Laser Beam Profiling Applications

Laser Beam Profiling Applications

Characterize Time

Takes less than 30 minutes

Compatibility

With Low (LM) & High (HM) lenses

Compatibility

With Low (LM) & High (HM) lenses

Performances

Fluorescent-based imaging systems

Performances

Fluorescent-based imaging systems

Characterize Time

Takes less than 30 minutes

Category:

LASER BEAM PROFILER APPLICATIONS PAGE

This application pages focuses on parametrics used for choosing the right beam profiler. Laser beam profiling recommendations, M² measurements and measurement divergence.

How to choose the right beam profiler for my application?

When it comes to choosing a laser beam profiler, the choice can often be overwhelming. What follows are suggestions to make the right choice for you. All our laser beam profilers are based on 2D arrays (not scanning slits).  

1- Wavelength

What is my wavelength and am I working with 1 or several wavelengths? This will determine which technology to use (Si based CMOS sensors, InGaAs based Infrared sensors etc) for your laser beam profiling application

For wavelengths <1150 nm and in some cases <1320 nm, a CMOS or CCD based sensor will do the job. All CMOS and CCD based laser beam profilers we offer have no cover-glassNowadays, CMOS sensors are very performant and will be a cost-effective solution in >95% of the cases. CCD sensors have the advantage of being available with larger active areas for applications having multiple beams or large beams (>10mm). The type of neutral density (ND) filter used impacts the cut-on of the sensitivity. 

400 – 1150 nm (or 1320 nm)

Use an absorptive type filter. Each filter is fabricated from a glass substrate that has been selected for its spectrally flat absorption coefficient in the visible region. By varying the type and thickness of the glass used, an entire line of absorptive ND filter is possible. 

By default, all CinCam CMOS laser beam profilers are delivered with a built-in OD3.0 absorptive filter with a wedge to minimize interference effects due to parallel surfaces. 

320 – 1150 nm (or 1320 nm)

Use a reflective type filter. Reflective ND filters consist of thin film optical coatings, typically metallic, that has been applied to a glass substrate. The coating optimization is available for specific wavelength ranges such as UV, VIS or NIR. The thin film coating primarily reflects light back toward the source. User should take special care to ensure the reflected light does not interfere with the system setup. 

240 – 1150 nm 

This range can be achieved by removing the micro-lens array used typically to increase the fill-factor of each pixel. The glass used blocks UV light and therefore, by removing it, sensitivity as low as 240 nm is achievable. 

<150 – 1150 nm

This range can be achieved using a special fluorescent coating directly on the CMOS sensor. A thin layer of  UV to VIS converting coating which absorbs UV light and emits visible  light instead is covering the sensor. The robust fluorescent material is ideal for UV imaging. The material shows an excellent quantum yield of nearly 100% for wavelengths below 450 nm and down to 100 nm. In contrast there is a high transparency of the material for wavelengths above 480 nm which gives a very good response even in the visible and near infrared wavelengths.

~1550 nm

Can be achieved using a special phosphor coating directly on the CMOS sensor. The coating used is based on a complex and non-charge anti-stokes material with unique emission properties and converts 1495 nm-1595 nm photons to visible and detectable wavelengths without fading or image lag. We offer a non-linearity software correction. 

Because of the particles’ size, the effective resolution is 5-9µm no matter how small the pixel pitch of the sensor is. 

900 – 1700 nm

This requires the use of an InGaAs based sensor. You can achieve high QE from 1µm to 1.6µm. Even though QE can be very small before 900 nm, it is possible to some sensitivity as low as 800nm. 

2- Beam Size

How to choose the right laser beam profiler model given my beam size for laser beam profiling? Beam size is often taken at 1/e2 for a Gaussian beam. It is important to understand that a 1mm beam size for instance, does not mean that there is 0% energy outside a circle of 1mm of diameter. The tail of the beam, although of small intensity, is necessary in order to compute accurate ISO standard measurements on the beam. 

