w(z)2 = w2 Beam quality [Insert Figure 1] and the Strehl ratio
Characterising the quality of a laser beam and other optics in an optical system is critical when looking to understand the overall performance of the system. There are a variety of methods
that can be used to determine the performance of the laser, such as the M2
factor, the beam
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Beam quality and the strehl ra:o
quality and the strehl ra:o uality of a laser beam and other op7cs in an op7cal system is cri7cal when looking to all performance of the system. There are a variety of methods that can be used to mance of the laser, such as the M2 factor, the beam parameter product, and power ape of the beam itself must also be considered. When analysing the overall op7cal vidual components, the Strehl ra7o is used to describe the performance compared se methods gives a comprehensive understanding of the real performance of a be used to predict the final performance of the system.
23 - Feature Case Study: Op:cs - 1 page (Edmund Op:cs) sored content: Op:cs
quality and the strehl ra:o uality of a laser beam and other op7cs in an op7cal system is cri7cal when looking to all performance of the system. There are a variety of methods that can be used to mance of the laser, such as the M2 factor, the beam parameter product, and power ape of the beam itself must also be considered. When analysing the overall op7cal vidual components, the Strehl ra7o is used to describe the performance compared se methods gives a comprehensive understanding of the real performance of a be used to predict the final performance of the system.
parameter product, and power in the bucket. The shape of the beam itself must also be considered. When analysing the overall optical system as well as individual components, as individual components, the Strehl ratio is used to compare its actual vs ideal performance. Using these methods gives a comprehensive understanding of the real performance of a laser system and can be used to predict the final performance of the system.
The M2 factor
mon ways to characterise beam quality is with the M2 factor. This quan7ty quality by comparing the shape of the beam to an ideal Gaussian beam. According 11146, the M2 factor is dependent on the beam waist (w0), the divergence angle of lasing wavelength (λ), such that:1
describes the beam quality by comparing the shape of the beam to an ideal Gaussian beam. According to the ISO Standard 11146, the M2
mon ways to characterise beam quality is with the M2 factor. This quan7ty quality by comparing the shape of the beam to an ideal Gaussian beam. According 11146, the M2 factor is dependent on the beam waist (w0), the divergence angle of lasing wavelength (λ), such that:1
on the beam waist (w0
factor is dependent ), the
ctor
ost common ways to characterise beam quality is with the M2 factor. This quan7ty beam quality by comparing the shape of the beam to an ideal Gaussian beam. According ndard 11146, the M2 factor is dependent on the beam waist (w0), the divergence angle of and the lasing wavelength (λ), such that:1
divergence angle of the laser (θ), and the lasing wavelength (λ), such that:1
M2 = M2 =
r the divergence angle of a gaussian beam: r the divergence angle of a gaussian beam:
Additionally, consider the divergence angle of a gaussian beam:
πω0θ λ
πω0θ λ
consider the divergence angle of a gaussian beam:
θgaussian = λ πω0
M2 =
ian ian
that the M2 factor for a diffrac7on limited gaussian beam is equal to 1 by for θ in equa7on 1. The equa7on simplifies as follows:
that the M2 factor for a diffrac7on limited gaussian beam is equal to 1 by for θ in equa7on 1. The equa7on simplifies as follows:
θgaussian = λ πω0
n θgaussian M2 =
o show that the M2 factor for a diffrac7on limited gaussian beam is equal to 1 by (3) πω0
M2 =
o the real-world performance of a laser, this value must be greater than or equal to er than this are not possible. Lower M2 factors more efficiently u7lise the beam’s ter focus. The M2 factor is also used when approxima7ng the radius of the
for θ in equa7on 1. The equa7on simplifies as follows: πω0
It is possible to show that the M2 factor for a diffraction-limited gaussian beam is equal to 1 by substituting in for θ in equation 1. The equation simplifies as follows:
πω0 λ * λ
πω0 λ * λ
o the real-world performance of a laser, this value must be greater than or equal to er than this are not possible. Lower M2 factors more efficiently u7lise the beam’s ter focus. The M2 factor is also used when approxima7ng the radius of the
M2 =
πω0 λ * λ
πω0 = 1 Beam parameter product
the M2 factor to understand the real world beam quality of a laser, ISO 11146 adius measurements at varying posi7ons on the op7cal axis in both the near and far e actual beam radius (w(z)) is related to the wavelength (λ), beam waist (w0) and M2
