Integrating sphere for solar transmittance measurement ofplanar and nonplanar samples

J. G. Symons, E. A. Christie, and M. K. Peck

A new apparatus that incorporates an integrating sphere is described, which enables the solar transmittanceof test samples to be measured as a function of both angle of incidence and azimuth angle. This apparatuswas developed to perform measurements on both planar and nonplanar samples of larger dimensions thancan be accommodated in a spectrophotometer. Solar transmittance measurements from this apparatus arecompared with those from a Gier & Dunkle spectrophotometer for a range of sample materials, and excellentagreement has been found. Errors in solar transmittance measurement may arise from changes in the inte-grating sphere entrance port reflectance due to placement and then the removal of the test sample from theport. A correction procedure is derived to take account of these errors and is applicable to all single-beamintegrating spheres.

1. Introduction

A. General StatementThe transmittance of a material to incident solar ra-

diation is usually evaluated by some integration pro-cedure, such as a selected ordinate method,1' 2 frommeasured spectral data. These measurements areconducted on small test samples mounted at the en-trance port to an integrating sphere so that both directand diffused components of the transmitted radiationare included in the measurement. Most instrumentsused for spectral transmittance analysis irradiate onlya few square millimeters of the sample, and their ap-plication is, therefore, restricted to relatively thin planarmaterials with minimal variations from uniform com-position and structure.

Solar transmittance of a particular sample is the ratioof transmitted radiation flux, both direct and diffuse,to the incident flux summed over all wavelengths in theincident beam and is of obvious importance in radiationheat transfer calculations involving, for example,building windows, greenhouses, and solar collectors.

The authors are with Commonwealth Scientific & Industrial Re-search Organization, Division of Energy Technology, Highett, Vic-toria, Australia 3190.

Received 12 November 1981.0003-6935/82/152827-06$01.00/0.

While measurement of solar transmittance on smallplanar samples is adequate for many applications, thereis now an interest in the transmittance of more com-plex-shaped nonplanar structures. In solar collectors,for example, plain glass covers, shaped covers, extrudedplastic covers, and honeycombs are all being used, andin greenhouses, plain glass heets, profiled sheets,multiple plastic skins, and bubble plastic sheets areemployed.

To measure the transmittance of these materials, anapparatus has been developed which will enable totalsolar transmittance to be determined for samples ofcomplex shapes at various angles of incident radiation.The test procedure is rapid and allows testing overlarger sample areas than was previously possible witha spectrophotometer.

B. Nomenclature

Ad area of the detector cavity port, M2 ;Ap,Ap areas of entrance port for the sample trans-

mittance and sample reflectance tests, re-spectively, M 2

;

As area of side sphere port, M2 ;AU,A' areas of sphere wall, excluding port openings,

for the sample transmittance and sample re-flectance tests, respectively, M2 ;

E,E' diffuse flux densities inside the sphere withthe sample covering one of the ports for thesample transmittance and sample reflectancetests, respectively, W m- 2 ;

Eo,E diffuse flux densities inside the sphere withno sample in place for the sample transmit-tance and sample reflectance tests, respec-tively, W m-2 ;

1 August 1982 / Vol. 21, No. 15 / APPLIED OPTICS 2827

FDP configuration factor from the sphere wall areadirectly irradiated by source radiation toA .

FDS configuration factor from the sphere wall areadirectly irradiated by source radiation toA.;

a°,,h hemispherical absorptance of sphere wall;cxw, absorptance of sphere wall for radiation at

incident angle 0;Pdh hemispherical reflectance of the detector

cavity;Psh hemispherical reflectance of sample;Pso reflectance of sample, to beam radiation at

incidence angle 0;Pw,h hemispherical reflectance of sphere wall;

Pw,bq5 reflectance of sphere wall in direction of in-cident radiation at angle s;

Ts,o solar transmittance of sample, to beam ra-diation at incident angle 0;

b source radiation flux, W.

11. Apparatus

The equipment is illustrated in Fig. 1 and comprisesa source directing radiation through a collimator intoa large integrating sphere used for the transmittancemeasurement. The test sample is placed over a port inthe integrating sphere in the path of the collimatedbeam. The solar transmittance of the test sample isdetermined from measurements of radiation flux den-sity in the sphere with the sample in place and then withthe sample removed. Correction is made for the in-fluence of the sample reflectance on the sphere losses.Various angles of incidence of radiation on the testsample are achieved by rotating the source and colli-mator with respect to the sample and integratingsphere, as in Fig. 1, while various azimuth angles areachieved by rotating the sample.

