Optic equation - optic solution
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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.
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This module also supports M² calculations based on a series of images collected at various distances from the focused beam.
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Here is an analysis of a set of images that do not meet the ISO 11146 requirements for determining M² (because the image locations are not taken in right locations relative to the focus). These beam images are from a HeNe laser with slightly misaligned mirrors to primarily lase in a TEM₀₁ transverse mode. The laser resonator had a fixed rotation of 38.7° from the plane of the optical table.:
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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:
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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 semi-major axis 2.6±0.7 is consistent with the expected value of 3 for the TEM₁₀ mode.
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