Gentec Beamage M2 User manual

Beamage-M² User Manual Revision 6

Beamage-M² User Manual Revision 6 i
WARRANTY
First-Year Warranty
The Gentec-EO Beamage series beam profiler carries a one-year warranty (from the date of shipment) against
material and/or workmanship defects, when used under normal operating conditions. The warranty does not cover
damages related to battery leakage or misuse.
Gentec-EO Inc. will repair or replace, at Gentec-EO Inc.’s discretion, any Beamage that proves to be defective
during the warranty period, except in the case of product misuse.
Any attempt by an unauthorized person to alter or repair the product voids the warranty.
The manufacturer is not liable for consequential damages of any kind.
Contacting Gentec Electro-Optics Inc.
In case of malfunction, contact your local Gentec-EO distributor or nearest Gentec-EO Inc. office to obtain a return
authorization number. The material should be returned to:
Gentec Electro-Optics, Inc.
445, St-Jean-Baptiste Avenue, Suite 160
Québec, QC
Canada G2E 5N7
Tel: [phone]
Fax: [phone]
E-mail: [e-mail]
Website: gentec-eo.com
CLAIMS
To obtain warranty service, contact your nearest Gentec-EO agent or send the product, with a description of the
problem, and prepaid transportation and insurance, to the nearest Gentec-EO agent. Gentec-EO Inc. assumes no
risk of damage during transit. Gentec-EO Inc. will, at its discretion, repair or replace the defective product free of
charge or refund your purchase price. However, if Gentec-EO Inc. determines that the failure is caused by misuse,
alterations, accident, or abnormal conditions of operation or handling, it would therefore not be covered by the
warranty.

Beamage-M² User Manual Revision 6 ii
SAFETY INFORMATION
Do not use a Beamage-M² if the device or the detector appears damaged, or if you suspect that a Beamage-M² is
not operating properly.
Note: This equipment has been tested and was found to comply with the limits for a Class A digital
device, pursuant to part 15 of the FCC Rules. These limits are designed to provide reasonable
protection against harmful interference in a residential installation. This equipment generates,
uses, and can radiate radio frequency energy. If not installed and used in accordance with the
instructions, it may cause harmful interference to radio communications. However, there is no
guarantee that interference will not occur in a particular installation. If this equipment does cause
harmful interference to radio or television reception, which can be determined by turning the
equipment off and on, try to correct the interference by taking one or more of the following steps:
•Reorient or relocate the receiving antenna.
•Increase the distance between the equipment and receiver.
•Connect the equipment to an outlet that is on a different circuit than the receiver.
•Consult the dealer or an experienced radio/TV technician for help.
Caution: Changes or modifications not expressly approved in writing by Gentec-EO Inc. may void the
user’s authority to operate this equipment.

