Infrared Spectral Emittance Measurements of Optical Materials D. L. Stierwalt Optical properties of solids are usually determined by measurements of either the transmittance or the re- flectance. Each of these methods has advantages and disadvantages, depending upon the spectral region and the nature of the material being studied. A third method, the measurement of emittance, although little used has definite advantages under certain conditions. Theory If electromagnetic radiation is incident upon a solid body, some of the radiation is reflected, some absorbed, and the rest is transmitted. If we define the absorp- tance A as the fraction absorbed, the reflectance R as the fraction reflected, and the transmittance T as the fraction transmitted, A +R+T= l. (1) The emittance E can be defined as the ratio of the thermal radiation per unit area emitted by an object to that emitted by a blackbody at the same temperature. McMahon 1 has shown that E + R + T = 1. (2) This can be shown to hold at each wavelength so that the spectral absorptance A;< equals the spectral emit- tance Ex. For a plane parallel sample with optically smooth surfaces and for which k/n <<1, the following relation- ships can be derived: 2 A = E = (1 - r 2 )(1 - e-d)/(l - r2e-ad) (3) R = r 2 [1 + e-2ad(l - 2r 2 )]/(l - r4e-2ad) (4) T = (1 - r2)2ed/(l - r4e-2ad), (5) where r = (n - 1)/(n + 1), n is the real part and k is the imaginary part of the complex index of refraction, the absorption coefficient a = 47rk/X,and d is the sam- ple thickness. When ad <<1, which is frequently the case for mate- rials used for windows or lenses, Eq. (3) reduces to E= ad. (6) This indicates one advantage of the emittance mea- The author is in the Infrared Division, Research Department, U.S. Naval Ordnance Laboratory, Corona, California 91720. Received 1 August 1966. surement over the transmittance measurement for find- ing the absorption coefficient of highly transparent samples. To find a from a transmittance measure- ment, the index must be known in order to calculate the reflectance loss. When Eq. (6) is valid, the reflectance has a negligible effect on the emittance so the absorp- tion coefficient can be determined without precise knowledge of the index of refraction. Of course, the fact that a is directly proportional to E is an obvious advantage in that it simplifies data reduction. Going to the other extreme, when ad >>, the transmittance approaches zero, and we have E= 1-R. (7) In this case, an emittance measurement provides the same information as a reflectance measurement with the advantage that the emittance can be measured normal to the sample. In the more general case, solving Eq. (3) for ad yields the following expression: ad = ln[(1 - r- r 2 E)/(1 -r - E)] (8) We can find a from Eq. (8) when r 2 is unknown by measuring the emittance of two samples of different thickness. Then we have two simultaneous transcen- dental equations which can best be solved graphically. Another method we have developed recently is mea- suring both emittance and emittance plus transmittance for the same sample. Knowing both E and T, Eqs. (3) and (5) may be solved for r 2 and a, and from these we can derive n and k. Method To measure the spectral emittance, we compare radiation from a sample with that from a blackbody at the same temperature. If the sample compartment, monochromator, and detector compartment shown in the schematic diagram of Fig. 1 form an isothermal enclosure, the radiation inside the enclosure will obey the Planck radiation law WR = C- 5 /(ec 2 XTR - 1), (9) December 1966 / Vol. 5, No. 12 / APPLIED OPTICS 1911
Transcript
Infrared Spectral Emittance Measurements of Optical Materials
D. L. Stierwalt
Optical properties of solids are usually determined by measurements of either the transmittance or the re-flectance. Each of these methods has advantages and disadvantages, depending upon the spectral regionand the nature of the material being studied. A third method, the measurement of emittance, althoughlittle used has definite advantages under certain conditions.
Theory
If electromagnetic radiation is incident upon a solidbody, some of the radiation is reflected, some absorbed,and the rest is transmitted. If we define the absorp-tance A as the fraction absorbed, the reflectance R asthe fraction reflected, and the transmittance T as thefraction transmitted,
A +R+T= l. (1)The emittance E can be defined as the ratio of the
thermal radiation per unit area emitted by an object tothat emitted by a blackbody at the same temperature.McMahon 1 has shown that
E + R + T = 1. (2)
This can be shown to hold at each wavelength so thatthe spectral absorptance A;< equals the spectral emit-tance Ex.
