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Background The design of optical delivery systems for laser systems is highly dependent on the laser's beam quality. The beam quality, given by the parameter M^{2}, ranges from 1 for a diffractionlimited TEM_{00} laser beam, to several hundred for a distorted, poor quality beam. The National Institute for Standards and Technology (NIST) and the International Standards Organization (ISO) are in the process of establishing standards for laser beam quality measurement. The proposed standards are based upon calculating M^{2} from a set of beam diameter measurements. Several diameter measurement techniques have been endorsed by NIST. One of these methods, which has been adopted by U.S. Laser, involves the use of a CCD camera near the focus of an imaging lens. The beam waist diameter and Rayleigh range are measured, and are then used to calculate M^{2}. The technique is similar to focal plane divergence measurement technique with two major differences: (1) two diameters (instead of one) are taken at different locations along the beam; (2) the measurement of the actual beam waist and its position, not the diameter at the ideal waist position is used. Definition of M^{2} The beam quality M^{2} is the ratio of the laser beam's multimode diameterdivergence product to the ideal diffraction limited (TEM_{00}) beam diameterdivergence product. It can also be given by the square of the ratio of the multimode beam diameter to the diffractionlimited beam diameter.
In the equation above, D_{m} is the measured beam waist diameter, Θ_{m} is the measured fullangle divergence, d_{0} is the theoretical "imbedded Gaussian" beam diameter, and θ_{0} is the theoretical diffractionlimited divergence. The diameterdivergence products are given in units of mm•mrad. In addition to the quantities above we will use a quantity known as the Rayleigh range, denoted by z_{R}. The Rayleigh range is the distance a beam must propagate for its diameter to grow by a factor of factor . See Figure 1 for an illustration. Selection of an Imaging Lens It is important that two conditions are met by the lens:
Note: For M^{2} measurements the longest focal length lens that does not overfill the CCD camera should be used. Longer focal length lenses afford more precise Rayleigh range measurement. Better Rayleigh range measurements, in turn, enhance the quality of M^{2} measurements. Setup and Procedure A schematic of the setup for M^{2} measurements is shown below in Figure 1. The procedure for measuring M^{2} is as follows:
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