Method for more accurate transmittancemeasurements of low-angle scatteringsamples using an integrating sphere
with an entry port beam diffuser
Annica M. Nilsson,1,* Andreas Jonsson,1 Jacob C. Jonsson,2 and Arne Roos1
1Department of Engineering Sciences, Uppsala University, Box 534, SE-751 21 Uppsala, Sweden2Environmental Energy Technology Division, Lawrence Berkeley National Laboratory,
1 Cyclotron Road MS 25A-119, Berkeley, California 94720, USA
The light-scattering and diffusing properties of pat-terned glass make them suitable for daylightingapplications and to create architectural effects inbuildings. However, the light-scattering propertiesalso make patterned glass notoriously difficult tocharacterize even in cases when hemispherical infor-mation is sufficient. There are several contributingfactors to these hardships, but a fundamental pro-blem for all relative integrating sphere measure-
ments arises from the discrepancy between thereference signal and the sample signal. Given thatmost standard instruments employ relative mea-surement techniques, simple methods for improvedaccuracy are desirable.
In this paper, a method for more accurate trans-mittance measurements of patterned glass with low-angle scattering is proposed. Because of the forwardtransmitting properties of these samples, a large por-tion of the transmitted light hits the recessed edge ofthe reflectance sample port (i.e., specular transmit-tance exit port), resulting in a reduced signal. Theproposed measurement method uses a thin light dif-fusing material to reduce the discrepancy between
the reference and the sample signal. The light diffus-ing material has the additional effect that the trans-mitted light from the sample is scattered over alarger portion of the sphere wall, hence reducing theabsorption effect of the recessed port edge. The meth-od is developed for measurements at normal angle ofincidence, but a similar approach can in principlebe applied to measurements at oblique incidenceangles. However, very few standard instrumentsequipped with a specular transmittance exit portare designed to facilitate oblique angle of incidence.
Three samples are used to study the accuracy ofthe method and a model to account for multiple re-flections is proposed. The presented results are spe-cific for the instrument, a Perkin-Elmer Lambda 900spectrophotometer equipped with a 150mm Spectra-lon-coated integrating sphere from Labsphere, butthe method can be applied to any integrating spherespectrophotometer.
A. Background
Spectrophotometers with integrating sphere detec-tors are widely used to determine the hemisphericaltransmittance and reflectance of a sample. The inte-grating sphere theory has been covered in detailby several authors [1–3], and will not be reviewedfurther here. The basic principle, however, is the es-tablishment of radiation balance within the sphere,creating a true average light intensity monitored bythe detector. It is assumed that all light entering thesphere contributes equally to the detected signal. Toachieve this, the ideal integrating sphere geometryshould be perfectly symmetrical, portholes infinitelysmall, and the interior surface should be an ideal dif-fuse reflector. Naturally, ideal integrating spheresare impossible to attain in reality. The interior sur-face is never perfectly Lambertian, and the introduc-tion of ports, detectors, and baffles is inevitable. Anexcellent overview of the effect of various sources oferror is given by Clarke and Compton [4]. Althoughthe authors review errors occurring for hemispheri-cal reflectance measurements in particular, severalof the concepts presented can be applied to integrat-ing sphere measurements in general since many ofthe errors are associated to portholes, baffles, and de-tectors. These features are introduced to facilitate amultipurpose instrument, but also lead to deviationsfrom ideal integrating sphere properties. For specu-lar samples, the discrepancies generally do not poseserious problems, but for light-scattering samples,systematic measurement errors that are hard toquantify usually occur. Anomalies due to anisotropi-cally light-scattering samples have been reported inprevious studies. Roos et al. showed anomalies indetector response depending on the orientation ofa polished Cu plate with directional properties [5].Lindseth et al. reported similar findings in reflec-tance intensity variations for rolled and etched Alplates [6]. Analogous problems occur for transmit-tance measurements of light-scattering samples.Milburn and Hollands showed a strong dependency
between directional response error and transmit-tance distribution for conically transmitting andtranslucent samples [7]. The study emphasized theimportance of avoiding high light intensities scat-tered into the sphere at angles with large variationin directional response. To account for directionalproperties and light losses through portholes of inte-grating spheres, a simple model for nonideal trans-mitting samples was proposed by Roos [8]. Themodel is based on the separation of the diffuse partinto three different parts depending on scattering so-lid angles and is primarily intended for samples withwide angle scattering. Integrating sphere methodswhere the sample is mounted in the sphere have alsobeen proposed for characterization of imperfectlydiffuse samples. These methods are primarily usedfor reflectance [9] or for combined reflectance andtransmittance measurements [10,11]. The reportedaccuracy of the methods is satisfying, but the mea-surements can be complicated to perform and usual-ly require specific sphere designs. To the authorsknowledge, there are currently no simple measure-ment methods available for improved accuracy ofhemispherical transmittance measurements of low-angle scattering sample.
