Rajeev Gupta, John H. Burnett, Ulf Griesmann, and Matthew Walhout, "Absolute refractive indices and thermal coefficients of fused silica and calcium fluoride near 193 nm," Appl. Opt. 37, 5964-5968 (1998)

The refractive indices of several fused silica and calcium fluoride
samples from different suppliers were measured with the minimum
deviation method in the deep UV between 191 and 196 nm with a standard
uncertainty of 7 ppm. For both materials the dispersion
dn/dλ near 193 nm and 20 °C was determined. In
addition, we measured the thermal coefficients of the refractive index
near 193 nm and between 15 and 25 °C.

F. J. Micheli, “Ueber den Einfluss der Temperatur auf die Dispersion ultravioletter Strahlen in Flusspat, Steinsalz, Quarz und Kalkspat,” Ann. Phys. (Leipzig) 7, 772–789 (1902).

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, UK, 1980), pp. 177–180.

D. Tentori, J. R. Lerma, “Refractometry by minimum deviation: accuracy analysis,” Opt. Eng. 29, 160–168 (1990).
[CrossRef]

V. Kaufman, B. Edlén, “Reference wavelengths from atomic spectra in the range 15 Å to 25000 Å,” J. Phys. Chem. Ref. Data 3, 825–895 (1974).
[CrossRef]

J. Reader, C. H. Corliss, W. L. Wiese, G. A. Martin, “Wavelengths and transition probabilities for atoms and atomic ions,” U.S. Department of Commerce, National Bureau of Standards, Natl. Stand. Ref. Data Ser. NSRDS-NBS 68 (1980).

K. P. Birch, M. J. Downs, “An updated Edlén equation for the refractive index of air,” Metrologia 30, 155–162 (1993).
[CrossRef]

F. J. Micheli, “Ueber den Einfluss der Temperatur auf die Dispersion ultravioletter Strahlen in Flusspat, Steinsalz, Quarz und Kalkspat,” Ann. Phys. (Leipzig) 7, 772–789 (1902).

F. J. Micheli, “Ueber den Einfluss der Temperatur auf die Dispersion ultravioletter Strahlen in Flusspat, Steinsalz, Quarz und Kalkspat,” Ann. Phys. (Leipzig) 7, 772–789 (1902).

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, UK, 1980), pp. 177–180.

Ann. Phys. (Leipzig) (1)

F. J. Micheli, “Ueber den Einfluss der Temperatur auf die Dispersion ultravioletter Strahlen in Flusspat, Steinsalz, Quarz und Kalkspat,” Ann. Phys. (Leipzig) 7, 772–789 (1902).

V. Kaufman, B. Edlén, “Reference wavelengths from atomic spectra in the range 15 Å to 25000 Å,” J. Phys. Chem. Ref. Data 3, 825–895 (1974).
[CrossRef]

Metrologia (1)

K. P. Birch, M. J. Downs, “An updated Edlén equation for the refractive index of air,” Metrologia 30, 155–162 (1993).
[CrossRef]

Opt. Eng. (1)

D. Tentori, J. R. Lerma, “Refractometry by minimum deviation: accuracy analysis,” Opt. Eng. 29, 160–168 (1990).
[CrossRef]

Other (2)

J. Reader, C. H. Corliss, W. L. Wiese, G. A. Martin, “Wavelengths and transition probabilities for atoms and atomic ions,” U.S. Department of Commerce, National Bureau of Standards, Natl. Stand. Ref. Data Ser. NSRDS-NBS 68 (1980).

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, UK, 1980), pp. 177–180.

Absolute refractive index of a fused silica sample as a
function of wavelength between 191 and 196 nm at
20 °C. Uncertainties are too small to be shown with error
bars.

Temperature dependence of the absolute refractive index
of a fused silica sample at 194.5 nm. Between 15 and 25 °C the
temperature coefficient dn/dt is (19.4
± 2.2) × 10^{-6}/°C.

Refractive indices of calcium fluoride samples at 193.39
nm and 20 °C from suppliers A and B. Here A1 and A2 represent
two measurements of the same sample, A.

We follow the usual convention whereby
the wavelengths of the visible lines Vis 1 to Vis 4 are air wavelengths
whereas vacuum wavelengths are used below 200 nm.