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the M2 factor to understand the real world beam quality of a laser, ISO 11146 adius measurements at varying posi7ons on the op7cal axis in both the near and far
θgaussian = λ πω0
= 1 = 1
Circular vs ellip:cal beams
ng this to the real-world performance of a laser, this value must be greater than or equal to s smaller than this are not possible. Lower M2 factors more efficiently u7lise the beam’s heir 7ghter focus. The M2 factor is also used when approxima7ng the radius of the beam.2
The shape of the beam plays a cri7cal role in determining the overall performance of the laser system. Most commonly, a laser beam is either circular or ellip7cal. Different beam shapes have different effects on the laser system's performance. For example, ellip7cal beams have a larger focused spot size than circular beams, resul7ng in overall lower irradiance. When characterising ellip7cal beams, the axis with the larger divergence is defined as the fast axis, while the smaller axis is defined as the slow axis. It is possible to change the shape of the laser beam using a variety of op7cs. When minor adjustments need to be made to the beam shape, a cylindrical lens can be used to either stretch or shrink the beam along the desired axis.
(3)
Ver t ical Beam Qualit y = Actual Beam Radius at Given Power Ideal Beam Radius at Given Power
(3) [Insert Figure 1] Beam parameter product
When evalua7ng the quality of a laser beam, the beam parameter product (BPP) is a valuable metric frequently used to characterise fiber or semiconductor lasers with large M2 factors. The BPP is defined as the product of the beam radius at the beam waist and the half-angle beam divergence. It is related to the M2 factor through the following equa7on:
g the quality of a laser beam and other op7cs in an op7cal system is cri7cal when looking to he overall performance of the system. There are a variety of methods that can be used to e performance of the laser, such as the M2 factor, the beam parameter product, and power The shape of the beam itself must also be considered. When analysing the overall op7cal ll as individual components, the Strehl ra7o is used to describe the performance compared sing these methods gives a comprehensive understanding of the real performance of a and can be used to predict the final performance of the system.
One of the most common ways to characterise beam quality is with the M2
factor. This quantity Power in the bucket w(z)2 = w2
Figure 1: Despite containing 0% of the TEM00 mode, this beam cross sec7on s7ll looks to be Gaussian at this given plane. This demonstrates why mul7ple measurements are necessary to fully ensure the laser’s M2 factor accurately measured.
The power in the bucket (PIB) technique for characterising beam quality is most frequently used with high-power laser systems. It is calculated by integra7ng the laser power over a specific "bucket," which refers to a par7cular spot on the material's surface being processed. The specifica7ons of the ideal near- field bucket shape are cri7cal for making accurate comparisons to ideal scenarios. Addi7onally, the far- field bucket shape must be well-defined. PIB is commonly reported in terms of horizontal and ver7cal beam quality, as follows:4
Hor izontal Beam Qualit y = Ideal Power in Bucket Actual Power in Bucket
Ver t ical Beam Qualit y = Actual Beam Radius at Given Power Ideal Beam Radius at Given Power
Figure 1: Despite containing 0% of the TEM00 mode, this beam cross sec7on s7ll looks to be Gaussian at this given plane. This demonstrates why mul7ple measurements are necessary to fully ensure the laser’s M2 factor accurately measured.
w(z)2 = w2 [Insert Figure 1] 0 1 + (z − z0)2 (
M2λ πw2
2 References: 0 )
πω0θ λ
Power in the bucket
The power in the bucket (PIB) technique for characterising beam quality is most frequently used with high-power laser systems. It is calculated by integra7ng the laser power over a specific "bucket," which refers to a par7cular spot on the material's surface being processed. The specifica7ons of the ideal near- field bucket shape are cri7cal for making accurate comparisons to ideal scenarios. Addi7onally, the far- field bucket shape must be well-defined. PIB is commonly reported in terms of horizontal and ver7cal beam quality, as follows:4
Power in the bucket The power in the bucket (PIB) technique for characterising beam quality is most frequently used with high-power laser systems. It is calculated by integrating the laser power over a specific “bucket”, which refers to a particular spot on the material’s surface being processed. The specifications of the ideal near- field bucket shape are critical for making accurate comparisons to ideal scenarios. Additionally, the far-field bucket shape must be well defined. PIB is commonly reported in terms of horizontal and vertical beam quality, as follows:4
(1) (1)
(2) (2)
BPP = M2λ π
(1) (2)
Since M2 must be ≥1, the minimum value for BPP would be equal to λ/π. Thus, a larger BPP equates to worse beam quality.
