Refractive indices of water and icein the 0.65- to 2.5-gm spectral range

Linhong Kou, Daniel Labrie, and Petr Chylek

New accurate values of the imaginary part, k, of the refractive index of water at T = 22 C, supercooledwater at T = -8 C and polycrystalline ice at T = -25 0C are reported. The k spectrum for water in thespectral region 0.65-2.5 pLm is found to be in excellent agreement with those of previous studies. The kvalues for polycrystalline ice in the 1.44-2.50-ptm region eliminate the large uncertainties existing amongpreviously published conflicting sets of data. The imaginary part of refractive index of supercooled watershows a systematic shift of absorption peaks toward the longer wavelengths compared with that of waterat warmer temperatures.

Key words: Refractive index, optical constant, near-infrared, ice, water.

1. Introduction

Refractive indices of water and ice play a special rolein the field of atmospheric science. They must beknown if the radiative properties of clouds and hazeare to be determined. It has been recognized thatthe cloud feedback mechanism is one of the mostimportant and least understood climate mecha-nisms'- 5 that may significantly modify currently pre-dicted warming68 resulting from the increase ofatmospheric greenhouse gases. An accurate calcula-tion of the cloud radiative parameters is not possiblewithout a precise knowledge of the refractive indicesof water and ice in the spectral range of solar (0.25-4.0-pm) and terrestrial (3-150-pm) radiation.

Refractive indices used most frequently in atmo-spheric applications are those listed in the Hale andQuerry9 compilation of the refractive indices of waterand in Warren's 0 compilation of indices of refractionof ice. A major effort was devoted to the determina-tion and parameterization of the cloud radiativeproperties with an error not larger than a few percent.At the same time it was assumed that the refractiveindices of such common materials as water and ice areknown with a high degree of accuracy. Those whonot only use the tables but also study carefully the

The authors are with the Atmospheric Science Program, Depart-ment of Physics, Dalhousie University, Halifax, Nova Scotia B3H3J5, Canada.

Received 11 August 1992.0003-6935/93/193531-10$06.00/0.© 1993 Optical Society of America.

analysis given in the text of the above-mentionedcompilations are well aware that this is not true.The uncertainty in the imaginary part of the refrac-tive index (which determines the absorption of radia-tion) is significant especially in the case of ice,'0 whereit can reach as high as 100% in some spectral regions.

One of the regions of large uncertainty is in thenear-infrared part of the solar spectrum. War-ren's 0 compilation of the refractive indices of ice isbased in this range on measurements done in theearly- and mid-1950's"" 2 on ice in the temperaturerange -30° to -78 0C. The estimated uncertainty'0of the compilation in this region is a factor of 2.

To reduce the uncertainty in the imaginary part kof the refractive index of ice in the near-infraredregion, we have performed new accurate measure-ments in the 1.45-2.5-pim spectral region. Althoughour primary goal was to obtain new accurate values ofk for ice, we have also measured k for water. Thelatter measurement was made to test the experimen-tal equipment (k for water is known with a musthigher accuracy than that of ice) and procedures.

The measured k values for water differ by as muchas 15% from those listed by Hale and Querry9;however, they are in good agreement with thoseobtained by Palmer and Williams 3 and Downing andWilliams.' 4 We present new measurements of k forsupercooled water at -8 C. Obtained refractiveindices (imaginary parts) of ice differ as much as 22%from those listed by Warren.' 0

This paper is divided into four parts. In Section 2we describe the experimental setup and discuss the

1 July 1993 / Vol. 32, No. 19 / APPLIED OPTICS 3531

procedure used to measure k for water and ice. InSection 3 we present new results for water and ice,and Section 4 provides a discussion of the results andsuggestions for future work.

2. Experimental Setup and ProceduresThe transmission measurements through water andice were carried out with a Bomem DA3.02 Fourier-transform infrared spectrometer at a spectral resolu-tion of 16 cm-'. The instrument has an absolutewavelength calibration. During the course of themeasurements, no adjustment of the light intensitywas necessary for 100% transmission to be obtainedin the spectral regions where the absorption is negligi-ble.

We derived the Lambert absorption coefficient, a,of freshly distilled filtered water, using the ratio oftransmittances obtained with different absorptionpath lengths. In this way, reflection losses occurringat the air-window and window-water interface andabsorption losses caused by the windows of theabsorption cell were exactly canceled out. Opticalpath lengths d in water ranging from 100 ALm to 20cm were selected in such a way that a could bedetermined from transmittance values varying from20% to 60%.

Measurements of a of supercooled water and poly-crystalline ice were taken in a temperature-controlled

20000

2.0 Tv

1 .5

t 1.0

0.5

0.01 0

5

0

WAVE NUMBER (cm- 1)1 0000 6666.7 5000

0.5 1.0 1.5 2.0WAVELENGTH (em)

4000

2.5

Fig. 1. (a) Imaginary part of the refractive index, k, of water: thepresent work (KLC, solid curves) at T = 22 'C and the PW and DWdata (dashed curves) at 27 'C (b) Standard deviation of k forwater at T = 22 'C.

cryostat with sample temperatures ranging from+22 C to -40 C. For the case of ice and super-cooled water, at a given path length oa was calculatedby using the ratio of the transmittance taken below0 C temperature to that at 22 C. Using our previ-ous measurements of absorption coefficient of waterat 22 C, we determined the absorption coefficient atsubzero temperature. Using this method, we foundthat reflection and absorption losses caused by thecell windows were eliminated. Optical path lengthsvarying between 100 pum and 2 cm were used forsupercooled water, while those for ice were between116 and 269 Rm.

We utilized the following procedure for the forma-tion of ice sample. A droplet of water was placedbetween two optical windows in such a way that thedroplet was free to expand during cooling in thedirection normal to the thickness of the sample.Using the above procedure, we found that the waterthickness was nearly the same as that of ice.

We obtained an a spectrum by calculating theaverage spectrum of a set of as many as 20 a spectracollected under the same experimental conditions.The corresponding error can be evaluated by usingthe standard deviation of the same set of a spectraand the uncertainty in the path length.

2.0

1 .5

v 1.0

0.5

0.01 0

N

0

wd

5

0

1 0000WAVE NUMBER (cm-1 )

6666.7 5000 4000

1.0 1.5 2.0 2.5WAVELENGTH (m)

Fig. 2. (a) Imaginary part of the refractive index of water at T =22 'C (solid curves), supercooled water at T = -8 'C (longer-dashedcurves), and polycrystalline ice at T = -25 'C (shorter-dashedcurves). (b) Standard deviation of k for supercooled water at T =-8 'C.