The radiation source is a Thorn Compact Source Io-dine lamp with a nominal power dissipation of 1 kW.This lamp is chosen for its high irradiance (which isinsensitive to changes in lamp inclination and appliedvoltage) and for its spectral distribution, which is sim-ilar, when summed over wavelength bands of 200 nm,to that of the airmass 2 solar spectrum. The relativespectral irradiance of the lamp has been measured overthe 372-2484-nm wavelength range by comparing itsspectral output with that of a standard tungsten fila-ment lamp. Results are compared to the solar spectrumfor airmass 23 in Fig. 2.

The collimator comprises a series of metal baffleseach with a 100-mm circular aperture. The collimatorwhich is painted mat black inside serves to absorb allscattered radiation. The radiation emerging from thecollimator is nearly parallel with a deviation of not morethan 4.5° from the central axis. This simple collimatorarrangement provides uniform irradiance across the testbeam and avoids changes to the spectral distribution ofthe radiation source. The irradiance distribution acrossthe sphere port was measured with a silicon detectorand is shown in Fig. 3 for three angles of incidence. For0 = 0 (illumination normal to the test sample), the ir-

I \KL FRADIATION SOURCE

CHOPPER

COLLIMATOR

CS) (E W (N)SAMPLE

INTEGRATING SPHERE

DETECTOR (IN WALL)

Fig. 1. Integrating sphere apparatus for measuring solartransmittance.

radiated test area of 100-mm diam has a near uniformirradiance in both the NS and EW directions with amaximum variation of 3% from the mean. The maxi-mum irradiance for this orientation is 615 W m-2. Atan angle of inclination of 600, the irradiance is uniformin the EW direction; however, in the NS direction itincreases toward the collimator (indicated as north).

The integrating sphere, spun from a 1.6-mm alumi-num sheet, is 914 mm in diameter and coated internallywith Eastman White Reflectance Coating (Pwh = 0.94)providing a highly reflecting diffuse surface with min-imum selectivity. The radiation entrance port is 350mm in diameter to maximize acceptance of radiationemerging from the test sample into the sphere. Theneed for a large entrance port is particularly importantfor large angles of incidence and for test samples whichscatter the incident beam radiation. The test sampleis mounted at the port on a rotatable horizontal plat-form to allow the azimuth angle to be varied.

An Eltec Pyroelectric 404 VM/6 detector with aquartz window is inserted in the wall of the sphere ona radial axis 900 to the sample port axis. The detectoris located in a 8.5-mm diam cavity in the sphere wall,and a 20-mm diam shield is positioned in front of thedetector cavity to shield the detector from direct ra-diation emerging from the sphere port and from thesphere wall area directly irradiated by the incidentbeam. The output from the detector is measured usinga linear variable gain ac amplifier with a three-digitnumerical display. The radiation is chopped at a fre-quency of 12.5 Hz immediately before entering thecollimator using a segmented rotating disk. As theamplifier has a filtered response matched to that of thechopping frequency, stray radiation entering the inte-grating sphere does not affect the radiation flux reading.The approximate spectral response of the detector hasbeen checked (with a Perkin-Elmer model 98 mono-chromator by comparing the output from the Pyro-

2828 APPLIED OPTICS / Vol. 21, No. 15 / 1 August 1982

we~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~s

z4~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

0~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~I-4 -2 5

IL w

n 140 1500 2000 . 2500 spectral irradiance with the lamp

>3

-l ~ ~ ~ ~ AE ENT bn5 pcrliraine

1000 -

z I LAMP a600

I ~~~~~~~~~~~~~SOLAR/ i,,. . -/ ~~~~~~~~~~~~~~~~~~~~~200

Fig 2 Comparison of the solar566 1"0 1500 2000 2500 spectral irradiance with the lamp

WAVELENGTH (n,) spectral irradiance.

electric detector with that of a Reeder RP-3W137thermocouple over wavelengths of the solar spectrum)

NORT H 8. o SOUTH and found to be uniform over the wavelength range of600 the solar spectrum.

'E Mlk -) Ill. Correction for Large Entrance Port AreaE

400 A large integrating sphere entrance port increasesU uncertainties in solar transmittance measurements. As4

200 / a test sample is placed over the entrance port, the re-4 200 _ / ] _ flectance of the entrance port is increased, thus reducing

200 the radiation flux leaving the sphere through the port.In most integrating spheres, the entrance port area isso small with respect to the total sphere wall area that

80 40 0 40 so placement of a sample over the port will not cause aDISTANCE FROM CENTRAL AXIS (mn) significant change in the radiation flux leaving the

WEST EAST sphere. Initially the detector was located in the bottomfl^00 of the integrating sphere with a detector shield posi-

600 tioned in the center of the sphere, as recommended inthe British Standard.4 Using this arrangement, the

E incident beam radiation on entering the sphere was4" g / \ intercepted by the detector shield when 0 = 0 but by-

U Q I \ passed the shield at other angles. The resulting change0 < { _ @.60' \ in view factor between the area first intercepting the

= 200 | | 4 > \ beam radiation and the entrance port also influencedthe radiation flux leaving the integrating sphere. Hencethe detector and shield location recommended in Ref.