Table 2

Measured Refractive Indices of Fused Silica and Calcium
Fluoride at 20 °C

Absolute refractive indices (column
2) and dispersions (column 3) at 193.39 nm of fused silica
samples from three suppliers A, B, and C. The coefficients of a
quadratic polynomial that was fitted to the refractive-index data
between 191 and 196 nm for 20 °C are listed in the rightmost
column. Since the refractive-index values for samples from one
supplier are nearly equal, only the polynomial coefficients for the
sample with the median index is tabulated. The uncertainty of the
refractive index is 10.1 × 10^{-6}, corresponding to 7
ppm. The uncertainty in the dispersion is 2 ppm.

Table 4

Uncertainty Budget of Refractive-Index Measurements

Source of Uncertainty

Value

Index uncertainty

Apex angle measurement

0.24″

0.8 × 10^{-6}

Wild spectrometer measurement

Temperature uncertainty

0.12 °C

1.5 × 10^{-6}

Deviation measurement uncertainty

1.1″

3.6 × 10^{-6}

Gaertner spectrometer measurement

Temperature uncertainty

0.07 °C

1.4 × 10^{-6}

Deviation measurement uncertainty

1.9″

5.9 × 10^{-6}

Refractive index of air

Index uncertainty in DUV

0.2 × 10^{-6}

Barometric pressure variation

7.0 × 10^{-6}

Humidity variation

0.2 × 10^{-6}

Combined index uncertainty (1σ)

10.1 × 10^{-6}

Table 5

Refractive Index and Dispersion of Calcium Fluoride at
193.39 nma

Absolute refractive indices (column
2) and dispersions (column 3) at 193.39 nm and 20 °C of
calcium fluoride samples from two suppliers. A1 and A2 represent
two measurements of the same sample A. Column 4 contains the
coefficients of the second-order polynomial that were fitted to the
data to obtain the refractive index in the range between 191 and 196
nm. These coefficients are valid for a sample temperature of
20 °C. The uncertainty of the refractive index is 10.1 ×
10^{-6}, corresponding to 7 ppm. The uncertainty in the
dispersion is 2 ppm.

We follow the usual convention whereby
the wavelengths of the visible lines Vis 1 to Vis 4 are air wavelengths
whereas vacuum wavelengths are used below 200 nm.

Table 2

Measured Refractive Indices of Fused Silica and Calcium
Fluoride at 20 °C

Absolute refractive indices (column
2) and dispersions (column 3) at 193.39 nm of fused silica
samples from three suppliers A, B, and C. The coefficients of a
quadratic polynomial that was fitted to the refractive-index data
between 191 and 196 nm for 20 °C are listed in the rightmost
column. Since the refractive-index values for samples from one
supplier are nearly equal, only the polynomial coefficients for the
sample with the median index is tabulated. The uncertainty of the
refractive index is 10.1 × 10^{-6}, corresponding to 7
ppm. The uncertainty in the dispersion is 2 ppm.

Table 4

Uncertainty Budget of Refractive-Index Measurements

Source of Uncertainty

Value

Index uncertainty

Apex angle measurement

0.24″

0.8 × 10^{-6}

Wild spectrometer measurement

Temperature uncertainty

0.12 °C

1.5 × 10^{-6}

Deviation measurement uncertainty

1.1″

3.6 × 10^{-6}

Gaertner spectrometer measurement

Temperature uncertainty

0.07 °C

1.4 × 10^{-6}

Deviation measurement uncertainty

1.9″

5.9 × 10^{-6}

Refractive index of air

Index uncertainty in DUV

0.2 × 10^{-6}

Barometric pressure variation

7.0 × 10^{-6}

Humidity variation

0.2 × 10^{-6}

Combined index uncertainty (1σ)

10.1 × 10^{-6}

Table 5

Refractive Index and Dispersion of Calcium Fluoride at
193.39 nma

Absolute refractive indices (column
2) and dispersions (column 3) at 193.39 nm and 20 °C of
calcium fluoride samples from two suppliers. A1 and A2 represent
two measurements of the same sample A. Column 4 contains the
coefficients of the second-order polynomial that were fitted to the
data to obtain the refractive index in the range between 191 and 196
nm. These coefficients are valid for a sample temperature of
20 °C. The uncertainty of the refractive index is 10.1 ×
10^{-6}, corresponding to 7 ppm. The uncertainty in the
dispersion is 2 ppm.