Minimum beam size measurable: The accuracy of the size measurement depends on the number of illuminated pixels. 15 pixels will give very high accuracy. Under 12 pixels, the accuracy is acceptable. It is not recommended to profile a laser beam with less than 10 illuminated pixels.  Therefore, the minimum measurable beam size of a laser beam profiler is pixel_ pitch (µm) x ~10For example: the CinCam CMOS 1201 laser beam profiler has a pixel pitch of 5.2µm. Therefore, the minimum beam size recommended is >52µm. The smallest pixel pitch available is 2.2µm (see CinCam CMOS 1204 laser beam profiler and CinCam CMOS PICO laser beam profiler)

Maximum beam size measurable: The active area of the laser beam profiler sensor will define the maximum beam size measurable. A rule of thumb is to take ~75% of the length in one direction. For example: The CinCam CMOS Nano 1.001 laser beam profiler has an active area of 11.3 x 11.3 mm. Therefore, the maximum beam size measurable is ~8.5mm. 

The largest CMOS sensor is the CinCam CMOS Nano 1.001 laser beam profiler with 11.3 x 11.3 mm active area. The largest CCD sensor is the CinCam CCD 3501 laser beam profiler with 36 x 24 mm active area. 

3- Pulsed or CW?

Is my laser continuous-wave or pulsed, and if so, what is its repetition rate? Some sensors have a rolling shutter which means all the pixels are not read at the same time but rather in a row-by-row fashion. For CW lasers, a rolling or global shutter is suitable. However for pulsed lasers with a repetition rate <1kHz, a global shutter is necessary. Pulsed lasers with a repetition rate >1kHz or >>1kHz, a global shutter or rolling shutter is suitable as such frequency will be ‘seen’ as CW by the laser beam profiler. In other words, the sensor will not see the difference. 

4- Power

What is my beam power and what OD or attenuation do I need? Whether using an absorptive or reflective type ND filter, laser beam profilers allows the maximum peak power of~1W. For power greater than 1W, a attenuation unit can be added directly to the laser beam profiler (works on all CMOS, CCD and InGaAs models thanks to a large spectral range of 190 nm to 2000 nm). The attenuator is based on two uncoated fused silica wedges and is designed for pre-attenuation of high intensity laser beams. The principle is based on the polarization effect by reflection on an optical surface. The s-pol. and p-pol. parts of the laser beam have different reflection factors. Orthogonal arrangement of the wedges compensates the polarization effect and allows neutral attenuation of the laser beam

You can use the prism attenuator up to intensities of 2GW/cm2 for pulse wave and 25kW/cm2 for continuous wave. It is possible to combine with neutral density filters for final power adjustment to the beam profiler sensitivity level. The high performance optical design in compact housing allows precise beam attenuation. 

3 models are available: 5W, 100W or 200W. 

5- Form factor

Do I have limited space in my optical setup? For the CMOS laser beam profilers, there are 3 body styles depending on the available room in the optical setup. 

The standard CinCam CMOS laser beam profiler models measure 40 x 40 x 20 mm. 

The CinCam CMOS Nano laser beam profiler models measure 29 x 29 x 20 mm with standard body. 

The CinCam CMOS PICO laser beam profiler is the smallest beam profiler in the world with only 15 x 15 x 11.5 mm. 

Click for more information and technical specs on: CinCam CMOS ,

6- Calibrations

Do I need a special calibration for my application? Go beyond standard laser beam profiling by enabling high performance features for your applications!

RayCi software automatically perform corrections but some corrections require user activation. Please refer to the Rayci Laser Beam Profiling Software user manual for more information. Additional calibrations such as absolute power calibration or angular calibration for divergent sources such as VCSEL are available and must be requested at the time of order. 

Power calibration

Saturation level is in some cases linear with input power. Based on this simple principle, the laser beam profiler can be power calibrated to show the absolute laser power in real time. Because the sensor sensitivity depends strongly on the laser wavelength, the calibration has to be done for each target wavelength. 

  • Price: $ per wavelength (specify wavelength upon order)
  • Accuracy: 5-7% 
  • Hardware availability: CinCam CMOS 1201 Nano, CinCam CMOS 1.001 Nano, CinCam CCD 3501
  • RayCi version availability: Lite, Standard, Pro
  • Type: Factory calibration

NEW! Angular calibration

For laser beam profiling applications with a highly divergent beam (typically > ±10°), QE and therefore the sensor response decreases with the angle of incidence. The angular response calibration corrects this effect, thus allowing accurate results. 