3532 APPLIED OPTICS / Vol. 32, No. 19 / 1 July 1993

I-N

ry0

wy

Table 1. Imaginary Part of the Refractive Index, k, and the Standard Deviation of k for Water at T = 22 °C, Supercooled Water at T = -8 °C, andPolycrystalline Ice at T = -25 °C in the Spectral Range From 4000 to 6920 cm-'

Water Ice

T = 22°C T = -8 C T= -25°C

Wave Wave Error Error ErrorNumber (1/cm) Length (m) k (% k (% k (%

3.6 1.76 x 10-3

3.3 1.68 x 10-3

3.9 1.56 x 10-3

3.1 1.42 x 10-3

2.0 1.25 x 10-3

1.4 1.17 x 10-3

1.4 1.08 x 10-3

1.4 9.94 x 10-4

1.2 9.20 x 10-4

1.0 8.50 x 10-4

0.8 7.81 x 10-4

0.9 7.31 x 10-4

0.9 6.73 x 10-4

1.0 6.19 x 10-4

0.9 5.70 x 10-4

1.0 5.31 x 10-4

0.9 4.90 x 10-4

0.8 4.55 x 10-4

1.0 4.26 x 10-4

1.1 4.01 x 10-4

1.1 3.80 x 10-4

1.0 3.63 x 10-4

1.2 3.48 x 10-4

1.1 3.45 x 10-4

1.2 3.43 x 10-4

1.1 3.37 x 10-4

1.2 3.35 x 10-4

1.3 3.41 x 10-4

1.3 3.43 x 10-4

1.0 3.52 x 10-4

1.0 3.61 x 10-4

1.0 3.72 x 10-4

0.9 3.89 x 10-4

1.0 4.08 x 10-4

1.0 4.31 x 10-4

1.0 4.58 x 10-4

1.1 4.87 x 10-4

1.2 5.23 x 10-4

1.1 5.61 x 10-4

1.3 6.03 x 10-4

1.3 6.47 x 10-4

1.5 7.00 x 10-4

1.6 7.50 x i0-4

2.0 8.25 x 10-4

1.8 8.91 x 10-4

2.0 9.54 x 10-4

1.8 1.03 x 10-3

1.7 1.11 x 10-3

1.5 1.19 x 10-3

2.5 1.28 x 10-3

2.9 1.37 x 10-3

2.5 1.46 x 10-3

2.7 1.56 x 10-3

2.5 1.68 x 10-3

2.0 1.77 x 10-3

2.1 1.87 x 10-3

2.0 1.95 x 10-3

2.1 2.00 x 10-3

4.3 8.04 x4.1 7.72 x4.3 7.44 x3.8 7.20 x3.0 6.91 x2.3 6.61 x2.2 6.40 x1.8 6.21 x1.5 5.99 x1.5 5.77 x1.3 5.54 x1.2 5.27 x1.1 4.97 x1.2 4.61 x1.3 4.20 x1.3 3.81 x1.3 3.40 x1.5 3.03 x1.4 2.72 x1.4 2.46 x1.7 2.28 x1.3 2.16 x2.1 2.10 x1.7 2.12 x1.7 2.17 x1.7 2.27 x1.6 2.38 x1.8 2.54 x1.7 2.71 x1.3 2.93 x1.5 3.17 x1.2 3.48 x1.6 3.83 x1.4 4.28 x1.4 4.85 x1.2 5.50 x1.1 6.28 x1.4 7.19 x1.3 8.20 x1.4 9.30 x1.4 1.02 x1.5 1.13 x1.7 1.23 x1.9 1.32 x1.8 1.40 x2.0 1.45 x3.1 1.52 x3.1 1.55 x2.9 1.59 x2.8 1.63 x2.7 1.64 x2.4 1.64 x2.5 1.63 x2.3 1.59 x1.8 1.52 x1.9 1.42 x1.8 1.31 x2.0 1.16 x

1 July 1993 / Vol. 32, No. 19 / APPLIED OPTICS 3533

4000402040404060408041004120414041604180420042204240426042804300432043404360438044004420444044604480450045204540456045804600462046404660468047004720474047604780480048204840486048804900492049404960498050005020504050605080510051205140

2.50002.48762.47522.46312.45102.43902.42722.41552.40382.39232.38102.36972.35852.34742.33642.32562.31482.30412.29362.28312.27272.26242.25232.24222.23212.22222.21242.20262.19302.18342.17392.16452.15522.14592.13682.12772.11862.10972.10082.09212.08332.07472.06612.05762.04922.04082.03252.02432.01612.00802.00001.99201.98411.97631.96851.96081.95311.9455

2.00 x 10-3

1.87 x 10-3

1.71 x 10-3

1.56 x 10-3

1.40 x 10-3

1.27 x 10-3

1.17 x 10-3

1.07 x 10-3

9.84 x 10-4

9.05 x 10-4

8.35 x 10-4

7.70 x 10-4

7.11 x 10-4

6.75 x 10-4

6.07 x 10-4

5.64 x 10-4

5.24 x 10-4

4.89 x 10-4

4.60 x 10-4

4.34 x 10-4

4.12 x 10-4

3.95 x 10-4

3.80 x 10-4

3.70 x 1O-4

3.62 x 10-4

3.56 x 10-4

3.53 x 10-4

3.53 x 10-4

3.54 x 10-4

3.59 x 10-4

3.64 x 10-4

3.73 x 10-4

3.83 x 10-4

3.96 x 10-4

4.13 x 10-4

4.32 x 10-4

4.54 x 10-4

4.80 x 10-4

5.09 x 10-4

5.43 x 10-4

5.80 x 10-4

6.20 x 10-4

6.65 x 10-4

7.20 x 10-4

7.77 x 10-4

8.31 x 10-4

8.96 x 10-4

9.69 x 10-4

1.05 x 10-3

1.13 x 10-3

1.23 x 10-3

1.33 x 10-3

1.44 x 10-3

1.56 x 10-3

1.68 x 10-3

1.80 x 10-3

1.92 x 10-32.02 x 10-3

10-4

10-4

10-4

10-4

10-4

10-4

10-4

10-4

0-4

10-4

0-4

10-4

10-4

10-4

10-4

10-4

10-4

10-4

10-4

10-4

10-4

10-4

10-4

10-4

10-410-4

10-4

10-410-4

10-4

10-4

10-410-4

10-4

10-4

10-4

0-4

10-4

10-4

10-4

10-310-3

10-3

o-3

10-3

10-3

10-3

10-3

10-3

10-3

0-3

10-3

0-3

10-3

10-3

10-3

10-3

10-3

6.04.73.83.83.02.12.01.91.61.51.31.41.51.71.82.12.32.73.33.63.94.14.34.34.34.23.93.73.43.13.02.72.42.22.01.81.61.61.51.23.33.02.92.72.52.12.22.12.12.22.22.02.42.42.22.52.73.6

