lifetime.) Thus, Q = ωτ. This is an extremely simple equation to measure Q in large rings. The photon lifetime τ is measured on an oscilloscope, as the times are of the order of microseconds to milliseconds. Shape of rings In order to maximize the signal/noise ratio of a ring inside a given circle of radius r with n mirrors, a planar ring is advantageous over an equivalent nonplanar ring. Furthermore, a regular polygon has a maximal A/Ln ratio, with A/Ln = which itself has a maximum at n = 4, hence a planar square ring is optimal. Mirrors It is essential for a high quality ring to use mirrors of very high reflectivity. Metallic mirror surfaces are inadequate for laser work (household Al-covered mirror surfaces are 83% reflective, Ag is 95% reflective). However, multilayer dielectric mirrors with 20–30 alternate (low L and high H index of refraction) — λ/4 layers achieve reflection losses (1 - r) of single parts per million, and an analysis shows that losses of parts per billion can be achieved, if materials technology is pushed as far as is done with fiber optics. The losses are composed of scattering S, absorption A, and transmission T, such that 1 - r = S + A + T. Scattering is not treated here, because it is largely dependent on details of surface and interface treatment, and not easily analyzed. r, A, and T are amenable to analysis. The losses are analyzed with a matrix method that, given the success of surface treatment and reduction of absorption, shows how many layers have to be applied to reduce transmission accordingly. The goal is to increase the quality factor of the cavity until Rayleigh scattering of the HeNe gas in the cavity or other unavoidable loss mechanisms set a limit. For simplicity we assume normal incidence. Introducing the complex index of refraction (nh - jkh) (where nh is the real index of refraction and kh is the extinction coefficient) of the high-index material h []), and a corresponding complex index for the low-index material l [], the stack is described by two matrices: Mr = r = l,h, which are multiplied in pairs, according to the size of the stack: Mh Ml MhMl..............Mh Ml. Hereby, all calculations are strictly carried out up to the first power in the ks, assuming the materials are weakly absorbing. The final result, after the