I 

DETERMINING THE OPTICAL 

QUALITY OF FOCUSING COLLECTORS 

WITHOUT LASER RAY TRACING 

Solar Energy Research Institute 

1536 Cole Boulevard 

Golden, Colorado 80401 

A Division of Midwest Research Institute 

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Contract No. EG.77.C.01.4042 
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NOTICE 

This report was prepared as an account of work sponsored by the United States Government. Neither the United States nor the United States Department of Energy, nor any of 

their employees, nor any of their contractors, subcontractors, or their employees, makes 

any warranty, express or implied, or assumes any legal liability or responsibility for the 

accuracy, completeness or usefulness of any information, apparatus, product or process 

disclosed, or represents that its use would not infringe privately owned rights. 
FOREWORD 

A preliminary version of this report (How to Ideasure the Optical 

Quality of Focussing Solar Collectors Without Laser Ray Tracing; 

SERI/TT-~~-~~~) was presented at the 1979 Silver Jubilee International Congress of the International Solar Energy Society in Joint 

Meeting with the American Section of the International Solar Energy Society, Inc., May 28 through June 1, 1979 in Atlanta, Georgia. 

The authors thank F. Biggs and his colleagues at Sandia Laboratories for a careful review of this report. 

Frank Kreith 

Branch Chief 

Thermal Conversion Branch 

Approved for: 

SOLAR EmRGY 

7 

RESEARCH INSTITUTE 

iii 
This paper describes a novel alternative to the laser ray trace 

technique for evaluating the optical quality of focusing solar 

collectors. The new method does not require any equipment beyond 

that which is used for measuring collector efficiency; it could 

therefore become part of routine collector testing. The total optical errors resulting from imperfect specularity and from inaccuracies in reflector position or slope are characterized by an angular standard deviation floptical, the rms deviation of the reflected rays from the design direction. The method is based on 

the fact that the off-axis performance of a concentrator depends 

on Goptical. An angular scan is performed; i.e., the collector 

output is measured as a function of misalignment angle over the 

entire range of angles for which there is measurable output (typically a few degrzes). This test should be carried out on a very 

clear day, with the receiver close to ambient temperature (if the 

latter condition cannot be satisfied, appropriate corrections are 

necessary). The parameter ooptical is then determined by a leastsquares fit between the measured and the calculated angular 

scan. We tested the method on a parabolic trough collector manufactured by Hexcel, but it is suitable for parabolic dishes as 

well. 
TABLE OF COKTENTS 

Page 

Nomenclature ............................................................. ix 

1.0 Introduction ........................................................ 1 

2.0 Theory .............................................................. 3 

3.0 Experiment* ......... .......................................... 11 

4.0 Conclusions ......................................................... 15 

References ............................................................... 17 

vii 
S1PI TR-359 

LIST OF TABLES 

Page 

2-1 Coefficients of Angular Acceptance Function for a Parabolic 

Dish with Flat Receiver............,................................ 5 

LIST OF FIGURES 

Page 

2-1 Intercept Factor vs. Misalignment Angle for aoptical = 0, 5, 

and 10 mrad....................................................... 10 

3-1 Test Data of Optical Efficiency vs. Nisalignment Angle.. ............ 10 
NOMENCLATURE 

Effective source obtained as convolution of Bsu, with error 

distribution 

Bsun, radial(6) Angular brightness distribution of the sun for point focus 

geometry (w/rn2 sterad) 

asun,linear[ gl) Angular brightness distribution of the sun for line focus 

geometry (w/n2 rad) 

