malitson_1963#
I. H. Malitson, “A Redetermination of Some Optical Properties of Calcium Fluoride”, Appl. Opt. 2, 1103 (1963)
Source record · Catalogue · Review register
DOI: 10.1364/ao.2.001103
Source kind: measurement
Recorded technique: Minimum deviation on the NBS modified Gaertner precision spectrometer (reflecting optics, uniform-rate spectrum scanning, Golay pneumatic detector, recording potentiometer; Fig. 1), at controlled room temperatures near 14 and 24 degrees C, at 46 calibrated wavelengths, 0.2288-9.724 um: emission lines (Cd, Hg, H, Na, He, K, Cs) and absorption bands of 1,2,4-trichlorobenzene, polystyrene, methylcyclohexane, CO2 and water vapour (Table II; p. 1104). Prisms: a synthetic CaF2 prism from a Stockbarger-grown crystal deposited at NBS, measured in 1959 (faces about 55 x 73 mm, refracting angle near 70 degrees), and a natural fluorite prism at NBS for more than fifty years, ‘believed to be of European origin’ (faces about 50 x 50 mm, angle near 60 degrees), both at 24 C. Table I reproduces 1944 NBS measurements of two synthetic prisms at 15, 35 and 55 C (nine visible lines; Geneva Society spectrometer with a temperature-controlled housing), previously published by Stockbarger (p. 1103). dn/dt of the synthetic prism from its 14 and 24 C indices (pp. 1106-1107).
Materials in structured entries: CaF2
Dataset quantities: refractive_index, refractive_index_deviation, thermo_optic_coefficient
Contents: 10 datasets; 1 formula.
Curation notes#
Journal pages 1103-1107 are pdf pages 1-5. Identity checked against the first page.
AIR OR VACUUM. The paper does not say whether the index is relative to air or reduced to vacuum, and gives no air correction; the measurements were made ‘at controlled room temperatures’ (p. 1104) on the instrument of Rodney and Spindler (1954) and Malitson (1965), which were in room air (TC-323, TC-399; rodney_1954, malitson_1965). Daimon and Masumura (daimon_2002, pp. 5279-5280) state it: ‘Malitson’s data are 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.’ The Table II datasets and the formula are recorded as relative to the room air at 24 C (index_medium = ‘air’, pressure not stated). A check (2026-09-27): the formula times the index of dry air at 24 C and 101 325 Pa (Edlen), at the standard-air wavelength, against daimon_2002’s 20 and 25 C formulas interpolated to 24 C times the index of N2 there (peck_1966/eq4): +1.5, +3.3, +2.5, +1.4, +0.8, +0.1, -0.2, -0.2, -0.4 x 1e-5 at 0.25, 0.3, 0.4, 0.5, 0.6, 0.8, 1.0, 1.5-2.0, 2.3 um. Read as absolute, the formula would be about 3.9e-4 below Daimon’s absolute index. The 1944 data of Table I were measured in a temperature-controlled housing, gas not stated (‘not stated’). WAVELENGTHS are the lines’ air wavelengths (Hg 0.546074 um in Table II, 0.5460740 um in Table I; Cd 0.643847 um), recorded as standard air; Table IV’s regular wavelengths are the formula’s variable, likewise in air.
ACCURACY. Table I: ‘The uncertainty of these index measurements is estimated at 2 x 10^-6’ (p. 1103). Table II: ‘The average of the absolute values of the residuals for 46 measured wavelengths is 2.46 x 10^-5 with only three residuals larger than 5 x 10^-5’ (p. 1104); at 0.2537 um (residual +9 x 1e-5) ‘there is observational uncertainty because emission lines of cadmium, zinc, and mercury are present in the spectral source’; in the 6 um region ‘exact wavelength identification was confusing because ... many overlaying atmospheric water-vapor bands’. ‘values of index may be interpolated to five decimal places’ (p. 1107). No per-point uncertainty is stated for the 24 C measurements; the residual datasets state none. The natural prism’s indices are ‘higher in each case by an average value of 2.83 x 10^-5’ than the synthetic’s computed values (p. 1105); ‘the lack of uniformity of refractive index of both the synthetic and natural fluorite is of the order of 3 x 10^-5’ (p. 1107).