  • Price: $ per wavelength (specify wavelength upon order)
  • Accuracy: 10-15% @ ±40° (Level 1 calibration) or 3-5% @ ±40°  (Level 2 calibration)
  • Hardware availability: CinCam CMOS 1.001 Nano and CinCam CCD 3501
  • RayCi version availability: Standard, Pro
  • Type: Factory calibration & requires sensor position calibration

Sensor position calibration

Know the exact optical position of sensor surface relative to the housing with high accuracy. 

  • Price: $ 
  • Accuracy: 50µm
  • Hardware availability: CinCam CMOS 1.001 Nano, CinCam CMOS 1201 Nano, and CinCam CCD 3501
  • RayCi version availability: Lite, Standard, Pro
  • Type: Factory calibration 

Flat-field calibration

The calibration removes pixel sensitivity variations achieved by an illuminated flat field (White homogeneous image). If available, the 2D-View will be permanently corrected with these pixel sensitivity variations. 

  • Price: $ 
  • Accuracy: 2-3% over the whole sensor area
  • Hardware availability: CinCam CMOS 1.001 Nano, CinCam CMOS 1201 Nano, and CinCam CCD 3501
  • RayCi version availability: Lite, Standard, Pro
  • Type: Factory calibration 

Background calibration

The background calibration is a process to permanently subtract an acquired background image (reference image) from the live stream. This correction eliminates undesired illumination effects and it includes also a cold and hot pixel correction. 

  • Price: included 
  • Hardware availability: All
  • RayCi version availability: Lite, Standard, Pro
  • Type: Acquired image by the user

Baseline correction

RayCi laser beam profiling software calculates a correction plane from every live frame. This correction plane is a dynamically baseline correction. The software subtracts the correction plane from the live data and corrects the dynamical non-uniformities in the background. Additionally this eliminates the temporal changes in the background level. 

  • Price: included 
  • Hardware availability: All
  • RayCi version availability: Lite, Standard, Pro
  • Type: Acquired image 
  • Activation: by the user

Click for more information and technical specs on: CinCam CMOS CinCam CCDCinCam InGaAs and Rayci Software

What is M²?

In laser science, the parameter M²,M^2, also known as the beam quality factor, represents the degree of variation of a beam from an ideal Gaussian beam. It is calculated from the ratio of the beam parameter product (BPP) of the beam to that of a Gaussian beam with the same wavelength. It relates the beam divergence of a laser beam to the minimum focussed spot size that can be achieved. For a single mode TEM00 (Gaussian) laser beam, M²,M^2, is exactly one.

The M², M^2, value for a laser beam is widely used in the laser industry as a specification, and its method of measurement is regulated as an ISO Standard (11146-1 and 11146-2).

Why is M² important?

M² is useful because it reflects how well a collimated laser beam can be focused to a small spot, or how well a divergent laser source can be collimated. It is a better guide to beam quality than Gaussian appearance because there are many cases in which a beam can look Gaussian, yet have an M² value far from unity. Likewise, a beam intensity profile can appear very “un-Gaussian”, yet have an M² value close to unity.

The value of M² is determined by measuring D4σ or “second moment” width. Unlike the beam parameter product, M² is unitless and does not vary with wavelength.

The quality of a beam is important for many applications. In fiber-optic communications beams with an M² close to 1 are required for coupling to single-mode optical fiber.

M²,,M2, determines how tightly a collimated beam of a given diameter can be focused: the diameter of the focal spot varies as M², M2, and the irradiance scales as 1/M4. For a given laser cavity, the output beam diameter (collimated or focused) scales as M, and the irradiance as 1/M². This is very important in laser machining and laser welding, which depend on high fluence at the weld location.

Generally, M², M2, increases as a laser’s output power increases. It is difficult to obtain excellent beam quality and high average power at the same time due to thermal lensing in the laser gain medium.

How is M² measured?

Siegman’s proposal became popular because of its simplicity, but experimentally it isn’t so straightforward, and some uncertainties arise from these principles. For example, if you want to measure the waist radius in the lab, how can you be sure that your measurement device is positioned exactly at the focus?