Geometric concentration ratio (for example, a trough of 

aperture width D and receiver tube diameter d has C = ~/nd) 

f(O) Angular acceptance function 

Beam irradiance as measured by pyrheliometer (lJ/rn2), aiso 

called direct insolation 

a Absorptance of receiver 

Intercept factor if collector is misaligned, that is, with 

its optical axis pointing an angle 8, away from the sun 

rl qnet /Ib = collector efficiency 

rlo Optical efficiency = (p ~a)y 

Projection of incidence angle on plane perpendicular to 

tracking axis 

Projection of incidence angle on plane of tracking axis and 

optical axis 

Misalignment angle = angle from center of sun to axis or 

plane of symmetry of collector 

Xeflectance of reflector 

Effective reflectance-transmittance-absorptance product of 

collector 

'contour mas angular deviation of contour from design direction 

'displacement Equivalent rms angular spread that accounts for imperfect 

placement of receiver relative to reflector 

c specular rms spread of reflected beam due to imperfect specularity 

of reflector material 

'optical rms angular spread caused by all optical errors 

0 rns angular width of sun in line focus geometry sun 

'tracking rms angular tracking error 

0 Total rms bean spread 

T Transmittance of collector glazing, if any 

4) Rim angle 
SECTION 1.0 

INTRODUCTION 

Evaluation of the optical quality of a solar concentrator is important: to 

the designer, to tell him whether a collector needs improvement; and to the 

manufacturer, to ensure proper quality control. In addition to the optical 

efficiency no, it is important to have a measure of optical errors and of 

losses due to reflected radiation missing the receiver. The methods that are 

available or have been proposed for measuring the contour accuracy of solar 

concentrators require either laser ray tracing or flux mapping at the receiver 

surface. Both approaches can provide accurate results, but the equipment is 

specialized and expensive and demands a good deal of time and/or 

expertise [l,2]. 

The question arises, therefore, whether the instantaneous efficiency neasurements that are performed as part of a standardized performance evaluation [3] 

could somehow be used to determine croptical the rms angular beam spread caused 

by optical imperfections. This paper shows that this can indeed be accomplished by misaligning the collector slightly away from the sun and measuring the efficiency for several values of the misalignment angle. The optical 

error ooptical is then extracted by finding the theoretical curve that best 

fits these misalignment data. Thus, the determination of Oopticalr could become part of the standard test procedures for concentrating solar colleccors. In a sense, this method employs the receiver itself as flux mapper. 

Compared to conventional flux mapping with point-like detectors, the present 

method is much simpler experimentally. The method is suitable for both photovoltaic and thermal collectors. * 

The theory underlying this technique is described in Section 2.0. Section 3.0 

presents the test results for a parabolic trough collector with cylindrical 

receiver, manufactured by Hexeel. The data obtained with this collector indicate that the reproducibility of this method is good (on the order of 25%). 

Unfortunately, a laser ray trace apparatus was not available for an 

independent determination of o optical. 

*In some photovoltaics concentrators, the reflector is designed for uniformity 

of flux distribution and is not a parabola. The method is still applicable, 

but the angular acceptance function f(8) in Eq. 2-9 would have to be recalculated for the data analysis. 

SECTION 2.0 

Since the theory of focusiEg solar collectors has been described elsewhere 

[4,5], a brief summary suffices at this point. The crucial concepts are the 

angular acceptance function and the intercept factor. The angular acceptance 

function f(8) is defined as that fraction of a uniform beam of parallel rays 

incident on the aperture at an angle 8 from the symmetry axis that reaches the 

receiver if the optics are perfect; f(8) accounts for off-axis aberrations. 

Eqs. 2-1 and 2-2 list the angular acceptance function for parabolic trough and 

dish reflectors with round and with flat receivers. The rim angle is Q and 

the geometric concentration ratio C, defined as the ratio of the aperture area 

to the absorber surface areaFor a parabolic trough with cylindical receiver, the angular acceptance function is 

for 01 < 101 < 92 

oforlel>e2 . 

where 

sin Q el = - TTC 

2 tan (4/2) 

TC 

For a parabolic dish with spherical receiver, the angular acceptance function 

is the square of Eq. 2-la, with the replacement of nC by ~Jc: 

10 for e2 < -, 
with 

sin (6 61 = -

2Jc 

and 

- 62 - 

2 tan ($12) 

