daimon_2002#
M. Daimon and A. Masumura, “High-accuracy measurements of the refractive index and its temperature coefficient of calcium fluoride in a wide wavelength range from 138 to 2326 nm”, Appl. Opt. 41, 5275 (2002)
Source record · Catalogue · Review register
DOI: 10.1364/ao.41.005275
Source kind: measurement
Recorded technique: Minimum deviation (double minimum-deviation angle, Eq. (1)) on one prism of synthetic single-crystal CaF2 (‘not made for a dedicated application for photolithography at a wavelength of 157 nm’; apex 65 degrees, faces 25 mm high and 40 mm wide, flatness about lambda/5), on a Moller-Wedel goniometer-spectrometer (model 1 UV-VIS-IR) with mirrors M1-M5 recoated for use below 150 nm (p. 5276). 69 wavelengths, 137.9-2326 nm: a Pt-Ne hollow-cathode lamp below 283 nm (line wavelengths from Reader et al. and Sansonetti et al.), Hg, Cd, He and Cs lamps above 297 nm; photomultiplier (Cs-Te) below 283 nm, UV-enhanced CCD 297-1014 nm, cooled PbS above 1129 nm. The light path was purged with nitrogen (oxygen 20 ppm or less), the prism held at 20 +- 0.1 and 25 +- 0.1 degrees C by the room temperature (K-type thermocouple; quartz thermometers for the junction and the nitrogen), pressure by a silicon-oscillator barometer (pp. 5276-5277). Apex angle the mean of 8 readings, minimum deviation of 3.
Materials in structured entries: CaF2
Dataset quantities: refractive_index, thermo_optic_coefficient
Contents: 3 datasets; 3 formulas.
Curation notes#
Journal pages 5275-5281 are pdf pages 1-7. Identity checked against the first page (the PDF prints no DOI; the library found it by title).
MEDIUM (the key fact about this paper). The index is relative to NITROGEN, not air and not vacuum: ‘we applied the minimum-deviation method to determine the relative refractive index of CaF2 ... in a nitrogen environment’ (p. 5275); ‘We used the refractive index of nitrogen given in Refs. 11-13 [Koch 1913; Peck and Khanna 1966; Griesmann and Burnett 1999] to convert measured values of the relative refractive index to those values, n(lambda, t), at 1013.25 hPa’ (p. 5276); Table 1’s heading, ‘Relative Refractive Index in Nitrogen (1013.25 hPa)’. The nitrogen is at the prism temperature: Figs. 3 and 4 compare ‘in nitrogen gas at 25 C and 1013.25 hPa’ and ‘at 20 C and 1013.25 hPa’ (pp. 5279-5280). optmat’s index_medium (vacuum, air or not stated) cannot say this, so the datasets omit it and state the reference gas in their parameters (reference_gas = N2, its pressure and temperature). The formulas state index_medium = nitrogen, which the formula models take (added at review, TC-545). To make the index absolute, multiply by the index of N2 at 1013.25 hPa and the stated temperature: n_N2 - 1 is 2.80e-4 at 500 nm, 2.75e-4 at 1 um and 2.74e-4 at 2 um at 20 C (Peck and Khanna’s formula, peck_1966/eq4, recomputed here 2026-09-27), 0.5-0.6e-5 above dry air’s (Edlen) at the same temperature and pressure. The absolute index is therefore about 4e-4 above the tabulated one (n_rel x 2.75e-4 = 3.9e-4 at 1 um). WAVELENGTHS are vacuum wavelengths (‘Vacuum Wavelength (nm)’, Table 1; ‘lambda is the wavelength in vacuum ... To convert the wavelength in air to that in vacuum we used Edlen’s equation’, p. 5276).
dn/dt. Relative (to nitrogen at 1013.25 hPa, at the temperature of the prism), from the indices at t1 near 20 C and t2 near 25 C, Eq. (2) (p. 5276); the indices at exactly 20 and 25 C then follow from Eqs. (3)-(4). Table 1’s dn/dt equals (n(25) - n(20))/5 to within the rounding (largest difference 0.02e-6/K, checked 2026-09-27). Being relative to nitrogen whose refractivity falls with temperature at constant pressure (by 0.93e-6/K at 20-25 C and 1 um, peck_1966/eq4), the absolute dn/dT is n_N2 dn_rel/dt + n_rel dn_N2/dt, about 1.3e-6/K below the tabulated relative values (e.g. -11.4e-6/K absolute for the printed -10.06e-6/K at 587.7 nm). Not discussed in the paper, which says that Eq. (6) of Hoffmann et al. for the absolute dn/dT ‘is equally applicable to’ the relative one (p. 5277).