(Table continued)

Table 1. (continued)

Water Ice

T = 22 C T = -8°C T = -25 C

Wave Wave Error Error ErrorNumber (1 /cm) Length (.m) k (% k (% k (%

2.3 2.00 x 10-3

2.2 1.95 x 10-3

2.3 1.82 x 10-3

2.5 1.66 x 10-3

2.7 1.44 x 10-3

2.9 1.17 x 10-3

2.4 8.83 x 10-4

2.7 5.91 x 10-4

2.8 3.90 x 10-4

4.0 2.69 x 10-4

3.6 1.98 x 10-4

1.9 1.65 x 10-4

1.4 1.45 x 10-4

1.4 1.34 x 10-4

1.3 1.29 x 10-4

1.1 1.26 x 10-4

1.2 1.25 x 10-4

1.4 1.24 x 10-4

1.5 1.25 x 10-4

1.2 1.26 x 10-41.2 1.26 x 10-4

1.4 1.27 x 10-4

1.3 1.27 x 10-4

1.5 1.26 x 10-4

1.2 1.23 x 10-4

1.1 1.09 X 10-4

1.4 1.14 x 10-4

1.0 1.09 X 10-4

1.2 1.05 x 10-4

1.1 1.0 X 10-4

1.1 9.74 x 10-5

1.3 9.50 x 10-5

1.1 9.30 x 10-5

1.0 9.15 x 10-5

1.3 9.01 x 10-51.1 8.94 x 10-5

1.2 8.94 x 10-5

1.3 8.92 x 10-5

1.0 8.93 x 10-5

1.1 8.97 x 10-51.2 9.00 x 10-51.3 9.08 x 10-5

1.4 9.16 x 10-5

1.1 9.29 x 10-5

1.4 9.40 x 10-5

1.1 9.56 x 10-51.2 9.72 x 10-5

1.3 9.86 x 10-5

1.2 1.00 x 10-41.4 1.03 x 10-41.2 1.05 x 10-4

1.1 1.07 x 10-4

1.2 1.11 x 10-41.5 1.13 x 10-4

1.0 1.17 x 10-4

1.2 1.20 x 10-4

1.0 1.24 x 10-41.2 1.29 x 10-4

1.2 1.34 x 10-4

2.3 9.91 x 10-4

2.3 8.38 x 10-4

2.7 6.82 x 10-4

3.3 5.53 x 10-4

3.8 4.84 x 10-4

4.3 4.00 x 10-4

3.2 2.98 x 10-4

3.5 2.33 x 10-4

3.5 1.87 x 10-4

4.9 1.56 x 10-4

4.7 1.42 x 10-4

2.6 1.33 x 10-4

1.9 1.26 x 10-4

1.9 1.26 x 10-4

1.7 1.23 x 10-4

1.3 1.23 x 10-4

1.4 1.25 x 10-41.6 1.26 x 10-41.6 1.28 x 10-4

1.3 1.30 x 10-4

1.2 1.31 x 10-4

1.5 1.33 x 10-4

1.3 1.35 x 10-4

1.6 1.37 x 10-4

1.2 1.38 x 10-4

0.8 1.39 x 10-4

1.4 1.40 x 10-4

1.1 1.42 x 10-4

1.2 1.45 x 10-4

1.0 1.48 x 10-41.1 1.49 x 10-4

1.3 1.52 x 10-4

1.2 1.54 x 10-4

1.1 1.59 x 10-4

1.5 1.63 x 10-4

1.4 1.67 x 10-4

1.4 1.72 x 10-4

1.5 1.78 x 10-4

1.5 1.82 x 10-4

1.5 1.87 x 10-4

1.6 1.92 x 10-4

1.7 1.97 x 10-4

1.7 2.05 x 10-4

1.7 2.11 x 10-4

1.9 2.16 x 10-4

1.7 2.23 x 10-4

1.7 2.29 x 10-4

1.8 2.35 x 10-4

1.9 2.40 x 10-4

1.9 2.44 x 10-4

1.9 2.47 x 10-4

1.7 2.49 x 10-4

1.9 2.53 x 10-4

1.9 2.59 x 10-4

1.8 2.66 x 10-4

1.8 2.74 x 10-4

1.9 2.84 x 10-4

1.9 2.97 x 10-41.9 3.11 x 10-4

3534 APPLIED OPTICS / Vol. 32, No. 19 / 1 July 1993

51605180520052205240526052805300532053405360538054005420544054605480560055205540556055805600562056405660568057005720574057605780580058205840586058805900592059405960598060006020604060606080610061206140616061806200622062406260628063006320

1.93801.93051.92311.91571.90841.90111.89391.88681.87971.87271.86571.85871.85191.84501.83821.83151.82481.81821.81161.80511.79861.79211.78571.77941.77311.76681.76061.75441.74831.74221.73611.73011.72411.71821.71231.70651.70071.69491.68921.68351.67791.67221.66671.66111.65561.65021.64471.63931.63401.62871.62341.61811.61291.60771.60261.59741.59241.58731.5823

2.08 x 10-3

2.10 x 10-3

2.06 x 10-3

1.96 x 10-3

1.78 x 10-3

1.49 x 10-3

1.10 X 10-3

7.31 x 10-4

4.75 x 10-4

3.21 x 10-4

2.34 x 10-4

1.89 x 10-41.64 x 10-4

1.48 x 10-4

1.42 x 10-4

1.37 x 10-4

1.34 x 10-4

1.33 x 10-4

1.32 x 10-4

1.33 x 10-41.31 x 10-4

1.31 x 10-4

1.30 x 10-4

1.27 x 10-4

1.23 x 10-4

1.18 x 10-41.11 X 10-4

1.06 x 10-4

1.01 X 10-4

9.59 x 10-5

9.19 X 10-5

8.87 x 10-58.61 x 10-58.39 x 10-5

8.19 x 10-58.04 x 10-5

7.97 x 10-5

7.89 x 10-5

7.84 x 10-5

7.82 x 10-57.79 x 10-57.82 x 10-5

7.85 x 10-57.91 x 10-5

7.97 x 10-58.09 x 10-58.20 x 10-5

8.29 x 10-5

8.44 x 10-5

8.63 x 10-58.79 x 10-59.00 X 10-5

9.23 x 10-59.44 x 10-5

9.70 x 10-5

1.00 X 10-4

1.03 x 10-4

1.07 x 10-41.11 X 10-4

4.75.47.09.2

11.014.710.4

9.99.1

10.610.411.011.912.313.012.110.911.410.2

9.810.0

9.99.38.38.18.28.07.67.07.07.26.46.55.95.45.55.34.74.84.74.14.24.23.53.53.43.43.53.23.33.23.22.82.93.12.82.82.72.7

