malitson_1964#
I. H. Malitson, “Refractive Properties of Barium Fluoride”, J. Opt. Soc. Am. 54, 628 (1964)
Source record · Catalogue · Review register
Source kind: measurement
Recorded technique: Minimum deviation. Commercial sample (Harshaw Chemical Company, footnote 6; available 1958): one prism, faces 18 x 18 mm, refracting angle near 61 degrees, measured on the NBS Gaertner precision spectrometer modified for non-visible wavelengths (reflecting optics, spectrum scanning, Golay detector; Fig. 1) and a Wild precision spectrometer in the visible, at 46 calibrated wavelengths of emission lines and absorption bands, 0.2652-10.346 um; ‘The room temperature was regulated and maintained very near 25 C’ (pp. 628-629). MIT sample (an experimental melt grown by D. C. Stockbarger): one prism measured at NBS in 1944 on a Geneva Society spectrometer ‘equipped with a water-jacketed housing for precise control of temperature’, nine visible lines, at 15, 35 and 55 C (p. 628).
Materials in structured entries: BaF2
Dataset quantities: refractive_index, thermo_optic_coefficient
Contents: 7 datasets; 1 formula.
Curation notes#
Journal pages 628-632 are pdf pages 1-5. Identity checked against the first page. Received 27 September 1963.
AIR OR VACUUM. Not stated. The commercial prism was measured in the room, whose temperature ‘was regulated and maintained very near 25 C’ (p. 629), on the NBS instrument of Rodney and Spindler and Malitson (1963, 1965), with the lines’ air wavelengths (Hg 0.546074, Cd 0.643847 um): as for those papers (TC-323, TC-399; malitson_1963, which Daimon and Masumura read as ‘in air’), the index is recorded as relative to the room air at 25 C (pressure not stated) and the wavelengths as standard air. An inference from the method, not a statement of the paper. The 1944 data were measured in a water-jacketed housing; the gas is not stated.
ACCURACY. Table I: ‘The uncertainty of these index measurements is estimated at 3 x 10^-6’ (p. 628). Table II: ‘An average absolute residual of 1.9 x 10^-5 indicates that values of index may be interpolated to five decimal places’ (‘1.91 x 10^-5’ in the abstract); the residuals -9 and +9 x 1e-5 at 2.5766 and 6.6331 um (water-vapour bands) ‘may be attributed to erroneous assignment of wavelengths, rather than errors in index measurement’ (p. 630). No per-point uncertainty is stated for Table II. ‘The index data of Table II are final results for this particular sample and supersede all preliminary data which were released for earlier publication’ (Ballard et al., ref. 3; p. 630); ‘the values of refractive index given in Table II refer only to the particular commercially produced sample’ (p. 632).
TABLE II RESIDUALS are the measured minus the computed column to the last digit (all 46 rows, checked 2026-09-27); not extracted. The computed column against the formula: 44 of 46 values are the formula’s rounded to five decimals; at 0.334148 um the formula gives 1.4936354 (printed 1.49363, a rounding edge) and at 0.486133 um 1.4785462 (printed 1.47856, 1.4e-5 higher); the measured 1.47855 and the residual -1 at 0.486133 um are consistent with the printed computed value. Not corrected.
TABLE I. ‘-dn/dt x 10^-6 per C’: ‘The coefficients were averaged for both ranges at each wavelength since no significant variation with temperature was noted’ (p. 631); every value equals (n(15) - n(55))/40 of the table to the rounding (checked 2026-09-27), so it is the mean over 15-55 C (temperature_k 35 C). ‘A general value, averaged over lambda, for the temperature interval 15 to 55 C is -15.2 x 10^-6/C’. Rows 0.589262 and 0.767858 um carry the mark ‘a’, ‘Intensity weighted mean of doublet’. Abbe numbers 81.82, 81.76, 81.67 at 15, 35, 55 C (last row, not extracted).
dn/dt OF THE COMMERCIAL SAMPLE (text only, pp. 631-632): measured ‘at room temperatures in the neighborhood of 15 and 30 C. However, because of excessive fluctuations ... only tentative values of dn/dt ... negative over the entire measured wavelength range ... increases from an average of about -11 x 10^-6/C in the near ultraviolet to a high of about -17 x 10^-6/C in the near infrared, then decreases to an average of about -9 x 10^-6/C at the long wavelength limit. The coefficients for this sample were more reliably determined for the visible region on the Wild spectrometer and found to have an average value of about -15 x 10^-6/C’; the abstract’s ‘tentative average thermal coefficient of index dn/dt for the measured spectral range is -12 x 10^-6/C’. Not recorded as data (averages over wavelength ranges, ‘tentative’). All relative to air.
TWO SAMPLES (Fig. 6, p. 632): computed at 25 C from Table I with its dn/dt, the MIT sample is below the commercial one ‘by an average of 46 x 10^-5’ in the visible, with the same dispersion (Abbe numbers 81.78 and 81.66), attributed to annealing rather than composition.