ACCURACY. Table 1 gives the uncertainty of each index (8-17 x 1e-7 without the wavelength’s, up to 21 x 1e-7 with it below 283 nm) and of each dn/dt (0.15-0.43 x 1e-6/C); text: ‘Without the wavelength uncertainty, the uncertainties in the relative refractive index and in dn_rel/dt are estimated to be 8e-7-17e-7 and 0.15e-6/C-0.43e-6/C, respectively’ (p. 5279). The level is not stated. Table 4 (main sources): apex angle 0.2 arcsec, double minimum deviation 0.4 arcsec, temperature 0.05 C, nitrogen pressure 0.1 hPa, wavelength 4-20 x 1e-5 nm (apex angle and wavelength do not affect dn/dt). Standard deviation of the fit residuals 6.1e-7 (20 C) and 5.7e-7 (25 C), and 0.130e-6/C for dn/dt (Table 1, last row; abstract).
TABLE 1 RESIDUALS (x 1e-7 for n, x 1e-6/C for dn/dt) are measured minus the Table 2 Sellmeier at the same temperature, and measured minus Eq. (7) with Table 3 for dn/dt; not extracted as data (they are the formulas’ checks). Every residual is reproduced (see each formula’s check).
COMPARISONS (figures, not digitised). Fig. 3: Malitson’s (1963) measured indices and formula, ‘measurements in air at 24 C. As there was no value of atmospheric pressure given for those data we assumed that they were corrected to 1013.25 hPa. We converted those data to the values in nitrogen gas at 25 C and compared the result with our dispersion formula at 25 C’ (pp. 5279-5280). Fig. 4: the NIST absolute indices near 193 and 157 nm (Gupta et al. 1998; Burnett et al. 2000), converted to nitrogen at 20 C. Fig. 5: dn/dt against Malitson’s, Gupta’s and Burnett’s, ‘converted ... to those of nitrogen gas’ (p. 5280). The figures’ axes: Delta n (x 1e-5 or 1e-6) against wavelength.
REFRACTIVEINDEX.INFO (main/CaF2/nk/Daimon-20.yml and Daimon-25.yml, compared 2026-09-27): formula 2 with coefficients identical to Table 2 (0.443749998, 0.00178027854, ... 8.85319946, 2752.28175 at 20 C; ... 13.0020420, 4039.76541 at 25 C), range 0.138-2.326 um, comment ‘20 C [25 C], Nitrogen atmosphere’. The pages give the relative index as n with no conversion: used as an absolute index (as solprop’s default CaF2 does), it is about 3.9e-4 low.
Recorded bibliographic identity status: VALIDATED_WITH_WARNINGS. This concerns identification of the source; it does not establish the scientific correctness of its contents.
Datasets#
daimon_2002/n_20C#
{
"id": "n_20C",
"material": "CaF2",
"file": "CaF2/daimon_2002__n_20C.csv",
"table": "tbl_8ae247914098",
"quantity": "refractive_index",
"abscissa_unit": "nm",
"use": "primary",
"parameters": {
"temperature_k": 293.15,
"form": "bulk",
"technique": "minimum deviation",
"reference_gas": "N2",
"reference_gas_pressure_pa": 101325,
"reference_gas_temperature_k": 293.15
},
"uncertainty": {
"column": true,
"level": "not stated"
}
}
Table 1 (pdf pp. 4-5, both parts: tbl_8ae247914098 and its continuation tbl_b68ea97710c0), ‘Relative Refractive Index in Nitrogen (1013.25 hPa)’, At 20 C, Measured: 69 vacuum wavelengths, 137.9-2326 nm. The index is relative to nitrogen at 1013.25 hPa and 20 C, not to vacuum or air (see the source notes); it is about 3.9e-4 below the absolute index. Reduced to exactly 20 C from t1 near 20 C by Eq. (3). The sigma column is Table 1’s uncertainty, including the wavelength’s where printed (below 283 nm); level not stated.