2. Measurement Methods
A. Integrating Sphere Spectrophotometers
Two spectrophotometers, one commercial doublebeam instrument and one single beam spectrophot-ometer constructed at Uppsala University, wereused to investigate the proposed method. Bothinstruments are equipped with integrating spheredetectors. The commercial spectrophotometer, aPerkin-Elmer Lambda 900 (here referred to as L900)with a 150mm Spectralon-coated integrating spherefrom Labsphere, is commonly used at research insti-tutions and in industry for standard measurements.Before using the commercial instrument, the trans-mittance sample holder was removed. This is a minorand reversible modification aimed at reducing lightlosses through side shift by moving the sample closerto the sphere port and increasing the port’s diameterfrom 19 to 26mm.
The university-constructed spectrophotometer,here denoted Tsphere, is fitted with a 200mm inte-grating sphere with an interior BaSO4 coating [12].It is a multipurpose instrument that can be modifiedto accommodate different sample sizes and mea-suring requirements. Furthermore, the integratingsphere has only one porthole for the incident light,leaving the far end of the sphere wall intact. Conse-quently, the detected signal is not reduced due to ab-sorption in sphere anomalies and, for this reason, theuniversity-built spectrophotometer was used as a re-ference instrument.
B. Goniospectrophotometer
An Optronic OL750-75MA goniospectrophotom-eter was used to determine the light-scattering
distribution of the sample. Goniometric measure-ments are not needed for the proposed method,but were used to verify the low-angle scattering prop-erties of the sample.
3. Optical Model
A. Proposed Method of Measurement
As previously mentioned, the idea of an integratingsphere is to detect the averaged light intensity. Toachieve this, the light entering the sphere should bereflected off the diffuse and highly reflective spherewall before reaching the detector.
For a nonscattering transmitting sample, the re-ference and the sample measurement are identical,and errors caused by the directional response of thesphere are therefore canceled out. For diffusingsamples with nearly Lambertian properties, themeasured intensity needs to be corrected for the re-flectance of the sphere wall, due to the difference be-tween the reference and the measurement reading.In principle this does not pose a problem, providedthat the reflectance of the sphere wall is known.For a light-scattering sample, the difference betweenthe specular reference scan and the sample scan is insome cases significant. Depending on the specificproperties of the sample and the design of the inte-grating sphere, a number of systematic errors mighttake place, due to, for example, the detector’s field ofview, the position of baffles, and the size and numberof portholes in the sphere. For a sample with pre-dominantly low-angle scattering, a large fraction ofthe transmitted light hits the edge of the speculartransmittance porthole. Because the port is recessed,it inevitably absorbs more light than the wall aroundit and, consequently a reduced signal is detected.
The difference in detector response can be signifi-cant depending on the position of the light spot on thesphere wall. This is illustrated in Fig. 1, which showsthe difference in detector response for five differentlight spot positions on and in the vicinity of the spec-ular transmittance exit port in the L900 spectrophot-
ometer. The specular transmittance exit port islocated at the far end of the sphere, as indicatedin the side view in Fig. 2.
To address the systematic errors for low-anglescattering samples, a method based on reducingthe difference between the reference scan and thesample scan is proposed. The method homogenizesthe scattering over a larger portion of the sphere wallby using a thin diffusing material. The diffusing ma-terial, here referred to as diffuser, is placed across thesample port of the integrating sphere for both refer-ence and sample measurements. The diffuser shouldbe thin, have high diffuse (ideally Lambertian) trans-mittance, and low reflectance. However, even if thediffuser fulfills all these requirements, an obviousdrawback of the method is the occurrence of multiplereflections between the sample and the diffuser. InSubsection 3.B a simple correction model that ac-counts for the multiple reflections is presented.