REFRACTIVEINDEX.INFO (main/BaF2/nk/Malitson.yml, compared 2026-09-27): formula 1 with 0.643356, 0.057789, 0.506762, 0.10968, 3.8261, 46.3864, identical to Table III; range 0.2652-10.346 um; comment ‘25 C’; temperature 298 K. No mention of air. solprop’s BaF2 uses these coefficients as an absolute index at vacuum wavelengths: about 4e-4 low if the index is relative to air.
REPRODUCTIONS. adair_1989’s ‘n (1.06 um)’ of BaF2, 1.4682, cites Dodge in the Handbook of Laser Science and Technology (CRC, 1986); this paper’s formula gives 1.46817 at 1.06 um (air wavelength), which rounds to it (checked 2026-09-27).
FIGURES (not digitised): 1, the spectrometer; 2, n of BaF2, 0.2-10.4 um; 3-5, the relative dispersion (minimum near 2.0 um), its reciprocal and (lambda dn/dlambda)^-1; 6, the MIT and commercial samples’ indices in the visible.
Recorded bibliographic identity status: VALIDATED_WITH_WARNINGS. This concerns identification of the source; it does not establish the scientific correctness of its contents.
Datasets#
malitson_1964/measured_25C#
{
"id": "measured_25C",
"material": "BaF2",
"file": "BaF2/malitson_1964__measured_25C.csv",
"table": "tbl_85b36c3e0390",
"quantity": "refractive_index",
"abscissa_unit": "um",
"wavelength_medium": "standard_air",
"use": "primary",
"parameters": {
"temperature_k": 298.15,
"grade": "Harshaw (commercial, 1958)",
"form": "bulk",
"technique": "minimum deviation",
"index_medium": "air",
"air_temperature_k": 298.15
}
}
Table II, ‘Refractive index, Measured’: the commercial (Harshaw) prism at 25 C, 46 wavelengths 0.2652-10.346 um. Relative to the room air (inferred; see the source notes). No per-point uncertainty is stated (average absolute residual from the formula 1.9e-5; the residuals of -9 and +9 x 1e-5 at 2.5766 and 6.6331 um are attributed to the assigned wavelengths).
malitson_1964/computed_25C#
{
"id": "computed_25C",
"material": "BaF2",
"file": "BaF2/malitson_1964__computed_25C.csv",
"table": "tbl_85b36c3e0390",
"quantity": "refractive_index",
"abscissa_unit": "um",
"wavelength_medium": "standard_air",
"use": "check",
"parameters": {
"temperature_k": 298.15,
"grade": "Harshaw (commercial, 1958)",
"form": "bulk",
"index_medium": "air",
"air_temperature_k": 298.15
}
}
Table II, ‘Refractive index, Computed’: the formula at the 46 wavelengths, 25 C; the formula’s own column (two values depart from the formula: see the source notes).
malitson_1964/mit_n_15C#
{
"id": "mit_n_15C",
"material": "BaF2",
"file": "BaF2/malitson_1964__mit_n_15C.csv",
"table": "tbl_a7ee026029c3",
"quantity": "refractive_index",
"abscissa_unit": "um",
"wavelength_medium": "standard_air",
"use": "primary",
"parameters": {
"temperature_k": 288.15,
"grade": "MIT experimental melt (Stockbarger), 1944",
"form": "bulk",
"technique": "minimum deviation",
"index_medium": "not stated"
},
"uncertainty": {
"absolute": 3e-06,
"level": "not stated"
}
}
Table I, 15 C: the MIT experimental sample (Stockbarger’s melt) measured at NBS in 1944, nine visible lines; ‘The uncertainty of these index measurements is estimated at 3 x 10^-6’ (p. 628). Rows 0.589262 and 0.767858 um are doublet means (footnote a). About 46e-5 below the commercial sample (Fig. 6). Gas in the water-jacketed housing not stated.
malitson_1964/mit_n_35C#
{
"id": "mit_n_35C",
"material": "BaF2",
"file": "BaF2/malitson_1964__mit_n_35C.csv",
"table": "tbl_a7ee026029c3",
"quantity": "refractive_index",
"abscissa_unit": "um",
"wavelength_medium": "standard_air",
"use": "primary",
"parameters": {
"temperature_k": 308.15,
"grade": "MIT experimental melt (Stockbarger), 1944",
"form": "bulk",
"technique": "minimum deviation",
"index_medium": "not stated"
},
"uncertainty": {
"absolute": 3e-06,
"level": "not stated"
}
}
Table I, 35 C: as mit_n_15C.
malitson_1964/mit_n_55C#
{
"id": "mit_n_55C",
"material": "BaF2",
"file": "BaF2/malitson_1964__mit_n_55C.csv",
"table": "tbl_a7ee026029c3",
"quantity": "refractive_index",
"abscissa_unit": "um",
"wavelength_medium": "standard_air",
"use": "primary",
"parameters": {
"temperature_k": 328.15,
"grade": "MIT experimental melt (Stockbarger), 1944",
"form": "bulk",
"technique": "minimum deviation",
"index_medium": "not stated"
},
"uncertainty": {
"absolute": 3e-06,
"level": "not stated"
}
}
Table I, 55 C: as mit_n_15C.