Beamage-M² User Manual Revision 6 iii
TABLE OF CONTENTS
1. BEAMAGE-M²...................................................................................................................................................0
1.1. INCLUDED WITH YOUR BEAMAGE-M2.............................................................................................................0
1.2. INTRODUCTION.............................................................................................................................................0
1.3. SPECIFICATIONS...........................................................................................................................................1
1.4. MECHANICAL DESCRIPTION............................................................................................................................3
1.4.1. Mechanical properties.........................................................................................................................3
1.4.2. Schematic ...........................................................................................................................................5
2. BEAMAGE-M² SETUP......................................................................................................................................6
2.1. MECHANICAL AND ELECTRICAL SETUP............................................................................................................6
2.2. LASER ALIGNMENT........................................................................................................................................7
2.3. SOFTWARE AND DRIVERS SETUP....................................................................................................................9
3. QUICK M2MEASUREMENT ......................................................................................................................... 10
4. THEORY......................................................................................................................................................... 13
4.1. UNDERSTANDING THE M2FACTOR .............................................................................................................. 13
4.1.1. Propagation Parameters.................................................................................................................. 13
4.1.2. Practical Measurement .................................................................................................................... 15
5. M2MEASUREMENT CONTROLS................................................................................................................. 16
5.1. M² IMAGES CONTROLS............................................................................................................................... 17
5.1.1. M2button.......................................................................................................................................... 17
5.1.2. M2Advanced button......................................................................................................................... 18
5.1.3. Image index...................................................................................................................................... 18
5.1.4. Previous Image and Next Image buttons......................................................................................... 18
5.1.5. Clear M² Buffer button...................................................................................................................... 19
5.1.6. M2Buffer Size.................................................................................................................................. 19
5.2. M² FILE CONTROLS ................................................................................................................................... 19
5.2.1. Open M² File .................................................................................................................................... 20
5.2.2. Export M² Data Only button ............................................................................................................. 22
5.2.3. Save All M² Images and Data button............................................................................................... 22
5.2.4. Print M² Report button...................................................................................................................... 23
5.3. M² SETUP TAB........................................................................................................................................... 24
5.3.1. M2Fixed Values............................................................................................................................... 25
5.3.2. Automatic Settings........................................................................................................................... 25
5.3.3. User-Defined Scan........................................................................................................................... 26
5.3.4. Manual Frames................................................................................................................................ 29
5.3.5. Data.................................................................................................................................................. 29
5.4. M² RESULTS.............................................................................................................................................. 32
5.4.1. Before lens....................................................................................................................................... 33
5.4.2. After Lens......................................................................................................................................... 33
5.4.3. M2Calculation.................................................................................................................................. 34
5.4.4. Definition scheme ............................................................................................................................ 34
5.5. DISPLAY WINDOW...................................................................................................................................... 35
6. M² MANUAL METHOD.................................................................................................................................. 36
6.1. PROCEDURE FOR MANUAL MEASUREMENT .............................................................................................. 37
7. TROUBLESHOOTING AND TIPS................................................................................................................. 39
7.1. THE PROGRAM CANNOT START BECAUSE MSVCR100.DLL IS MISSING […]...................................................... 39
7.2. BEAMAGE IS NOT DETECTED....................................................................................................................... 39
7.3. THE DISPLAY AREA IS COMPLETELY WHITE................................................................................................... 39
7.4. THERE IS NO SERIAL NUMBER DISPLAYED ON THE BEAMAGE SELECTOR WINDOW.......................................... 39
7.5. TIPS TO INCREASE THE FRAME RATE........................................................................................................... 39
7.6. THE BEAM DISAPPEARS FROM THE SENSOR................................................................................................. 40
7.7. ACTUAL SETTINGS DO NOT ALLOW AN M2MEASUREMENT............................................................................. 40
7.8. LENS CHOOSING GUIDE.............................................................................................................................. 40
7.9. THE BEAM IS TOO WEAK TO START AN AUTOMATIC ACQUISITION.................................................................... 41

Beamage-M² User Manual Revision 6 iv
7.10. OTHER ISSUES....................................................................................................................................... 42
8. DECLARATION OF CONFORMITY.............................................................................................................. 43
9. UKCA DECLARATION OF CONFORMITY................................................................................................... 45
APPENDIX A. ISO11146 AND ISO11670 DEFINITIONS .................................................................................... 47
APPENDIX B. RECYCLING AND SEPARATION PROCEDURE FOR WEEE ................................................... 50

