Use of an integrating sphere in solar energy research

Solar Energy Materials and Solar Cells 30 (1993) 77-94 North-Holland

Solar Energy Materials and Solar Cells

Use of an integrating sphere in solar energy research A. Roos Department of Technology, Uppsala University, Box 534, S-751 21 Uppsala, Sweden Received 7 December 1992 Models for the evaluation of total diffuse and specular reflectance and transmittance components for scattering samples measured on an integrating sphere are presented. It is demonstrated that for typical solar energy surfaces serious errors can be the result of incorrect interpretation of the detector signals. Methods to avoid such errors are presented.

1. Introduction Solar energy is utilized in many different applications and there are several branches of solar energy research. In all these it is important to experimentally determine the optical properties of the investigated materials. Two separate wavelength intervals can be distinguished in solar energy. The primary one is the solar spectrum which provides the energy we wish to utilize and the other is the thermal infrared spectrum. The solar spectrum is usually taken as the interval 0.3-2.5 p.m with a spectral distribution which depends on the atmospheric conditions. The thermal infrared spectrum of interest is the blackbody radiation from the investigated surfaces at their normal temperatures of operation. The solar and the thermal spectra do not overlap and it is, in fact, an experimental coincidence that these two spectra are handled by two different types of spectrophotometers. The solar spectrum is covered by the UV-VIS-NIR type of instrument and the thermal infrared by the IR type. In the infrared part of the spectrum the optical property of interest is usually the emission of radiation by the studied surface. This can be measured directly, but it is also common, and often more convenient, to measure this quantity indirectly by measuring the reflectance with a IR spectrophotometer. The emittance, which is always equal to the absorptance, is obtained as 1 - R for opaque samples. The utilization of solar energy always requires large surfaces since the energy density is low. In most cases such large surfaces cannot be produced with an optical quality equivalent to vacuum deposited films on small substrates. This means that most surfaces of interest will have a surface structure which causes scattering of incident radiation. This structure can be anything from microscopic surface roughness with a dimension smaller than the incident radiation to large scale waviness, grooves or scratches from 0927-0248/93/$06.00 © 1993 - Elsevier Science Publishers B.V. All rights reserved

78

A. Roos / Use of an integrating sphere in solar energy research

various production processes. The microscopic roughness causes scattering which is usually fairly homogeneously distributed over the hemispere, while macroscopic roughness tends to scatter light into a fairly small solid angle around the collimated beam. In all these cases an integrating sphere must be used to correctly measure transmittance and reflectance of the scattering samples. For the UVVIS-NIR type instrument most spectrophotometer manufacturers provide an integrating sphere as a standard accessory, while in the IR range it is more common to buy a separate sphere and design your own system, Spheres for the solar wavelength range are usually coated with BaSO 4 powder while IR spheres are gold coated. Basic integrating sphere theory has been described in detail by several authors [1-4] and several aspects on the design [5,6] and on errors [7,8] of integrating spheres have been published. Special problems have to be considered in the infrared [9,10]. In this paper some techniques to use integrating spheres will be described and special attention will be paid to errors caused by the distribution of scattered radiation within the sphere and how to minimize these errors. Port losses, and the fact that the throughput of the sphere depends on the angular distribution of the scattered light, can cause serious errors in both transmittance and reflectance values unless the samples are correctly positioned on the sphere and the instrument signals correctly interprated. The starting point will be the bidirectional distribution of the scattered radiation which is schematically shown in fig. 1 for a transmitting and a reflecting sample. As can be seen in the figure the scattered radiation is divided into the components Toj, To2 and Td3 for the

Td3

saml~'-

R~

Fig. 1. Schematicrepresentationof the angulardistributionof reflectedand transmittedradiation.