malitson_1964/mit_dndt_15_55C#
{
"id": "mit_dndt_15_55C",
"material": "BaF2",
"file": "BaF2/malitson_1964__mit_dndt_15_55C.csv",
"table": "tbl_a7ee026029c3",
"quantity": "thermo_optic_coefficient",
"unit": "1/K",
"scale": -1e-06,
"abscissa_unit": "um",
"wavelength_medium": "standard_air",
"use": "primary",
"parameters": {
"temperature_k": 308.15,
"grade": "MIT experimental melt (Stockbarger), 1944",
"form": "bulk",
"technique": "minimum deviation",
"index_medium": "not stated"
}
}
Table I, ‘-dn/dt x 10^-6 per C’: the MIT sample’s coefficient averaged over 15-35 and 35-55 C (p. 631), equal to (n(15) - n(55))/40 of the table; temperature_k is the midpoint, 35 C. The scale -1e-6 gives dn/dT (about -15e-6/K). Gas not stated (if air, the absolute dn/dT is about 1.4e-6/K more negative).
malitson_1964/table4_n_25C#
{
"id": "table4_n_25C",
"material": "BaF2",
"file": "BaF2/malitson_1964__table4_n_25C.csv",
"table": "tbl_3302616c5282",
"quantity": "refractive_index",
"abscissa_unit": "um",
"wavelength_medium": "standard_air",
"use": "check",
"parameters": {
"temperature_k": 298.15,
"grade": "Harshaw (commercial, 1958)",
"form": "bulk",
"index_medium": "air",
"air_temperature_k": 298.15
}
}
Table IV, n: the formula at regular wavelengths, 0.26-1.00 um by 0.02 and 1.00-10.40 um by 0.2 (85 points), 25 C; a sampling of the formula, not measurements. Rows in reading order (left column pair, then right). -dn/dlambda (1/um) is not extracted (no quantity).
Formulas#
malitson_1964/sellmeier#
{
"id": "sellmeier",
"form": "n2_sellmeier_wavelength",
"terms": {
"B": [
"0.643356",
"0.506762",
"3.8261"
],
"L": [
"0.057789",
"0.10968",
"46.3864"
]
},
"wavelength_medium": "standard_air",
"index_medium": "air",
"air_temperature_k": 298.15,
"range_nm": [
265.279,
10348.82
],
"material": "BaF2",
"parameters": {
"temperature_k": 298.15,
"grade": "Harshaw (commercial, 1958)"
},
"equation": "The abstract's equation (p. 628) and Table III (p. 629)",
"printed": "n^2 - 1 = 0.643356 lambda^2/[lambda^2 - (0.057789)^2] + 0.506762 lambda^2/[lambda^2 - (0.10968)^2] + 3.8261 lambda^2/[lambda^2 - (46.3864)^2]; Table III: A_1 = 0.643356, lambda_1 = 0.057789, lambda_1^2 = 0.0033396; A_2 = 0.506762, lambda_2 = 0.10968, lambda_2^2 = 0.012030; A_3 = 3.8261, lambda_3 = 46.3864, lambda_3^2 = 2151.70",
"variable": "lambda: wavelength in um ('where lambda is expressed in microns'), the air wavelengths of Table II's lines (see the source notes)",
"range": "0.2652-10.346 um (the 46 wavelengths fitted), 25 C; 'valid for interpolation to five decimal places over the measured wavelength range' (Fig. 2 caption)",
"coefficients": {
"A1": "0.643356",
"lambda1": "0.057789",
"lambda1_sq": "0.0033396",
"A2": "0.506762",
"lambda2": "0.10968",
"lambda2_sq": "0.012030",
"A3": "3.8261",
"lambda3": "46.3864",
"lambda3_sq": "2151.70"
},
"check": "Reproduces Table II's computed index at 44 of 46 wavelengths to its five printed decimals (rounded); at 0.334148 um 1.4936354 against 1.49363 (a rounding edge) and at 0.486133 um 1.4785462 against 1.47856 (1.4e-5). Reproduces Table IV's n at 83 of 85 wavelengths rounded, the other two truncated (within 1e-5). With the printed lambda_j^2 instead of lambda_j, 43 of 46. Checked 2026-09-27 against the printed coefficients."
}
Fitted by least squares (Sutton and Stavroudis, IBM 7090) to Table II’s measured indices, ‘no physical interpretation of the parameters is claimed’ (p. 630). The poles are printed as lambda_j (the abstract and Table III) and lambda_j^2 (Table III, rounded); the form uses lambda_j. Relative to the room air at 25 C (inferred). Identical to refractiveindex.info main/BaF2/nk/Malitson and to solprop’s BaF2.
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.