(Table continued)

Table 1. (continued)

Water Ice

T = 22°C T =-8 C T =-25 C

Wave Wave Error Error ErrorNumber (1/cm) Length (pum) k (%) k (%) k (%)

6340 1.5773 1.15 x 10-4 1.4 1.39 x 10-4 2.0 3.24 x 10-4 2.56360 1.5723 1.19 x 10-4 1.0 1.44 x 10-4 2.0 3.42 x 10-4 2.66380 1.5674 1.24 x 10-4 1.6 1.46 x 10-4 4.1 3.58 x 10-4 2.36400 1.5625 1.30 x 10-4 1.2 1.54 x 10-4 3.8 3.75 x 10-4 2.2

6420 1.5576 1.36 x 10-4 1.4 1.63 x 10-4 4.4 3.92 x 10-4 2.46440 1.5528 1.44 x 10-4 1.9 1.71 x 10-4 3.8 4.08 x 10-4 2.16460 1.5480 1.50 x 10-4 1.9 1.81 x 10-4 2.8 4.25 x 10-4 1.8

6480 1.5432 1.57 x 10-4 2.3 1.88 x 10-4 3.0 4.37,x 10-4 1.86500 1.5385 1.69 x 10-4 2.2 2.00 x 10-4 3.7 4.51 x 10-4 2.0

6520 1.5337 1.78 x 10-4 2.2 2.09 x 10-4 3.1 4.62 x 10-4 1.86540 1.5291 1.87 x 10-4 3.5 2.23 x 10-4 3.4 4.75 x 10-4 1.9

6560 1.5244 1.95 x 10-4 2.9 2.35 x 10-4 2.6 4.87 x 10-4 1.66580 1.5198 2.06 x 10-4 2.8 2.48 x 10-4 2.4 4.98 x 10-4 1.56600 1.5152 2.18 x 10-4 3.2 2.61 x 10-4 2.7 5.09 x 10-4 1.76620 1.5106 2.31 x 10-4 3.0 2.75 x 10-4 2.6 5.17 x 10-4 1.66640 1.5060 2.45 x 10-4 2.4 2.91 x 10-4 2.1 5.27 x 10-4 1.5

6660 1.5015 2.58 x 10-4 2.5 3.04 x 10-4 2.2 5.33 x 10-4 1.56680 1.4970 2.73 x 10-4 2.4 3.20 x 10-4 2.2 5.38 x 10-4 1.5

6700 1.4925 2.86 x 10-4 2.4 3.33 x 10-4 2.2 5.34 x 10-4 1.66720 1.4881 3.05 x 10-4 2.5 3.50 x 10-4 2.3 5.27 x 10-4 1.76740 1.4837 3.18 x 10-4 2.0 3.61 x 10-4 1.8 5.03 x 10-4 1.6

6760 1.4793 3.32 x 10-4 1.9 3.74 x 10-4 1.8 4.71 x 10-4 1.6

6780 1.4749 3.48 x 10-4 2.2 3.85 x 10-4 2.1 4.33 x 10-4 2.06800 1.4706 3.58 x 10-4 1.7 3.91 x 10-4 1.6 3.86 x 10-4 1.9

6820 1.4663 3.68 x 10-4 2.2 3.97 x 10-4 2.0 3.42 x 10-4 2.66840 1.4620 3.77 x 10-4 1.7 3.99 x 10-4 1.7 2.99 x 10-4 2.66860 1.4577 3.79 x 10-4 1.9 3.95 x 10-4 1.9 2.58 x 10-4 3.1

6880 1.4535 3.79 x 10-4 1.9 3.87 x 10-4 1.9 2.20 x 10-4 3.5

6900 1.4493 3.77 x 10-4 2.0 3.80 x 10-4 2.0 1.89 x 10-4 4.36920 1.4451 3.74 x 10-4 2.0 3.67 x 10-4 2.1 1.60 x 10-4 5.1

3. Imaginary Part of Refractive Index of Water and IceThe results of the Kou-Labrie-Chylek (KLC) mea-surements for the case of water at 22 C are shown inFig. 1. We determined the imaginary part of therefractive index, k, from the absorption coefficient a,using the relationship k = Xa/47r. We checked theresults for internal consistency by comparing the kspectra obtained with different d values (differentpath length). When the transmittance values werein the range 15% to 80%, excellent agreement wasfound among spectra obtained with several differentd values. Figure 1(a) also shows the k spectrumobtained from the data of Palmer and Williams 3

(PW) and Downing and Williams' 4 (DW). To withinPW and DW uncertainties, good agreement is foundbetween the two spectra. Figure 1(b) shows theerror of our measurements, which was calculated byusing the standard deviation of the data and theuncertainty in the path length, d. The error spec-trum typically varies between 1% and 2%, with someexcursions above 3%. The error increases dramati-cally below 0.6 [um because of the weak absorptionmeasured in the longest cell used. Recent measure-ments of Wieliczka et al.'5 that used a wedge-shapedcell are in considerable disagreement with our results

for wavelengthsas much as a

shorter than 1.25 tLm. The error offactor of 12 between the data of

Wieliczka et al. and ours is caused by the hightransparency of their very thin (d 22 m) watersamples used in their study.

The k spectrum of supercooled water taken at anaverage temperature of -8 0C is shown in Fig. 2.The water temperature in the 2-cm-long cell was-4 C. To our knowledge, this is the first reportedmeasurement of the absorption coefficient of super-cooled water. The k spectrum is similar to that ofwater; the main difference is that the k bands ofsupercooled water are shifted toward longer wave-lengths than those of water measured at T = 22 C.The k error spectrum, which varies in amplitude from1% to 8%, is shown in Fig. 2(b).

The k spectrum of ice in the spectral range from1.45 to 2.5 Vlm is also shown in Fig. 2(a). The kspectrum for ice exhibits absorption bands that areshifted toward longer wavelengths and have differentstrengths from those in the spectrum of water.Figure 3(a) shows a direct comparison between ourmeasurement (KLC) of the ice spectrum and thespectrum obtained from Warren's 0 compilation.Good agreement is observed between the spectra.