B. Correction for Multiple Reflections
To correct the detected signal for multiple reflectionsit is necessary to know the reflectance of both thesample and the diffuser. In principle, the angle-dependent reflectance is needed, because both thesample and the diffuser scatter light, resulting in ob-lique incidence angles. A first-order correction, how-ever, only requires the near normal hemisphericalreflectance of the sample and the diffuser. The correc-tion can be further improved by accounting for thechange in reflectance due to the oblique incidence an-gles, and obviously determined with an even greaterprecision if the full reflectance distribution is known.Going through the effort to determine the angle-dependent reflectance distribution is, however, con-trary to the purpose and simplicity of the model anddoes not significantly improve the accuracy.
Fig. 1. Detected light intensities, normalized to the highest in-tensity, for different positions of the light spot on the speculartransmittance exit port.
Fig. 2. Side view of the integrating sphere that illustrates the po-sition of the sample and the diffuser for the two scans that are re-quired to determine the correction coefficient kexp. When the signalS1 is detected the distance between the clear glass and the diffuseris sufficient to reduce all contributions from multiple reflections.During the second scan multiple reflections contribute to the de-tected signal S2.
To derive a correction factor for the multiple reflec-tions between the sample and the diffuser, the totaltransmittance, T, of the combination is first ex-pressed as the infinite series
T ¼ TsTd þ TsRdRsTd þ TsðRdRsÞ2Td þ…
¼X∞
m¼0
TsTdðRsRdÞm ¼ TsTd
1 − RsRd; ð1Þ
where Ts, Rs, Td, and Rd denote the transmittanceand reflectance of the sample and diffuser, respec-tively. Equation (1) is exact when two specular sam-ples are combined and measured at normal angle ofincidence. For light-scattering or diffusing samples,the multiple reflections are dominated by obliqueincidence angles and the equation is thereby an ap-proximation. However, for low-angle scattering, thisis a fair approximation given that the reflectance ofmanymaterials is relatively constant at low angles ofincidence. Solving for the sample transmittance, Ts,Eq. (1) can be rewritten as
Ts ¼Tð1 −RsRdÞ
Td: ð2Þ
If the reference signal is taken with the diffuseracross the transmittance entrance port, the detectedsignal, ST , can be expressed as ST ¼ T=Td. Substi-tuted into Eq. (2), this gives the corrected sampletransmittance, Ts;Corr1, as a function of the detectedsignal, the reflectance of the sample, and the reflec-tance of the diffuser according to
Ts;Corr1 ¼ STð1 − RsRdÞ: ð3Þ
C. Compensation for Non-Normal Incidence
As previously mentioned, Eq. (1), and the equationsfollowing from it, are exact for a combination of twospecular samples at normal angle of incidence. How-ever, in this case, both the sample and the diffuserare scattering, and the reflectance values should ide-ally account for the oblique incidence angles betweenthe sample and the diffuser. One way to correct forthis is to determine the reflectance distribution ofthe sample and the diffuser using a goniophotometer,but the aim of this paper is to characterize low-angle scattering samples using a single standardintegrating sphere spectrophotometer. Therefore, acorrection coefficient, kexp, was determined experi-mentally to account for the oblique angle reflectance.With kexp incorporated into the correction formula,Eq. (3) becomes
Ts;Corr2 ¼ STð1 − kexpRsRdÞ: ð4Þ
The correction coefficient was determined using alow-iron clear glass in combination with the diffuser.The determination requires two measurement scans,as shown schematically in Fig. 2. For the first scan,
the clear glass was positioned as far away from thesphere as the instrument permits and, for the secondscan, it was moved close to the sphere port. The dif-fuser was positioned across the port of the sphereduring both the reference and the measurementscans. The distance between the clear glass andthe diffuser during the first scan effectively removesthe contribution frommultiple reflections and the de-tected signal, S1, becomes equal to the transmittanceof the clear glass. When the clear glass is moved clo-ser to the diffuser, multiple reflections are introducedand the detected signal, S2, must therefore be cor-rected. The relation between the two signals canhence be expressed according to
S1 ¼ S2ð1 − kexpRcgRdÞ; ð5Þ
where Rcg is the reflectance of clear glass at normalangle of incidence. By using Eq. (5), the correctioncoefficient can be determined according to
kexp ¼�1 −
S1S2
�
RcgRd: ð6Þ
This correction coefficient accounts for the obliqueincidence angles when multiple reflections occurbetween a clear glass and a diffuser. Ideally, a similarsample-specific correction coefficient should be ob-tained for the two patterned glass samples. Giventheir light-scattering properties, this is, however, amore challenging task. Using the kexp as a correctioncoefficient for samples exhibiting light scattering isstill an approximation. This approximation is, how-ever, reasonable when the reflectance of the samplehas a low angle spread and is of the same order ofmagnitude as the clear glass. It is also worth notingthat the application of the correction coefficient is asecond-order correction, making a small relative er-ror more acceptable.