0 JJJ . SS4 are unsuitable for integrating spheres when 0 is to be0 40 0 40 80 varied, particularly when the entrance port is large.

DISTANCE FROM CENTRAL AXIS (mm) The integrating sphere detector and shield locationsFig. 3. Irradiance distributions across the entrance port: (top) adopted in the apparatus substantially reduced mea-

north-south traverse; (bottom) east-west traverse. surement errors caused by varying the sphere losses, and

1 August 1982 / Vol. 21, No. 15 / APPLIED OPTICS 2829

through the sample equals the sum of the following: thedirect beam flux reflected from the sphere wall andtransmitted back through and absorbed by the sample;the direct beam flux absorbed by the sphere wall; thediffuse flux absorbed by the sphere wall; the diffuse fluxabsorbed in the detector cavity; and the diffuse fluxtransmitted through and absorbed by the sample. Aradiant flux balance, therefore, yields

'I'rs,0 = sr8 ,oPW,0FD(1 - Ps,6) + 4Ts,0aw,q + EAwawh+ EAd(1 - d,h) + EAp(1 Psh) (1)

where FDP is the configuration factor from the spherewall area directly illuminated by the source radiationto the radiation entrance port. FDP is equal to the ratioof the radiation entrance port area to the total spherearea.

By rearrangement

E = 4br.,(1 - wOFDP + Pw.,OFDPPs,O -w,)

Awtw,h + Ad - AdPdh + AP - ApP8,h

When the sample is removed from the port, Tso = 1and Pso = Psh = 0. Under this open port condition, thediffuse radiation flux inside the sphere is uniformlyequal to E0 in all directions, and Eq. (2) becomes

Eo= 1(1 - p,0,jFDP aw,o)-Awa.,h + Ad - AdPd,h + Ap

Hence from Eqs. (2) and (3)

E-= p50.

Fig. 4. Integrating sphere test configurations: (top) measurementof r,O; (bottom) measurement of Ps,h-

1

1+ Pw,00FDPPs,61 - w,OOFDP - wO

ApPsh

A. a.,h + Ad - Adpd,h + Ap

If the integrating sphere wall is opaque to solar ra-diation wavelengths and closely approximates Lam-bert's cosine law for diffuse reflections,

a correction factor is derived below to estimate the re-maining error.

IV. Measurement of Solar Transmittance

The integrating sphere with a test sample at the ra-diation entrance port is shown schematically in Fig. 4.A collimated beam with radiation flux -lb is directed intothe sphere through the entrance port of area AP. Adetector cavity with hemispherical reflectance Pd,h islocated behind a detector port of area Ad. The testsample has a solar transmittance and solar reflectanceto beam radiation at incidence angle 0 of rs,o and psO,respectively, and a hemispherical reflectance of Ps,h-The sphere wall of area AW is coated with a diffusingsurface with hemispherical reflectance Pw,h, hemi-spherical absorptance a°wh, absorptance to radiationat incident angle 0 of a ,O and reflectance Pw6,0 to in-cident radiation at incident angle q, which is reflectedback in the same direction as the incident beam. Underthese conditions, the diffuse flux density inside thesphere is uniformly equal to E in all directions. Allradiation entering the sphere is either lost from thesphere port, absorbed in the sphere wall, or absorbedby the detector; i.e., the total flux entering the sphere

°1w, = aw,h, Pw,00 = Pw,h, and Pw,h = 1 - wh,

and so from Eqs. (4) and (5) rearrangement gives

1 - ApPs,hE A. a.,h + Ad - AdPd,h + AP

(5)

(6)

1 + FDPPsO1 - FDP

From Eq. (6) the solar transmittance ro is equal tothe product of the ratio E/Eo and a correction factor.Equation (6) is applicable to all single-beam integratingspheres when used for measuring transmittance andcompensates for the change in reflectance of the ra-diation entrance port due to the presence of the sample.The numerator of the correction factor accounts forchanges in the sphere flux density due to reflection ofdiffuse radiation by the underside of the sample. Thedenominator accounts for changes in the sphere fluxdensity caused by radiation reflected by the area ofsphere wall directly irradiated by the source, which issubsequently reflected by the sample. The influenceof the detector is only significant if it occupies an areacomparable with the entrance port area.