0 1 + (z − z0)2 (
[Images] Figure 1 (as per copy, no cap:on required)
Circular vs elliptical beams The shape of the beam plays a critical role in determining the overall performance of the laser system. Most commonly, a laser beam is either circular or elliptical. Different beam shapes have different effects on the laser system’s performance. For example, elliptical beams have a larger focused spot size than circular beams, resulting in overall lower irradiance. When characterising elliptical beams, the axis with the larger divergence is defined as the fast axis, while the smaller axis is defined as the slow axis. It is possible to change the shape of the laser beam using a variety of optics. When minor adjustments need to be made to the beam shape, a cylindrical lens can be used to either stretch or shrink the beam along the desired axis.
(4)
M2λ πw2
2 0 )
(5) (6)
(7) More information
Hor izontal Beam Qualit y = Ideal Power in Bucket Actual Power in Bucket
(5) (6)
For more from Edmund Optics on assessing beam quality and laser system performance, visit www.
edmundoptics.co.uk/knowledge- center/application-notes/lasers/
When evalua7ng the quality of a laser beam, the beam parameter product (BPP) is a valuable metric frequently used to characterise fiber or semiconductor lasers with large M2 factors. The BPP is defined as the product of the beam radius at the beam waist and the half-angle beam divergence. It is related to the M2 factor through the following equa7on:
3. 4. as follows:3
Figure 1: Despite containing 0% of the TEM00 mode, this beam cross sec7on s7ll looks to be Gaussian at this given plane. This demonstrates why mul7ple measurements are necessary to fully ensure the laser’s M2 factor accurately measured.
Power in the bucket
Three ways to assess laser beam quality, and what they mean for system performance
When applying this to the real-world performance of a laser, this value must be greater than or equal to 1 as M2
values smaller
the beam’s power with their tighter focus. The M2
than this are not possible. Lower M2
factors more efficiently utilise
used when approximating the radius of the propagating beam.2 When looking to use the M2
The power in the bucket (PIB) technique for characterising beam quality is most frequently used with high-power laser systems. It is calculated by integra7ng the laser power over a specific "bucket," which refers to a par7cular spot on the material's surface being processed. The specifica7ons of the ideal near- field bucket shape are cri7cal for making accurate comparisons to ideal scenarios. Addi7onally, the far- field bucket shape must be well-defined. PIB is commonly reported in terms of horizontal and ver7cal beam quality, as follows:4
Figure 1: Despite containing 0% of the TEM00 mode, this beam
cross-section still looks to be Gaussian at this given plane. This demonstrates why multiple measurements are necessary to fully ensure the laser’s M2
factor is accurately measured
Hor izontal Beam Qualit y = Ideal Power in Bucket Actual Power in Bucket
Ver t ical Beam Qualit y = Actual Beam Radius at Given Power Ideal Beam Radius at Given Power
Beam parameter product factor is also
factor to understand the real-world beam quality of a laser, ISO 11146 required five beam radius measurements at varying positions on the optical axis in both the near and far field of the beam. The actual beam radius (w(z)) is related to the wavelength (λ), beam waist (w0
) and M2 factor
Beam parameter product When evaluating the quality of a laser beam, the beam parameter product (BPP) is a valuable metric frequently used to characterise fibre or semiconductor lasers with large M2
factors. The BPP
When evalua7ng the quality of a laser beam, the beam parameter product (BPP) is a valuable metric frequently used to characterise fiber or semiconductor lasers with large M2 factors. The BPP is defined as the product of the beam radius at the beam waist and the half-angle beam divergence. It is related to the M2 factor through the following equa7on:
Strehl ra:o
The Strehl ra7o is used to analyse the performance of an op7c or op7cal system by c performance to its ideal performance. It is defined as the ra7o of the actual maximu irradiance of the op7c from a point source to the ideal maximum irradiance from a t diffrac7on-limited op7c. This ra7o is approximately related to the RMS transmihed w that:5
is defined as the product of the beam radius at the beam waist and the half-angle beam divergence. It is related to the M2
factor through the following equation:
BPP = M2λ π
Since M2 must be ≥1, the minimum value for BPP would be equal to λ/π. Thus, a larger BPP equates to worse beam quality.