2Jc 

For a parabolic trough with flat one-sided receiver, f( 6) is given by 

(1 for 161 < 61 , 

1 / 2 

mt + 

ftrough, flat = 

for el < 8 < 82 

0 for 62 < 161 , (2-2a) 

-- 

tan 3 t:nL'] 

0 C 

with 

sin cp cos 4 611 C 

and 

2 G2 = - 4 

C tan - 2 ' 

For a parabolic dish with flat one-sided receiver, the exact expression for 

the angular acceptance function is more complicated. For practical applications, however, the following polynomial fit is acceptable: 

(0 for vz < eJc . 

The coefficients a, by c, vl, and v2 depend on rim angle and are tabulated in 

Tabl~ 2-la; a more accurate four-tsrm expansion with an additional term 

d(~0")~ is given in Table 2-lb. Iinplicit iil Eq. 2-1 and 2-2, and throughout 

this paper, is the assumption that the concentration is high enough (C >, 10 

for line-focus and C >, 100 for point-focus concentrator) to permit the approximation of sin 6 by 0. 
Table 2-1. COEFFICIENTS OF AHGULLVI ACCEPTANCE FUNCTION FOR A PARABOLIC DISH 

NITH FLAT RECEIVEX: THUS-PAmlETEK FIT (a), FOUR-PXA?lETER FIT (b) 

-- - 

(a) 9 

[degrees] a b c "1 v2 

(b) 0 

[degrees] a b c d v1 
The intercept factor y(em) is that fraction of rays from the sun that reaches 

the receiver of a collector with real optical errors when the optical axis is 

misaligned by an angle 9, from the center of the sun. The intercept factor is 

the convolution of the normalized angular brightness distribution of the sun, 

the distribution of optical errors, and the angular acceptance function for 

perfect optics. 

The brightness distribution of the sun has been measured by the Lawrence 

Berkeley Laboratory circumsolar telescope as brightness BSun, radial(9) in 

w/m2 steradians at an angle 8 from the center of the solar disk. To yield the 

dimensionless intercept factor, Bsun must be normalized by the beam 

irradiance: 

(The upper integration limit corresponds to the acceptance half-angle of the 

pyrheliometer, the instrument which is customarily used for measuring the socalled direct or beam insolation.) For line focus collectors it is convenient to transform to the linear brightness distribution (in v/D?): 

where is the angular coordinate in the plane normal to the focal line 

and el, che angular coordinate parallel to the focal line. 

To standardize the tests described in this paper, it is advisable to take data 

only when the sky is very clear. The rms width of the sun under such conditions is 

usun, linear = 2 -6 f 0.1 mrad (2 -5a) 

for line focus collectors, and 

as,,, = 3.5 f 0.1 mrad (2-5b) 

for point focus collectors. The variation of the brightness distribution between clear days (ratio of circumsolar over beam irradiance less than one percent) is sufficiently small that the analysis of the misalignment data can be 

based on the standard scan in Table 4-1 of Ref. [6] if a circumsolar telescope 

is not available. 

In a solar concentrator, several statistically independent factors contribute 

to the optical error: contour errors, lack of perfect specularity [7], tracking errors (when averaged over time), and deformation and displacement of the 

receiver. 
Each error type can be characterized by its rms angular width (one-sided deviation from the design direction). The dispersion aoptical for the total 

optical error is obtained by adding the squares of the individual dispersions: 

('contour is multiplied by two because of Snell's law; in Fresnel reflectors, 

'tracking must also be multiplied by two.) 

Note that this rule for combining standard deviations is valid regardless of 

the shape of the individual error distributions; they could be Gaussian, boxlike, or anything else, since all distributions under discussion have zero 

mean. The total beam width a is obtained by adding the rms width of the sun 

according to 

14easurements of reflector surfaces [I] have shown that the distributions torresponding to ocontour and Ospecular can be treated as Gaussian. The other 

terms nay or may not be Gaussian.* However, when many statistically independent distributions are convoluted, the result is nearly Gaussian unless a 

single non-Gaussian contribution dominates [$I. In the case of focusing solar 

collectors, the Gaussian contour errors appear to be the largest, and a Gaussian approximation for the total optical error is reasonable; this is assumed 

for the rest of the paper. 