4. Characteristics of the Samples and the Diffuser
Three samples, two low-angle scattering andone specular, were measured using the proposedmethod. The specular sample, a low-iron float glass,is straightforward to characterize and was chosen totest the validity of the model. The two low-angle scat-tering samples were both of the type patterned glass,but with a regular and an irregular surface pattern.
Fig. 3. (Color online) Transmitted scattering image when lightfrom a laser pointer is incident upon the smooth front side, in(a) for the Pyramidal sample and in (b) for the Peel sample.
The sample with a regular surface structure hassmall inverted pyramids and is in this paper referredto as Pyramidal. The appearance of the irregularlystructured sample bears resemblance to an orangepeel and is, therefore, referred to as Peel. For bothsamples, the period of the surface structure was sig-nificantly smaller than the light spot in the spectro-photometers, making the measurements relativelyinsensitive to the position of the sample on thesphere port.
In order to determine whether the sampleswere suitable for the model the light-scatteringproperties were estimated using a laser pointer withwavelength 633nm directed toward the sample.The transmitted light was displayed onto a targetscreen showing the approximate scattering angles,as shown for the Pyramidal sample in Fig. 3(a)and for the Peel sample in Fig. 3(b). The distinct lightpattern is a result of the small illuminated area ofthe laser pointer, and a larger light beam, similarto that of the spectrophotometers, provides an inte-grated light intensity. It can be noted that the 5° cir-cle in Fig. 3 corresponds approximately to the edge ofthe specular transmittance exit port in the commer-cial instrument.
The scatter patterns displayed by the laser pointerwere verified by measuring the angle-dependentlight scattering at normal angle of incidence. Thelight-scattering distribution was determined usinga goniophotometer and can be viewed in Fig. 4(a)for the Pyramidal sample and in Fig. 4(b) for the Peelsample. Both samples scatter primarily in the for-ward direction, although the slightly narrower lightdistribution of the Pyramidal sample makes it parti-cularly suitable for the model.
The transmittance and reflectance of the diffuserused to reduce the effect of absorption at the portedge are shown in Fig. 5. The optical properties weremeasured using the L900 standard instrument, andhave been corrected for the Spectralon reflectance.
The diffuser is a thin glass sample that has beenetched on one side, giving it light-scattering proper-ties. It has a high diffuse transmittance with a rela-tively flat spectral response, and low absorption.Because of the light-scattering properties, the trans-mittance is not identical from the two sides. Thediffuse transmittance is slightly higher and thereflectance slightly lower when the etched side(side b) faces the beam. Both these properties aredesirable and this side was, therefore, orientedtoward the patterned glass sample during themeasurements.
Although the diffuser is not completely Lamber-tian, its spreading of the illuminated area is suffi-cient when combined with the patterned glasssamples. This is illustrated in Fig. 6, where the in-plane light intensity at normal angle of incidence
Fig. 4. (Color online) The bidirectional transmittance distribution function (BTDF) in (a) for the Pyramidal sample and in (b) for the Peelsample. The BTDF was determined using a goniophotometer.
