Theoretical background

Introduction

Note

This section covers the very minimum concepts one should understand in order to run BeamProfiler. For more detailed information check out the References, in special reference 1.

Several ISO and non-ISO characterizing parameters must be associated with a user-defined value called clip-level (denoted by the Greek letter eta \(\eta\)). The clip-level defines a fraction of the characterizing parameter associated with it, and it is mathematically defined as (\(0 \leq \eta < 1\)). For instance, if the maximum power density (\(E_{max}\)) of a laser beam is \(1000 ADC/px\), then the clip-level power density \(E_{\eta CL}\) considering \(\eta = 0.8\) is \(800 ADC/px\).

Similarly, some ISO and non-ISO characterizing parameters must be associated with two clip-levels, namely the upper clip-level (denoted by the Greek letter eta \(\eta\)) and the lower clip-level (denoted by the Greek letter epsilon \(\epsilon\)). The upper clip-level and the lower clip-level are mathematically expressed as \(0 \leq \epsilon < \eta < 1\). The values of eta and epsilon largely depend on the quality requirements of the process that uses the laser beam.

Lastly, a few ISO and non-ISO characterizing parameters depend on a normal fit of the the histogram associated with the pdd of the laser beam. Often times a single Gaussian distribution does not provide a proper fit, therefore BeamProfiler offers the option to use a mixture of up to three Gaussian distributions. You can set the variable mix to define the number of normal mixtures used in the normal fit.

References

On this section you will find a list of relevant references that will get you started on the theory of laser beam analysis and deepen your understanding on the field.

  1. Characterization of laser beams: theory and application in laser-assisted bonding process

    This tutorial paper offers a pedagogical introduction to the theory and application of laser beam analysis through the use of a minimum working example. It is ideal for newcomers to the field of laser beam characterization.

    Authors:

    Braganca, Wagno Alves and Kim, KyungOe

    Journal:

    Optical Engineering, 60(6), 060801 (2021)

    Access:

    https://doi.org/10.1117/1.OE.60.6.060801

    Parameters:

    clip-level beam width, clip-level edge width.

  1. ISO 136944:2018

    The official ISO document that specifies the test methods and parameters for the characterization of laser beam power density distribution. It is handy for those already familiar to the field of laser beam characterization.

    Authors:

    ISO/TC 172/SC 9 Laser and electro-optical systems

    Access:

    https://www.iso.org/standard/72945.html

    Parameters:

    total power, clip-level power, maximum power density, clip-level, power density, clip-level average power density, clip-level irradiation area, beam aspect ratio, fractional power, flatness factor, beam uniformity, plateau uniformity, edge steepness.

  1. ISO 11145:2018

    The official ISO document that defines basic terms, symbols, and units of measurement for the field of laser technology. It is suitable for those already familiar to the field of laser beam characterization.

    Authors:

    ISO/TC 172/SC 9 Laser and electro-optical systems

    Access:

    https://www.iso.org/standard/72944.html

    Parameters:

    beam centroid, beam width.

  1. Flat-top shaped laser beams: reliability of standard parameters

    This paper proposes a slight modification to the ISO standards in order to improve its reliability. It is ideal for those who fully understand the ISO standards and recognize its limitation.

    Authors:

    Chang, Chao and Cramer, Larry and Danielson, Don and Norby, James

    Proceedings:

    XV International Symposium on Gas Flow, Chemical Lasers, and High-Power Lasers

    Access:

    https://doi.org/10.1117/12.611248

    Parameters:

    modified plateau uniformity.

  1. Specifying excimer beam uniformity

    This paper defines the top-hat factor, a non-ISO definition that serves a a general indicator of beam quality with a single number. It is relevant for those already familiar with the ISO standards and want to explore other characterizing parameters commonly used in the industry.

    Authors:

    Abele, Chris Christian and Bunis, Jenifer Lynn and Caudle, George F and Klauminzer, Gary K

    Proceedings:

    Laser Energy Distribution Profiles: Measurement and Applications

    Access:

    https://doi.org/10.1117/12.143846

    Parameters:

    top-hat factor