Beamage-M² User Manual Revision 6 1
TABLE OF FIGURES
FIGURE 1-1:ASSEMBLED AUTOMATED M2MEASUREMENT SYSTEM...................................................................3
FIGURE 1-2:COMPLETE MECHANICS TOP VIEW .................................................................................................3
FIGURE 1-3:BEAMAGE-M² MODULE TOP,SIDE AND FRONT VIEW ........................................................................4
FIGURE 1-4:AUTOMATED M2MEASUREMENT SYSTEM SCHEMATIC ....................................................................5
FIGURE 2-1:COMPLETE ASSEMBLY OF BEAMAGE-M² SETUP..............................................................................6
FIGURE 2-2:BAD ALIGNMENT VS.GOOD ALIGNMENT..........................................................................................7
FIGURE 2-3: ALIGNMENT TUBE.........................................................................................................................8
FIGURE 2-4:BEAMAGE INSTALLER ...................................................................................................................9
FIGURE 3-1:PC-BEAMAGE LOGO...................................................................................................................10
FIGURE 3-2:BEAMAGE CAMERA SELECTOR POP-UP ........................................................................................10
FIGURE 3-3:SOFTWARE SETUP:STEP 4.........................................................................................................10
FIGURE 3-4:SOFTWARE SETUP:STEP 5.........................................................................................................11
FIGURE 3-5: SELECT THE ACTION FOLLOWING THE SETUP PHASE.....................................................................11
FIGURE 3-6: SOFTWARE REQUIRES THE LASER BEAM TO BE BLOCKED..............................................................12
FIGURE 3-7:M2ROUTINE DONE PROMPT.........................................................................................................12
FIGURE 4-1:GAUSSIAN BEAM PARAMETERS....................................................................................................13
FIGURE 4-2:POSITIONING OF THE BEAM DIAMETERS WHEN MEASURING A M2...................................................15
FIGURE 5-1:M2MAIN CONTROL BUTTONS.......................................................................................................16
FIGURE 5-2: M2IMAGES CONTROLS ...............................................................................................................17
FIGURE 5-3: M2BUTTON................................................................................................................................17
FIGURE 5-4: M2ADVANCED BUTTON ..............................................................................................................18
FIGURE 5-5: IMAGE INDEX .............................................................................................................................18
FIGURE 5-6: PREVIOUS IMAGE AND NEXT IMAGE BUTTONS..............................................................................18
FIGURE 5-7: CLEAR M² BUFFER.....................................................................................................................19
FIGURE 5-8: M² BUFFER SIZE........................................................................................................................19
FIGURE 5-9: M² FILE CONTROLS....................................................................................................................19
FIGURE 5-10: OPEN M² FILE..........................................................................................................................20
FIGURE 5-11: LESS THAN 20% OF AVAILABLE SPACE ON THE HARD DISK..........................................................20
FIGURE 5-12: LESS THAN 10% OF AVAILABLE SPACE ON THE HARD DISK..........................................................20
FIGURE 5-13: LESS THAN 255 MB OF AVAILABLE SPACE ON THE HARD DISK .....................................................21
FIGURE 5-14: EXPORT M² DATA ONLY BUTTON ..............................................................................................22
FIGURE 5-15: SAVE ALL M² IMAGES AND DATA BUTTON..................................................................................22
FIGURE 5-16: PRINT M² REPORT BUTTON ......................................................................................................23
FIGURE 5-17: M2PRINT REPORT ....................................................................................................................23
FIGURE 5-18:M² SETUP TAB .........................................................................................................................24
FIGURE 5-19:FIXED PARAMETERS .................................................................................................................25
FIGURE 5-20:TRANSLATION STAGE USER-DEFINED SCAN CONTROLS...............................................................26
FIGURE 5-21:STAGE SETTINGS WINDOW .......................................................................................................26
FIGURE 5-22: START BUTTON ........................................................................................................................27
FIGURE 5-23: STOP BUTTON..........................................................................................................................27
FIGURE 5-24:ROUTINE DONE POP-UP WINDOW...............................................................................................27
FIGURE 5-25: CURVE FIT PASSES UNDER ZERO.............................................................................................28
FIGURE 5-26: SAVE PREVIOUS DATA ..............................................................................................................28
FIGURE 5-27: CALCULATE M² BUTTON ...........................................................................................................29
FIGURE 5-28:MANUAL DISTANCE SETTING .....................................................................................................29
FIGURE 5-29: DATA BOX...............................................................................................................................29
FIGURE 5-30:DATA SECTION.........................................................................................................................30
FIGURE 5-31:CALCULATE M² BUTTON............................................................................................................30
FIGURE 5-32:M² RESULTS TAB......................................................................................................................32
FIGURE 5-33:CALCULATION RESULTS OF THE NATURAL BEAM BEFORE LENS....................................................33
FIGURE 5-34:CALCULATION RESULTS OF THE FOCUSED BEAM AFTER THE LENS ...............................................34
FIGURE 5-35 :M2AND BPP RESULTS ............................................................................................................34
FIGURE 5-36 :GAUSSIAN BEAM PARAMETERS SCHEMATIC BEFORE AND AFTER THE LENS..................................34
FIGURE 5-37:DISPLAY WINDOW SHOWING THE MEASURED DATA .....................................................................35
FIGURE 6-1: OPTICAL SETUP FOR THE M² MEASUREMENT ...............................................................................36
FIGURE 6-2: M2BUTTON................................................................................................................................37
FIGURE 6-3: M2FIXED VALUES WINDOW ........................................................................................................37