1 July 1993 / Vol. 32, No. 19 / APPLIED OPTICS 3535

Table 2. ImagInary Part of the Refractive Index, k, and the Standard Deviation of k for Water at T = 22 °C and T = -8 °C in the Spectral Range From6940 to 15,000 cm-'

Water Water

T = 22°C T= -8°C T = 22°C T = -8 CWave Wave Wave Wave

Number Length Error Error Number Length Error Error(1/cm) (pm) k (%) k (%) (1/cm) (Pim) k (%) k (%)

2.0 3.53 x 10-4

1.9 3.39 x 10-4

2.3 3.18 x 10-4

1.9 2.99 x 10-4

2.3 2.79 x 10-4

2.1 2.57 x 10-4

2.4 2.38 x 10-4

2.9 2.18 x 10-4

2.5 1.94 x 10-4

3.6 1.69 x 10-4

3.9 1.45 x 10-4

5.4 1.18 x 10-4

3.1 9.23 x 10-52.7 7.35 x 10-5

3.1 6.07 x 10-5

2.3 5.09 x 10-51.9 4.46 x 10-51.7 4.08 x 10'1.8 3.76 x 10-51.3 3.58 x 10-5

1.3 3.40 x 10-51.8 3.27 x 10-51.9 3.14 x 10-5

2.1 3.03 x 10-1.6 2.91 x 10-51.7 2.76 x 10-51.1 2.60 x 10-51.3 2.45 x 10-5

1.2 2.30 x 10-5

1.1 2.16 x 10-51.3 2.02 x 10-51.1 1.90 x 10-5

1.2 1.78 x 10-51.5 1.68 x 10-51.1 1.59 x 10-11.4 1.52 x 10-`1.3 1.45 x 10-51.3 1.39 x 10-51.1 1.35 x 10-51.8 1.30 x 10-'1.4 1.27 x 10-51.1 1.24 x 10-51.5 1.21 x 10-51.9 1.20 x 10-51.4 1.19 x 10-11.2 1.18 x 10-51.6 1.17 x 10-51.6 1.17 x 10-5

1.6 1.17 x 10-1i1.6 1.17 x 10-61.8 1.19 x 10-5

1.5 1.20 x 10-51.7 1.19 x 10-5

1.6 1.21 x 10-52.0 1.22 x 10-51.5 1.23 x 10-51.5 1.24 x 10-51.6 1.24 x 10-r)

2.2 81002.1 81202.6 81402.4 81602.9 81802.7 82003.2 82203.9 82403.5 82605.1 82805.4 83007.5 83204.8 83404.2 83604.7 83803.7 84003.3 84202.7 84402.8 84602.2 84802.1 85002.5 85202.5 85402.7 85602.2 85802.2 86001.5 86201.6 86401.6 86601.3 86801.5 87001.3 87201.3 87401.6 87601.1 87801.5 88001.4 88201.4 88401.2 88601.8 88801.5 89001.3 89201.6 89401.9 89601.6 89801.4 90001.7 90201.7 90401.7 90601.7 90801.8 91001.6 91201.9 91401.7 91602.0 91801.6 92001.6 92201.7 9240

1.23461.23151.22851.22551.22251.21951.21651.21361.21071.20771.20481.20191.19901.19621.19331.19051.18761.18481.18201.17921.17651.17371.17101.16821.16551.16281.16011.15741.15471.15211.14941.14681.14421.14161.13901.13641.13381.13121.12871.12611.12361.12111.11861.11611.11361.11111.10861.10621.10381.10131.09891.09651.09411.09171.08931.08701.08461.0823

1.15 x 10-51.16 x 10-51.17 x 10-51.17 x 10-51.18 x 10-51.18 x 10-51.20 x 10-51.20 x 10-51.21 x 10-51.21 x 10-51.22 x 10-51.21 x 10-51.22 x 10-51.22 x 10-r1.21 x 10-51.20 x 10-51.19 x 10-5

1.18 x 10-i1.17 x 10-51.16 x 10-51.15 x 10-51.15 x 10-51.13 x 10-51.12 x 10-51.11 x 10-5

1.10 x 10-5

1.08 x 10-51.05 x 10-51.01 x 10-5

9.54 x 10-68.68 x 10-67.84 x 10-66.86 x 10-65.92 x 10-65.05 x 10-64.26 x 10-63.64 x 10-63.18 x 10-62.84 x 10-62.59 x 10-62.43 x 10-62.30 x 10-62.18 x 10-62.09 x 10-62.07 x 10-61.99 x 10-6

1.91 x 10-6

1.83 x 10-61.76 x 10-61.69 x 10-61.63 x 10-61.55 x 10-61.49 x 10-61.44 x 10-61.39 x 10-61.35 x 10-61.31 x 10-61.27 x 10-6

1.8 1.25 x 10-51.7 1.25 x 10-51.5 1.25 x 10-51.4 1.26 x 10-5

2.0 1.26 x 10-51.5 1.25 x 10-5

1.6 1.26 x 10-51.7 1.25 x 10-51.2 1.25 x 10-5

1.8 1.24 x 10-5

1.5 1.25 x 10-5

1.9 1.22 x 10-5

1.2 1.22 x 10-51.3 1.20 x 10-5

1.7 1.19 x 10-51.6 1.16 x 10-51.5 1.15 x 10-51.4 1.12 x 10-5

1.5 1.10 x 10-51.7 1.08 x 10-i1.4 1.05 x 10-5

1.4 1.03 x 10-51.8 9.99 x 10-61.6 9.79 x 10-61.5 9.52 x 10-6

1.6 9.21 x 10-62.0 .8.89 x 10-62.0 8.47 x 10-61.9 8.06 x 10-61.8 7.53 x 10-61.3 7.07 x 10-62.0 6.43 x 10-61.6 5.68 x 10-61.4 4.97 x 10-61.7 4.30 x 10-62.6 3.67 x 10-61.6 3.20 x 10-62.6 2.84 x 10-61.9 2.58 x 10-62.6 2.38 x 10-62.5 2.28 x 10-62.9 2.17 x 10-63.2 2.09 x 10-6

3.0 2.02 x 10-63.2 1.96 x 10-63.0 1.90 10-62.9 1.84 x 10-6

2.7 1.78 x 10-62.7 1.72 x 10-62.6 1.66 x 10-62.5 1.61 x 10-62.5 1.56 x 10-62.4 1.51 x 10-62.5 1.44 x 10-62.4 1.41 x 10-62.4 1.38 x 10-62.4 1.35 x 10-62.3 1.31 x 10-6

3536 APPLIED OPTICS / Vol. 32, No. 19 / 1 July 1993

6940696069807000702070407060708071007120714071607180720072207240726072807300732073407360738074007420744074607480750075207540756075807600762076407660768077007720774077607780780078207840786078807900792079407960798080008020804080608080