For a particular integrating sphere, AP, Ad, AW, awh,

Pdh, and FDP are constants. For the device being de-

2830 APPLIED OPTICS / Vol. 21, No. 15 / 1 August 1982

I

(2)

(3)

(4)

- 3=, E

scribed, substitution of the appropriate values in Eq.(6) gives

E 1 - .3881ps,7

Eo 1 + 0.0381p,, (7)

For convenience, it is preferable to express Eq. (7) interms of only one independent variable. From Eq. (7)it may be noted that Ps,h has the greater influence onrs,O, and for 0 < 60°, Ps,O - Ps,h. Therefore, for practicalmeasurements it is assumed that

Ps,O = Psh- (8)

It should be noted that Ps,O and Ps,h would need to bemarkedly different before this assumption leads tosignificant errors in the resulting estimate of r.,,.Therefore, for the integrating sphere described, Eq. (7)becomes

E 1 - .388lPshBr' = -________9_

Eo 1 - 0.038lPsh

Therefore, to determine Ts,O, E/EO is found from ex-perimental measurement, and an estimate of P,h isrequired.

V. Measurement of Hemispherical DiffuseReflectance

The integrating sphere was constructed with twoports, a large entrance port and a smaller side port.During transmittance measurements the side port iscovered with a disk having the same internal radius andcoating as the sphere wall. Similarly the entrance portaperture can be reduced in diameter with another disk.For reflectance measurement, the side port of area A,is opened, and the entrance port is reduced in diameteras shown in Fig. 4. If the test sample is placed over theside port, the (top) radiation entrance port is reducedin area to A, and the assumptions of Eq. (5) againapply. Then a radiant flux balance yields

= 4P,hFDS(l - Ps,0) + I)Pw,hFDP + aw,h + EAaWCa,h+ EA + E'A,(1 - P,h) + E'Ad(1 - Pd,h). (10)

Hence

E 1(1 - Pw,hFDS + P,hFDSPs, - Pw,hFDP - 01w,h) 1AW awh + Ap + As - AP8,h + Ad-Adpdh

Again if the sample is removed from the port, re-flectance over the side port area is zero, and the diffuseflux density in the sphere is E, Eq. (11) becomes

I =1 (- w,hFDS - Pw.,hFDP - aw,h) (12)=wawh + Ap + A + Ad - AdPd,h

As the assumptions leading to Eq. (8) are again valid,Eqs. (5), (8), (11), and (12) give

1 + FDSPSh1 -FDS - FDP

A1 -o,

A' aW,h + AP + A, + Ad - AdPd,h

The similarity between Eqs. (4) and (13) should benoted. On substituting the values of A8, A', A' , Ad,awh, Ps,h, Pd,h, FDS, and FDP for the device being de-scribed, Eq. (13) becomes

E' 1 + 0.0110PshE 1 - 0.l 4 8 lPsh

(14)

and hence(E'/E) -1

P .0.0110 + 0.1481(E'/E'o)(15)

It follows that the diffuse reflectance of a test sampleto solar radiation may be evaluated by a simple exper-imental procedure using a second port in the integratingsphere. Solar transmittance may then be determinedby substituting the experimental measurement of E/Eoand the estimate of Ps,h into Eq. (9).

While Eqs. (6) and (13) are general expressions thatcan be used for any single-beam integrating sphere, Eqs.(9) and (15) are applicable only to the device being de-scribed in this work.

The technique described here for measurement ofhemispherical diffuse reflection is believed to be newand is a modification of one of the Taylor methods.5

VI. Typical Results

Seven planar samples have been tested in both thisequipment and also in a Gier & Dunkle integratingsphere6 attached to a Perkin-Elmer model 98 mono-chromator to compare the results. The new device ir-radiates a nominal 100-mm diam test area, while theGier & Dunkle system has a maximum beam size of 12X 2 mm at the sample. The solar transmittances ofsamples tested in the Gier & Dunkle integrating spherewere determined by performing a weighted mean of thespectral transmittance according to the airmass 2 solarspectrum. The tests were performed for a range of in-cident angles, and results are shown in Table I.

Four of the samples tested had minimal spectral se-lectivity, while three further samples had significantspectral-dependent transmittance characteristics asshown in Fig. 5. The samples with significant variationsin spectral transmittance were included to verify use ofthe radiation source and collimator as a suitable solarsimulator.

