BeamSquared® - Measurement of Long Rayleigh Range Lasers with Small Focal Spot

The development of remote material processing techniques requires increasing the accuracy of the process to permit creating smaller features. Laser systems, used for various industrial applications like material processing and micromachining, require small focal spots and at the same time, greater focal lengths. To achieve that, lasers systems combining larger beams, and lower M2, combined with longer focal length lenses are used. This results in smaller focal spots at longer distances from the laser and Rayleigh length, up to 20 meters.

A variety of single-mode fiber and solid-state lasers designated to meet the specifications of both a long-waist location and small focal spot size is now available on the markets. The laser systems require a new approach to their beam analysis technique.

Beam Propagation and Caustic analysis of lasers with small focal spot and long Rayleigh range performed by BeamSquared® (BSQ) equipped with conventional focusing lenses of 400 to 500 mm may not be ISO11146 Standard compliant due to pixel limitation of Beam Profiler camera. The limitation occurs if the measured beam covers an area on the camera sensor less than 20 pixels in diameter. Even when the beam waist diameter is larger than 20 pixels, more accurate measurement results are achieved when more pixels are covered. An additional parameter of ISO11146 defines that the caustic propagation measurement space should be at least 4 times the Rayleigh length of the laser.

To support ISO11146 standard measurement of such lasers, longer focal length lenses with high focal length accuracy are required.

Ophir introduces a set of lenses calibrated for accurate and repeatable propagation measurements of lasers having long Rayleigh length and small focal spot.

The Technique

The BeamSquared® (BSQ) measures laser beam widths after a focusing lens at several positions along the light propagation axis (Z), resulting in measurements of the laser M², size and location of laser beam waist, both for the focused beam after the lens and original laser.

Standard BSQ includes SP920 camera with Pixel pitch of 4.4μm, and Lens Kit includes focal lengths of 400mm and 500mm lenses.

In order to meet Laser Beam Profiling ISO11146 Standard, A Beam Waist diameter (W02) after focusing lens should preferably cover 20 of sensor area which is 88 μm, however, in some applications where high accuracy is required, covering more pixels is recommended.

A laser, with remote waist position and small waist size, analyzed using BSQ equipped with conventional 400 to 500 mm lenses, will result in a small beam waist and low coverage beam profiler camera sensor. For example, single mode lasers with very long Rayleigh lengths may not be suitably measured with the BeamSquared if standard, 400 to 600mm focal length lenses are used.

To improve the propagation measurement accuracy lasers with long Rayleigh lengths, larger beam waist diameters should be obtained by using longer focal length (f) lenses.

Model  Region  Focal length 
SP90554 UV 266-440 nm 750 mm
SP90558 UV 266-440 nm 1000 mm
SP90557 XNIR 1000-1550 nm 750 mm
SP90556 NIR 650-1000 nm 750 mm
SP90555 VIS 430-700 nm 750 mm
SP90559 VIS 430-700 nm 1000 mm

New Lens Implementation

The new lenses were chosen based on a special software tool capable to simulate various laser systems and parameters such as M2, BPP, focused beam waist size, Wavelength, and Rayleigh range. This simulation enabled Ophir to emulate a wide variety of existing laser systems to fit an optimal set of lenses for maximum coverage and accurate results. It was found that 750 and 1000 focal length lenses are the most compatible for these types of lasers.

Comparison of simulated and real measurement provides an accurate prediction of laser caustic parameters:

Before lens M² X Fitted Divergence X Waist Width X Waist Location X Rayleigh Length X
Simulation 1.028 0.203 mrad 4080 μm 6100 mm 20084 mm
BSQ Measured results 1.026 0.203 mrad 4077 μm 6103 mm 20091 mm

Lens Calibration

All BeamSquared lenses are subject to scrupulous tests to provide the most accurate instrument performance. However, for long Rayleigh range lasers, due to the increased focal length of the lenses, the precision of measurement becomes even more important as small errors can cause a significant offset of the results. Ophir have implemented a new BeamSquared® lenses calibration techniques to ensure the most accurate and repeatable Caustic and Beam Propagation measurements, with a maximum of 10% relative error in Rayleigh range and Waist Location, compared to >30% of uncalibrated lenses.

Example of Measurement using long focal length lenses

As demonstrated below, the Caustic measurement of a 633nm laser, having a 20-meter Rayleigh Length and M²=1.03, using a calibrated 750 mm lens, The BeamSquared provides the result of 147 μm Waist Width and 26 mm Rayleigh Length. The BeamSquared provides over 800 mm measurement range which makes it easy to make ISO11146 compliant measurements of well over 4 Rayleigh lengths.

BeamSquared® Users have conducted some trials comparing different lenses used for long, ~20 meter Rayleigh range, small focal spot, real-life laser systems. The results show, that when a 500 mm lens is used the Waist diameter covers only 10-13 pixels but when a longer focal length lens is used, Waist diameter covers 20 pixels and still BSQ's rail range covers more than 2 x Rayleigh length.

Laser Source (Before Lens)

Focal Length Waist Location Rayleigh length Beam Waist diameter after lens  Pixels on CCD
Laser 343 nm, M²=1.0
Rayleigh Length = 28M
Beam diameter = 3.5 mm
500 mm 480 mm 8.25 mm 60 μm 13
750 mm 720 mm 18.5 mm 90 μm 20
Laser 355 nm, M²=1.0
Rayleigh Length = 23M
Beam diameter = 5.0mm
500 mm 483 mm 4.38 mm 40 μm 10
1000 mm 964 mm 17.5 mm 87.4 μm 20

BeamSquared Lens Finder

To optimize Beam Propagation measurements using BeamSquared, Ophir has developed an addition to its Beam Profiler Finder, enabling users to choose the best lens for their laser. In case the power density of the focal spot occurs above the thermal lensing threshold of the BSQ optics, causing beam deformation, the tool suggests an optimal attenuator for the system.


  • The new sets of BeamSquared® 750mm and 1000mm lenses, designated for UV, VIS and NIR regions provide accurate Beam Propagation and Caustic analysis of lasers having both small focal spot and long Rayleigh length.
  • Accurate calibration techniques, used at Ophir, provide less than 10% relative error in Waist location and Rayleigh length measurement and less than 5% in other parameters such as M², BPP, and Waist Size.
  • The new long focal length lenses are sold separately and are not a part of the standard BeamSquared® kit.
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