Selecting the Correct Lens for M² Measurements with NanoModeScan

NanoModeScan is perhaps the most versatile of the available instruments for measuring M2 , since it can be used with lasers of any wavelength and power level. Nonetheless, with this versatility comes the complexity of selecting the proper test lens with which to make the measurements. There are several considerations to be taken into account.
With the broad range of wavelengths that can be measured with this instrument, the first consideration is the material and anti-reflective coating of the lens. There are a number of lenses that are standardly available for order from Ophir-Spiricon that cover the most widely used wavelengths. For the UV there are fused-silica lenses AR coated for 266 and 355nm; for the visible there are BK-7 lenses with broadband visible AR coatings. In the IR, things get a bit more complex. Although in the near IR the BK-7 material is the same, there are different AR coatings depending on the wavelength range. Basically, these are the very near IR, principally the wavelengths around the Nd:YAG emission bands at 1.06 to 1.08µm, the telecom wavelength from 1.3 to 1.7µm, and others around 2µm. In the Far IR, lenses are made of zinc-selenide and coated for the principal CO2 emission band at around 10.6µm. Wavelengths in between 2µm and 10.6µm are a bit more problematic. These lenses are made of Zn-Se or other specific materials and generally must be custom coated for the wavelengths of use. It is really not possible to stock these at Ophir-Spiricon, and they are better sourced from the specialty lens makers themselves.
The next consideration is what focal length lens should be used. In some cases there is little choice; for example the Zn-Se lens for 10.6µm is only available as a 190mm focal length. The other lenses that we supply are available standard as either 200mm or 400mm (the longer UV is actually 350mm).
Why do we provide these two focal lengths? The test lens is used to form a waist in the 500mm test space of the NanoModeScan rail. This is the distance from front to back of the rail travel. The lens must form this waist within this space and provide a waist that is easily measurable. For this reason it should not be too small or too big or formed too close to either end of the rail.
What is too small or too big? NanoScan can measure a beam size as small as 20µm accurately, but in many cases the power density of such small beams may well exceed the damage threshold of the slits. In addition, a very small beam will have a very short Rayleigh range, and therefore getting a good measurement of the beam caustic can be difficult. This will lead to erratic results. It is much better to aim for a beam waist size between 100 and 300µm. If the beam waist is too large, the beam measurements 2 Rayleigh ranges away from the waist may be too large for the aperture or may not fall within the test space.
From the thin lens equation we know that the waist size is dependent on the divergence, focal length, and the M2 value. Using the following equation we can get an estimate of the waist that a particular focal length lens will create, given the input diameter of the beam to be measured.


  • d0 is the test waist
  • f is the focal length
  • λ is the wavelength
  • D is the input beam’s diameter

In order to make this calculation come out easily, convert all values to µm
You can use this to determine the right focal length or to see if a particular configuration will result in a waist that is too large or too small. Obviously, since you are measuring M2 to determine its value, you do not know it exactly, but if you assume the value to be 1, you will have the smallest waist theoretically possible. Anything larger will probably be safer.