ISO 11146 Calculation of Laser Beam Center, Diameter, and M²
Project description
by Scott Prahl
Simple and fast calculation of beam sizes from a single monochrome image based on the ISO 11146 method of variances. Some effort has been made to make the algorithm less sensitive to background offset and noise.
This module also supports M² calculations based on a series of images collected at various distances from the focused beam.
Extensive documentation can be found at <https://laserbeamsize.readthedocs.io>
Using laserbeamsize
Install with pip:
pip install user laserbeamsize
or run this code in the cloud using Google Collaboratory by selecting the Jupyter notebook that interests you.
use binder which will create a new environment that allows you to run Jupyter notebooks. This takes a bit longer to start, but it automatically installs laserbeamsize.
clone the laserbeamsize github repository and then add the repository to your PYTHONPATH environment variable
Determining the beam size in an image
Finding the center and dimensions of a good beam image:
import imageio import numpy as np import matplotlib.pyplot as plt import laserbeamsize as lbs beam = imageio.imread("thene.pgm") x, y, dx, dy, phi = lbs.beam_size(beam) print("The center of the beam ellipse is at (%.0f, %.0f)" % (x,y)) print("The ellipse diameter (closest to horizontal) is %.0f pixels" % dx) print("The ellipse diameter (closest to vertical) is %.0f pixels" % dy) print("The ellipse is rotated %.0f° ccw from horizontal" % (phi*180/3.1416))
to produce:
The center of the beam ellipse is at (651, 491) The ellipse diameter (closest to horizontal) is 334 pixels The ellipse diameter (closest to vertical) is 327 pixels The ellipse is rotated 29° ccw from the horizontal
A visual report can be done with one function call:
lbs.beam_size_plot(beam) plt.show()
produces something like
or:
lbs.beam_size_plot(beam, r"Original Image $\lambda$=4µm beam", pixel_size = 12, units='µm') plt.show()
produces something like
Nongaussian beams work too:
# 12bit pixel image stored as highorder bits in 16bit values tem02 = imageio.imread("TEM02_100mm.pgm") >> 4 lbs.beam_size_plot(tem02, title = r"TEM$_{02}$ at z=100mm", pixel_size=3.75) plt.show()
produces
Determining M²
Determining M² for a laser beam is also straightforward. Just collect beam diameters from five beam locations within one Rayleigh distance of the focus and from five locations more than two Rayleigh distances:
lambda1=308e9 # meters z1_all=np.array([200,180,160,140,120,100,80,60,40,20,0,20,40,60,80,99,120,140,160,180,200])*1e3 d1_all=2*np.array([416,384,366,311,279,245,216,176,151,120,101,93,102,120,147,177,217,256,291,316,348])*1e6 lbs.M2_radius_plot(z1_all, d1_all, lambda1, strict=True) plt.show()
produces
Here is an analysis of a set of images that were insufficient for ISO 11146:
lambda0 = 632.8e9 # meters z10 = np.array([247,251,259,266,281,292])*1e3 # meters filenames = ["sb_%.0fmm_10.pgm" % (number*1e3) for number in z10] # the 12bit pixel images are stored in highorder bits in 16bit values tem10 = [imageio.imread(name)>>4 for name in filenames] # remove top to eliminate artifact for i in range(len(z10)): tem10[i] = tem10[i][200:,:] # find beam in all the images and create arrays of beam diameters options = {'pixel_size': 3.75, 'units': "µm", 'crop': [1400,1400], 'z':z10} dy, dx= lbs.beam_size_montage(tem10, **options) # dy and dx in microns plt.show()
produces
Here is one way to plot the fit using the above diameters:
lbs.M2_diameter_plot(z10, dx*1e6, lambda0, dy=dy*1e6) plt.show()
In the graph on the below right, the dashed line shows the expected divergence of a pure gaussian beam. Since real beams should diverge faster than this (not slower) there is some problem with the measurements (too few!). On the other hand, the M² value the semimajor axis 2.6±0.7 is consistent with the expected value of 3 for the TEM₁₀ mode.
License
laserbeamsize is licensed under the terms of the MIT license.
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