Hello. I am learning about M2 test. In the experiment, a lens has to be used to focus the laser beam which is not TEM00. I am wondering if M2 is the same after the lens with that before the lens.Thanks!
Good lenses with small spherical aberrations (http://en.wikipedia.org/wiki/Spherical_aberration) typically introduce very small M2 changes. When different lenses deliver different M2 values, this may easily be caused by the following errors, rather than by the lenses themselves:
1. The beam radius is measured with a simple criterion, not based on the full intensity profile, although the beam profiles are not all close to Gaussian. Only for nearly Gaussian beam shapes, such simple measurement methods are allowed. For others, the D4σ method based on the second moment of the intensity distribution must be used.
2. The beam is focused too tightly, so that the beam waist is too small to measure its beam radius precisely. For example, a CCD camera has a limited spatial resolution; it cannot be used for precise measurements if the beam diameter corresponds only to a few pixels.
3. Background subtraction, a sensitive issue for the second-moment method, is not correctly done. Camera images can exhibit some background intensity level, which may either really be belonging to the laser beam (and should not be removed then) or is an artifact which must be removed. If such a background results from ambient light, the most reliable measure is to switch this off, or to carefully shield it with a black tube in front of the camera. (Subtracting a fixed level for all images is problematic since ambient light levels may change, e.g. when somebody moves in the room.) The background issue is particularly serious when the beam size is only a fraction of the camera's sensitive area.
4. The beam intensity on a camera is too high or too low. If it is too high, the center pixels may be saturated, so that the beam intensity at the center is underestimated and the measured beam radius is too large. For too low intensities, intensity background issues may become more severe.
5. The beam radii are not measured sufficiently far from the focus. In order to properly judge the beam divergence, the ISO 11146 standard demands that about half of the measurement points must be more than two effective Rayleigh lengths away from the beam focus (whereas the other half of the points is close to the focus, i.e., within one Rayleigh length). This may be difficult in practice when the beam waist is made relatively large, leading to a long Rayleigh length and correspondingly large space requirements for a correct measurement.
[http://www.rp-photonics.com/m2_factor.html]
In fact M2 is a measure of laser beam quality (beam profile) . It may be distorted traversing a non ideal lens even with low abbrration.
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