A set of continually factorized uniformly convergent series is introduced for optical refractivities. Upper and lower bounds on the refractivities are obtained by truncating two such adjacent series, which alternately converge from above and below, after finite numbers of terms. The extent to which the present method complements the Padé method for extrapolating the refractive index from infrared and visible to ultraviolet frequencies is demonstrated by calculations on heavy inert gases. With exactly the same original data, the present method sometimes helps to reduce the Padé bounds to one third. The present method also complements Wolfsohn’s method in obtaining bounded estimates of oscillator strengths from refractivity measurements. This is illustrated in the case of argon, for which the oscillator strengths of two close lines are separately determined. In the case of atomic hydrogen, the results of the present method for oscillator strengths and the refractivity, below as well as above the first resonance line, are compared with exact values. Finally, as an illustrative example of estimating the refractivity at frequencies above the first resonance line, we extend a Sellmeier dispersion equation for argon in the normal-dispersion region to frequencies between the first and third excitation levels.
K. T. Tangand and K. K. Poon, "Continued-factorization method for optical dispersion," J. Opt. Soc. Am. 64, 1582-1590 (1974)