daimon_2002/n_25C#
{
"id": "n_25C",
"material": "CaF2",
"file": "CaF2/daimon_2002__n_25C.csv",
"table": "tbl_8ae247914098",
"quantity": "refractive_index",
"abscissa_unit": "nm",
"use": "primary",
"parameters": {
"temperature_k": 298.15,
"form": "bulk",
"technique": "minimum deviation",
"reference_gas": "N2",
"reference_gas_pressure_pa": 101325,
"reference_gas_temperature_k": 298.15
},
"uncertainty": {
"column": true,
"level": "not stated"
}
}
Table 1 (both parts), ‘Relative Refractive Index in Nitrogen (1013.25 hPa)’, At 25 C, Measured: 69 vacuum wavelengths, 137.9-2326 nm. Relative to nitrogen at 1013.25 hPa and 25 C (see the source notes). Reduced to exactly 25 C from t2 near 25 C by Eq. (4). The sigma column is Table 1’s uncertainty (one column for both temperatures), including the wavelength’s where printed; level not stated.
daimon_2002/dndt#
{
"id": "dndt",
"material": "CaF2",
"file": "CaF2/daimon_2002__dndt.csv",
"table": "tbl_8ae247914098",
"quantity": "thermo_optic_coefficient",
"unit": "1/K",
"scale": 1e-06,
"abscissa_unit": "nm",
"use": "primary",
"parameters": {
"temperature_k": 295.65,
"form": "bulk",
"technique": "minimum deviation",
"reference_gas": "N2",
"reference_gas_pressure_pa": 101325
},
"uncertainty": {
"column": true,
"level": "not stated"
}
}
Table 1 (both parts), ‘Relative dn/dt in Nitrogen (1013.25 hPa), (x 10^-6/C)’, Measured, with the Uncertainty column as sigma (level not stated): 69 vacuum wavelengths. From the indices near 20 and 25 C by Eq. (2); temperature_k is the midpoint, 22.5 C. RELATIVE to nitrogen at 1013.25 hPa and the prism temperature: the absolute dn/dT is about 1.3e-6/K lower (see the source notes). Negative above 173 nm, positive below.
Formulas#
daimon_2002/sellmeier_20C#
{
"id": "sellmeier_20C",
"material": "CaF2",
"form": "n2_sellmeier",
"index_medium": "nitrogen",
"nitrogen_temperature_k": 293.15,
"nitrogen_pressure_pa": 101325,
"equation": "Eq. (5), p. 5276, with Table 2 (p. 5277), 20 C",
"printed": "n^2(lambda, t) - 1 = sum_{i=1}^{4} A_i lambda^2 / (lambda^2 - lambda_i^2)",
"variable": "lambda: vacuum wavelength in um ('lambda is given in units of micrometers', p. 5276; vacuum, p. 5276)",
"range": "137.9-2326 nm, the 69 wavelengths fitted; 20 C; the index relative to nitrogen at 1013.25 hPa (and 20 C)",
"coefficients": {
"A1": "4.43749998 x 10^-1",
"lambda1_sq": "1.78027854 x 10^-3",
"A2": "4.44930066 x 10^-1",
"lambda2_sq": "7.88536061 x 10^-3",
"A3": "1.50133991 x 10^-1",
"lambda3_sq": "1.24119491 x 10^-2",
"A4": "8.85319946",
"lambda4_sq": "2.75228175 x 10^3"
},
"terms": {
"B": [
"4.43749998e-1",
"4.44930066e-1",
"1.50133991e-1",
"8.85319946"
],
"C": [
"1.78027854e-3",
"7.88536061e-3",
"1.24119491e-2",
"2.75228175e3"
]
},
"range_nm": [
137.89572,
2326.05
],
"parameters": {
"temperature_k": 293.15,
"reference_gas": "N2",
"reference_gas_pressure_pa": 101325,
"reference_gas_temperature_k": 293.15
},
"check": "Reproduces Table 1's 20 C residuals (measured minus formula, x 1e-7) at all 69 wavelengths to within 0.95e-7, the rounding of the seven-decimal index and of the integer residual; the rms residual is 6.12e-7 against the printed standard deviation 6.1e-7. Checked 2026-09-27 against the printed coefficients."