A. Roos / Use of an integrating sphere in solar energy research

79

transmitting sample and Rdl and Rd2 for the reflecting one. The significance of these components will be made clear later. Models for the interpretation of the sphere signal output as functions of these components for the reflectance mode [11] and the transmittance mode [12] are described in detail elsewhere. In this paper these models are summarized and some experimental results are presented which show the importance of these aspects in solar energy research. All results have been obtained in the solar wavelength range and on the Beckman standard integrating sphere, but the basic ideas are generally valid and can easily be adapted to any sphere system.

2. Integrating sphere design The integrating sphere used in this work is the Beckman standard integrating sphere for the 5240 spectrophotometer. The design of this sphere with all the ports and their relative positions is shown in fig. 2. This sphere is a multipurpose instrument designed for measurements of both transmittance and reflectance. The positions of ports and baffles are therefore not ideal, and as we shall see, this leads to errors in several cases. The sphere as well as the reference plates are coated with BaSO 4 and the two detectors cover the wavelength range 0.3-2.5 p,m. A special feature of this sphere design is that the collimated beam can be allowed to escape out of the sphere through a port and thus only the scattered radiation is recorded. This possibility to distinguish between the scattered and collimated radiation is necessary for the interpretation of the signal output.

2.1. Reflectance measurements In figs. 3a and 3b the sphere is shown in reflectance mode. The reference beam has been omitted for convenience and the ports shown are ports Nos. 2, 3 and 5 in fig. 2. With a BaSO 4 plate covering the specular exit port (No. 5) all the reflected light is contained within the sphere exept for the fraction which escapes through side view

top view

7

5

1 ~

2

3 ~

4

Fig. 2. Design of the Beckman integrating sphere. (1) entrance Imrt-reference beam, (2) entrance port-sample beam, (3) sample port, (4) reference port, (5) specular exit I~rt, (6) PbS detector, (7) PM detector.

80

A. Roos / Use of an integrating sphere in solar energy research

(a)

8amplo

,~zmpie

(b)

Fig. 3. ]ntegrating sphere in reflectance mode set for (a) total reflectance, (b) diffuse reflectance.

the entrance ports. When the specular exit port is open, as in 3b, the specular beam is lost and only the scattered part of the radiation contributes to the detector signal. The two components Rdl and Rd2 of the scattered radiation are also shown in this figure. The significance of this division is that Rd2 is assumed to be scattered homogeneously into all solid angles in the same way as light is reflected off the BaSO4 coating. Ral, on the other hand, is close to the collimated beam and is not completely diffused into the sphere until it has been reflected by the sphere wall around the exit port. Ra2 is in this way equivalent to the reference beam which is scattered into the sphere from the BaSO4 reference plate covering port 4 (cf. fig. 2). The fraction F of both these two signals is contained in the sphere and for the Beckman sphere this factor has been experimentally determined to be equal to 0.98 [11]. Depending on the character of the sample, different fractions Fs of the component Rdl are contained within the sphere, or conversely, fractions 1 - Fs are lost through the two entrance ports 1 and 2 (cf. fig. 2). The factor Fs can in general not be determined exactly but a simple geometrical consideration can often lead to a reasonable estimation. This means that the three components R~, Ral and Ra2 contribute to the detector signal according to S I =ARsRB,

(1)

S 1I = A R d l R B F s ,

(2)

S III = A R d E F ,

(3)

where R a is the reflectance of the BaSO 4 coating and A is the instrument amplification factor.

2.2. Transmittance measurements In transmittance measurements the sample is positioned in front of entrance port 2 in fig. 2. This means that two different modes of operation can be performed. Port No. 3, which is the sample port in the reflectance mode can be covered either by a BaSO 4 plate or by an evaporated mirror, usually aluminium.

A. Roos / Use of an integrating sphere in solar energy research

81

) jli Sample

ght trap

Fig. 4. Integrating sphere in BaSO 4 mode for transmittance: (a) total transmittance, transmittance.