Beamage User Manual Revision 0
1. BEAMAGE-M²
1.1. INCLUDED WITH YOUR BEAMAGE-M2
The following items are included with BEAMAGE-M2:
Description
Part name
Part number
Beamage-M2 module
Beamage-M2 Module
203616
Beamage-4M camera with ND4.0 filter mounted
Beamage-4M
202884
3 m elbowed USB-3 cable
90° USB-3 cable
105048
USB-A to USB-B module control cable
M2 control cable
203617
Power supply 48V M2
M2 Power Supply
203465
Fluoresent card and 85 mm alignment tube
Alignment kit
203848
1/8”Flat head screwdriver
3/32”L-key
9/64”L-key
1.5 mm L-key
Planoconvex lenses (f = 500, 400, 300, 250 and 200 mm)
Camera’s calibration certificate
Beamage-M2 module conformity certificate
SM1-BNC adapter
USB stick
Pelican transport case
1.2. INTRODUCTION
Gentec-EO’s Beamage beam profiler now has a powerful ally in its quest towards M2measurement: The
Automated M2Measurement System, Beamage-M². With its low profile and smart hardware, Beamage-M²
is easy to set up on any optical table. Intended for use with a Beamage camera, equipped with a rapid
translation stage, and integrated in the PC-Beamage software, an M2measurement can be done in less
than 1 minute. It comes with a complete set of 2″optics, the only one on the market allowing you to directly
measure >1″beams. No need to add uncertainties by further shrinking the beam!
The M2factor can be considered a quantitative indicator of a laser beam quality. In terms of propagation, it
is an indicator of closeness to an ideal Gaussian beam at the same wavelength. Paired with a Beamage-
4M beam profiling camera, the Beamage-M² module provides a very quick M² measurement directly in the
PC-Beamage software.
6

Beamage-M² User Manual Revision 6 1
1.3. SPECIFICATIONS
M² System
Beamage-M²
Wavelength Range
350-1100 nm
Attenuation Range
ND0 - ND0.5 - ND1 - ND2 - ND1.5 - ND2.5 - ND3 - ND3.5
Beam Diameter Range
55 µm to 11.3 mm (at Beamage)
Damage Threshold
See specifications for Beamage-4M
Translation Stage
Travel Range
200 mm
Effective Optical Path
180 –587 mm
Lens Focal Length
200 mm
250 mm
300 mm
400 mm
500 mm
Optical Axis Height
86 mm
Typical Estimated M² Accuracy (depending
on the beam quality and optical
configuration)
5%
2% repeatability
Applicable Light Sources
CW and pulsed
Typical Measurement Time
45 sec