TABLE II COMPUTED INDEX against the formula (checked 2026-09-27): 44 of 46 values are the formula’s value rounded to five decimals (the others within 0.5e-5 too, except two). At 0.2537 um the table prints 1.46602 where the formula gives 1.465989 (3.1e-5 lower), and at 0.365015 um 1.44490 where it gives 1.444913 (1.3e-5 higher). Neither is explained (no nearby line reproduces 1.46602 at 0.2537 um); the residuals at those two wavelengths are relative to the printed computed index, so the observed index there is uncertain by that amount (1.46611 or 1.46608 at 0.2537 um). Not corrected.
TABLE IV (n and -dn/dlambda at regular wavelengths, computed from the formula) is TRUNCATED, not rounded, to five and four decimals: 83 of its 84 n values equal the formula truncated to five decimals, and every -dn/dlambda equals the formula’s derivative truncated. The 84th, 1.44548 at 0.36 um, is a misprint for 1.44543 (erratum).
TABLE I dn/dt against its own indices: 16 of the 18 printed values are (n(t1) - n(t2))/20; two are not: 0.6678149 um, 35-55 C, printed 10.85 (the indices give 11.00) and 0.4046563 um, 35-55 C, printed 10.12 (the indices give 10.50). The paper says ‘the observed averaged indices and observed temperatures listed in Table I were used’ (p. 1106); the observed temperatures are not listed beyond the nominal 15, 35 and 55 C. Not corrected. Table I rows 0.767858 and 0.589262 um carry the mark ‘a’: ‘Intensity weighted mean of doublet’. Abbe numbers (last row): 95.13, 95.13, 94.93 at 15, 35, 55 C.
dn/dt. Table II’s column is for the mean temperature 19 C, from the 14 and 24 C measurements of the synthetic prism (pp. 1106-1107), negative throughout (-5.6 to -10.6 x 1e-6/C). Relative to the room air: at constant pressure the air’s refractivity falls by about 0.9e-6/K, so the absolute dn/dT is about 1.3e-6/K more negative (not discussed in the paper). Fig. 4 caption: ‘An average value of -dn/dt for the temperature interval of 15 C to 24 C over the entire measured wavelength range is 8.65 x 10^-6’.
REPRODUCED IN TABLE I: ‘The averaged index values of both prisms, published previously by Stockbarger^3,4 are reproduced in Table I’ (p. 1103): D. C. Stockbarger and M. Early, O.S.R.D. Rept. No. 4690 (1944), and D. C. Stockbarger, J. Opt. Soc. Am. 39, 731 (1949) (not in the library). The dn/dt columns of Table I are Malitson’s, computed from them.
FORMULA. See the formula entry. REFRACTIVEINDEX.INFO (main/CaF2/nk/Malitson.yml, compared 2026-09-27): formula 1 with 0.5675888, 0.050263605, 0.4710914, 0.1003909, 3.8484723, 34.649040, identical to Table III; range 0.23-9.7 um; comment ‘24 C’; no statement that the index is relative to air or that the wavelengths are air wavelengths. solprop’s alternative CaF2 (‘malitson’) uses these coefficients as an absolute index at vacuum wavelengths: about 3.9e-4 low.
FIGURES (not digitised): 1, the spectrometer; 2, n of synthetic CaF2 at 24 C, 0.2-10 um; 3, the dispersive quantities (dn/dlambda)/(1 - n), its reciprocal and (lambda dn/dlambda)^-1, relative dispersion minimum near 1.5 um; 4, -dn/dt against wavelength (NBS 19 C, Micheli 61.25 C at 0.185-0.508 um, Liebreich 60 C at 0.589-6.5 um); 5, Coblentz’s and Kohlrausch’s (Paschen) natural-crystal indices at 20 C minus NBS, average differences 2.18e-5 (57 wavelengths) and 2.36e-5 (28) (p. 1107).
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_1963/computed_24C#
{
"id": "computed_24C",
"material": "CaF2",
"file": "CaF2/malitson_1963__computed_24C.csv",
"table": "tbl_519685ce8f61",
"quantity": "refractive_index",
"abscissa_unit": "um",
"wavelength_medium": "standard_air",
"use": "check",
"parameters": {
"temperature_k": 297.15,
"grade": "synthetic (Stockbarger-grown, NBS)",
"form": "bulk",
"index_medium": "air",
"air_temperature_k": 297.15
}
}
Table II, ‘Computed index’: the Table III formula at the 46 wavelengths, 24 C; the formula’s own column (two values depart from the formula: see the source notes). The synthetic prism’s measured index is this plus residual_synthetic_24C.
