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.

F. A. Hagen and K. T. Tang J. Opt. Soc. Am. 60(3) 365-367 (1970)

References

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All refractivity values quoted are at NTP (0 °C, 1 atm). n − 1 = 2πN_{0}α(ω), with 2πN_{0} = 0.2502 × 10^{−4}.
Calculated from Eq. (17) with Cauchy coefficients in Table I.
Calculated with the method described in Ref. 5.
Calculated from Eqs. (17) and (51) with Cauchy coefficients in Table I.
Interpolated estimates based on α(ω) given in Ref. 10.

All refractivity values quoted are at NTP (0 °C, 1 atm). n − 1 = 2πN_{0}α(ω), with 2πN_{0} = 0.2502 × 10^{−4}.
Calculated from Eq. (17) with Cauchy coefficients in Table I.
Calculated with the method described in Ref. 5.
Calculated from Eqs. (17) and (51) with Cauchy coefficient in Table I.
Taken directly from Ref. 12.

All refractivity values quoted are at NTP (0 °C, 1 atm). n − 1 = 2πN_{0}α(ω), with 2πN_{0} = 0.2502 × 10^{−4}.
Calculated from Eq. (17) with Cauchy coefficients in Table I.
Calculated with the method described in Ref. 5.
Calculated from Eqs. (17) and (51) with Cauchy coefficients in Table I.
Taken directly from Ref. 12.

All refractivity values quoted are at NTP (0 °C, 1 atm). n − 1 = 2πN_{0}α(ω), with 2πN_{0} = 0.2502 × 10^{−4}.
Calculated from Eq. (17) with data set (1) in Table I.
Calculated from Eq. (51) with data set (1) in Table I.
Calculated from Eq. (29) with data set (1) in Table I.
Taken directly from Ref. 12.

All refractivity values quoted are at NTP (0 °C, 1 atm). n − 1 = 2πN_{0}α(ω), with 2πN_{0} = 0.2502 × 10^{−4}.
Calculated from Eq. (17) and Eq. (51) with our recommended Cauchy coefficients [data set (2) in Table I].
Reference 12.
Reference 13.
Reference 15.
Reference 14.

All refractivity values quoted are at NTP (0 °C, 1 atm). n − 1 = 2πN_{0}α(ω), with 2πN_{0} = 0.2502 × 10^{−4}.
Calculated from Eq. (17) with Cauchy coefficients in Table I.
Calculated with the method described in Ref. 5.
Calculated from Eqs. (17) and (51) with Cauchy coefficients in Table I.
Interpolated estimates based on α(ω) given in Ref. 10.

All refractivity values quoted are at NTP (0 °C, 1 atm). n − 1 = 2πN_{0}α(ω), with 2πN_{0} = 0.2502 × 10^{−4}.
Calculated from Eq. (17) with Cauchy coefficients in Table I.
Calculated with the method described in Ref. 5.
Calculated from Eqs. (17) and (51) with Cauchy coefficient in Table I.
Taken directly from Ref. 12.

All refractivity values quoted are at NTP (0 °C, 1 atm). n − 1 = 2πN_{0}α(ω), with 2πN_{0} = 0.2502 × 10^{−4}.
Calculated from Eq. (17) with Cauchy coefficients in Table I.
Calculated with the method described in Ref. 5.
Calculated from Eqs. (17) and (51) with Cauchy coefficients in Table I.
Taken directly from Ref. 12.

All refractivity values quoted are at NTP (0 °C, 1 atm). n − 1 = 2πN_{0}α(ω), with 2πN_{0} = 0.2502 × 10^{−4}.
Calculated from Eq. (17) with data set (1) in Table I.
Calculated from Eq. (51) with data set (1) in Table I.
Calculated from Eq. (29) with data set (1) in Table I.
Taken directly from Ref. 12.

All refractivity values quoted are at NTP (0 °C, 1 atm). n − 1 = 2πN_{0}α(ω), with 2πN_{0} = 0.2502 × 10^{−4}.
Calculated from Eq. (17) and Eq. (51) with our recommended Cauchy coefficients [data set (2) in Table I].
Reference 12.
Reference 13.
Reference 15.
Reference 14.