Beamage-M² User Manual Revision 6 2
Camera Specifications
See Beamage-4M manual
Sensor Technology
CMOS without cover glass
Pixel Dimension
5.5 µm
Pixel Count
4.2 MPixels
ADC
12 bits
Frame Rate
See Beamage-4M Manual
Minimum and Maximum Exposure Time
0.06 ms - 200 ms
USB Port
USB 3.0 ports for optimal performance
USB 2.0
General Specifications
Size
602 mm (L) x 193 mm (W) x 172 mm (H)
Weight
6.8 kg (15 lb)
Power Supply
48V DC, 1.25A out
Environmental
Storage Temperature
10 °C to 60 °C
Storage Humidity
RH < 90%
Operating Temperature
15 °C to 28 °C
Operating Humidity
RH < 80% (without condensation)
Measurements
M-Square
, 
Beam Parameter Product
, 
Width at Waist
, 
Divergence angle
, 
Waists Location and Offset
, , 
Rayleigh Length
, 
Astigmatism
Tip
This guide contains the software information needed to operate the
Beamage-M² automation. More information about the PC-Beamage
software and interface can be found in the Beamage User Manual.

Beamage-M² User Manual Revision 6 3
1.4. MECHANICAL DESCRIPTION
1.4.1.Mechanical properties
The overall appearance of the fully assembled Beamage-M² is shown below. A casing covers the moving
parts to protect them from dust and to prevent accidental misalignment of the factory-adjusted mirror (M4).
Figure 1-1: Assembled Automated M2Measurement System
Figure 1-2:Complete mechanics top view
Automated M2Measurement System with the casing removed.

Beamage-M² User Manual Revision 6 4
Figure 1-3: Beamage-M² module top, side and front view
#10–32 Camera set screw (use 3/32” hex screwdriver)

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1.4.2.Schematic
Figure 1-4: Automated M2 Measurement System schematic
Alignment mirrors
M1 and M2 allow the user to align the beam through the lens and on the Beamage. M1
is mounted on a translation stage that allows a better centring on the mirror pair, while
M2 is mounted on a fixed post. They both allow the usual “X” and “Y” angle alignment.
Variable neutral density filters (ND)
Three ND filters are held in separate toggle mounts, allowing the user to rapidly change the
beam attenuation factor. A sufficient attenuation factor set for the far field will usually be too
weak around the focal spot for the camera to adjust its exposure time. The variable density
filter eliminates the hassle of setting a cage system or multiple posts-mounted ND filters
during the measurement.
Lens
Five cage-mounted 2″lenses are supplied with every M2 system: 200 mm, 250 mm,
300 mm, 400 mm and 500 mm. The cages screw onto SM2 female thread.
Translation stage
A 200 mm motorized rail allows a computer-controlled position of the folding mirrors (M3 and
M4), which in turn allow a 400 mm beam path difference. The automation of the translation
stage allowed by the software is the key to a fast measurement.
Folding mirrors
M3 is glued to the TS while M4 allows an angular adjustment. This enables the best
possible beam alignment inside the translation chamber. M4 is factory-aligned.
Beamage camera
A Beamage profiling camera (BC) is held in a smooth borehole by a set screw and can
easily be removed when the M2measurement is completed. Use the provided 3/32” L-
key to unscrew.
Iris aperture
An iris aperture is used in order to facilitate the alignment.
M1
TS
M4
M3
ND
L1
M2
BC
Iris
TS
M4
M3
ND
L1
BC
M2
M1
Iris

Beamage-M² User Manual Revision 6 6
2. BEAMAGE-M² SETUP
Before a measurement, make sure that the entire device is in good condition and ready to work. This section
shows how to perform the set-up and verify that each component is working properly.
2.1. MECHANICAL AND ELECTRICAL SETUP
Figure 2-1: Complete assembly of Beamage-M² setup
1. Make sure the Beamage-4M camera is in place as shown in the image above. The connectors must be
facing upwards.
2. Verify the focal length of the lens placed into the SM2 threaded hole.
3. Plug the camera into a USB-3 port on your computer, equipped with the latest PC-Beamage software
version.
4. Connect the Beamage-M² rail to a USB-2 or USB-3 port. Note that the translation stage will only work
with the provided USB cable.
5. Connect the power cable to a power outlet. Upon connection, the rail should run by itself for a few
seconds.
6. Verify that the translation stage is in good working condition by turning the translation knob towards the
“far” and “near” positions, respectively. “Far” and “near” refer to the position of the stage relative to the
lens. Be sure to return the stage to the end of the “far” position prior to the laser alignment.

