M² measurement withImagine Optic, 18 rue Charles de Gaulle, 91400 Orsay, France

Summary
One way to characterize a laser beam is to compute the beam quality factor called M² or Msquared. This factor is used to compare the divergence and the waist size of a beam to aGaussian one. It is equal to one in the case of a perfect TEM00 gaussian beam and its value
increases when the tested laser quality decreases (it won’t be possible to focus or collimate itperfectly).
This measurement is defined by the standard ISO 11146: the measurement of 10 differentframes is required to get the M² value. However, Imagine Optic developed a variation to accessto this value which needs one single measurement to generate the 10 frames. This approach isbased enabled by CAM SQUARED sensor, used together with the Application ‘M2’ based on theWAVEVIEW 4.3.2 metrology software.
This application note first introduces the new M² factor acquisition method developed byImagine Optic. It then presents the results obtained with CAM SQUARED by laser
manufacturers on three different sources.

Measurement of M2 with CAM SQUARED
B. Renard

23 March 2023 – Property of Imagine Optic

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I. M² computation: how does Imagine
Optic challenge the status quo?
The M² factor is defined by the international standard ISO11146 as:πw0 θM2 =λWhere Θ is the beam divergence, w_0 is the beam waistand λ is the wavelength (cf. Figure 1).

Figure 1: Beam parameters used to compute the M²
M² is greater or equal to 1. Unity means the laser presents
a perfect Gaussian beam and can be perfectly collimated(if divergent) or focused (if collimated) as in Fig. 2 below.

wavefront measurement and an intensity map at thesame time. Then, from these N intensity maps, the M²
value is computed -according to the standard ISO 11146as well as other characteristics. Note that N can be any
value above 10 so one can access the measurement inany plane of interest without moving and aligning thesensor.
Therefore, the measurement is faster, easier andrequires less space in the lab. Advantageously, it does
not require focusing lenses that can affect the opticalquality of the M2 measured.
Here is an example of twelve different planes when a553 nm circular beam is measured with the sensor
CAM SQUARED:

Figure 2: Example of a beam with a M² = 1.01 (left) and abeam with a M² = 2.44 (right)
M² acquisition according to the Standard ISO 11146:
The Standard ISO 11146 requires at least 10measurements: the beam is measured at 10 different
observation planes using a camera moving among the zaxis. Then, each of the 10 images is analyzed to computelaser characteristics.
Classic M² measurement:
Usually, measuring the M² requires a camera mounted ona translation stage or a graduated rail so the camera canbe moved to the 10 different positions. This method canbe time consuming and can be affected by any
perturbation during the measurement (vibrations,ambient light…). It also requires to choose a lens focusing
the beam within the travel range so that acquisition
points can be taken at different position away from thewaist.
Imagine Optic’s solution:
Based on feedback from its customer in the laser
manufacturing industry, Imagine Optic has developed
another method to measure the M² which consists inusing the propagation tool to generate N observation
planes from one single shot. This is possible because
Shack-Hartmann technology allows to acquire both aFigure 3: PSF slices in 12 different planes of a 553 nm circularlaser, M² = 1.07
The main advantage of this new approach to beam quality
testing is that only one shot is needed to acquire thedataset required to calculate the M² value. Indeed, thisfast measurement allows a live visualization and cantherefore be used to align optical benches in R&D labs
or in a production line. In addition, it can be used forthe characterization of pulsed laser and dynamic
effects such as thermal effects.
Measurement of M2 with CAM
SQUARED Application note
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II. Application ‘M2’: an easy-to-use
interface based on WAVEVIEWTM
The Application corresponds to an optimized display oflaser quality metrics based on WAVEVIEWTM long-provenmetrology software. It provides an instant visualization ofthe M² factor and of the intensity map at any observation
plane. One can access this value in only one shot.
The User Interface is divided in two main parts (cf. Fig 4):+ Diagrams (left): the first diagram represents the beamaccording to the yz axis. Users can move the red line inorder to choose the z position on which he.she wants tovisualize the xy beam intensity (second diagram below).
Note that 3D plots are available too.
+ Data (right): acquisition parameters are displayed in“General information” and one can find the following
metrics: M², waist position, waist size and Rayleighdistance in “Results”.

Figure 4: Application ‘M²‘
Users can choose the Standard ISO 11146 methodaccording to the beam to characterize:+ ISO 11146 – II+ ISO 11146 – circular+ ISO 11146 – astigmatic+ ISO 11146 – general astigmatism
Below are screenshots of two different measurements: aperfect gaussian beam (left) and a beam with astigmatism(right). For those two beams, the Application ‘M2’
computes the M² values: 1.01 and 3.64.

Figure 5: M² values and WAVEVIEWTM screenshots for a
perfect gaussian beam (left) and an aberrated beam (right)

III. Use case with experts at Oxxius
Setup:
Imagine Optic works hand in hand with laser
manufacturers and laser diagnostics experts to identify
customers’ needs and implement metrology solutions
that meet their requirements. This use case reported hereis the result of our collaboration with the laser
manufacturer Oxxius and presents data acquired by
Oxxius engineers while using the CAM SQUARED sensor
with the Application ‘M2’ based on the version WAVEVIEW
4.3.2 to measure and reconstruct the M² on threedifferent sources.
In order to do so, they placed each laser source in front of
the wavefront sensor and adjusted the distance betweenthem so that the analysis pupil is fully covered by thelaser beam while ensuring it was not cropped.
Here are the main specifications of CAM SQUARED usedby laser engineers in these tests:
Pupil size
Max frame
Wavelength
Total bench(mm²)
rate (Hz)(nm)
size (mm3)6.9 x 5.1
125
350 - 1100
50 x 50 x 55
Oxxius experts used the CAM SQUARED because it isworking from 350 to 1100 nm and therefore, only one
sensor was used to measure the three different laser
sources. According to them, measuring the M² withthis sensor was faster than their previous protocols:“only few seconds instead of more than two minutes”.
Moreover, as it is a very accurate and fast wavefront
sensor, it was also used to align the optical bench.

Measurement of M2 with CAM
SQUARED Application note
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Results:
Below are reported results on different beam shapes ofthree different laser references:

Conclusion
We report a laser diagnostic application consisting in themeasurement of the M2 parameter with a simple
wavefront sensor. M2 calculation is performed following
the reconstruction proposed in the standard ISO 11146,
while taking advantage of beam propagation ability of theShack-Hartmann wavefront sensors to drastically reducethe duration of the measurement procedure. In thisspecific case, Imagine Optic customer reduced
characterization time during production from 2 minutes
to a few seconds, therefore reducing metrology costs
associated to the manufactured lasers.

References
Laser at λ = 553 nm, circular

1. Standard ISO 11146:
https://www.iso.org/obp/ui/#iso:std:iso:11146:-1:ed2:v1:en
2. Imagine Optic would like to thank Oxxius team for their
feedback and assistance in the acquisition of this data.
Oxxius website: https://www.oxxius.com/

Laser at λ = 488 nm, astigmatic

Laser at λ = 375 nm, circular

Measurement of M2 with CAM SQUARED
Application notewww.imagine-optic.com
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