1.44091.43681.43271.42861.42451.42051.41641.41241.40851.40451.40061.39661.39281.38891.38501.38121.37741.37361.36991.36611.36241.35871.35501.35141.34771.34411.34051.33691.33331.32981.32631.32281.31931.31581.31231.30891.30551.30211.29871.29531.29201.28871.28531.28211.27881.27551.27231.26901.26581.26261.25941.25631.25311.25001.24691.24381.24071.2376

3.69 x 10-4

3.66 x 10-4

3.54 x 10-4

3.44 x 10-4

3.30 x 10-4

3.13 x 10-4

2.97 x 10-4

2.77 x 10-4

2.50 x 10-4

2.20 x 10-4

1.89 x 10-4

1.55 x 10-4

1.22 x 10-4

9.70 x 10-57.94 x 10-56.58 x 10-55.68 x 10-55.07 x 10-r4.60 x 10-54.30 x 10-54.04 x 10-53.84 x 10-53.66 x 10-53.48 x 10-53.32 x 10-53.09 x 10-52.88 x 10-52.70 x 10-52.50 x 10-52.33 x 10-52.16 x 10-52.01 x 10-51.88 x 10-51.75 x 10-51.65 x 10-51.55 x 10-51.47 x 10-51.40 x 10-r1.34 x 10-51.29 x 10-51.25 x 10-51.21 x 10-51.19 x 10-

1.16 x 10-51.13 x 10-51.12 x 10-51.10 x 10-5

1.09 x 10-5

1.09 x 10-5

1.09 x 10-5

1.10 x 10-5

1.10 x 10-5

1.10 x 10-5

1.11 x 10-5

1.12 x 10-51.13 x 10-51.14 x 10-51.14 x 10-5

1.81.81.81.62.11.71.81.81.32.01.82.01.31.51.91.71.61.61.82.01.71.72.22.12.02.22.72.92.72.62.22.82.42.12.43.32.23.22.73.33.43.73.93.83.94.43.74.85.04.85.24.85.95.34.66.36.46.1

(Table continued)

Table 2. (continued)

Water Water

T = 22°C T= -8°CW T = 22°C T= -8°CWave Wave Wave Wave

Number Length Error Error Number Length Error Error

(1/cm) (Pm) k (%) k (%) (1/cm) (Pm) k (%) k (%)

2.3 1.30 x 10-62.3 1.27 x 10-62.3 1.26 x 10-62.3 1.28 x 10-62.2 1.26 x 10-62.2 1.29 x 10-62.2 1.30 x 10-62.2 1.30 x 10-62.2 1.35 x 10-6

2.2 1.35 x 10-62.2 1.37 x 10-62.1 1.44 x 10-62.1 1.47 x 10-62.1 1.53 x 10-62.1 1.57 x 10-6

2.1 1.63 x 10-6

2.1 1.71 x 10-62.1 1.75 x 10-62.1 1.83 x 10-62.1 1.90 x 10-62.1 1.97 x 10-62.1 2.04 x 10-62.1 2.13 x 10-62.1 1.23 x 10-62.1 2.29 x 10-6

2.1 2.36 x 10-62.1 2.48 x 10-62.2 2.53 x 10-62.2 2.61 x 10-61.2 2.70 x 10-60.6 2.75 x 10-60.9 2.84 x 10-6

0.6 2.92 x 10-60.6 2.95 x 10-60.9 3.05 x 10-60.4 3.11 x 10-60.8 3.15 x 10-60.7 3.15 x 10-60.5 3.22 x 10-60.8 3.22 x 10-6

0.6 3.26 x 10-60.7 3.35 x 10-60.9 3.37 x 10-60.6 3.37 x 10-60.8 3.34 x 10-60.8 3.32 x 10-60.6 3.31 x 10-60.9 3.33 x 10-60.8 3.28 x 10-60.5 3.26 x 10-60.9 3.23 x 10-60.5 3.18 x 10-60.7 3.16 x 10-6

0.9 3.05 x 10-6

0.5 3.00 x 10-60.9 2.94 x 10-60.8 2.88 x 10-60.5 2.80 x 10-61.1 2.66 x 10-6

6.1 104406.3 104606.7 104806.6 105005.8 105207.0 105406.8 105605.2 105805.8 106006.2 106206.5 106405.5 106605.3 106805.9 107005.2 107204.8 107405.8 107605.4 107805.4 108004.3 108205.0 108404.8 108603.7 108803.8 109004.5 109203.2 109403.2 109604.5 109803.7 110004.1 110203.9 110403.4 110603.7 110803.1 111002.7 111203.0 111402.7 111603.2 111803.3 112004.4 112203.1 112402.7 112604.3 112803.8 113004.1 113203.2 113403.9 113603.8 113804.0 114004.1 114204.1 114403.0 114604.5 114803.8 115003.4 115205.1 115405.2 115603.3 115805.2 11600

(Table continued)

1 July 1993 / Vol. 32, No. 19 / APPLIED OPTICS 3537

2.57 x2.39 x2.19 x2.04 x1.82 x1.70 x1.56 x1.42 x1.32 x1.24 x1.17 x

10-6

10-6

10-6

10-6

10-6

10-6

10-6

10-6

10-6

10-6

10-6

5.24.84.65.46.27.54.87.19.06.57.8

9260928093009320934093609380940094209440946094809500952095409560958096009620964096609680970097209740976097809800982098409860988099009920994099609980

10000100201004010060100801010010120101401016010180102001022010240102601028010300103201034010360103801040010420

1.07991.07761.07531.07301.07071.06841.06611.06381.06161.05931.05711.05491.05261.05041.04821.04601.04381.04171.03951.03731.03521.03311.03091.02881.02671.02461.02251.02041.01831.01631.01421.01211.01011.00811.00601.00401.00201.00000.99800.99600.99400.99210.99010.98810.98620.98430.98230.98040.97850.97660.97470.97280.97090.96900.96710.96530.96340.96150.9597

1.24 x 10-61.23 x 10-61.21 x 10-61.20 x 10-61.20 x 10-61.20 x 10-61.21 x 10-61.22 x 10-61.23 x 10-61.26 x 10-61.28 x 10-61.31 x 10-61.35 x 10-61.39 x 10-61.43 x 10-61.49 x 10-61.55 x 10-61.61 x 10-61.67 x 10-61.74 x 10-61.81 x 10-61.89 x 10-61.96 x 10-62.05 x 10-62.14 x 10-62.22 x 10-62.31 x 10-62.40 x 10-62.50 x 10-62.58 x 10-62.66 x 10-62.74 x 10-62.83 x 10-62.92 x 10-63.01 x 10-63.09 x 10-63.16 x 10-63.24 x 10-63.31 x 10-63.38 x 10-63.45 x 10-63.50 x 10-63.57 x 10-63.62 x 10-63.67 x 10-63.71 x 10-63.74 x 10-63.76 x 10-63.78 x 10-63.78 x 10-6