For a plane parallel sample with optically smoothsurfaces and for which k/n <<1, the following relation-ships can be derived:2
A = E = (1 - r2)(1 - e-d)/(l - r2e-ad) (3)
R = r2[1 + e-2ad(l - 2r2)]/(l - r4e-2ad) (4)
T = (1 - r2)2ed/(l - r4e-2ad), (5)
where r = (n - 1)/(n + 1), n is the real part and k isthe imaginary part of the complex index of refraction,the absorption coefficient a = 47rk/X, and d is the sam-ple thickness.
When ad <<1, which is frequently the case for mate-rials used for windows or lenses, Eq. (3) reduces to
E= ad. (6)
This indicates one advantage of the emittance mea-
The author is in the Infrared Division, Research Department,U.S. Naval Ordnance Laboratory, Corona, California 91720.
Received 1 August 1966.
surement over the transmittance measurement for find-ing the absorption coefficient of highly transparentsamples. To find a from a transmittance measure-ment, the index must be known in order to calculate thereflectance loss. When Eq. (6) is valid, the reflectancehas a negligible effect on the emittance so the absorp-tion coefficient can be determined without preciseknowledge of the index of refraction. Of course, thefact that a is directly proportional to E is an obviousadvantage in that it simplifies data reduction. Goingto the other extreme, when ad >>, the transmittanceapproaches zero, and we have
E= 1-R. (7)
In this case, an emittance measurement provides thesame information as a reflectance measurement with theadvantage that the emittance can be measured normalto the sample. In the more general case, solving Eq.(3) for ad yields the following expression:
ad = ln[(1 - r- r2 E)/(1 -r - E)] (8)
We can find a from Eq. (8) when r2 is unknown bymeasuring the emittance of two samples of differentthickness. Then we have two simultaneous transcen-dental equations which can best be solved graphically.
Another method we have developed recently is mea-suring both emittance and emittance plus transmittancefor the same sample. Knowing both E and T, Eqs.(3) and (5) may be solved for r2 and a, and from thesewe can derive n and k.
Method
To measure the spectral emittance, we compareradiation from a sample with that from a blackbody atthe same temperature. If the sample compartment,monochromator, and detector compartment shown inthe schematic diagram of Fig. 1 form an isothermalenclosure, the radiation inside the enclosure will obeythe Planck radiation law
Fig. 1. Simplified schematic diagram of the optical path.
where T is the reference temperature, i.e., the tem-perature of the sample compartment.
Now we introduce the sample at temperature Ts intothe sample compartment and assume that this has anegligible effect on the blackbody characteristics of thecompartment. Let us also put in a chopper to modu-late the radiation entering the monochromator. Theac signal from the detector will be given by
S = K(EWs + RTVR + TWR - WR), (10)
where the first term is the power density emitted by thesample, the second term is the amount reflected, thethird term is the amount transmitted, and the fourthterm is that emitted by the chopper when it interruptsthe beam. The constant K depends upon the transferfunction of the optical system and the responsivity ofthe detector.
By use of Eq. (2), Eq. (10) reduces to
Ss = KE(TVs - VR). (11)
With a blackbody in place of the sample, we have
SB = K(Ws - WR), (12)
and solving Eqs. (11) and (12) for E we find that
E = (S/SBB). (13)
Note that the measured emittance is independent of Kand Ws - WR. The sample temperature may be aboveor below the reference temperature as long as Ws- WRis large enough to give a usable signal. When W;s <WR, both Ss and SBB are negative.
To make the E + T measurement mentioned in theprevious section, we place the blackbody in the sampleholder behind the sample so that both are at sampletemperature. Now, instead of Eq. (10), we have
S = K(EWs + RIVR Jr TWs - VR),
1.0
w 0.8
I- 0.6I-
: 0.4
0.2
0
WAVELENGTH (MICRONS)00 IV
0 00 0 0 000 0 0 00 0 00 0 0 0 00 0 0 0 0O Cu 0 (D L1 0 c D t
In cli cl _ _ _
(14)
0 0 0CC) I I
0U- 00 00 C) 0I) N N
cm-,
Fig. 2. Spectral emittance of 2-mm thick Irtran 1 at 77 0K.
0 0 2 0 0
0 0 000 00 00 0 0 OOo O < N 0 I W 0 OO I0 0 - CD CA V. N. 11J 1 - -_ _ _
0
Fig. 3. Spectral emittance of 2-mm thick77 0K, and 373 0K.
00 0 0 0 0 0O dD o N 0 0
Irtran 2 at 4.20K,
which reduces to
S, = K(E + T)(V, - WR)
and
E + T = (SS/SBB).