(b) diffuse

2.2.1. BaS04 mode In the BaSO 4 mode, as in fig. 4, transmitted radiation is partly scattered, Td, and partly transmitted specularly, T~. The specular component, Ts, is then scattered into the sphere by the BaSO 4 plate. When the BaSO4 plate is replaced by a light trap, the specular signal is absorbed and does not contribute to the detector signal. Owing to the size of the port, however, a fraction of the scattered radiation Td, is also trapped in this light trap. This is the componerit labelled Tdl in fig. 1. This means that in this mode the instrument defines a specular signal as the sum of Tspec and Tdl in fig. 1. The component Td2 is equivalent to the the component Rdl in the reflectance mode and enters the sphere after having been reflected off the sphere wall in the immediate vicinity of the BaSO 4 port. All of the components Ts, Tax and Td2 are reflected by the BaSO 4 from a position opposite the two entrance ports 1 and 2 and hence only the fraction F of these signals is contained in the sphere. The component Td3 is directly diffused by the sample in the same homogeneous way as light reflected off the BaSO4 coating. This component cannot "see" the two entrance ports and is therefore completely contained in the sphere. The four components thus contribute to the detector signal according to

S l =ATsRBF,

(4)

S n =ATdlRBF,

(5)

S nI =ATd2RBF,

(6)

S TM= ATd3.

(7)

2.2.2. Al mode In the other mode for transmittance measurements an Al mirror with negligible scattering is placed on port 3. The collimated beam is reflected in this mirror and is scattered into the sphere by the BaSO 4 plate covering the specular exit port opposite the mirror. This is depicted in fig. 5, where it can also be seen that the component Tdl in this case is contained in the sphere (dashed beams in fig. 5b). Tdl is scattered from the BaSO 4 wall in the vicinity of the specular exit port in the

82

A. Roos / Use of an integrating sphere in solar energy research

)

Sample

(a)

AI-mlrrot

AI - mirror

(b)

Fig. 5. Integrating sphere in AI mode for transmittance: (a) total transmittance, (b) diffuse transmittance. same way as the specular signal T~, but only the fraction F M of Tdl which does not escape through the two entrance ports. The two components Td2 and Ta3 enter the sphere in the same way as in the BaSO 4 mode. Thus we can write the contributions to the detector signals from the four components T~, Tdl, Td2 and Td3 as S I =ATsRMRB,

S |I = A T d l R M F M R B , S nt = A T d 2 R B F ,

S TM =ATd3 ,

(8) (9) (a0) (11)

where RM is the reflectance of the AI mirror. 3. Mathematical model

Since the specular and the different diffuse components give rise to different detector signals depending on how they are scattered into the sphere, it is essential to be able to measure the specular and the diffuse signals separately. The determination of the specular, diffuse and total reflectance or transmittance thus requires three scans; a reference reading without the sample, a reading of the total signal and a reading of the diffuse signal. These readings are labeled $1, $2 and S 3 in the following. The signal output from the instrument is, for a double beam instrument, always the ratio between the sample beam signal and the reference beam signal. The reference readings in the reflectance mode and in the BaSO 4 mode are then S 1 = AFRB/FR B = A.

(12)

In the AI mode the reference reading is S x = A R MR B / F R B = A R M / F .

(13)

The total reading S z can for the reflectance mode be written S I -.I--S II + S III

S2 =

(14) FRB

A. Roos / Use of an integrating sphere in solar energy research

83

and for the two transmittance modes S I --[-S II q- S II1 --b S TM

Sz =

(15)

FR B

The diffuse readings for the reflectance, BaSO 4 and AI modes can be written as S ii ..{_SIII

S3 =

,

FRB

(16)

SIII d- S TM

S3 -

,

FRB

(17)

S n -.{-SIII ..~ S TM

S3 =

,

FRB

(18)

respectively. It is convenient to normalize the diffuse components and we write for the reflectance mode: R d =Rdl +Rd2 = (1-B)R

d + B R d,

(19)

i.e. the fraction B of the scattered reflectance is completely diffuse. For the BaSO4 transmittance m o d e both T~ and Tdl escape for the diffuse reading and we can write for the two remaining components Ta = Td2 + Td3 = (1 -- B ) r d + BTd.