The order of carrying out the convolution of angular acceptance function, 

solar brightness, and optical errors is immaterial. Let us first convolute 

the solar brightness distribution with a Gaussian distribution of optical errors to obtain the so-called effective source. For line focus geometry, the 

effective source depends only on 9 L. 

*Receiver displacements nay be parallel or perpendicular to the aperture (or 

some combination), and the corresponding error distribution will in general 

not be Gaussian for a single collector module. Averaged over a large array of 

collectors, a Gaussian approximation for the displacement error distribution 

is likely, however, to be quite good. 
The point focus case requires two-2imensional con-~olytions, and it is convenient to write the angles as two-dimensional vactors 8. Because of azimuthal 

symeJry, the effective source for point focus collectors depends only on 

e = 161. 

Finally, the. intercept factor as a function of misalignment angle Om is obtained as a convolution of effective source and angular acceptance fun? 

tions. For line focus collectors, 6 is measured in the plane normal to the 

rp focal line, and the intercept factor 1s 

(If the incidence angle along the trough is nonzero, for example in a collector with an east-west tracking axis at times other than solar noon, 8, is the 

projection of the incidence angle on the plane normal to the tracking axis.) 

For point focus coll.ctors with azimuthal symmetry, the intercept factor depends only on 3, = le,], the angle between the center 02 the sun and the symmetry axis of the collector: 

In a real point focus collector, axial symmetry may be violated by gravity induced deformations and by manufacturing defects. To test for such a possibility, the angular scan should be performed in different aziauthal directions. 

For parabolic reflectors, flinear and fradial are given in Eqs. 2-1 and 2-2; 

for other linear concentrator-types, they can be calculated by the method described in Refs. 4 and 5. 

A convenient approximation is permitted if the optical errors are sufficiently 

large. If under clear sky conditions "Optical is larger than 5 mrad for line 

focus and 10 mrad for point focus collectors, the intercept factor is quite 

insensitive to details of the sun shape and the effective source can be replaced by a Gaussian distribution [2,4]. Since this is the case for the cur 

rent generation of parabolic trough collectors [I], we have made this approximation for the data analysis in this paper; in other words, we have calculated 

the intercept factor according to 

2 2 

exp ( - e1 /2a ) 

Ycrough, ~auss($m) = del f trough( aa-el) 5 & 9 

with the total width a of Eq. 2-7. 8 
Figure 2-1 shows schematically what the angular scan looks like for a parabolic trough with cylindrical receiver, rim angle @ = 90°, and concentration 

ratio C = 25, for three values of the optical error: 0, 5, and 10 mrad. For 

this example, (prcr) was assumed to be one; hence, the intercept factor equals 

the optical efficiency. From these curves, one sees that this test is raost 

sensitive to data taken around the curved portion of the graph; data 

corresponding to the halfway point, on the other hand, do not provide any 

information on ooptical. 

Due to reflection and absorption losses, the radiation incident on the collector is attenuated by a factor (pra) , where 

p = solar reflectance of reflector; 

r = solar transmittance of receiver glazing, if any; and 

a = solar absorptance of absorber. 

(The parentheses indicate that the factor is an effective transrni ttancereflectance-absorptance product, including secondary effects such as multiple 

reflections [9].) When the absorber surface is at ambient temperature, the 

heat loss is zero and the efficiency TI equals the optical efficiency: 

If the heat loss is not zero, an appropriate correction must be applied. 

Variation of (PTO) with is sufficiently small to be negligible for the present purpose. 