Instrumentation
(15)
(16)
Three Beckman IR-3 spectrophotometers have beenmodified for making these measurements, each coveringa different spectral region. The IR-3 has characteris-tics which make it especially suitable for this particularapplication. It is evacuable, which not only eliminatesatmospheric absorption but also minimizes heat transferbetween the sample and holder and the source compart-ment. Each compartment of the IR-3 is lined withcopper sheet on which are soldered tubes that carrywater at a controlled temperature. The water ispumped from a thermostatted bath below the instru-ment. This temperature control system ensures thatthe instrument is, indeed, an isothermal enclosure, aswe have assumed previously.
The IR-3 is not a double beam instrument, but uses aprogrammed reference. It has a servo system thatvaries the slit width to maintain constant output fromthe detector while scanning the spectrum. This slit
15 20 25 30 35 40WAVELENGTH (MICRONS)
45 50
Fig. 4. Spectral emittance of 0.37-mm thick Irtran 4 at 4.20K,770K, and 195'K. d = 0.37 mm.
Fig. 5. Spectral emittance of 2.11-mm thick Irtran 5 at 77°K.
drive and wavelength drive program are recorded onmagnetic tape. If a blackbody is in the sample holderwhen this program is recorded, the 100% line on thechart recorder will represent an emittance of unity,i.e., in Eq. (13), SBB = 1. If the blackbody is nowreplaced by the sample and the same taped program isused to control the slit and wavelength drives, thespectral emittance is traced out directly on the chartrecorder.3 This assumes that the amplifier gain, de-tector response, sample temperature, blackbody tem-perature, and reference temperature are all constantduring the two runs. For samples having low emit-tance, it is sometimes convenient to increase the gainon the sample runs. For example, if the gain were in-creased by a factor of ten, full scale on the chart wouldrepresent an emittance of 0.1. Reference 2 shows someexamples of this technique.
Equation (10) assumes that radiation from the chop-per is blackbody radiation at reference temperature.At first, a black chopper blade was used, driven by asmall motor with an input power of about 100 mW.However, it was found that the blade ran about 0.50Cabove the reference temperature, causing an objection-able error at wavelengths short of 5 u. This problemwas eliminated by using a polished aluminum chopperblade angled so that the detector sees the side of thesample compartment when the chopper blade inter-rupts the beam.
The samples and standardizing blackbody are heatedor cooled by thermal conduction from a copper oraluminum block. For measurements above referencetemperature, the block is heated by resistance elements.A platinum resistance sensor is used in a bridge circuitto control the power to the heaters. The block ismounted on a long, thin stainless steel tube to minimizethermal conduction to the sample compartment. Forlow-temperature measurements, three types of holdersare used. The simplest is a well of thin-wall stainlesssteel tubing with the block mounted on the end. Thewell can be filled with ice water, dry ice and alcohol, orliquid nitrogen. For operating at liquid helium tem-perature, a similar well is used, but it has a liquid-nitrogen-cooled radiation shield. For other operatingtemperatures, a Cryotip* expansion cooler is used.
* Air Products and Chemicals, Inc., Allentown, Pa.
Z
4C-
"0 00 0 000 00 0 00 0 0 0 0 0 000 00 00 0000 0 0 0000 0 0 CC OCD-NOOCC\ O L, 0 W C i D ° A ° C.o , 0 ° L - -
cm1 -'
Fig. 6. Spectral emittance of 0.79-mm thick sapphire at 4.20K,770K, and 200'K. Crystal orientation was not determined.
With this device, a range of 20-200'K can be covered.The sample compartment is maintained about 10-6torr by a Vac Ion pump so windows are not neces-ary on the sample dewars.
MeasurementsThe Irtran materials made by Eastman Kodak Com-
pany are used in many ir optical systems. Some typi-cal emittance spectra are presented. Figure 2 showsthe emittance of Irtran 1 from 3.5-45 at 770 K. Inthe low emittance region at short wavelengths, thismaterial is transparent. The low emittance regionsbeyond 15 u are reststrahlen bands.
Figure 3 presents the spectral emittance of Irtran 2from 3-125 , illustrating the temperature dependence.The sharp dips in emittance at 15 ,u and 18 in the770 K spectrum are windows which are absent at roomtemperature. The reststrahlen band is seen at about30-35 u. Beyond this band, Irtran 2 shows strongtemperature dependence. At 4.2°K, it is a goodwindow beyond 70 ,.