(20)

In the Al m o d e we write the three scattered components as T d = Tdl + Td2 + Td3 = BIT d + B 2 T d + B 3 T d,

(21)

where B 1 + B 2 + B 3 --- 1 by definition. Using eqs. (12)-(21) we can now find the final expressions for the desired reflectance and transmittance values as functions of the signal readings $1, S 2 and $3. In the reflectance mode we get: (22)

Rs = F ( S2 - $3)/$1, FRBS 3 Rd = [ F B +Fs(1 - B ) R B ] S

, '

(23) (24)

R t = R d + Rs.

For the transmittance in the BaSO 4 mode, r~b = ( S z - S3)//Sl ,

S3 Tab = S1(1 - B + B / F B R B ) '

(25) (26) (27)

A. Roos / Use of an integrating sphere in solar energy research

84

and, finally, in the AI mode, Ts =

(S 2-

(28)

53)/S1,

$3 SI( B 1 F M + B i F B / R M +

(29)

B3/RMRB) '

(30)

Tt = T~ + Td .

4. Results

In this section some results are presented which demonstrate the importance of correct positioning of samples and correct usage of eqs. (22)-(30).

4.1. Reflector surfaces A solar reflector surface is a surface which reflects as much as possible of the incoming solar radiation, usually onto another surface where it is absorbed. Aluminium is one of the most common reflector materials owing to its high reflectivity. A problem is its low corrosion resistance and aluminium needs a protective coating if it is exposed to environmental conditions. In fig. 6 the diffuse, specular and total reflectance spectra are shown for ordninary rolled uncoated aluminium. The two sets of spectra are recorded with the sample oriented with the direction of rolling vertical (O = 0 °) and turned 80 ° clockwise (O = 80 °) on the sample port (No. 3 in fig. 2). The difference between the total and the diffuse spectra recorded with the two sample orientations is dramatic. The specular signals, on the other hand, are nearly identical. The reason behind this extraordinary difference is that a rolled surface has a surface texture with the grains oriented along the direction of rolling and sometimes small grooves or scratches along this direction. The surface then acts as a grating; light is only scattered in

100

i

i

Rtot

Rolled lllumlnlum

i

0=80 °

~

8o

0=0"

w

z°eO .

~ 40

0=0 ° 0=80 °

w

2O

0 0.25

015

~ WAVELENGTH

(,urn)

Fig. 6. Total, diffuse and specular reflectance spectra for a rolled aluminium surface for two different orientations of the sample.

85

(a)

Fig. 7. Schematic picture of the illumination of the sphere wall for the two situations in fig. 6.

directions perpendicular to the direction of rolling. This means that light reflected from the rolled aluminium sample illuminates the sphere wall opposite the sample port according to the configuration depicted in fig. 7. For 19--0 ° a large proportion of the scattered light escapes out of the two entrance ports 1 and 2, while for the 80 ° orientation all of this light is contained inside the sphere and contributes to the detector signal. The specular signal is independent of the sample orientation since the same amount of radiation hits the specular exit port in all cases. A more detailed description of this effect can be found elsewhere [8]. Since 19 = 80° is the better choice this orientation is used in fig. 8 to demonstrate how the parameter B affects the reflectance spectra. It can be seen that the difference between the choices B = 0 and B = 1 is quite considerable, especially in the infrared part of the spectrum. The B = 0 and B = 1 curves are only shown for the total spectra. The diffuse spectra will differ in exactly the same way as the total, while the specular spectra are identical for all values of B. Looking at the total spectra in detail it is clear that in the infrared part we can see a characteristic structure, which originates from the BaSO 4 coating of the sphere. In particular the dip in the B -- 1 curve at A = 2 ~ m is easy to recognize. Eq. (23) reduces to R d = R B S 3 / / S I in the limit B = 1. This overcorrects for the BaSO 4 reflectance R B and hence we get the

100 --

~ ao .1 <

i

~

O=~ e

i

i

Rolled alumln|um .