And how far do you need to go to be in the far field to measure the divergence? Are these two data points enough? The folks at the International Organization for Standardization, or ISO, decided to put an end to all this confusion, so they wrote a norm explaining how to measure and calculate M2, M2, properly: ISO 11146.

The ISO norm explains a method to calculate M², M2, from a set of beam diameter measurements, in a way that minimizes sources of error. Here are the main steps:

  • Focus it with an aberration-free lens
  • Use the regression equations detailed in the norm to fit a hyperbola to your data points for both the X and Y axes. This improves the accuracy of the calculation by minimizing measurement error.
  • From this fit, extract the values for θ, w0, R and M², M2, for each axis.

The ISO norm also states a few extra rules about the measurement of diameters (especially when using array sensors such as CCD or CMOS sensors):

  • Use a region of interest of 3 times the diameter
  • Always remove the background noise before taking a measurement

Using CinSquare to accurately measure your laser beam quality.

CINOGY’s CinSquare is a compact and fully automated tool to measure the beam quality of CW and pulsed laser systems from the UV to SWIR spectral range. The system consists of a fixed focusing lens in front of a motorized translation stage carrying the camera-based CinCam beam profiler. Its operational robustness and reliability ensures continuous use applications in industry, science, research and development.

According to ISO 11146-1/2 the CinSquare system measures the complete beam caustic and determines M², M^2, waist position, divergence, etc., related to the reference plane. To facilitate its use, the CinSquare system is equipped with two alignment mirrors for exact positioning of the laser beam and a filter wheel for incremental beam attenuation.

RayCi software in action: an example of measurement

How to measure laser beam divergence ?

There are several ways to measure the laser beam divergence  We describe here 2 methods for laser beam divergence measurement.

Method 1:

Far-field laser beam divergence measurement using a lens of known focal length. By definition, the full divergence Θ=D/f where D is the diameter of the beam at the focal distance and f the focal length.

By placing the CinCam profiler at the focus distance and inputting the focal length directly in RayCi software, laser beam divergence measurement can be easily achieved.

Method 2:

Measurement by direct beam size calculation at several positions in the beam path

By definition, the divergence (full angle) Θ is given by:

Θ=2 arctan(D1-D2)/2L where D1,D2 are the beam diameter at different positions and L the distance between the measurement positions.

Description

LASER BEAM PROFILER APPLICATIONS PAGE

This application pages focuses on parametrics used for choosing the right beam profiler. Laser beam profiling recommendations, M² measurements and measurement divergence.

How to choose the right beam profiler for my application?

When it comes to choosing a laser beam profiler, the choice can often be overwhelming. What follows are suggestions to make the right choice for you. All our laser beam profilers are based on 2D arrays (not scanning slits).  

1- Wavelength

What is my wavelength and am I working with 1 or several wavelengths? This will determine which technology to use (Si based CMOS sensors, InGaAs based Infrared sensors etc) for your laser beam profiling application

For wavelengths <1150 nm and in some cases <1320 nm, a CMOS or CCD based sensor will do the job. All CMOS and CCD based laser beam profilers we offer have no cover-glassNowadays, CMOS sensors are very performant and will be a cost-effective solution in >95% of the cases. CCD sensors have the advantage of being available with larger active areas for applications having multiple beams or large beams (>10mm). The type of neutral density (ND) filter used impacts the cut-on of the sensitivity. 

400 – 1150 nm (or 1320 nm)

Use an absorptive type filter. Each filter is fabricated from a glass substrate that has been selected for its spectrally flat absorption coefficient in the visible region. By varying the type and thickness of the glass used, an entire line of absorptive ND filter is possible. 

By default, all CinCam CMOS laser beam profilers are delivered with a built-in OD3.0 absorptive filter with a wedge to minimize interference effects due to parallel surfaces. 

320 – 1150 nm (or 1320 nm)

Use a reflective type filter. Reflective ND filters consist of thin film optical coatings, typically metallic, that has been applied to a glass substrate. The coating optimization is available for specific wavelength ranges such as UV, VIS or NIR. The thin film coating primarily reflects light back toward the source. User should take special care to ensure the reflected light does not interfere with the system setup. 