3.77 x 10-63.75 x 10-63.72 x 10-63.69 x 10-63.66 x 10-63.61 x 10-63.55 x 10-63.47 x 10-63.35 x 10-6

0.95790.95600.95420.95240.95060.94880.94700.94520.94340.94160.93980.93810.93630.93460.93280.93110.92940.92760.92590.92420.92250.92080.91910.91740.91580.91410.91240.91070.90910.90740.90580.90420.90250.90090.89930.89770.89610.89450.89290.89130.88970.88810.88650.88500.88340.88180.88030.87870.87720.87570.87410.87260.87110.86960.86810.86660.86510.86360.8621

3.19 x 10-62.99 x 10-62.75 x 10-6

2.48 x 10-6

2.25 x 10-62.04 x 10-6

1.86 x 10-61.72 x 10-61.58 x 10-61.47 x 10-61.36 x 10-61.26 x 10-61.16 x 10-61.09 x 10-6

1.02 x 10-69.49 x 10-7

8.83 x 10-7

8.22 x 10-7

7.68 x 10-7

7.22 x 10-76.80 x 10-7

6.45 x 10-7

6.15 x 10-7

5.90 x 10-7

5.68 x 10-7

5.50 x 10-7

5.34 x 10-7

5.21 x 10-7

5.09 x 10-7

4.98 x 10-7

4.88 x 10-7

4.80 x 10-74.71 x 10-7

4.63 x 10-7

4.55 x 10-7

4.48 x 10-7

4.41 x 10-7

4.34 x 10-7

4.27 x 10-7

4.20 x 10-7

4.13 x 10-74.06 x 10-7

3.99 x 10-7

3.92 x 10-7

3.84 x 10-7

3.78 x 10-7

3.71 x 10-7

3.64 x 10-7

3.57 x 10-7

3.52 x 10-7

3.45 x 10-7

3.40 x 10-7

3.35 x 10-7

3.29 x 10-7

3.25 x 10-7

3.21 x 10-7

3.17 x 10-7

3.13 x 10-7

3.09 x 10-7

0.80.81.42.72.52.42.42.42.42.32.42.32.42.31.01.01.00.90.90.90.90.80.80.90.80.80.90.90.90.90.90.90.90.90.90.90.91.01.01.01.01.01.01.01.11.01.01.01.01.01.01.01.01.01.01.01.01.01.0

Table 2. (continued)

Water, T = 22 C

Errork (%)

3.06 x 10-7 1.0

3.30 x 10-7 1.0

2.99 x 10-7 1.0

2.97 x 10-7 1.1

2.93 x 10-7 1.0

2.90 x 10-7 1.0

2.86 x 10-7 1.0

2.84 x 10-7 1.1

2.84 x 10-7 1.0

2.80 x 10-7 1.0

2.77 x 10-7 1.0

2.74 x 10-7 1.1

2.71 x 10-7 1.1

2.68 x 10-7 1.0

2.64 x 10-7 1.0

2.61 x 10-7 1.1

2.57 x 10-7 1.1

2.52 x 10-7 1.1

2.46 x 10-7 1.22.39 x 10-7 1.32.29 x 10-7 1.42.18 x 10-7 1.62.05 x 10-7 1.71.92 x 10-7 1.71.82 x 10-7 1.81.72 x 10-7 1.81.65 x 10-7 1.71.60 x 10-7 1.71.56 x 10-7 1.61.52 x 10-7 1.61.50 x 10-7 1.61.48 x 10-7 1.61.46 x 10-7 1.71.44 x 10-7 1.71.43 x 10-7 1.71.42 x 10-7 1.71.41 x 10-7 1.71.41 x 10-7 1.71.40 x 10-7 1.71.41 x 10-7 1.71.41 x 10-7 1.71.41 x 10-7 1.71.42 x 10-7 1.71.43 x 10-7 1.71.43 x 10-7 1.61.45 x 10-7 1.71.47 x 10-7 1.71.48 x 10-7 1.71.49 x 10-7 1.61.50 x 10-7 1.61.52 x 10-7 1.51.54 x 10-7 1.61.55 x 10-7 1.51.57 x 10-7 1.51.58 x 10-7 1.51.60 x 10-7 1.41.62 x 10-7 1.51.63 x 10-7 1.51.64 x 10-7 1.5

WaveNumber(1/cm)

1280012820128401286012880129001292012940129601298013000130201304013060130801310013120131401316013180132001322013240132601328013300133201334013360133801340013420134401346013480135001352013540135601358013600136201364013660136801370013720137401376013780138001382013840138601388013900139201394013960

WaveLength(Pm)

0.78130.78000.77880.77760.77640.77520.77400.77280.77160.77040.76920.76800.76690.76570.76450.76340.76220.76100.75990.75870.75760.75640.75530.75410.75300.75190.75080.74960.74850.74740.74630.74520.74400.74290.74180.74070.73960.73860.73750.73640.73530.73420.73310.73210.73100.72990.72890.72780.72670.72570.72460.72360.72250.72150.72050.71940.71840.71740.7163

Water, T = 22 °C

Errork (%)

1.65 x 10-7 1.41.67 x 10-7 1.41.68 x 10-7 1.31.69 x 10-7 1.41.70 x 10-7 1.41.70 x 10-7 1.31.71 x 10-7 1.41.71 x 10-7 1.31.72 x 10-7 1.31.73 x 10-7 1.31.73 x 10-7 1.41.73 x 10-7 1.31.73 x 10-7 1.21.74 x 10-7 1.31.74 x 10-7 1.31.74 x 10-7 1.31.74 x 10-7 1.31.74 x 10-7 1.41.73 x 10-7 1.31.73 x 10-7 1.41.73 x 10-7 1.31.73 x 10-7 1.31.73 x 10-7 1.31.72 x 10-7 1.41.72 x 10-7 1.41.71 x 10-7 1.31.71 x 10-7 1.41.70 x 10-7 1.41.70 x 10-7 1.41.69 x 10-7 1.31.69 x 10-7 1.4