~

...-B:0 B.0.4 Bml

R~

0

~ 40 L

RePe~ j

2O

J 0

0.25

01.5 WAVELENGTH

(~m)

Fig. 8. Total diffuse and specular reflectance spectra for a rolled aluminium surface for different values of parameter B.

86

A. Roos / Use o f an integrating sphere in solar energy research

Table 1 Calculated solar parameters and model parameters for the reflector surfaces Sample

0

B

Fs

Rsol

Rvi s

Rolled aluminium

0 80

0.5 0.5

1 1

57.6 70.4

53.3 65.6

6

80 80 80

0 1 0.4

1 1 1

71.5 69.3 70.6

66.4 64.8 65.7

7

80 0

0.4 0.4

1 0.6

70.6 70.2

65.7 65.4

8

-

0 0

0.7 1

1

1

85.5 63.3 61.8

10

-

86.9 64.4 62.1

-

-

-

87.4

86.1

-

Anodized AI hammered

Anodized AI smooth

Cf. fig.

dip in the reflectance curve. For B = 0, on the other hand, eq. (23) reduces to and no correction for the sphere coating is made. In this situation the dip becomes a small peak and the reflectance curve tends to increase too rapidly with wavelength. For the value of B = 0.4 the reflectance curves do not show this influence of the BaSO 4 coating. This indicates that in this particular case we have a way of estimating the parameter B and in this way obtain more reliable reflectance values of the sample. If the sample itself has absorption bands in the near infrared this becomes more difficult. In table 1 we can see how the integrated solar parameters Rso ~ and Rvis are affected by sample orientation and choice of parameter B. The disastrous result for O = 0 ° in fig. 6 can be improved by a correct choice of the factor F~ in eq. (23). This factor gives the fraction of Rdl which is contained in the sphere. Going back to fig. 7 it is possible to estimate this factor by considering the port sizes and the distribution of the reflected component Rdl. For a sample with a distribution according to fig. 7 F~ = 0.6 is a reasonable estimate and the reflectance curves for this choice are shown in fig. 9. The agreement between this and the case with O = 80 ° and B = 0.4 is now quite good, especially the solar parameters in table 1. The reason why the curves for the two cases intercept is probably due to the fact that the scattering from a rough surface is usually wavelength dependent and in this case this would lead to a distribution of the scattered light which varies with the wavelength. The F s factor then becomes wavelength dependent. This difficulty is not treated in this paper. The reflectance spectra of a surface with a different character are shown in fig. 10. This sample is an anodized aluminium sample with a hammered surface. The typical lateral size of the surface irregularities is in the range 5-10 mm and the vertical around 1 mm. Apart from this large scale surface structure the surface is very smooth and mirror like. This type of sample is difficult to measure accurately

R d = F S 3 / F s S 1,

A. Roos / Use of an integrating sphere in solar energy research i

100

!

87

i

e . I m O ; l l . 0A ; VI. I

Rolled m l u m l n l u m

~ 80 Railf

i~. 40 Ik tU

20

;

o..

WAVELENGTH

"

(,urn)

•

Fig. 9. Total diffuse and specular reflectance spectra for two different sample orientations and values of parameter F s. i

100

i

i RIn

80 la

~ "-"'"~"-'~.. -~'v%p~ ,,,, , , - ~v,%-/~o~/

=°co

~v~-,t,i

< I,,0

.,__.~ . . . . .