Since y(0 ) depends on ooptical, it is clear that an angular scan 

m of r1(8 ) versus 0, contaiils enough information to determine both (pra) and 

rn ooptical, at least in principle. 
19 

0 .5 1 1.5 2 2.5 

MISALIGNMENT ANGLE (DEGREES) 

Figure 2-1. Intercept Factor vs. Misalignment 

Angle for ooptical = 0,5, and 10 

mrad 

@ positive angles 1 

angles 

MISALIGNMENT ANGL-E (DEGREES) 

Figure 3-1. Test Data of Optical Efficiency 

vs. Misalignment Angle (Best Fit) 
SECTION 3.0 

EXPERIMENT 

In order to determine whether this method is accurate enough to be useful in 

practice, we decided to test a parabolic trough collector manufactured by 

Hexcel [lo]. The test setup is described in another publication [Ill. The 

collector has a cylindrical receiver coated with black chrome. The heat 

shield and receiver glazing originally supplied by Hexcel were removed for 

this test, so (p~a) is simply pa. The reflector is made of an aluminum honeycomb substrate, coated with FEK-163, an aluminized second-surface acrylic film 

manufactured by the 3M Company. The rim angle of the collector is = 72', 

and the geometric concentration ratio is C = 20-9. The tracking axis is horizontal in the east-west direction, and the tests were carried out at solar 

noon, so that the longitudinal incidence angle 0 vanishes. The collector 

time constant was less than one minute, sufficient!ly short to perform an entire angular scan in half an hour. (If the time constant is much longer, a 

rotating test stand may be desirable.) 

Inspection of the Hexcel collector after reassembly at SERI revealed that a 

significant amount of radiation missed the receiver. This suggested the possibility that receiver placement away from the design focal length of 0.915 m 

(36 in.) might improve the performance. We therefore set the receiver at sev- / 

era1 different distances from the reflector apex and each time visually realigned the two reflector halves (which are hinged at the apex) to maximize 

the intercept of radiation. We facilitated this visual reflector alignment by 

covering one reflector half while working on the other. By this procedure, we 

found that the thermal collector efficiency was maximized for a receiver 

placement slightly (1.25 cm) further away from the apex than the design focal 

length. All subsequent tests were carried out with the receiver in this new 

position. 

h typical scan of n,(9,) versus (0,) is shown in Fig. 3-1. Positive and negative values of 0, have been included on the same side because of symmetry. 

Plotting +Om and -8, together has the advantage of pointing out any systematic 

error in the zero alignment. A nonlinear least-squares fit to these data 

yields the values 

and 

F'pa = 0.690 

a = 6.5 mrad . 

In the test procedure, inlet and outlet temperatures of the fluid were measured and only the product Ftrlo of heat extraction efficiency (zlso called 

collector efficiency factor [9]) and optical efficiency could be determined. 

The theoretical scan corresponding to these parameters .is shown by the solid 

line in Fig, 3-1. To evaluate the accuracy of this method, the scan was repeated several times, and F'pa and o were calculated for each scan. The results are: 
F'pa a (mrad) (3-3 

0.691 6.4 

0.658 6.1 

0.685 6.8 

0.690 6.5 

0.708 6.1 

- 

mean 0.686 6.4 

The sample standard deviation for these five a measurements is 0.3 mrad, and 

indicates that the reproducibility of this method is about 5%. 

Lacking a reflectometer, we could not measure p and a seperately. Published 

values for clean materials suggest p 0.85 and a 0.95. F' is calculated to 

be close to unity and certainly larger than 0.95 (in fact, it did not change 

noticeably when spirals were inserted within the receiver to increase the turbulence). Hence, we would have expected F'pa values greater than 0.77. T'ne 

low measured values may be because of materials degradation (for example, the 

reflector was visibly scratched), but the issue remains unresolved without 

further data. 