Beamage-M² User Manual Revision 6 7
2.2. LASER ALIGNMENT
The first time the Beamage-M² is being used, the laser must be aligned correctly to ensure that the beam
fits entirely on the camera’s sensor.
The mechanics simplify this task by putting all the optics at the same height. The mirrors on the moving
stage are factory-aligned so that the user should never need to adjust them. The only adjustment remaining
is the entry angle, controlled by mirrors M1 and M2.
The beam must be centred on the lens and the Beamage camera at the same time; this is our success
criteria.
1. Alignment:
a. Place the Beamage-M² on an optical table.
b. Fix at least two of the 5 anchoring points to the optical table in order to keep the module
from moving during or after alignment.
c. Install the Alignment Tube in front of the Iris (i.e., screw the tube on the Iris).
Note: the orange surface on the disk is fluorescent from 800 nm to 1700 nm.
d. Make sure the Beamage-M² mirrors are parallel to their mount prior to the alignment, it will
make it easier.
e. Block the output of the laser you wish to measure with the detector card or with a suitable
beam blocker then turn it on.
f. Be sure not to damage the system:
i. If your laser beam has a power higher than 100 mW, put some attenuation in the beam
path before mirror M1.
ii. Use ND-Filters for beams with a power lower than 1 W.
iii. Use a Beam Splitter for beams with a power higher than 1 W.
g. Align the beam towards the center of mirror M1 while trying to have it as parallel as
possible to the optical table. Use the detector card to help you align the beam from now on.
h. Use mirror M1 to align the beam at the center of the mirror M2.
i. Make sure the beam reaches the first disk of the alignment tube. Use mirror M1 to target
the center of the disk P1 (see Figure 2-3)
j. Once the beam passes through the disk P1, look through the tube’s slot to find where it hits
the disk P2.
k. Use mirror M2 to center the beam on the disk P2.
l. Repeat steps h. to k. until the beam is centred and passes through both the disks P1 and
P2.
m. Remove the alignment tube while keeping the iris in place.
n. Turn on the PC-Beamage software, press Start Capture and click on 2D Display.
Figure 2-2: Bad alignment vs. good alignment.
Left side: Bad alignment, causes the beam to shift a great distance on the sensor when the stage
is moving.
Right side: Good alignment, the beam is centered on both the lens and the camera.

Beamage-M² User Manual Revision 6 8
o. In the Advanced tab, click on the M² button. Two (2) new tabs open and the translation
stage automatically connects to the computer.
p. Click on the right arrow in the Manual Settings, this moves the stage to the farthest
possible position.
q. Observe the beam in the Display screen and use mirror M2 (see Figure 2-3: Alignment
tube) to center the beam on the sensor.
r. Click on the left arrow in Manual Settings, this moves the stage to the closest possible
position, then center the beam using mirror M1.
s. Repeat steps q. to s. if needed.
Figure 2-3: Alignment tube
On the left, the alignment tube mounted with its 2 fluorescent pinholes. On the right, schematics of the
alignment tube with mirrors M1 and M2 aligning a laser beam.
M1
M2
P1
P2
Alignment Tube