---.,...,.-

lldm

~ -~'~'-'~,,.-.,,,x.,Vv~,,.,,r.~

~ 4o E

Anodized Jumlnlum

- h a m m e r e d sun'ace

20 o

Bx0;

Fs = 0.7

B.0;

Fl=l

I

o. 5

o'.E

2 WAVELENGTH

,

(`urn)

Fig. 10. Total and diffuse reflectance spectra for an anodized aluminium surface with large scale surface irregularities and two different values of parameter F s.

and practically all of the scattering is confined to a small solid angle around the specular beam. This means we can set B = 0 in eq. (23). Assuming that all the scattered radiation, R d = Rdl, hits the sphere wall within the shadowed area in fig. 11 we can again estimate the F, factor for this component. This gives F s = 0.7 in this case. The total reflectance curve for Fs = 0.7 in fig. 10 is what we should expect

Fig. 11. Schematic picture of the illumination of the sphere wall for the anodized sample in fig. 10.

88

A. Roos / Use of an integrating sphere in solar energy research I

100

I

I

C u O ] S t a i n l e s s steel

~ 8O

R tot

0=0° ~=T/.5% ~

6o

Z

0 = 7 0 ° (x=75.8 %

t--

~

LI.40 2O

R eltff

o.2s

I

o15

1

4

WAVELENGTH

(,urn)

Fig. 12. Total and diffuse reflectance spectra for a solar absorber surface. Sample orientation and a-values as indicated. for this type of surface. This is verified by measuring the same type of anodized sample with a macroscopically fiat surface. The solar parameters in table 1 for such a sample compare well with the case F s = 0 . 7 for the hammered surface. 4.2. Absorber surfaces

The same considerations as in the previous section have to be made when studying absorber surfaces. The sample orientation and the distribution of the scattered radiation affects the result in a similar way. In fig. 12 the influence of the sample orientation for copper oxide on stainless steel is demonstrated. In this case the ~9 = 0 ° position is incorrect and leads to a a-value which is too high. The diffuse component is in this case very small. In fig. 13 the B-factor is varied for a sample with a very rough surface. The reflectance is totally diffuse with R d = R t. In fig. 14, finally, it is shown how a combination of sample orientation and scattering distribution can lead to serious errors in the reflectance spectrum and

i

100

t

C u O / S t a l n l e l m eteet ; matt velvet s u r f a c e .~80

B=I

; az, 80.9 %

B=0

; (x=79.7%

uJ

zUeo

i

i

.j~/"

4o!

0.25

01.5

i 1

WAVELENGTH

i 2

4

(,~m)

Fig. 13. Total reflectance spectra for a solar absorber surface for the two extreme values of parameter B. a-values as indicated.

89

A. Roos / Use of an integrating sphere in solar energy research --'

100

i

i

i

Pigmented snodlxed slumlnlum

~80 v

~6o

.......

e:80

; B:0

; rt182.6%

Ou0

; B:I

; a:86.0%

Z ,< I--

~ 4o i, w E

2O I

0.25

O15

I

1 WAVELENGTH

2 (~um)

Fig. 14. Total reflectance spectra for a solar absorber surface for two orientations of the sample and two values of p a r a m e t e r B. a-values as indicated.

hence in the integrated solar absorption a. In table 2 the integrated solar parameters RsoI = 1 - a and R~s are given for the samples from figs. 12-14. Owing to the lower reflectance values of the absorber surfaces the relative errors are less important for the evalueation of a -- 1 - R. Nevertheless, variations in the a-value of the order of several percent are obtained for different sample alignment and detector signal interpretation.

4.3. Transmission In many applications of solar energy it is c o m m o n to use various plastic films as convection barriers and glass or plastic panes as covers on solar absorbes and solar cells. These need to h a v e high transmission for solar radiation and they can be either clear or diffuse. In buildings windows can be used for daylighting purposes or passive solar heating. In both these cases they do not need to give clear vision and the materials used can therefore be more or less scattering. It is in all these cases necessary to be able to accurately measure both the specular and diffuse components of the transmittance and to use these data in calculations of solar parameters, efficiency, etc. Transmittance measurement on an integrating sphere

Table 2 Calculated solar parameters and model parameters for the absorber surfaces Sample

0

B

Fs

Rsol

Rvls

Cf. fig.