In these tests, the misalignment angle was monitored quite accurately, hence 

the tracking error does not contribute significantly to the beLm spread and 

Assuming an rms width of 2.6 mrad for the sun, 'one therefore obtains from 

Eq. 2-3 the optical error 

aoptical = (6.5' - 2.62)1'2 mrad 

= 6.0 * 0.3 mrad 

for this experiment. 

Unfortunately, we did not have a laser ray trace apparatus for an independent 

evaluation of the optical error. Measurements of Uspecular and Ucontour have 

been reported by Sandia Laboratories for reflectors also manufactured by 

Hexcel of a sinilar type but different focal length [1,12, and a cornnunicaticn 

with R. B. Pettit]. The contour errcr ranged from 1.8 mrad, before environmental exposure, to 2.2 mrad, after three months in an environmental test 

chamber, and aspecular was on the order of 1 mrad. However, the values of 

uspecular and aContour depend very much on how the FEK-163 film is bonded to 

the substrate. 
- If these values of Ocontour and ~~~~~~l~~ were applicable to the Hexcel collector tested at SERI, they would imply that the contribution odisplacement, 

caused by displacement of the rec~iver and deformations of the parabola, is 

fairly large, on the order of 4 nrad. Visual inspection of the solar image at 

the receiver shows that the reflector is deformed; its curvature tends to be 

less than the design shape either because of the manufacturing process or because of weight-induced sag. A value of 4 mrad for the associated beam spread 

may be realistic. In view of the difficulty of measuring gdisplacement directly, and in view of the lack of laser ray trace data for the collector 

tested at SERI, one can invoke the Sandia data only for a qualitative comparison. To this extent, our results are certainly consistent with the Sandia 

data, but further work is needed to evaluate the accuracy of the method 

described in this paper. 

SECTION 4 .g 

CONCLUSIONS 

We have shown that the optical quality of focusing solar collectors can be determined by measuring the performance over a range of misalignment angles, and 

then comparing the data with calculated results. The calculated results depend on the nns angular optical error Oopticalr and doptical can be found by 

means of a nonlinear least-squares fit between data and calculation. The 

method has been tested on a parabolic trough collector and found to have acceptable reproducibility (better than 5%). For point focus collectors, the 

angular scan can be carried out in several different aziauthal directions in 

order to provide infomation on, for example, gravity induced deformations . 

REFERENCES 

1. Butler, B. L.; Pettit, R. 13. "Optical Evaluation Techniques for Ref lecting Solar Concentrators," Society of Photo-optical Pnstruriientation Engineers (SPIE). Optics Applied to Solar Znergy Conversion: 

Vol. 114; p. 43; 1977. 

2. Siggs, F.; Vittitoe, C, N. The Helios Model for the Optical Behavior 

of Reflecting Solar Concentrators. Albuquerque, iiTivI: Sandia iabs, ; 

SAND 76-0354; tlarch 1979. 

3. krterican Society of 'rieating , Refrigerating and Air-Conditioning Engineers, Inc. ASHW Standard, iiIethod of Testing to Determine the Tilerma1 Performance of Solar Collectors. Hew York, LNY: XSHKAE; 1978. 

4. Bendt, P.; Rabl, A,; Gaul, H, W.; Reed, K. A. Optical Analysis and 

Optimization of Line Focus Solar Collectors. Golden, CO: Solar Energy 

Zesearch Institute; SEKI/TK-~~-~~~. September 1979. 

5. Bendt, P,; bbl, A. Optical Analysis of Point Focus Parabolic 

Radiation Concentrators. Go1 den, CU: Solar Energy Research Institute; 

TR-333-336. In preparation. 

6 kndt, I?. ; hbl, A. Effect of Circumsolar Radiation on Performance of 

Focusing Collectors. Golden, CO: Solar Energy Research Institute; 

SERI/Ti<-34-093; 1980. 

7. Pettit, R. Y. "Characterization of the Reflected Beam Profile of Solar 

$lirror Materials." Solar Energy. Vol, 19: p, 733; 1977. 