}
Four-term Sellmeier, one infrared term and three ultraviolet terms, ‘because a three-term dispersion formula could not approximate the true dispersion sufficiently’ (p. 5276); eight constants fitted by least squares to n(lambda, 20). The poles are printed as lambda_i^2 (um^2). The formula’s index is relative to nitrogen at 1013.25 hPa and 20 C (index_medium nitrogen, TC-545); read as an absolute index it would be about 3.9e-4 too low. Identical to refractiveindex.info main/CaF2/nk/Daimon-20 and to solprop’s default CaF2 (which uses it as absolute).
daimon_2002/sellmeier_25C#
{
"id": "sellmeier_25C",
"material": "CaF2",
"form": "n2_sellmeier",
"index_medium": "nitrogen",
"nitrogen_temperature_k": 298.15,
"nitrogen_pressure_pa": 101325,
"equation": "Eq. (5), p. 5276, with Table 2 (p. 5277), 25 C",
"printed": "n^2(lambda, t) - 1 = sum_{i=1}^{4} A_i lambda^2 / (lambda^2 - lambda_i^2)",
"variable": "lambda: vacuum wavelength in um ('lambda is given in units of micrometers', p. 5276; vacuum, p. 5276)",
"range": "137.9-2326 nm, the 69 wavelengths fitted; 25 C; the index relative to nitrogen at 1013.25 hPa (and 25 C)",
"coefficients": {
"A1": "4.37387571 x 10^-1",
"lambda1_sq": "1.73799328 x 10^-3",
"A2": "4.49211397 x 10^-1",
"lambda2_sq": "7.82718648 x 10^-3",
"A3": "1.52068715 x 10^-1",
"lambda3_sq": "1.24086125 x 10^-2",
"A4": "1.30020420 x 10^1",
"lambda4_sq": "4.03976541 x 10^3"
},
"terms": {
"B": [
"4.37387571e-1",
"4.49211397e-1",
"1.52068715e-1",
"1.30020420e1"
],
"C": [
"1.73799328e-3",
"7.82718648e-3",
"1.24086125e-2",
"4.03976541e3"
]
},
"range_nm": [
137.89572,
2326.05
],
"parameters": {
"temperature_k": 298.15,
"reference_gas": "N2",
"reference_gas_pressure_pa": 101325,
"reference_gas_temperature_k": 298.15
},
"check": "Reproduces Table 1's 25 C residuals at all 69 wavelengths to within 1.04e-7 (the rounding of index and residual); rms residual 5.77e-7 against the printed standard deviation 5.7e-7. Checked 2026-09-27 against the printed coefficients."
}
As sellmeier_20C, fitted to n(lambda, 25). The infrared term differs strongly between the two temperatures (A4 = 8.85 at 20 C, 13.0 at 25 C; lambda4^2 = 2752 and 4040 um^2): the term is weakly determined by data ending at 2.33 um, so the two formulas must not be extrapolated beyond 2.33 um, and their difference is not a dn/dT outside the range. Relative to nitrogen at 1013.25 hPa and 25 C, as sellmeier_20C. Identical to refractiveindex.info main/CaF2/nk/Daimon-25.
daimon_2002/dndt#
{
"id": "dndt",
"material": "CaF2",
"equation": "Eq. (7), p. 5277, with Table 3 (p. 5277)",
"printed": "dn_rel(lambda)/dt = [n^2(lambda) - 1] [D_0 + E_0/(lambda^2 - lambda_0^2)] / [2 n(lambda)]",
"variable": "lambda: vacuum wavelength in um; n(lambda): the relative index at 20 C, n(lambda, 20) ('using n(lambda, 20) as the value of n(lambda)', p. 5277); dn_rel/dt in 1/C",
"range": "137.9-2326 nm; between 20 and 25 C (D, E and lambda_0 'considered constant', p. 5277); relative to nitrogen at 1013.25 hPa",
"coefficients": {
"D0": "-2.8422 x 10^-5",
"E0": "4.6988 x 10^-7",
"lambda0_sq": "1.3459 x 10^-2"
},
"check": "With n from sellmeier_20C, reproduces Table 1's dn/dt residuals (measured minus Eq. (7), x 1e-6/C) at all 69 wavelengths to within 0.011e-6/C (the rounding of two-decimal values); rms residual 0.130e-6/C, as printed. Checked 2026-09-27 against the printed coefficients."
}
Hoffmann et al.’s form (Proc. SPIE 1327, 219 (1990), Eq. (6)) with D, E and lambda_0 constant over 20-25 C (p. 5277); lambda_0^2 in um^2, units of D_0 and E_0 not printed (1/C and um^2/C by the equation). It gives the relative dn/dt (see the source notes for the absolute one).
Corrections#
No dataset errata are recorded in this source record.
Formula corrections, where recorded, appear with their formulas above. Curation notes may also discuss corrections or unresolved interpretation. Consult the review register for the checks and decisions.