240 – 1150 nm 

This range can be achieved by removing the micro-lens array used typically to increase the fill-factor of each pixel. The glass used blocks UV light and therefore, by removing it, sensitivity as low as 240 nm is achievable. 

<150 – 1150 nm

This range can be achieved using a special fluorescent coating directly on the CMOS sensor. A thin layer of  UV to VIS converting coating which absorbs UV light and emits visible  light instead is covering the sensor. The robust fluorescent material is ideal for UV imaging. The material shows an excellent quantum yield of nearly 100% for wavelengths below 450 nm and down to 100 nm. In contrast there is a high transparency of the material for wavelengths above 480 nm which gives a very good response even in the visible and near infrared wavelengths.

~1550 nm

Can be achieved using a special phosphor coating directly on the CMOS sensor. The coating used is based on a complex and non-charge anti-stokes material with unique emission properties and converts 1495 nm-1595 nm photons to visible and detectable wavelengths without fading or image lag. We offer a non-linearity software correction. 

Because of the particles’ size, the effective resolution is 5-9µm no matter how small the pixel pitch of the sensor is. 

900 – 1700 nm

This requires the use of an InGaAs based sensor. You can achieve high QE from 1µm to 1.6µm. Even though QE can be very small before 900 nm, it is possible to some sensitivity as low as 800nm. 

2- Beam Size

How to choose the right laser beam profiler model given my beam size for laser beam profiling? Beam size is often taken at 1/e2 for a Gaussian beam. It is important to understand that a 1mm beam size for instance, does not mean that there is 0% energy outside a circle of 1mm of diameter. The tail of the beam, although of small intensity, is necessary in order to compute accurate ISO standard measurements on the beam. 

Minimum beam size measurable: The accuracy of the size measurement depends on the number of illuminated pixels. 15 pixels will give very high accuracy. Under 12 pixels, the accuracy is acceptable. It is not recommended to profile a laser beam with less than 10 illuminated pixels.  Therefore, the minimum measurable beam size of a laser beam profiler is pixel_ pitch (µm) x ~10For example: the CinCam CMOS 1201 laser beam profiler has a pixel pitch of 5.2µm. Therefore, the minimum beam size recommended is >52µm. The smallest pixel pitch available is 2.2µm (see CinCam CMOS 1204 laser beam profiler and CinCam CMOS PICO laser beam profiler)

Maximum beam size measurable: The active area of the laser beam profiler sensor will define the maximum beam size measurable. A rule of thumb is to take ~75% of the length in one direction. For example: The CinCam CMOS Nano 1.001 laser beam profiler has an active area of 11.3 x 11.3 mm. Therefore, the maximum beam size measurable is ~8.5mm. 

The largest CMOS sensor is the CinCam CMOS Nano 1.001 laser beam profiler with 11.3 x 11.3 mm active area. The largest CCD sensor is the CinCam CCD 3501 laser beam profiler with 36 x 24 mm active area. 

3- Pulsed or CW?

Is my laser continuous-wave or pulsed, and if so, what is its repetition rate? Some sensors have a rolling shutter which means all the pixels are not read at the same time but rather in a row-by-row fashion. For CW lasers, a rolling or global shutter is suitable. However for pulsed lasers with a repetition rate <1kHz, a global shutter is necessary. Pulsed lasers with a repetition rate >1kHz or >>1kHz, a global shutter or rolling shutter is suitable as such frequency will be ‘seen’ as CW by the laser beam profiler. In other words, the sensor will not see the difference. 

4- Power

What is my beam power and what OD or attenuation do I need? Whether using an absorptive or reflective type ND filter, laser beam profilers allows the maximum peak power of~1W. For power greater than 1W, a attenuation unit can be added directly to the laser beam profiler (works on all CMOS, CCD and InGaAs models thanks to a large spectral range of 190 nm to 2000 nm). The attenuator is based on two uncoated fused silica wedges and is designed for pre-attenuation of high intensity laser beams. The principle is based on the polarization effect by reflection on an optical surface. The s-pol. and p-pol. parts of the laser beam have different reflection factors. Orthogonal arrangement of the wedges compensates the polarization effect and allows neutral attenuation of the laser beam

You can use the prism attenuator up to intensities of 2GW/cm2 for pulse wave and 25kW/cm2 for continuous wave. It is possible to combine with neutral density filters for final power adjustment to the beam profiler sensitivity level. The high performance optical design in compact housing allows precise beam attenuation. 