8. Cramst-, i-i. Mathematical Nethods of Statistics. Princeton, NJ: 

Princeton University Press; 1947. 

9. Duffie, J, A.; Beckman, W. A. Solar Energy Thernal Processes. New 

York, New York: John Wiley and Sons; 1976. 

10. Dudley, V, E.; CJorkhoven, K. M. Summary lieport: Concentrating Sofar 

Collector Test Results, Collector Module Test Facility. Albuquerque, 

1: Sandia Labs; SAND 78-0515; >lay 1978. 

11. Gaul, H. W. ; Rabl, A. "Incidence Angle Xodifier and Average Optical 

Efficiency of Parabolic Trough Collectors." ISES ~onf erence. )lay 

1379; Atlanta, Gh. SERI/TP-34-246, to be published in AS21E Journal %3f 

Solar Engineering. Vol. 1 (1980). 

12. Allred, LC, E. "Environmental Effects on Solar Reflector Structures," 

ISES Conference. Xay 1979; Atlanta, GA. To be published as a Sandia 

Labs report. 
1 Document Control 1' SEq4 &port "0 f 2'47s Accession No / 3 ;iec:clenr s Actess~on No. 1' 

I Page 1 rq-137-359 

1 P. Benlt. R. Gaul. A. 9abl 1 

1 :O ?r=jec~<ask/Wcrk Lnlr No 

I 

1 9 F?ncrm:n; Crcan~zat~cn Name inc Aaaress 1 

1 I 

1 Dezsrainicg the Optical Quality of Focusing Collectors 

Sclar Energy Research Institute 

1617 Cole Boulevard 

I Golden, CO 80001 

/ .: TI:!* anc S~cr~:ia j 5. ?uo~icar!cn ,>are 

1 

Task 43432.10 

11. Contrac: (C; or Granr !Gi NO. 

I Uithout Lassr Ray Tracing 1 d 

I I 

4 

Sconscr~ns Grgan~zat~on Name ana Aoaress Tv~e ar Reccn A ier~ca Saberel I 

I i Technical Report i 

I 

1 

I 

8-: 

, , Suc;tenen:a?j Notes 

I 

1s ios;rac:ti.m1r:2%worcs) This paper aescri'ses a novel alcernacive to the laser ray trace j 

cec3nique for evaluating the optic21 quality of focusing solar collectors. The new ' 

yethod does not reqilire any equipment beyond what is used For measuring collector I 

efficiency; Lt could therefore become part of routine collector testing. The total 1 

spiical errors resulting from iaperfect specularity and from inaccuracies in reflec- 1 

tor position or slope are characterized by an angular standard deviation G optical9 1 

the rT.s deviation of the reflected rays from the design direction. The method is I 

bassd on the fact that the off-axis perforaance of a concentrator depends on a I 

optica4' 

1-23 angxlar scan is zerforaed: i.e., c5e collsctor output is xeasured as a function 

- - LL xisalignxenc angle over the entire range of angles for which there is measurable 

out?ut (typically a few degrees). rhis test should be carried out on a very clear 

cay, xich receiver close to ambient tenFerature (if ihe latier condition cannot be 

stzisfied, appropriate corrections are r-ecessary). The parameter s is chen I optical 

,decerxined by a least-squares fLt betwsen the neasured and the calculated angular 

'scan. Ve tested the method on a parabolic trough collector nanufactured by Hescel, 

but it is suitable for parabolic dishes as well. The method appears to Se accurate 

'etough to deternine c- __, vithi2 about 10:;. I_- - ---- ,:~,men! Anat {~IS 

: 3. L--.-, -"--'CtorsCcncentrating Coiiectors ; Focusing Callectors ; ~leasurlng nethods ; 

1 / Efficiency 

1 ! 

I 

/ ?. ;de~i!fiersiC~erl-E?;aed Terms 

I 

, '5 I..~II~CIII!V S:ai?!?en: 

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i 15235 Torr Soya1 Xoad $4.50 

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