Since M2 Circular vs ellip:cal beams must be ≥1, the minimum
The shape of the beam plays a cri7cal role in determining the overall performance of the laser system. Most commonly, a laser beam is either circular or ellip7cal. Different beam shapes have different effects on the laser system's performance. For example, ellip7cal beams have a larger focused spot size than circular beams, resul7ng in overall lower irradiance. When characterising ellip7cal beams, the axis with the larger divergence is defined as the fast axis, while the smaller axis is defined as the slow axis. It is possible to change the shape of the laser beam using a variety of op7cs. When minor adjustments need to be made to the beam shape, a cylindrical lens can be used to either stretch or shrink the beam along the desired axis.
References: 1.
Here, S represents the op7c's Strehl ra7o, and σ is defined as the op7c's RMS wavefr in waves. When S is equal to 1, the op7c is said to be ideal and completely free of ab real-world lenses with a Strehl ra7o greater than or equal to 0.8 are considered to b limited."
value for BPP would be equal to λ/π. Thus, a larger BPP equates to worse beam quality.
Here, S represents the optic’s
1. Interna'onal Organiza'on for Standardiza'on. (2005). Lasers and laser-rela methods for laser beam widths, divergence angles and beam propaga'on ra
2. PaschoKa, Rüdiger. Encyclopedia of Laser Physics and Technology, RP Photon
www.rp-photonics.com/
encyclopedia.html.
Strehl ratio, and σ is defined as the optic’s RMS wavefront error reported in waves. When S is equal to 1, the optic is said to be ideal and completely free of aberrations. However, real-world lenses with a Strehl ratio greater than or equal to 0.8 are considered to be “diffraction-limited”. l
3. Hofer, Lucas. “M² Measurement.” DataRay Inc., 12 Apr. 2016,
www.dataray.
measurement.html.
4. Strehl, Karl W. A. “Theory of the telescope due to the diffrac'on of light,” Lei 5. Mahajan, Virendra N. "Strehl ra'o for primary aberra'ons in terms of their a JOSA 73.6 (1983): 860-861.
(4) 2.
International Organization for Standardization. (2005). ‘Lasers and laser- related equipment – Test methods for laser beam widths, divergence angles and beam propagation ratios’ (ISO 11146).
Paschotta, Rüdiger. Encyclopedia of Laser Physics and Technology, RP Photonics, October 2017,
www.rp-photonics.com/
encyclopedia.html.
Hofer, Lucas. ‘M² Measurement’. DataRay Inc., 12 Apr. 2016,
www.dataray.com/blog-
m2-measurement.html.
5.
Strehl, Karl W. A. ‘Theory of the telescope due to the diffraction of light,’ Leipzig, 1894.
Mahajan, Virendra N. ‘Strehl ratio for primary aberrations in terms of their aberration variance.’ JOSA 73.6 (1983): 860-861.
S = exp[ − (2πσ)2]
The Strehl ratio The Strehl ratio is used to analyse the performance of an optic or optical system by comparing its true performance with its ideal performance. It is defined as the ratio of the actual maximum focal spot irradiance of the optic from a point source to the ideal maximum irradiance from a theoretical diffraction-limited optic. This ratio is approximately related to the RMS transmitted wavefront error such that5
(5) (6)
: (7)
0 1 + (z − z0)2
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(
M2λ πw2
2 0 )
THE 2023 GUIDE TO LASER SYSTEMS LASER SYSTEMS EUROPE 43
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