From Table I it is clear that the solar transmittancevalues obtained with this equipment compare favorablywith the spectral measurements using a Gier & Dunkleintegrating sphere. For all the comparisons made, themaximum difference between this new apparatus andthe Gier & Dunkle integrating sphere is 0.01. Even forthe three heat absorbing glass (H/A) samples whichrepresent the most selective materials likely to be ofinterest for solar energy applications, no significantdifference in the solar transmittance could be de-tected.

Two sets of results are shown in Fig. 6 as a furtherexample of the tests that can be performed with thisapparatus. One set is for a parallel wall structure madefrom strips of FEP Teflon-type 50A (60 mm high and5 mm apart), called a slat convection suppression device,which may be used for reducing the heat loss fromflat-plate solar collectors. The other set is for a corru-gated fiber-reinforced polyester sheet. These non-planar materials cannot be tested in the Gier & Dunkle

1 August 1982 / Vol. 21, No. 15 / APPLIED OPTICS 2831

E' E',

Table I. Solar Transmittance of Planar Materials

Bronze H/AdIncidence Window glass Low iron glass FEP Teflon Bronze acrylic glass Green H/Ad glass Grey H/Ad glass

angle (4 mm) (5 mm) 50A (5 mm) (6 mm) (6 mm) (6 mm)(deg) a b a b a b a b a b a b a b

0 0.82 0.89 0.97 0.16 0.50 0.48 0.4310 0.82 0.89 0.97 0.16 0.50 0.47 0.4420 0.82 0.82 0.89 0.89 0.96 0.97 0.15 0.15 0.48 0.49 0.47 0.47 0.43 0.4330 0.82 0.81 0.88 0.88 0.97 0.14 0.14 0.47 0.48 0.46 0.46 0.42 0.4240 0.81 0.81 0.88 0.88 0.97 0.13 0.13 0.46 0.47 0.45 0.45 0.41 0.4050 C 0.78 c 0.86 C 0.95 c 0.12 C 0.44 c 0.42 c 0.3760 c 0.74 C 0.81 c 0.93 C 0.1 c 0.40 C 0.38 C 0.34

a From spectral data using a Gier & Dunkle spectrophotometer.b From the new integrating sphere, corrected using Eq. (9).c Outside range of instrumentation.d H/A, heat absorbing.

z4 080 REEN

Z 0U60

4 0-40

-2

00-4 O a 1 2 18 2

WAVELENGTH (urn)

Fig. 5. Spectral transmittance of three heat absorbing glasses.

CORRUGr.ATFD FRP

--.-~ N -,S~ -~~

. 1.... NN

1o L mu nX 00E 450

N1 \ \ Es1K

integrating sphere to give a comparison of the measuredsolar transmittance.

Vil. Conclusions

A simple apparatus has been described which enablesmeasurements to be made of the solar transmittance ofplanar and nonplanar transparent samples for variousangles of incidence. The results from this apparatuscompare favorably with those from a more sophisticatedspectrophotometer for the range of test samples com-pared.

The apparatus enables measurements to be made ofthe solar transmittance of nonplanar samples, includinghoneycombs, shaped plastic sheeting, and fabricatedmultiskinned films. None of these samples can betested with existing equipment. The apparatus usesa larger irradiated test area than usual, thus enablingthe overall solar transmittance of shaped structures tobe determined in one test.

A correction method has been developed whichminimizes errors arising from integrating spheres withlarge entrance ports. A technique is also suggested forapproximate measurement of diffuse reflectance of testsamples, a property required for the correctionmethod.

Support was provided under the National EnergyResearch Development and Demonstration Programadministered by the Australian Department of NationalDevelopment and Energy.

The assistance of F. Wilkinson, CSIRO Division ofApplied Physics, is acknowledged for providing therelative spectral intensity data in Fig. 2 and for hisconstructive criticism of this paper. The contributionof a number of colleagues to the design and manufactureof the apparatus is also acknowledged.

* go References1. A. V. Sheklion, Appl. Sol. Energy USSR 3, 2, 68 (1967).

\5c 2. 0. H. Olson, Appl. Opt. 2, 109 (1963).3. P. Moon, J. Franklin Inst. 230, 583 (1940).

1 1 4. British Standard: Aerospace Series, Specification for Reflection0 10 20 30 40 50 60 Reducing Coating of Instrument Windows and Lighting Wedges,

British Standards Institution G.211 (Mar. 1971).ANGLE OF INCIDENCE (DEG) 5. A. H. Taylor, J. Opt. Soc. Am. 4,9 (1920).

Fig. 6. Typical test results for nonplanar samples. 6. D. K. Edwards et al., J. Opt. Soc. Am. 51, 1279 (1961).

2832 APPLIED OPTICS / Vol. 21, No. 15 / 1 August 1982

0-8

0.9j

0-8t_AMNIDLr