Irtran 4 (Fig. 4) exhibits similar behavior. In the20-35 ,u region, the emission is mostly by two-phononprocesses which are strongly temperature dependent.Again, we see a material that is opaque at room tem-perature become transparent when cooled. At 40-45,u we observe the reststrahlen band.
Irtan 5 (Fig. 5) shows little temperature dependence
0.7 "
0.6 -
0.5
0.2 _ 77°>"
0.1 77 ~ -
- 6 1 8 20 22 24 26 28 30 32 34 36 38 40 42 44
WAVELENGTH (MICRONS)
Fig. 7. Spectral emittance of 2-mm thick single crystal n-typesilicon at 77°K, 203°K, and 373°K.
over the spectral region measured; so only the 770 Kcurve is shown. Again, the low emittance band atshort wavelengths is the transparent region, and theone at longer wavelengths is the reststrahlen band.
Sapphire (Fig. 6) exhibits a striking temperature de-pendence beyond 25 4. At 200"K, the sample isopaque, at 77 0K the transmission increases slowlytoward the longer wavelengths, and at 4.2 0 Ki the trans-mission increases rapidly between 26 u and 29 u.
The emittance of single crystal silicon at three tem-peratures is shown in Fig. 7. The predominant emis-sion mechanisms are the two-phonon processes.
Figures 8 and 9 show spectra from 3-40 gu of threeblack paints frequently used in optical equipment andfor thermal radiation control surfaces. The 3M black*and Cat-a-Lac blackt show little temperature depend-ence, while the emittance of Sicon black5 drops at longwavelengths and low temperature.
* Minnesota Mining and Manufacturing Co., Minneapolis,Minn.
t Finch Paint and Chemical Co, Torrance, Calif.§ Midland Industrial Finishes Co., Waukegan, Ill.
The examples given here show that the optical prop-erties of many materials used in ir optical systems arequite temperature dependent. In most cases, both thetransmittance and the emittance of the componentsmust be known at the operating temperature for properdesign of a system. The emittance and transmittancedepend upon n and k, which are determined by theabsorption or emission processes that are taking placein the material. Fundamental crystal lattice vibra-tions are relatively insensitive to temperature. Phononsummation bands and free carrier emission are fairlytemperature dependent, and phonon difference bandsdepend strongly upon the temperature.
Crystal quartz, sapphire, Irtran 2, and Irtran 4 arematerials which have been used as cold filters to blockbackground radiation in cooled ir detectors. All ofthese have low temperature windows that can affect theperformance of the detector. Even some paints havetemperature dependent optical properties. One cannotsafely use room temperature data for calculating opticalsystem characteristics at other temperatures.
Another area where knowledge of spectral emittanceis useful is in the calculation of heat exchange by radia-tion. The total emittance E is related to the spectralemittance Ex by the equation
E = f EXW.dx f WxdX.
The total emittance depends upon the temperature intwo ways. Since the spectral distribution of the black-body energy WA changes with temperature, E will alsochange unless E is independent of wavelength. IfEx is temperature dependent, E will probably be tem-perature dependent also, although there may be tem-perature regions where the shift in the blackbody dis-tribution will compensate the change in Ex.
The temperature dependence of the total emittancemay be either positive or negative. For example, thetotal emittance was calculated from spectral emittancemeasurements for a sample of cadmium sulfide and asample of sapphire over a range of temperatures. 4
Going from 770 K to 4730 K, the total emittance of thecadmium sulfide decreased by a factor of three whilethe total emittance of the sapphire increased by morethan a factor of three.
References
1. H. 0. McMahon, J. Opt. Soc. Am. 40, 376 (1950).2. D. L. Stierwalt and R. F. Potter, in Proceedings of the Inter-
national Conference on the Physics of Semiconductors (The In-stitute of Physics and the Physical Society, London, 1962.
3. D. L. Stierwalt, J. B. Bernstein, and D. D. Kirk, Appl. Opt.2, 1169 (1963).
4. D. L. Stierwalt, AIAA Progr. Astronautics Aeron. 18, 21(1966).
photosD. L. MacAdam
M. Beran speaks while G. Toraldo di Francia Florence chairs asession of the University of Rochester Conference on Coherence.
G. W. Series Clarendon Laboratory, Oxford addresses the SecondRochester Conference on Coherence and Quantum Optics.
D. E. TA\'cCumber Bell Telephone Labora-tories, a speaker at the Coherence Conference.
December 1966 /Vol. 5, No. 12 / APPLIED OPTICS 1915
