Yasuaki Hori, Akiko Hirai, Kaoru Minoshima, and Hirokazu Matsumoto, "High-accuracy interferometer with a prism pair for measurement of the absolute refractive index of glass," Appl. Opt. 48, 2045-2050 (2009)

We propose a variable-path interferometric technique for the measurement of the absolute refractive index of optical glasses. We use two interferometers to decide the ratio between changes in the optical path in a prism-shaped sample glass and in air resulting from displacement of the sample. The method allows precise measurements to be made without prior knowledge of the properties of the sample. The combined standard uncertainty of the proposed method is $1.6\times {10}^{-6}$.

H. Delbarre, C. Przygodzki, M. Tassou, and D. Boucher, “High-precision index measurement in anisotropic crystals using white-light spectral interferometry,” Appl. Phys. B 70, 45-51(2000).
[CrossRef]

J. Zhang, Z. H. Lu, B. Menegozzi, and L. J. Wang, “Application of frequency combs in the measurement of the refractive index of air,” Rev. Sci. Instrum. 77, 083104 (2006).
[CrossRef]

K. Fujii, E. R. Williams, R. L. Steiner, and D. B. Newell, “A new refractometer by combining a variable length vacuum cell and a double-pass Michelson interferometer,” IEEE Trans. Instrum. Meas. 46, 191-195 (1997).
[CrossRef]

J. Zhang, Z. H. Lu, B. Menegozzi, and L. J. Wang, “Application of frequency combs in the measurement of the refractive index of air,” Rev. Sci. Instrum. 77, 083104 (2006).
[CrossRef]

H. Delbarre, C. Przygodzki, M. Tassou, and D. Boucher, “High-precision index measurement in anisotropic crystals using white-light spectral interferometry,” Appl. Phys. B 70, 45-51(2000).
[CrossRef]

K. Fujii, E. R. Williams, R. L. Steiner, and D. B. Newell, “A new refractometer by combining a variable length vacuum cell and a double-pass Michelson interferometer,” IEEE Trans. Instrum. Meas. 46, 191-195 (1997).
[CrossRef]

H. Delbarre, C. Przygodzki, M. Tassou, and D. Boucher, “High-precision index measurement in anisotropic crystals using white-light spectral interferometry,” Appl. Phys. B 70, 45-51(2000).
[CrossRef]

H. Delbarre, C. Przygodzki, M. Tassou, and D. Boucher, “High-precision index measurement in anisotropic crystals using white-light spectral interferometry,” Appl. Phys. B 70, 45-51(2000).
[CrossRef]

K. Fujii, E. R. Williams, R. L. Steiner, and D. B. Newell, “A new refractometer by combining a variable length vacuum cell and a double-pass Michelson interferometer,” IEEE Trans. Instrum. Meas. 46, 191-195 (1997).
[CrossRef]

J. Zhang, Z. H. Lu, B. Menegozzi, and L. J. Wang, “Application of frequency combs in the measurement of the refractive index of air,” Rev. Sci. Instrum. 77, 083104 (2006).
[CrossRef]

J. Zhang, Z. H. Lu, B. Menegozzi, and L. J. Wang, “Application of frequency combs in the measurement of the refractive index of air,” Rev. Sci. Instrum. 77, 083104 (2006).
[CrossRef]

K. Fujii, E. R. Williams, R. L. Steiner, and D. B. Newell, “A new refractometer by combining a variable length vacuum cell and a double-pass Michelson interferometer,” IEEE Trans. Instrum. Meas. 46, 191-195 (1997).
[CrossRef]

H. Delbarre, C. Przygodzki, M. Tassou, and D. Boucher, “High-precision index measurement in anisotropic crystals using white-light spectral interferometry,” Appl. Phys. B 70, 45-51(2000).
[CrossRef]

Steiner, R. L.

K. Fujii, E. R. Williams, R. L. Steiner, and D. B. Newell, “A new refractometer by combining a variable length vacuum cell and a double-pass Michelson interferometer,” IEEE Trans. Instrum. Meas. 46, 191-195 (1997).
[CrossRef]

H. Delbarre, C. Przygodzki, M. Tassou, and D. Boucher, “High-precision index measurement in anisotropic crystals using white-light spectral interferometry,” Appl. Phys. B 70, 45-51(2000).
[CrossRef]

Wang, L. J.