Beamage-M² User Manual Revision 6 9
2.3. SOFTWARE AND DRIVERS SETUP
Always use the latest version of the PC-Beamage software to ensure an optimal operation of the Beamage-
M² system and the most up-to-date automation features. The automatic control of the M2module requires
at least the 1.04.00 version of PC-Beamage. Here, we will guide you through the software
update/installation procedure. Note that the following software and firmware can also be found on the
USB key provided.
1. If PC-Beamage is already installed on your computer, the version is automatically verified at
every software boot, provided you have an internet connection. The update begins automatically.
2. Download the latest Beamage Installer at the following address:
https://www.gentec-eo.com/resources/download-center.
3. Click on the Install All button and follow the installation instructions.
Figure 2-4: Beamage Installer
Tip
By pressing the Install All button, you will install the latest version of the
PC-Beamage software, the Beamage driver and the driver for the
translation stage.

Beamage-M² User Manual Revision 6 10
3. QUICK M2MEASUREMENT
1. Start-up the PC-Beamage software.
Figure 3-1: PC-Beamage logo
2. Select the serial number of the camera recognized on the Beamage Selector pop-up; click OK.
Figure 3-2: Beamage camera selector pop-up
3. Turn on the laser you want to measure and make sure it is aligned according to section 2.2.
4. In the software, under the Advanced tab, click the M2button to activate the M² measurement
functions and the tabs M2Results and M2Setup.
Figure 3-3: Software setup: step 4

Beamage-M² User Manual Revision 6 11
5. Under M² Setup, fill in the Laser Wavelength and Focal Length fields.
Figure 3-4: Software setup: step 5.
6. Click RUN M² SETUP.
7. Click Yes to automatically start an M² measurement once the SETUP phase is completed.
Figure 3-5: Select the action following the setup phase
8. Execute the tasks required to obtain good measurement conditions during the setup phase. The
software might show pop-up windows when one of the following actions is required:
a. Change lens
b. Add attenuation
c. Remove attenuation

Beamage-M² User Manual Revision 6 12
9. Block the laser beam when the following pop-up appears:
Figure 3-6: Software requires the laser beam to be blocked to execute the background noise subtraction
10. Release the laser blocking once the Please block your laser pop-up disappears to let the Beamage-
M² device execute an automatic measurement.
11. Once the measurement is done, a window pops up. Press OK to reach the results tab.
Figure 3-7: M2 routine done prompt

Beamage-M² User Manual Revision 6 13
4. THEORY
4.1. UNDERSTANDING THE M2FACTOR
The M2factor, which is unit-less, can be considered a quantitative indicator of a laser beam quality. It
indicates the deviation of the measured beam from a theoretical Gaussian beam of the same wavelength.
It can be mathematically defined as the ratio between the Beam Parameter Product (beam waist radius
w0multiplied by divergence half-angle θ) of the measured beam with the theoretical Gaussian beam. Thus,
for a single mode ideal TEM00 theoretical Gaussian beam, the M2factor is exactly one. Since an ideal
Gaussian beam diverges more slowly than any other beam, the M2value is always greater than one. An
M2value very close to 1 indicates an excellent beam quality. This is associated with a low divergence and
a good ability to focus. Multimode lasers have higher M2factors.
4.1.1.Propagation Parameters
In the following equations, “th” refers to theoretical values and “exp” to experimental or real values.
The beam waist is defined as the location along the beam propagation axis where the beam radius reaches
its minimum value (see Figure 4-1). For a theoretical Gaussian beam, the beam radius 󰇛󰇜at any
position z along the beam axis is given by the following equation
1
:
󰇛󰇜󰇧
󰇨
where is the laser wavelength and , the theoretical beam waist radius.
As depicted in Figure 4-1, the theoretical Rayleigh Length is the distance (along the propagation axis)
between the beam waist and the position where the beam radius is times larger than the beam waist
(doubled cross-section).
Figure 4-1: Gaussian beam parameters
1
Siegman, A. E., 1993. Defining, measuring, and optimizing laser beam quality. Proceedings of SPIE,
Volume 1868, pp. 2-12.