laserbeamsize 2.5.0

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

The image-loading examples below also use imageio:

pip install imageio

Or with conda:

conda install -c conda-forge laserbeamsize

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

Quick Start: Determining Beam Size

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

import imageio.v3 as iio
import matplotlib.pyplot as plt
import laserbeamsize as lbs

data_url = "https://raw.githubusercontent.com/scottprahl/laserbeamsize/main/docs/images/"
file = data_url + "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.

lbs.plot_image_analysis(beam)
plt.show()

Resulting example:

Astigmatic and Non-Gaussian Beams

The analysis also works for beams that are not well approximated by a Gaussian. For example, a TEM₀₂ mode.

import imageio.v3 as iio
import matplotlib.pyplot as plt
import laserbeamsize as lbs

data_url = "https://raw.githubusercontent.com/scottprahl/laserbeamsize/main/docs/images/"
tem02 = iio.imread(data_url + "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:

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.

import matplotlib.pyplot as plt
import numpy as np
import laserbeamsize as lbs

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:

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 TEM₀₁ mode and rotated -52°

import imageio.v3 as iio
import matplotlib.pyplot as plt
import numpy as np
import laserbeamsize as lbs

data_url = "https://raw.githubusercontent.com/scottprahl/laserbeamsize/main/docs/images/"
lambda0 = 632.8e-9  # meters
z = np.array([247, 251, 259, 266, 281, 292]) * 1e-3  # meters
filenames = [data_url + f"sb_{number * 1e3:.0f}mm_10.pgm" 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_major, d_minor = lbs.plot_image_montage(tem10, **options)
plt.show()

Example montage output:

Plotting the M² Fit

Continuing with the measured diameters returned by the montage:

lbs.M2_diameter_plot(z, d_major * 1e-6, lambda0, d_minor=d_minor * 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 TEM₁₀ mode, though the undersampling results in underestimated divergence.

Citation

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

Prahl, S. (2026). laserbeamsize: ISO 11146 Calculation of Laser Beam Center, Diameter, and M² (Version 2.4.1) [Computer software]. Zenodo. https://doi.org/10.5281/zenodo.8346799

@software{laserbeamsize_prahl_2026,
  author    = {Scott Prahl},
  title     = {laserbeamsize: ISO 11146 Calculation of Laser Beam Center, Diameter, and M²},
  year      = {2026},
  version   = {2.4.1},
  doi       = {10.5281/zenodo.8346799},
  url       = {https://github.com/scottprahl/laserbeamsize},
  publisher = {Zenodo}
}

License

laserbeamsize is distributed under the terms of the MIT license.