Fig. 5. (Color online) Transmittance and reflectance of the diffu-ser at normal angle of incidence with the smooth side (side f) andthe scattering side (side b) facing the beam. The diffuser has a highdiffuse transmittance and a low reflectance. The total reflectancewhen the scattering side (side b) faces the beam is especially lowand entirely diffuse.
is shown for the diffuser, the patterned glass, and acombination of the two.
The wavelength dependence of the scattering dis-tribution was also examined by measuring the trans-mittance of the diffuser at different distances fromthe sphere port, as seen in Fig. 7. The amount of lightscattered outside the integrating sphere increaseswith increasing distance between the diffuser andthe sphere. If the scattering distribution is wave-length dependent, then the intensity reduction isnot constant over the entire wavelength range. InFig. 7 it can be seen that the intensity reduction isslightly higher between 350 and 500nm when thedistance to the sphere is increased. Although thisis an indication that the scattering distribution iswider in this range, the difference is small and, forthe predominant part of the spectrum, the scatteringdistribution is close to wavelength independent.
5. Results and Discussion
Figure 8 shows the transmittance detected when thetwo patterned glass samples are characterized usinga standard instrument (L900) and the university-built spectrophotometer (Tsphere). The figure pres-ents standard measurements carried out without adiffuser and the discrepancy between the two instru-ments is presumably caused by absorption aroundthe specular transmittance port in the L900 spectro-photometer. The relative difference between the twoinstruments is smaller for the Peel sample, whichcan be explained by the larger scattering distributionof the sample.
When the samples are measured using the pro-posed method, the diffuser is positioned across thesphere port during the reference scan. For the mea-surement scan, the diffuser remains in this positionand the sample is positioned on its other side, so thatthe diffuser becomes sandwiched between the sphereand the sample.
In Fig. 9, the transmittance of the low-iron clearglass is presented. This nonscattering glass is un-complicated to characterize and, for a standard mea-surement, i.e., measured without a diffuser, thedetected transmittance is almost identical for thetwo instruments (labeled “Tsphere” and “L900” inthe figure). Here the use of a diffuser is, hence, notnecessary to improve the accuracy of the measure-ment. Instead, measurements with the diffuser areincluded to illustrate the validity of the correctionmodel. To show the effect of both the correctionmodeland the correction coefficient, kexp, both correctedand uncorrected transmittance spectra have been in-cluded in the figure. Before any corrections havebeen made, the signal detected using the methodis too high. This is due to the contribution frommulti-ple reflections and is seen in the spectra labeled“L900Uncorr”. By applying Eq. (3) to the uncorrected
Fig. 6. (Color online) In-plane scattering of the two patterned glass samples and the effect when a diffuser is introduced between thesample the and the detector. In (a) at 550nm and in (b) at 1500nm. At both wavelengths the diffuser helps to spread out and homogenizethe detected signal.
Fig. 7. Transmittance of the diffuser when it is positioned at dis-tance d from the integrating sphere port. The relatively constantintensity reduction over the wavelength range indicates that thescattering distribution of the diffuser is sufficiently wavelengthindependent.
transmittance signal, most of the error due to multi-ple reflections is accounted for (spectra labeled“L900Corr1”). The method correction can be improvedfurther by including the correction coefficient accord-ing to Eq. (4), and, by doing so, the method measure-ment (labeled “L900Corr2”) closely matches thestandard measurements in the L900 and Tspherespectrophotometers. The small difference that canbe seen between the standard measurements andthe corrected transmittance is within the accuracyof the instrument.
The transmittance spectra from the measure-ments of the patterned glass samples are presentedin Fig. 10(a) for the Pyramidal sample and in Fig. 10(b) for the Peel sample. As before, the spectra labeled“L900” and “Tsphere” are standard measurements,carried out without a diffuser, in the respectiveinstruments. For both samples, the uncorrected
signal detected using the proposed method (labeled“L900Uncorr”) is too high when compared to theTsphere measurements. This is due to multiple re-flections, and introduction of the correction factoraccording to Eq. (3) lowers the transmittance by0.5 percentage points for the Pyramidal sampleand 0.4 percentage points for the Peel sample(“L900Corr1”). The correction is further improved bythe addition of the correction coefficient accordingEq. (4), as seen in “L900Corr2.” By using the proposedmeasurement method together with the refined cor-rection, the average difference between a measure-ment in the standard instrument and in theuniversity-constructed instrument is reduced from2.6 to 0.1 percentage points for the Pyramidal
Fig. 8. (Color online) Transmittance of the two light-scatteringsamples Pyramidal and Peel. The transmittance has been deter-mined using standard measurements, i.e., measured without a dif-fuser, in the Tsphere and L900 instruments. The discrepancybetween the two instruments is addressed with the proposed mea-surement method.