malitson_1963/residual_synthetic_24C#
{
"id": "residual_synthetic_24C",
"material": "CaF2",
"file": "CaF2/malitson_1963__residual_synthetic_24C.csv",
"table": "tbl_519685ce8f61",
"quantity": "refractive_index_deviation",
"scale": 1e-05,
"abscissa_unit": "um",
"wavelength_medium": "standard_air",
"use": "primary",
"parameters": {
"reference": "malitson_1963/sellmeier",
"temperature_k": 297.15,
"grade": "synthetic (Stockbarger-grown, NBS)",
"form": "bulk",
"technique": "minimum deviation",
"index_medium": "air",
"air_temperature_k": 297.15
}
}
Table II, ‘Synthetic o-c’ x 10^5: the synthetic prism’s observed index minus the computed index, at 24 C, 46 wavelengths; the data the formula was fitted to. The residuals are relative to the printed computed index, which differs from the formula at 0.2537 um (by 3.1e-5) and 0.365015 um (1.3e-5): see the source notes. No per-point uncertainty is stated; the average absolute residual is 2.46e-5.
malitson_1963/residual_natural_24C#
{
"id": "residual_natural_24C",
"material": "CaF2",
"file": "CaF2/malitson_1963__residual_natural_24C.csv",
"table": "tbl_519685ce8f61",
"quantity": "refractive_index_deviation",
"scale": 1e-05,
"abscissa_unit": "um",
"wavelength_medium": "standard_air",
"use": "primary",
"parameters": {
"reference": "malitson_1963/sellmeier",
"temperature_k": 297.15,
"grade": "natural fluorite (NBS prism, believed European)",
"form": "bulk",
"technique": "minimum deviation",
"index_medium": "air",
"air_temperature_k": 297.15
}
}
Table II, ‘Natural o-c’ x 10^5: the natural fluorite prism’s observed index minus the computed index for the synthetic crystal, 24 C, 46 wavelengths (‘higher in each case by an average value of 2.83 x 10^-5’, p. 1105). Relative to the printed computed index (see residual_synthetic_24C).
malitson_1963/dndt_19C#
{
"id": "dndt_19C",
"material": "CaF2",
"file": "CaF2/malitson_1963__dndt_19C.csv",
"table": "tbl_519685ce8f61",
"quantity": "thermo_optic_coefficient",
"unit": "1/K",
"scale": -1e-06,
"abscissa_unit": "um",
"wavelength_medium": "standard_air",
"use": "primary",
"parameters": {
"temperature_k": 292.15,
"grade": "synthetic (Stockbarger-grown, NBS)",
"form": "bulk",
"technique": "minimum deviation",
"index_medium": "air"
}
}
Table II, ‘-dn/dt x 10^6’ for the mean temperature 19 C, from the synthetic prism’s indices at 14 and 24 C (pp. 1106-1107); 46 wavelengths. The printed values are -dn/dt: the scale -1e-6 gives dn/dT (negative throughout). Relative to the room air (the absolute dn/dT is about 1.3e-6/K more negative; see the source notes). No uncertainty stated.
malitson_1963/stockbarger_n_15C#
{
"id": "stockbarger_n_15C",
"material": "CaF2",
"file": "CaF2/malitson_1963__stockbarger_n_15C.csv",
"table": "tbl_ae8cd73c9fb7",
"quantity": "refractive_index",
"abscissa_unit": "um",
"wavelength_medium": "standard_air",
"use": "reproduced",
"reproduced_from": [
"D. C. Stockbarger and M. Early, \"Artificial Fluorite\", O.S.R.D. Rept. No. 4690 (December, 1944)",
"D. C. Stockbarger, J. Opt. Soc. Am. 39, 731 (1949)"
],
"parameters": {
"temperature_k": 288.15,
"grade": "synthetic (Stockbarger), average of two prisms",
"form": "bulk",
"technique": "minimum deviation",
"index_medium": "not stated"
},
"uncertainty": {
"absolute": 2e-06,
"level": "not stated"
}
}
Table I, 15 C: the average index of two synthetic prisms measured at NBS in 1944 (Geneva Society spectrometer with a temperature-controlled housing), nine visible lines; ‘published previously by Stockbarger’ and reproduced here (p. 1103). ‘The uncertainty of these index measurements is estimated at 2 x 10^-6’. Rows 0.767858 and 0.589262 um are intensity-weighted means of doublets (footnote a). The gas in the housing is not stated.
