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The objectives of this tutorial are to introduce the most important concepts and define some of the common terms involved in laser beam quality; to review briefly some of the beam quality definitions and measurement schemes employed t o date; to describe some of the problems associated with various approaches and with standardization efforts for beam quality measurement; and finally to express a few of the author's personal prejuduces on this subject. The "Maybe" in the title of this tutorial is intended to convey that measuring, or even rigorously defining, any single all-inclusive measure of laser beam quality is still a controversial an unsettled topic-and may remain so for some time.

Abstruct-Spontaneous, highly periodic, often permanent surface gratings or "ripples" can develop on the surface of almost any solid or liquid material illuminated by a single laser beam of sufficient intensity, under either pulsed or CW conditions. The grating periods are such that the incident laser beam is diffracted into a tangential wave which skims just along or under the illuminated surface. These spontaneously appearing surface ripples are generated by a runaway growth process analogous to stimulated Brillouin or Raman scattering or smallscale self focusing, but having many of the same properties as Wood's anomalies in diffraction gratings. Hence, it seems appropriate to refer to these spontaneous surface structures as "stimulated Wood's anomalies."

Optical-resonator modes and optical-beam-propagation problems have been conventionally analyzed using as the basis set the hermite-gaussian eigenfunctions tJn (x , z)consisting of a hermite polynomial of real argument Hn [V2x 1w (z)] times the complex gaussian function exp[-jkx 2 /2q (z)], in which q (z) is a complex quantity. This note shows that an alternative and in some ways more-elegant set of eigensolutions to the same basic wave equation is a hermite-gaussian set $n(x, z) of the form Hn [V/cx]exp [-c x 2 ], in which the hermite polynomial and the gaussian function now have the same complex argument VC cx=3 'kI2q)' ' 2 x. The conventional functions 'Pn are orthogonal in x in the usual fashion. The new eigenfunctions Vn, however, are not solutions of a hermitian operator in x and hence form a biorthogonal set with a conjugate set of functions An (VCx). The new eigenfunctions Xnare not by themselves