CuO/SS

0 70 °

0.5 0.5

1 1

22.5 24.2

16.2 18.2

12

CuO/SS

-

0 1

1 1

20.3 19.1

16.2 15.5

13

80 0

0 1

1 1

17.4 14.0

16.4 12.6

14

Pigmented anodized AI

90

A. Roos / Use of an integrating sphere in solar energy research 100

i

I

i

._

i

---_-:~

....

~80

TIot

,(

E

|40

-

<

B ~ 0 , 6 6 ;Taoi=81.4%

-

. . . . . .

B=I

; T~ol = 7 9 . 2 %

2O J

o 0.25

I

01.5

I

1

2

WAVELENGTH

"-4

(,~m)

Fig. 15. Total and specular transmittance spectra for a diffusely transmitting plastic film for different values of parameter B in the BaSO 4 mode. T~ol values as indicated.

is straightforward and causes no problems when the samples are perfectly specular, such as clear or vacuum coated float glass. For diffuse or partly diffuse samples the detector signal depends on the distribution of the scattered light in the same way as for reflectance measurements. For such samples the resulting error in transmittance values can be considerable. In fig. 15 the total and specular transmittance spectra for a highly diffuse plastic film are shown for three different values of the parameter B in the BaSO 4 mode. As in the reflectance mode the specular transmittance is independent of B. In this case the variation is far from negligible and the error in T~ot is several percent for an incorrect choice of B. The same sample measured in the Al mode with an aluminium mirror covering port 3 gives an even stronger variation with the parameters B1, B 2 and B a as can be seen in fig. 16. It may at first seem impossible to determine the B-factors but from the definition of B1 we can see that this component is equal to the difference between the specular components as measured in the two transmittance modes, and can therefore be determined experimentally (cf. figs. 4 and 5). Doing this gives the

100

~80 z 60 = 4o m

<~

T am

2O 8 =l;B

0.25

OI5

sT;O

1 - f

sl I

1 WAVELENGTH

i

2 ().Ira)

Fig. 16. Total specular and diffuse transmittance spectra recorded in the Al mode for the same diffusely transmitting sample as in fig. 15. Parameter values as indicated.

91

A. Roos / Use of an integrating sphere in solar energy research

Table 3 Calculated solar parameters and model parameters for the transmitting samples Sample

B

B1

Diffuse plastic film

0 0.66 1

. . .

-

1 0 0

0 1 0

0 0 1

0.1

0.3

Plastic pan e

0.16 -

. 0.7

B2 . . .

.

FM

B3 . . .

. . .

. 0.25

TsoI

Tvis

Cf. fig.

85.1 81.4 79.2

84.3 81.0 79.0

15

0.9 0.9 0.9

100.5 82.8 76.5

101.4 82.2 76.8

16

0.6

0.8

81.0

81.0

-

0.85

79.4 79.4

87.4 87.3

17

0.05

.

anticipated result that the factor B 1 is very small and that the homogeneously scattered fraction B 3 is the dominating contribution. The factor FM, which only affects the B~ component, is then of little importance. A strictly geometrical calculation from the dimensions of the ports and the sphere together with possible scattering angles for the component Td3, gives a value of F M = 0.8 in this case. Hence, choosing B~ = 0.1, B 2 = 0.3 and B 3 = 0.6 gives a total transmittance spectrum, which nearly completely coincides with the spectrum for the value of B = 0.66 in the BaSO4 mode in fig. 15. In table 3 the solar parameters are given for the different sets of parameters in figs. 15 and 16. It can be dearly seen that an incorrect interpretation of the signal output from the integrating sphere leads to serious errors for a highly diffuse transmitting sample. In fig. 17 the transmittance spectra for another type of sample are shown for both the BaSO 4 and the Al modes. In this case the sample is a plastic pane of 3 mm thickness and only moderately scattering. Moreover, most of the scattered radiation is found at small angles close to the specular beam. As can be seen in the

100 - -

'

'

D

N,k

~60

,An

411

0.25

0.5

1 WAVELENGTH

2 (,urn)

4

Fig. 17. Total specular and diffuse transmittance spectra for a 3 m m thick plastic pane. Parameters in

the BaSO4-and A1modes as indicated.

