laserbeamsize 2.3.1
ISO 11146 Calculation of Laser Beam Center, Diameter, and M²
Requires Python: >=3.10
Keywords: variance, gaussian, M-squared, d4sigma, M2, M², spotsize, laser beam, ISO11146, divergence, beam waist, TEM00, beam diameter, beam parameter product, BPP, laser propagation, beam profiling, beam optics, beam measurement, laser metrology, beam quality, beam analysis

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laserbeamsize
=============

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``laserbeamsize`` is a Python library for fast and reliable calculation of laser beam sizes from images.  
It implements the ISO 11146 variance method with enhancements that reduce sensitivity to background offset, noise, and nonideal beam profiles.

The package also provides automated tools for estimating M² from beam diameter measurements taken at multiple propagation distances.

Extensive documentation is available at:

    https://laserbeamsize.readthedocs.io


Features
--------

- Robust beam size extraction using the ISO 11146 variance method
- Automatic estimation of centroid, major/minor axes, and rotation
- Works with Gaussian, astigmatic, and strongly non-Gaussian beams (TEM modes)
- Handles 8-, 12-, and 16-bit grayscale images
- One-function visual reporting tools
- Convenient functions for M² fitting and plotting
- Minimal dependencies


Installation
------------

Install using ``pip``::

    pip install laserbeamsize

Or with ``conda``::

    conda install -c conda-forge laserbeamsize

You can also run the library immediately in the browser using JupyterLite:

|lite|


Quick Start: Determining Beam Size
----------------------------------

Example showing how to compute beam center, major/minor axes, and rotation.

.. code-block:: python

    import imageio.v3 as iio
    import laserbeamsize as lbs

    file = "https://github.com/scottprahl/laserbeamsize/raw/main/docs/images/t-hene.pgm"
    beam = iio.imread(file)

    x, y, d_major, d_minor, phi = lbs.beam_size(beam)

    print(f"Beam center: ({x:.0f}, {y:.0f})")
    print(f"Major axis:  {d_major:.0f} pixels")
    print(f"Minor axis:  {d_minor:.0f} pixels")
    print(f"Rotation:    {phi * 180/3.1416:.0f}° CCW")

results in::

    Beam center: (651, 492)
    Major axis:  369 pixels
    Minor axis:  347 pixels
    Rotation:    -12° CCW

To produce an annotated visual report.

.. code-block:: python

    lbs.plot_image_analysis(beam)
    plt.show()

Resulting example:

.. image:: https://raw.githubusercontent.com/scottprahl/laserbeamsize/main/docs/images/hene-report.png
   :alt: HeNe beam analysis example


Astigmatic and Non-Gaussian Beams
---------------------------------

The analysis also works for beams that are not well approximated by a Gaussian.  
For example, a TEM\ :sub:`02`\  mode.

.. code-block:: python

    tem02 = imageio.imread("TEM02_100mm.pgm") >> 4  # 12-bit data stored in 16-bit container
    lbs.plot_image_analysis(tem02, title="TEM$_{02}$ at z=100 mm", pixel_size=3.75)
    plt.show()

Example output:

.. image:: https://raw.githubusercontent.com/scottprahl/laserbeamsize/main/docs/images/tem02.png
   :alt: TEM02 beam example


M² Determination
----------------

Estimating M² requires beam diameters at several locations along the propagation axis.  
The beam diameters should be measured within ±1 Rayleigh distance and more than ±2+ Rayleigh distances.

.. code-block:: python

    lambda1 = 308e-9  # meters
    z1 = np.array([-200,-180,-160,-140,-120,-100,-80,-60,-40,-20,0,20,40,60,80,99,120,140,160,180,200]) * 1e-3
    d1 = 2*np.array([416,384,366,311,279,245,216,176,151,120,101,93,102,120,147,177,217,256,291,316,348]) * 1e-6

    lbs.M2_radius_plot(z1, d1, lambda1, strict=True)
    plt.show()

Example fit:

.. image:: https://raw.githubusercontent.com/scottprahl/laserbeamsize/main/docs/images/m2fit.png
   :alt: M² fit example


Example: Non-ISO-Conforming Measurement Set
-------------------------------------------

The following analysis uses images collected at non-ideal distances but illustrates the fitting process.  
The beam is a HeNe laser operating predominantly in the TEM\ :sub:`01`\  mode and rotated -52°

.. code-block:: python

    lambda0 = 632.8e-9  # meters
    z = np.array([247, 251, 259, 266, 281, 292]) * 1e-3  # meters
    filenames = [repo + "sb_%.0fmm_10.pgm" % (number * 1e3) for number in z]

    # the 12-bit pixel images are stored in high-order bits in 16-bit values
    tem10 = [iio.imread(name) >> 4 for name in filenames]

    # remove top to eliminate artifact
    for i in range(len(z)):
        tem10[i] = tem10[i][200:, :]

    # find beam in all the images rotated -52° and create arrays of beam diameters
    options = {
        "pixel_size": 3.75,
        "units": "µm",
        "crop": [1400, 1400],
        "z": z,
        "phi_fixed": np.radians(-52),
        "iso_noise": False
    }

    d_minor, d_major = lbs.plot_image_montage(tem10, **options)
    plt.show()

Example montage output:

.. image:: https://raw.githubusercontent.com/scottprahl/laserbeamsize/main/docs/images/sbmontage.png
   :alt: Montage of beam images


Plotting the M² Fit
-------------------

Using the measured diameters:

.. code-block:: python

    lbs.M2_diameter_plot(z10, dx*1e-6, lambda0, dy=dy*1e-6)
    plt.show()

In the example, the dashed curve indicates the ideal divergence of a Gaussian beam.  
The fitted M² of approximately 2.6 ± 0.7 agrees with the expected value of 3 for a TEM\ :sub:`10`\  mode,  
though the undersampling results in underestimated divergence.

.. image:: https://raw.githubusercontent.com/scottprahl/laserbeamsize/main/docs/images/sbfit.png
   :alt: M² divergence comparison plot


Citation
--------

If you use ``laserbeamsize`` in academic, instructional, or applied technical work, please cite:

Prahl, S. (2025). *laserbeamsize: ISO 11146 Calculation of Laser Beam Center, Diameter, and M²* (Version 2.3.0) [Computer software]. Zenodo. https://doi.org/10.5281/zenodo.8346799

BibTeX
^^^^^^

.. code-block:: bibtex

   @software{laserbeamsize_prahl_2025,
     author    = {Scott Prahl},
     title     = {laserbeamsize: ISO 11146 Calculation of Laser Beam Center, Diameter, and M²},
     year      = {2025},
     version   = {2.3.0},
     doi       = {10.5281/zenodo.8346799},
     url       = {https://github.com/scottprahl/laserbeamsize},
     publisher = {Zenodo}
   }


License
-------

``laserbeamsize`` is distributed under the terms of the MIT license.