malitson_1963/stockbarger_n_35C#
{
"id": "stockbarger_n_35C",
"material": "CaF2",
"file": "CaF2/malitson_1963__stockbarger_n_35C.csv",
"table": "tbl_ae8cd73c9fb7",
"quantity": "refractive_index",
"abscissa_unit": "um",
"wavelength_medium": "standard_air",
"use": "reproduced",
"reproduced_from": [
"D. C. Stockbarger and M. Early, \"Artificial Fluorite\", O.S.R.D. Rept. No. 4690 (December, 1944)",
"D. C. Stockbarger, J. Opt. Soc. Am. 39, 731 (1949)"
],
"parameters": {
"temperature_k": 308.15,
"grade": "synthetic (Stockbarger), average of two prisms",
"form": "bulk",
"technique": "minimum deviation",
"index_medium": "not stated"
},
"uncertainty": {
"absolute": 2e-06,
"level": "not stated"
}
}
Table I, 35 C: as stockbarger_n_15C.
malitson_1963/stockbarger_n_55C#
{
"id": "stockbarger_n_55C",
"material": "CaF2",
"file": "CaF2/malitson_1963__stockbarger_n_55C.csv",
"table": "tbl_ae8cd73c9fb7",
"quantity": "refractive_index",
"abscissa_unit": "um",
"wavelength_medium": "standard_air",
"use": "reproduced",
"reproduced_from": [
"D. C. Stockbarger and M. Early, \"Artificial Fluorite\", O.S.R.D. Rept. No. 4690 (December, 1944)",
"D. C. Stockbarger, J. Opt. Soc. Am. 39, 731 (1949)"
],
"parameters": {
"temperature_k": 328.15,
"grade": "synthetic (Stockbarger), average of two prisms",
"form": "bulk",
"technique": "minimum deviation",
"index_medium": "not stated"
},
"uncertainty": {
"absolute": 2e-06,
"level": "not stated"
}
}
Table I, 55 C: as stockbarger_n_15C.
malitson_1963/dndt_15_35C#
{
"id": "dndt_15_35C",
"material": "CaF2",
"file": "CaF2/malitson_1963__dndt_15_35C.csv",
"table": "tbl_ae8cd73c9fb7",
"quantity": "thermo_optic_coefficient",
"unit": "1/K",
"scale": -1e-06,
"abscissa_unit": "um",
"wavelength_medium": "standard_air",
"use": "primary",
"parameters": {
"temperature_k": 298.15,
"grade": "synthetic (Stockbarger), average of two prisms",
"form": "bulk",
"technique": "minimum deviation",
"index_medium": "not stated"
}
}
Table I, ‘-dn/dt x 10^6’, 15-35 C (temperature_k is the midpoint, 25 C): computed by Malitson from Stockbarger’s 1944 indices (p. 1106); every value equals (n(15) - n(35))/20 of the table. The scale -1e-6 gives dn/dT. Medium of the 1944 measurements not stated.
malitson_1963/dndt_35_55C#
{
"id": "dndt_35_55C",
"material": "CaF2",
"file": "CaF2/malitson_1963__dndt_35_55C.csv",
"table": "tbl_ae8cd73c9fb7",
"quantity": "thermo_optic_coefficient",
"unit": "1/K",
"scale": -1e-06,
"abscissa_unit": "um",
"wavelength_medium": "standard_air",
"use": "primary",
"parameters": {
"temperature_k": 318.15,
"grade": "synthetic (Stockbarger), average of two prisms",
"form": "bulk",
"technique": "minimum deviation",
"index_medium": "not stated"
}
}
Table I, ‘-dn/dt x 10^6’, 35-55 C (temperature_k is the midpoint, 45 C): computed by Malitson from Stockbarger’s 1944 indices. Seven of nine values equal (n(35) - n(55))/20; at 0.6678149 um the table prints 10.85 (the indices give 11.00) and at 0.4046563 um 10.12 (10.50): not explained (‘observed temperatures’ were used, p. 1105), not corrected. The scale -1e-6 gives dn/dT.