Fig. 9. (Color online) Transmittance of a low-iron clear glass sam-ple determined using the proposedmethod and standardmeasure-ments. The spectra labeled Tsphere and L900 are standardmeasurements, i.e., measured without a diffuser, in the respectiveinstruments. The subscripts Uncorr, Corr1, and Corr2 indicate un-corrected transmittance, transmittance corrected for multiple re-flections according to Eq. (3), and transmittance corrected formultiple reflections and non-normal-incidence angles accordingto Eq. (4), respectively.
Fig. 10. (Color online) Transmittance of the (a) Pyramidal and (b) Peel samples using the proposed method and standard measurements.The spectra labeled Tsphere and L900 are standard measurements, i.e., measured without a diffuser, in the respective instruments. Thesubscripts Uncorr, Corr1, and Corr2 indicate uncorrected transmittance, transmittance corrected for multiple reflections according toEq. (3), and transmittance corrected for multiple reflections and non-normal-incidence angles according to Eq. (4), respectively.
sample. The relative discrepancy improvement issmaller, from 1.0 to 0.3 percentage points, but stillnoticeable for the Peel sample.
It is worth pointing out that the optical propertiesof the diffuser are crucial for the function of themeth-od. A prerequisite, is a high diffuse transmittanceand a low reflectance. It is, furthermore, importantthat the diffuser scatters the light in sufficiently wideangles over the entire wavelength range. All theseproperties can, however, easily be evaluated with astandard instrument, as shown in Figs. 5 and 7.
6. Conclusions and Future Work
In this paper, a simple method for more accuratedetermination of the hemispherical transmittanceof low-angle scattering samples is proposed. Themethod is intended for standard instruments witha specular transmittance port and corrects for the ab-sorption that occurs around that port edge. The basicprinciple of the method is dual: to attain greater si-milarity between the reference and the sample scanand to spread the light spot over a greater portion ofthe sphere wall. The simplicity of the method is in-tentional and the aim is that only a standard spectro-photometer with an integrating sphere detector isneeded.
The method was tested for two low-angle scatter-ing glass samples and a clear low-iron glass sample.The transmittance determined using the methodwas compared to a reference integrating sphere in-strument without a specular transmittance port. Byusing the method, the average discrepancy betweenthe transmittance from the standard instrument andthe reference instrument was reduced from 2.6 to 0.1percentage points for one of the scattering samplesand from 1.0 to 0.3 for the other. The higher absolutereduction of one of the samples can be explained byits more forward-scattering properties, resulting inlarger port edge losses during a standard measure-ment scan in the L900 spectrophotometer.
In this case, a thin glass sample that was etched onone side was used as a diffuser. It is, however, possi-ble that the accuracy of the method can be improvedfurther by optimizing the properties of the diffuser.One approach would, for example, be to examinethe effect of etching time on the scattering propertiesof the diffuser.
Finally, this method is, in principle, also applicableto reflectance measurements. The diffuser wouldthen be positioned between the integrating sphereand the sample at the reflectance port of the
sphere. When compared to the transmittance modedescribed in this paper, there are two significant dif-ferences: the incident light would have a near normalangle of incidence and it would pass through the dif-fuser twice. The correction method would, hence,have to be adapted to account for this.
The samples studied in this paper were distributedwithin the International Commission on Glass,Technical Committee 10. The authors thank OliverKappertz at Interpane for providing the diffusingmaterial. The contributions from Jacob C. Jonssonwere supported by the Assistant Secretary forEnergy Efficiency and Renewable Energy, Office ofBuilding Technology, State, and CommunityPrograms, of the U.S. Department of Energy(DOE) under Contract No. DE-AC02-05CH11231.
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