3 models are available: 5W, 100W or 200W. 

5- Form factor

Do I have limited space in my optical setup? For the CMOS laser beam profilers, there are 3 body styles depending on the available room in the optical setup. 

The standard CinCam CMOS laser beam profiler models measure 40 x 40 x 20 mm. 

The CinCam CMOS Nano laser beam profiler models measure 29 x 29 x 20 mm with standard body. 

The CinCam CMOS PICO laser beam profiler is the smallest beam profiler in the world with only 15 x 15 x 11.5 mm. 

Click for more information and technical specs on: CinCam CMOS ,

6- Calibrations

Do I need a special calibration for my application? Go beyond standard laser beam profiling by enabling high performance features for your applications!

RayCi software automatically perform corrections but some corrections require user activation. Please refer to the Rayci Laser Beam Profiling Software user manual for more information. Additional calibrations such as absolute power calibration or angular calibration for divergent sources such as VCSEL are available and must be requested at the time of order. 

Power calibration

Saturation level is in some cases linear with input power. Based on this simple principle, the laser beam profiler can be power calibrated to show the absolute laser power in real time. Because the sensor sensitivity depends strongly on the laser wavelength, the calibration has to be done for each target wavelength. 

  • Price: $ per wavelength (specify wavelength upon order)
  • Accuracy: 5-7% 
  • Hardware availability: CinCam CMOS 1201 Nano, CinCam CMOS 1.001 Nano, CinCam CCD 3501
  • RayCi version availability: Lite, Standard, Pro
  • Type: Factory calibration

NEW! Angular calibration

For laser beam profiling applications with a highly divergent beam (typically > ±10°), QE and therefore the sensor response decreases with the angle of incidence. The angular response calibration corrects this effect, thus allowing accurate results. 

  • Price: $ per wavelength (specify wavelength upon order)
  • Accuracy: 10-15% @ ±40° (Level 1 calibration) or 3-5% @ ±40°  (Level 2 calibration)
  • Hardware availability: CinCam CMOS 1.001 Nano and CinCam CCD 3501
  • RayCi version availability: Standard, Pro
  • Type: Factory calibration & requires sensor position calibration

Sensor position calibration

Know the exact optical position of sensor surface relative to the housing with high accuracy. 

  • Price: $ 
  • Accuracy: 50µm
  • Hardware availability: CinCam CMOS 1.001 Nano, CinCam CMOS 1201 Nano, and CinCam CCD 3501
  • RayCi version availability: Lite, Standard, Pro
  • Type: Factory calibration 

Flat-field calibration

The calibration removes pixel sensitivity variations achieved by an illuminated flat field (White homogeneous image). If available, the 2D-View will be permanently corrected with these pixel sensitivity variations. 

  • Price: $ 
  • Accuracy: 2-3% over the whole sensor area
  • Hardware availability: CinCam CMOS 1.001 Nano, CinCam CMOS 1201 Nano, and CinCam CCD 3501
  • RayCi version availability: Lite, Standard, Pro
  • Type: Factory calibration 

Background calibration

The background calibration is a process to permanently subtract an acquired background image (reference image) from the live stream. This correction eliminates undesired illumination effects and it includes also a cold and hot pixel correction. 

  • Price: included 
  • Hardware availability: All
  • RayCi version availability: Lite, Standard, Pro
  • Type: Acquired image by the user

Baseline correction

RayCi laser beam profiling software calculates a correction plane from every live frame. This correction plane is a dynamically baseline correction. The software subtracts the correction plane from the live data and corrects the dynamical non-uniformities in the background. Additionally this eliminates the temporal changes in the background level. 

  • Price: included 
  • Hardware availability: All
  • RayCi version availability: Lite, Standard, Pro
  • Type: Acquired image 
  • Activation: by the user

Click for more information and technical specs on: CinCam CMOS CinCam CCDCinCam InGaAs and Rayci Software

What is M²?