Fig. 18. Photograph of the interior of the sphere taken through the reference port No. 4 and with an aluminium mirror covering port 3. (a) Moderate scattering plastic pane at port 2. (b) Highly scattering plastic film at port 2.

¢

A. Roos / Use of an integrating sphere in solar energy research

93

figure the total transmittance spectra for the given choice of parameter values are identical for the two modes of operation, while there is a dramatic difference in the diffuse and specular spectra. This is expected, since the two modes of operation define the specular, and therefore also the diffuse, components differently. This is evident from figs. 4 and 5 where it can be seen that the specular component in the BaSO4 mode consists of the two components Tspec+ Tdl in fig. 1. There is no contradiction in this result since what is specular and what is diffuse always depend on the particular instruments used, and also, as in this case, on the mode of operation. It should be pointed out here that, depending on this difference, even though the right hand side of eqs. (25) and (28) are identical, Tsb and T~ are not the same. The total component, however, is strictly a property of the sample and must be the same independent of the instrument used and the mode of operation. This is also the obtained result for both the highly and moderately scattering samples in figs. 15-17. Looking at the results summarized in table 3, we can also see that there is a simple relation between the factor B in the BaSO 4 mode and the factors B 2 and B 3 in the AI mode. This is also obvious from how these factors are defined. In the A1 mode the scattered component is Tdl + Tdz + Td3, while in the BaSO 4 mode the diffuse detector signal only originates from Td2 + Td3. B is thus given by B = B3//(B 2 + B3).

(31)

Finally in fig 18, a photograph of the interior of the sphere is shown with the two transmitting samples on the entrance port of the sphere. We can see the two entrance ports 1 and 2 on either side of the specular exit port No. 5 (cf. fig. 2). The photographs are taken through port No. 4 with an Al mirror on port 3. It is clearly seen that for the moderately scattering plastic pane most of the scattered light hits the sphere wall in the vicinity of the specular exit port while the diffuse film gives a very even distribution of the scattered light. This is consistent with the chosen parameter values in table 3.

5. Conclusions

It has been shown that correct sample alignment and interpretation of the signal output when using integrating spheres are of crucial importance for a correct result. Serious errors in the solar parameters will be present unless these factors are properly taken into consideration. Three models for the interpretation of the signal output are presented for reflectance and transmittance measurements. These models make a distinction between scattered radiation into different solid angles within the sphere, and the total, specular and diffuse components of transmitted or reflected radiation are calculated from the signals obtained from the instrument. The difference between the two transmittance modes can be used to obtain information about the scattering distribution of the sample, and make a correct interpretation possible. For samples with a macroscopic surface structure the error can amount to 10-30% in the reflectance value, and neglecting the

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A. Roos / Use of an integrating sphere in solar energy research

angular distribution of scattered radiation leads to errors in the order of several percent. The models presented provide a simple way of reducing these errors and of obtaining a correct distinction between the diffuse and specular components. These are important considerations in solar energy research where the integrated values of transmission, reflection or absorption of solar radiation need to be known accurately. In a solar absorber with one cover glass and one convection barrier the solar parameters for these two units plus the absorber need to be known. An error of only one percent in each of these can add to three percent for the direct optical efficiency of the absorber unit. In a complete solar heating plant this will lead to an error in the calculated annual efficiency of as much as 6-9%. The discrepancies between results obtained at different laboratories at various round robin tests are to a large extent likely to be due to the effects described in this paper.

Acknowledgement This work has been sponsored by the Swedish Council for Building Research.

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