J. Zhang, Z. H. Lu, B. Menegozzi, and L. J. Wang, “Application of frequency combs in the measurement of the refractive index of air,” Rev. Sci. Instrum. 77, 083104 (2006).
[CrossRef]

K. Fujii, E. R. Williams, R. L. Steiner, and D. B. Newell, “A new refractometer by combining a variable length vacuum cell and a double-pass Michelson interferometer,” IEEE Trans. Instrum. Meas. 46, 191-195 (1997).
[CrossRef]

J. Zhang, Z. H. Lu, B. Menegozzi, and L. J. Wang, “Application of frequency combs in the measurement of the refractive index of air,” Rev. Sci. Instrum. 77, 083104 (2006).
[CrossRef]

H. Delbarre, C. Przygodzki, M. Tassou, and D. Boucher, “High-precision index measurement in anisotropic crystals using white-light spectral interferometry,” Appl. Phys. B 70, 45-51(2000).
[CrossRef]

IEEE Trans. Instrum. Meas.

K. Fujii, E. R. Williams, R. L. Steiner, and D. B. Newell, “A new refractometer by combining a variable length vacuum cell and a double-pass Michelson interferometer,” IEEE Trans. Instrum. Meas. 46, 191-195 (1997).
[CrossRef]

J. Zhang, Z. H. Lu, B. Menegozzi, and L. J. Wang, “Application of frequency combs in the measurement of the refractive index of air,” Rev. Sci. Instrum. 77, 083104 (2006).
[CrossRef]

Principle of the proposed method. Ps, prism under measurement; Pi, incident prism; ML, refractive-index-matching liquid. Interferometer 1 detects the change in the optical path length in Ps ($\mathrm{\Delta}{x}_{1}$) and interferometer 2 detects the change in the optical path length in air ($\mathrm{\Delta}{x}_{2}$) generated by translation of Ps. From $\mathrm{\Delta}{x}_{1}$, $\mathrm{\Delta}{x}_{2}$, and the refractive index of the air, the absolute refractive index of Ps can be calculated by using Eq. (1).

Phase calculation procedure from the interferogram. The upper figure shows the intensity of the interferogram and the lower one shows the phase calculated from the interferogram, with a common horizontal axis of time. $\mathrm{\Delta}{\phi}_{i}(i=1,2)$ in the lower figure is the phase change from the point where the stage starts to the first point where the intensity crosses the zero line of the interferogram. ${N}_{i}(i=1,2)$ represents the integral number of fringes counted from points where the zero line is crossed. $\mathrm{\Delta}{\psi}_{i}(i=1,2)$ is the phase change from the final point where the zero line is crossed to the point where the stage stopped.

Experimental setup. Ps, prism under measurement; Pi, incident prism; M, mirror; BS, beam splitter; PD, photodiode; BPF, bandpass filter; W, wedge plate; CCD, charge-coupled device camera. The alignment system is used to maintain a constant separation between Pi and Ps during movement of the stage.

Results of a series of measurements. The filled circles and error bars represent the average and standard deviations, respectively, of a group of ten measurements. The average for a total of 120 measurements is 1.5154317 (dotted horizontal line). The vertical dotted lines represent removal and resetting of Ps.

$u({x}_{i})$, uncertainty of each factor; $\partial f/\partial {x}_{i}$, sensitivity coefficient; ${u}_{i}$, uncertainty for refractive-index measurement; ${\lambda}_{1}$, wavelength of interferometer 1 ($633\text{\hspace{0.17em}}\mathrm{nm}$); ${\lambda}_{2}$, wavelength of interferometer 2 ($543\text{\hspace{0.17em}}\mathrm{nm}$); ${n}_{s}$, refractive index of sample prism; ${n}_{L}$, refractive index of matching liquid; ${\theta}_{a}$, apex angle of sample prism; $\mathrm{\Delta}d$, offset between measurement passes of the two interferometers; $d{n}_{a}/dT$, temperature coefficient of refractive index of air; $d{n}_{a}/dP$, pressure coefficient of the refractive index of air; $dn/dT$, temperature coefficient of the refractive index of the sample prism.
Included in repeatability but not counted in the combined standard uncertainty or expanded uncertainty.
The uncertainty in refractive-index measurement ${u}_{\theta}$, which is caused by the uncertainty of alignment of perpendicularity $u(\theta )$ is shown as ${u}_{\theta}=({n}_{s}/6)\times u(\theta {)}^{2}$. The ${u}_{\theta}$ is split into $u(\theta )$ and $\partial f/\partial {x}_{i}=({n}_{s}/6)\times u(\theta )$ for description purposes.