1.68 x 10-7 1.4

1.68 x 10-7 1.41.67 x 10-7 1.41.66 x 10-7 1.51.65 x 10-7 1.41.63 x 10-7 1.51.61 x 10-7 1.41.57 x 10-7 1.51.53 x 10-7 1.51.48 x 10-7 1.71.43 x 10-7 1.71.35 x 10-7 2.01.28 x 10-7 2.11.21 x 10-7 2.21.14 x 10-7 2.31.07 x 10-7 2.51.02 x 10-7 2.49.63 x 10-8 2.59.20 x 10-8 2.48.80 x 10-8 2.58.45 x 10-8 2.68.09 x 10-8 2.77.75 x 10-8 2.97.43 x 10-8 2.87.11 x 10-8 3.06.80 x 10-8 3.26.51 x 10-8 3.26.24 x 10-8 3.5

3538 APPLIED OPTICS / Vol. 32, No. 19 / 1 July 1993

WaveNumber(1/cm)

1162011640116601168011700117201174011760117801180011820118401186011880119001192011940119601198012000120201204012060120801210012120121401216012180122001222012240122601228012300123201234012360123801240012420124401246012480125001252012540125601258012600126201264012660126801270012720127401276012780

WaveLength

(p'm)

0.86060.85910.85760.85620.85470.85320.85180.85030.84890.84750.84600.84460.84320.84180.84030.83890.83750.83610.83470.83330.83190.83060.82920.82780.82640.82510.82370.82240.82100.81970.81830.81700.81570.81430.81300.81170.81040.80910.80780.80650.80520.80390.80260.80130.80000.79870.79740.79620.79490.79370.79240.79110.78990.78860.78740.78620.78490.78370.7825

(Table continued)

-

Table 2. (continued)

WaveNumber(1/cm)

13980140001402014040140601408014100141201414014160141801420014220142401426014280143001432014340143601438014400144201444014460144801450014520145401456014580146001462014640146601468014700147201474014760147801480014820148401486014880149001492014940149601498015000

WaveLength

(plm)

0.71530.71430.71330.71230.71120.71020.70920.70820.70720.70620.70520.70420.70320.70220.70130.70030.69930.69830.69740.69640.69540.69440.69350.69250.69160.69060.68970.68870.68780.68680.68590.68490.68400.68310.68210.68120.68030.67930.67840.67750.67660.67570.67480.67390.67290.67200.67110.67020.66930.66840.66760.6667

Water, T = 22 C

k

5.97 x 10-85.72 x 10-85.50 x 10-8

5.27 x 10-8

5.08 x 10-84.89 x 10-8

4.74 x 10-8

4.59 x 10-8

4.46 x 10-84.34 x 10-8

4.22 x 10-84.12 x 10-8

4.00 x 10-83.90 x 10-83.81 x 10-83.72 x 10-8

3.63 x 10-8

3.55 x 10-8

3.47 x 10-83.40 x 10-8

3.33 x 10-83.27 x 10-8

3.20 x 10-83.15 x 10-8

3.10 x 10-83.04 x 10-82.98 x 10-8

2.94 x 10-8

2.91 x 10-82.87 x 10-8

2.84 x 10-8

2.82 x 10-82.79 x 10-82.76 x 10-8

2.73 x 10-8

2.73 x 10-8

2.71 x 10-8

2.69 x 10-82.66 x 10-82.64 x 10-82.64 x 10-8

2.61 x 10-8

2.61 x 10-8

2.58 x 10-8

2.56 x 10-8

2.55 x 10-8

2.54 x 10-82.53 x 10-82.52 x 10-82.48 x 10-82.48 x 10-82.47 x 10-8

2.0Error

(%)3.53.73.84.04.34.34.54.54.64.95.05.05.25.35.55.55.56.26.06.16.46.46.76.76.97.27.07.37.47.47.77.98.17.98.28.08.18.28.18.38.68.68.78.69.09.18.99.38.89.89.29.1

It seems that Warren's 0 estimate of an error as highas a factor of 2 was too pessimistic. The largestdeviation between Warren's compilation and ourmeasurements is 22%, around a wavelength of 1.85jim.

1 .5

no

o 1.0

0.5

0.0

1 5

0

uJ -:D

0

6666.7WAVE NUMBER (cm-1 )

5000 4000

1.5 2.0 2.5WAVELENGTH (,um)

Fig. 3. (a) Imaginary part of the refractive index of polycrystallineice at T = -25 CC from the present measurements (KLC, solidcurve) and Warren's 0 compilation (dashed curve). (b) Standarddeviation on k for polycrystalline ice at T = -25 C.

The error k spectrum shown in Fig. 3(b) indicatesthat the error is largest in the 1.8-1.9-jim range,where the transmission is correspondingly high.The KLC data of k and error, which are shown inFigs. 1-3, are listed with wave-number intervals of 20cm-' in Tables 1 and 2.

4. DiscussionGood agreement between KLC data and data ob-tained by Palmer and Williams 3 and Downing andWilliams 4 confirms the validity of the experimentaltechniques used in this study. The high quality ofKLC data is also reflected in the very low standarddeviation (typically 1-2%) presented in Fig. 1(b).For the first time to our knowledge, reported kspectrum of supercooled water at T = - 8 C is similarto that of water at T = +22 0C. The deviations aregenerally within 10% in the 1.0-2.5-jim spectralrange. The absorption peaks of supercooled waterare shifted slightly toward the longer wavelengths.

New accurate measurements of the imaginary partof the refractive index of polycrystalline ice taken atT = -25 C and in the spectral range 1.44-2.5 jim arein surprisingly good agreement with Warren's 0 com-pilation, who has estimated an uncertainty of a factor2 in k values for this spectral range. In his compila-tion, Warren used data collected by Ockman 2 on

1 July 1993 / Vol. 32, No. 19 / APPLIED OPTICS 3539

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102-jim-thick polycrystalline ice at T = -29 CC andby Reding" on 250-jm-thick polycrystalline ice takenat T = - 78 C. Reding's data are uncertain becausethey were corrected for the k temperature depen-dence and the ambiguous use of their vertical axis.Ockman's data and possibly Reding's data were notcorrected for reflection losses at the interface.Discrepancies between KLC data and Warren's compi-lation are observed mainly near 1.50, 1.85, and 2.5jim. The largest discrepancy occurs near 1.85 jim,at the minimum of the k spectrum. Reding's dataused here were smoothed out by Warren to correct forthe k temperature dependence. Our results have anuncertainty of 13% at the minimum because of thecorresponding high transmission (79%) at the consid-ered wavelength. New measurements with thickerice samples will be required if we are to increaseaccuracy in this region and to extend the measure-ments toward shorter wavelengths.

This work was supported in part by the Atmo-spheric Environment Service and the Natural Sci-ences and Engineering Research Council of Canada.

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3540 APPLIED OPTICS / Vol. 32, No. 19 / 1 July 1993