malitson_1963/table4_n_24C#
{
"id": "table4_n_24C",
"material": "CaF2",
"file": "CaF2/malitson_1963__table4_n_24C.csv",
"table": "tbl_9273a9ecad2b",
"quantity": "refractive_index",
"abscissa_unit": "um",
"wavelength_medium": "standard_air",
"use": "check",
"parameters": {
"temperature_k": 297.15,
"grade": "synthetic (Stockbarger-grown, NBS)",
"form": "bulk",
"index_medium": "air",
"air_temperature_k": 297.15
}
}
Table IV, n: the formula at regular wavelengths, 0.22-1.00 um by 0.02 and 1.00-9.80 um by 0.2 (84 points), 24 C, truncated to five decimals (see the source notes); a sampling of the formula, not measurements. Rows in reading order (left column pair, then right). -dn/dlambda (1/um) has no quantity and is not extracted.
Formulas#
malitson_1963/sellmeier#
{
"id": "sellmeier",
"form": "n2_sellmeier_wavelength",
"terms": {
"B": [
"0.5675888",
"0.4710914",
"3.8484723"
],
"L": [
"0.050263605",
"0.1003909",
"34.649040"
]
},
"wavelength_medium": "standard_air",
"index_medium": "air",
"air_temperature_k": 297.15,
"range_nm": [
228.874,
9726.65
],
"material": "CaF2",
"parameters": {
"temperature_k": 297.15,
"grade": "synthetic (Stockbarger-grown, NBS)"
},
"equation": "Table III, p. 1105 (the form in the abstract and p. 1104)",
"printed": "n^2 - 1 = Sum A_j lambda^2/(lambda^2 - lambda_j^2); lambda_1 = 0.050263605, lambda_1^2 = 0.002526430, A_1 = 0.5675888; lambda_2 = 0.1003909, lambda_2^2 = 0.01007833, A_2 = 0.4710914; lambda_3 = 34.649040, lambda_3^2 = 1200.5560, A_3 = 3.8484723",
"variable": "lambda: wavelength in um, the air wavelengths of Table II's lines (see the source notes)",
"range": "0.2288-9.724 um (the 46 wavelengths fitted), 24 C; 'The dispersion formula is valid for interpolation over the measured wavelength range' (Fig. 2 caption)",
"coefficients": {
"A1": "0.5675888",
"lambda1": "0.050263605",
"lambda1_sq": "0.002526430",
"A2": "0.4710914",
"lambda2": "0.1003909",
"lambda2_sq": "0.01007833",
"A3": "3.8484723",
"lambda3": "34.649040",
"lambda3_sq": "1200.5560"
},
"check": "Reproduces Table II's computed index at 44 of 46 wavelengths to its five printed decimals (rounded); at 0.2537 um it gives 1.465989 against the printed 1.46602 and at 0.365015 um 1.444913 against 1.44490 (see the source notes). Reproduces Table IV's n at 83 of 84 wavelengths and every -dn/dlambda as the formula truncated to the printed decimals (the 84th is the erratum at 0.36 um). The printed lambda_j and lambda_j^2 agree (lambda_j^2 rounded); either gives the same values to 1e-8. Checked 2026-09-27 against the printed coefficients."
}
A three-term Sellmeier fitted by least squares (L. E. Sutton’s program; refs. 5, 6) to the synthetic prism’s 24 C indices, ‘primarily a mathematical fit of the measured data’ (p. 1107). The poles are printed both as lambda_j and lambda_j^2; the form uses lambda_j (n2_sellmeier_wavelength). Relative to the room air at 24 C (see the source notes). Identical to refractiveindex.info main/CaF2/nk/Malitson and solprop’s ‘malitson’ CaF2 (both used there as absolute).
Corrections#
[
{
"dataset": "table4_n_24C",
"row": "0.36",
"column": "value",
"printed": "1.44548",
"corrected": "1.44543",
"reason": "Misprint of the last digit: Table IV is the formula truncated to five decimals (83 of its 84 values), and the formula gives 1.445432 at 0.36 um.",
"evidence": "Table IV image (pdf p. 3) prints 1.44548. The Table III formula gives 1.4454317 at 0.36 um (checked 2026-09-27), whose truncation is 1.44543; the neighbouring differences with 1.44543 (-0.00232 from 0.34 um, -0.00194 to 0.38 um) follow the printed -dn/dlambda (0.1272 at 0.34, 0.1056 at 0.36, 0.0888 at 0.38 um), while 1.44548 gives -0.00227 and -0.00199."
}
]
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.