The ISO standard defines a propagation factor known as k, the inverse of the widely advertised term M2. The quantity k can be thought of as a ratio of the diffraction limit that is the product of a laser beam's waist diameter (D0), divergence (q) and a constant related to beam wavelength (l).
Like the ISO methods, these alternative methods include recording measures of beam size in the far-field area of an artificial waist created by a lens.
METHOD 1
This method involves taking measurements exclusively through the waist of a lens similar to that which is specified in the ISO document. However, the method shown in Figure 1 offers greater ease and potentially less error.
To calculate the propagation factor, k, sample through the waist of the lens to determine Dmin. Next, translate the detector until the beam size increases to 1.414Dmin and record this location. Translate the detector back through the waist until the beam size measures 1.414Dmin on the other side of the waist. The distance between these points is 2ZR, or twice the Rayleigh range.
Then:
This approach relies on the fact that the propagation factor is a constant throughout an unaberrated optical system. Thus, the product of a beam's waist size and divergence in any section of an optical path will be equal to that in any other section. Therefore, the diameter of the waist of a lens, Dmin, and the angular spread affected by the lens, thetasubl, can be substituted for D0 and q, respectively, within the propagation formula. Since the Rayleigh range for any beam is defined as the waist divided by the divergence, this allows you to substitute the use of Dmin/ZR for qL.
A key advantage of using 2ZR in this method is the elimination of some potential sources of error in location determination. The depth of focus of a lens can provide a significant range of comparable readings of Dmin, thus making it difficult to precisely determine the distance from the lens to this hard-to-define location. At the extent of the Rayleigh range, however, the high rate of change of beam size makes it easy to locate these points. You need only measure the distance, 2ZR, between your two readings, thus eliminating the need to find the location of Dmin or any other distance from the lens.
METHOD 2
If you have a beam with negligible diffraction, and you have a good idea of approximately where its waist is located, you can calculate the propagation factor by recording two measures along the beam path (See Figure 2). Knowledge of the beam waist behavior is necessary in order to position the lens correctly within 1/3 Rayleigh range of the beam's waist.
Before installing the lens, measure the beam diameter, DL, at the point where the lens is to be placed. Next, install the lens of known focal length, f, and measure the resulting beam size, Df, at f. (Note: In most cases, Df does not coincide with Dmin.) The propagation factor can then be calculated as:
This method also gives the source divergence, since:
For more information about how Photon's beam profiling equipment can help you measure M2 and k-factor quickly and accurately, contact us at:
|
Application Note 230: Fast M2 (k-factor) Measures with Photon BeamProfilerTM
|
Rev. 1/00
|
