      1.7.4 Hard cutoff measures
      1.7.5 Mode maximization
1.8 Common Sources of Beam Quality Degradation
      1.8.1 Resonator modes
      1.8.2 Physical nonuniformities
      1.8.3 Unstable resonator
      1.8.4 Thermal nonuniformities
      1.8.4 Diffraction effects
1.9 Common Measures of Beam Quality
      1.9.1 M2
      1.9.2 Power in the bucket
      1.9.3 Strehl ratio
      1.9.4 Wavefront error
      1.9.5 Central lobe power
      1.9.6 Beam parameter product
      1.9.7 Brightness
      1.9.8 Times the diffraction limit
      1.9.9 Summary: What each metric is designed to determine

2 What Your Beam Analyzer Manual Didn't Tell You: How to Build Your Own M2 Device (or Understand Theirs)
2.1 Preparing to Purchase a Commercial Beam Analyzer
2.2 Resources
      2.2.1 Summary of the ISO standards on laser beam quality
2.3 Equipment
      2.3.1 Camera selection
      2.3.2 Stage tradeoffs
      2.3.3 Filters
2.4 Dark Current Noise and Zeroing
2.5 Data Windowing
      2.5.1 Noise equivalent aperture (NEA)
      2.5.2 Error terms due to data windowing
2.6 Curve Fitting
2.7 Error Determination in M2 Measurements
      2.7.1 Error estimation
      2.7.2 Variance of second-moment radius due to discretization error
      2.7.3 Variance of second-moment radius due to dark current noise
      2.7.4 Error in NEA estimation
      2.7.5 Variance of second-moment radius due to NEA estimation error
      2.7.6 Total variance in second-moment radius measurements
      2.7.7 Effect of averaging multiple shots on second-moment radius variance
2.8 Knife-Edge Measurements
      2.8.1 ISO two-point knife-edge method
      2.8.2 Single-point variable-aperture method
2.9 Conclusions: M2

3 How to Design Your Own Beam Quality Metric
3.1 Overview: Synthesis, Analysis, and Comparison
3.2 Requirements Synthesis
      3.2.1 Determining the nature of application requirements: producing a minimally effective beam
      3.2.2 Propagating minimally effective beams backward from target to aperture produces the best Strehl ratio
      3.2.3 Propagating a filled aperture forward from aperture to target produces the best spot size
      3.2.4 Bounding plausible aperture–target–beam combinations
      3.2.5 Choosing and documenting the metric
3.3 Specification Analysis
      3.3.1 Determining the reference beam
      3.3.2 Determining the basis of comparison between the actual beam and the reference beam
      3.3.3 Determining the definition of beam radius
      3.3.4 Completely specifying key metrics for measurement of beam quality
      3.3.5 Obtaining programmatic, technical, and contractual buy-in
      3.3.6 Fully documenting the beam quality specification
3.4 Comparative Beam Quality Metrics
3.5 Example: Generic VPIB-related Specifications
3.6 Example: Requirements Area
3.7 Example: System Beam Quality Metric
3.8 Example: Core and Pedestal Metrics

4 Beam Quality Metric Conversion
4.1 Gaussian Beam Quality Conversions
      4.1.1 Gaussian conversion: VPIB
      4.1.2 Gaussian conversion: HPIB
      4.1.3 Gaussian conversion: Strehl ratio
      4.1.4 Gaussian conversion: Phase aberration
      4.1.5 Gaussian conversion: Brightness
4.2 General Beam Quality Conversions
      4.2.1 Beam quality metrics versus uncorrelated Gaussian phase noise
      4.2.2 Beam quality metrics versus uncorrelated Gaussian amplitude noise

5 Arrays
5.1 Sources of Beam Quality Degradation
      5.1.1 Fill factor considerations
      5.1.2 Phasing errors
      5.1.3 Misalignment errors
      5.1.4 Emitter degradation
5.2 Adapting Beam Quality Metrics for Array Use
      5.2.1 Radius metrics in the near and far field
5.3 Thought Experiment: Loss of an Emitter

6 Cautionary Tales
6.1 Three Viewpoints on Gaussian Beam Propagation
6.2 Non-Gaussian Gaussians
6.3 The Effect of Truncation on Gaussian Beam Quality
6.4 Case Studies
      6.4.1 Fast cameras (jitter)
      6.4.2 Ever-changing near-field diameter (inscribed, circumscribed, square versus round, cutoffs, etc.)
      6.4.3 Creative time gating (taking only the good part)
      6.4.4 Gaming the beam profile (annular)
      6.4.5 Let's be fair to the laser (elliptic)
      6.4.6 Power and beam quality mismatch
      6.4.7 Adjusting data to get a "proper" PIB curve
6.5 What to Look for in Advertising

7 Conclusions

Appendix
A.1 Derivation of M2 from Gaussian modes
      A.1.1 Hermite–Gaussian
      A.1.2 Laguerre–Gaussian
A.2 Deconvolving the ISO Standard
      A.2.1 ISO propagation equation
A.3 Beam Waist Versus Focal Plane

References

Index

Preface

This book will help the reader to thread through the subtleties of laser beam quality analysis and requirements synthesis. It begins with a review of basic laser properties, moves to definitions and implications of the various standard beam quality metrics such as M2, power in the bucket, brightness, beam parameter product, and Strehl ratio. For those who are only interested in measuring Gaussian beams from commercial lasers, Chapter 1, Chapter 2 "What Your Laser Beam Analyzer Manual Didn't Tell You," and the first three sections of Chapter 6 "Cautionary Tales" will be sufficient. For the reader in more off-the-map areas such as unique lasers, unstable resonators, multikilowatt lasers, MOPAs, or requirements generation and development, a reading of the entire text is recommended.

The author got his start in laser metrics when assigned to align a parametric oscillator as a researcher fresh out of graduate school. After making the oscillator operational, he used a commercial beam profiler and discovered that it gave a number of either 1.3 or 7, sometimes alternating between the two in rapid succession. A perusal of the product manual added little light; everything of real interest was hidden behind the word proprietary. He put the commercial black box back on the shelf. Armed with a video capture card, digital camera, motion control stage, the ISO 11145:1999 standard, and LabVIEW, he built his own laser profiler, including automated M2 measurement using both the camera and knife edge. In so doing, he made just about every mistake possible and came to understand how these metrics work.

This system was used internally for several years and then retired when research needs changed. It was not until a few years later—when several hundred-million-dollar-plus laser development programs ran into trouble over the issue of laser beam quality specifications—that he realized how lacking this basic information was in the directed-energy community. It turned out to be all too easy to purchase a laser system that met specification but would not accomplish the intended task. His first beam quality publication, "Appropriate measures and consistent standard for high energy laser beam quality" was published in the Summer 2006 edition of the Journal of Directed Energy and won several awards. Other papers expanded the body of practical beam quality literature and were developed into a laser beam quality course that has been a regular feature of several Directed Energy Professional Society (DEPS) conferences and has been taught at SPIE's Defense, Security, and Sensing Symposia. This text is an outgrowth of these short courses.

T. Sean Ross
March 2013


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