In laser science, the parameter M²,M^2, also known as the beam quality factor, represents the degree of variation of a beam from an ideal Gaussian beam. It is calculated from the ratio of the beam parameter product (BPP) of the beam to that of a Gaussian beam with the same wavelength. It relates the beam divergence of a laser beam to the minimum focussed spot size that can be achieved. For a single mode TEM00 (Gaussian) laser beam, M²,M^2, is exactly one.

The M², M^2, value for a laser beam is widely used in the laser industry as a specification, and its method of measurement is regulated as an ISO Standard (11146-1 and 11146-2).

Why is M² important?

M² is useful because it reflects how well a collimated laser beam can be focused to a small spot, or how well a divergent laser source can be collimated. It is a better guide to beam quality than Gaussian appearance because there are many cases in which a beam can look Gaussian, yet have an M² value far from unity. Likewise, a beam intensity profile can appear very “un-Gaussian”, yet have an M² value close to unity.

The value of M² is determined by measuring D4σ or “second moment” width. Unlike the beam parameter product, M² is unitless and does not vary with wavelength.

The quality of a beam is important for many applications. In fiber-optic communications beams with an M² close to 1 are required for coupling to single-mode optical fiber.

M²,,M2, determines how tightly a collimated beam of a given diameter can be focused: the diameter of the focal spot varies as M², M2, and the irradiance scales as 1/M4. For a given laser cavity, the output beam diameter (collimated or focused) scales as M, and the irradiance as 1/M². This is very important in laser machining and laser welding, which depend on high fluence at the weld location.

Generally, M², M2, increases as a laser’s output power increases. It is difficult to obtain excellent beam quality and high average power at the same time due to thermal lensing in the laser gain medium.

How is M² measured?

Siegman’s proposal became popular because of its simplicity, but experimentally it isn’t so straightforward, and some uncertainties arise from these principles. For example, if you want to measure the waist radius in the lab, how can you be sure that your measurement device is positioned exactly at the focus?

And how far do you need to go to be in the far field to measure the divergence? Are these two data points enough? The folks at the International Organization for Standardization, or ISO, decided to put an end to all this confusion, so they wrote a norm explaining how to measure and calculate M2, M2, properly: ISO 11146.

The ISO norm explains a method to calculate M², M2, from a set of beam diameter measurements, in a way that minimizes sources of error. Here are the main steps:

  • Focus it with an aberration-free lens
  • Use the regression equations detailed in the norm to fit a hyperbola to your data points for both the X and Y axes. This improves the accuracy of the calculation by minimizing measurement error.
  • From this fit, extract the values for θ, w0, R and M², M2, for each axis.

The ISO norm also states a few extra rules about the measurement of diameters (especially when using array sensors such as CCD or CMOS sensors):

  • Use a region of interest of 3 times the diameter
  • Always remove the background noise before taking a measurement

Using CinSquare to accurately measure your laser beam quality.

CINOGY’s CinSquare is a compact and fully automated tool to measure the beam quality of CW and pulsed laser systems from the UV to SWIR spectral range. The system consists of a fixed focusing lens in front of a motorized translation stage carrying the camera-based CinCam beam profiler. Its operational robustness and reliability ensures continuous use applications in industry, science, research and development.

According to ISO 11146-1/2 the CinSquare system measures the complete beam caustic and determines M², M^2, waist position, divergence, etc., related to the reference plane. To facilitate its use, the CinSquare system is equipped with two alignment mirrors for exact positioning of the laser beam and a filter wheel for incremental beam attenuation.

RayCi software in action: an example of measurement

How to measure laser beam divergence ?

There are several ways to measure the laser beam divergence  We describe here 2 methods for laser beam divergence measurement.

Method 1:

Far-field laser beam divergence measurement using a lens of known focal length. By definition, the full divergence Θ=D/f where D is the diameter of the beam at the focal distance and f the focal length.

By placing the CinCam profiler at the focus distance and inputting the focal length directly in RayCi software, laser beam divergence measurement can be easily achieved.

Method 2:

Measurement by direct beam size calculation at several positions in the beam path

By definition, the divergence (full angle) Θ is given by:

Θ=2 arctan(D1-D2)/2L where D1,D2 are the beam diameter at different positions and L the distance between the measurement positions.