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NIST_method for Absolute Measurement of T, R, And a of Specular Samples

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Integrating-sphere system and Absolute Measurement of transmittance, reflectance, and absorptance of specular samples
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  Integrating-sphere system and method forabsolute measurement of transmittance,reflectance, and absorptance of specular samples Leonard Hanssen  An integrating-sphere system has been designed and constructed for multiple optical properties mea-surement in the IR spectral range. In particular, for specular samples, the absolute transmittance andreflectance can be measured directly with high accuracy and the absorptance can be obtained from theseby simple calculation. These properties are measured with a Fourier transform spectrophotometer forseveral samples of both opaque and transmitting materials. The expanded uncertainties of the mea-surements are shown to be less than 0.003   absolute   over most of the detector-limited working spectralrange of 2 to 18   m. The sphere is manipulated by means of two rotation stages that enable the portson the sphere to be rearranged in any orientation relative to the input beam. Although the spheresystem is used for infrared spectral measurements, the measurement method, design principles, andfeatures are generally applicable to other wavelengths as well. © 2001 Optical Society of America OCIS codes:  120.0120, 120.3150, 120.5700, 120.7000, 120.3940, 120.4570. 1. Introduction Integrating spheres have long been used for the mea-surement of diffuse reflectance and transmittance of materials in the UV, visible, and near-IR spectralregions,aswellassomewhatmorerecently  sincethe1970’s   in the mid- to far-IR regions. However, in-tegrating spheres have been used infrequently forspecifically measuring specular materials. This istrue despite the fact that, according to integrating-sphere theory, for an ideal sphere, a simple ratio of two measurements should result in the absolute re-flectance of a specular sample. The reason for thelack of use of integrating spheres for specular mea-surements of reflectance is that real integrating spheres are not ideal. The sphere-wall coating isnever a perfect Lambertian diffuser, baffles perturbthe light distribution within the sphere, and all de-tectors exhibit some angular dependence. Theseand other deviations from an ideal sphere can dras-tically affect the accuracy of the sphere equations. 1 Because of the deviations, all spheres have somedegree of nonuniformity of throughput. This meansthat the detector signal will vary as the direction of thereflectedorthetransmittedlight  andtheregionsupon which the light is incident   within the sphere is varied. The result may be errors in the quantitiesderived from the measurements. For this reason,measurements of reflectance of specular materialsare usually performed relative to a known specularstandard. When this is done, the regions of thespherewalluponwhichthereflectedlightofthesam-ple and the reference falls usually have similarthroughputs.For absolute regular   specular   reflectance mea-surements, various methods, including, V–W, V–N,and goniometer-based methods, are typically used. 2,3 Thesemethodstypicallydonotinvolveanintegrating sphere. They involve an input beam, several direct-ing mirrors, and the detector. Some subsets of themirrors, the sample, and the detector are rotated andtranslated between sample and reference measure-ments. For the V–N and the goniometer methods, asimple ratio of the two results produces the absolutesample reflectance, whereas for the V–W method, thesquare root is taken.The primary sources of error in the methods justmentioned are the result of alignment problems andthe spatial nonuniformity of the detector. Theseproblems can easily lead to errors of several percent L. Hanssen   hanssen@nist.gov   is with the Optical TechnologyDivision, National Institute of Standards and Technology, Gaith-ersburg, Maryland 20899.Received 17 October 2000; revised manuscript received 20March 2001.0003-6935  01  193196-09$15.00  0 © 2001 Optical Society of America 3196 APPLIED OPTICS    Vol. 40, No. 19    1 July 2001  or more. 4 With considerable effort to achieve accu-rate alignment, excellent results can be achieved forstandards quality samples. However, even in thesecases, characteristics of the sample surface can limitultimate measurement accuracy. 5,6 For transpar-ent materials, dealing properly with the transmittedlight and measuring the backsurface reflection accu-rately pose additional difficulties. An important application of integrating spheres istheir use as an averaging device for detectors. Be-cause of the useful properties of the sphere, an aver-aging sphere’s entrance port can be both significantlylarger and much more spatially uniform than a baredetector. The trade-off made for these improve-ments is a degradation of the signal-to-noise ratio.The benefits of using the integrating sphere for moreaccurate detection of light are used in the design of thesystemanddevelopmentofthemethodpresentedin this paper. The measurement of absolute trans-mittance (  ), reflectance (  ), and absorptance (  ) of specular samples is described and demonstrated.The inherent problems of sphere spatial nonunifor-mity are overcome through judicious use of the sym-metries of the sphere design to establish symmetriesin the measurement geometry. After describing thespecifics of the integrating sphere in Section 2, theother components of the sphere system in Section 3,and the absolute measurement method in Section 4,wepresentthespherecharacterizationmeasurementresults for error analysis in Section 5. The achieve-ment of measurement uncertainties of 0.002 to 0.004are demonstrated in Section 6 for several common IRmaterials. Finally, Section 7 contains the discus-sion of the results with conclusions about the useful-ness of the sphere method for specular materials. 2. Description of the Integrating Sphere The integrating-sphere system has been designedand constructed according to the specifications de-tailed in the following paragraphs. Figure 1 is aphotograph of the integrating sphere. Specific pa-rameters of the sphere, including a description andanalysis of the detector–nonimaging-concentratorsystem,havebeendescribedpreviously. 7 Theinsidewall of the sphere is coated with a material that isnearly a Lambertian diffuser and at the same timehas a high directional hemispherical   diffuse   reflec-tance    0.9   for the IR spectral range: plasma-sprayed Cu on a brass substrate, electroplated with Au.The sphere has entrance, sample, and referenceports, all centered on a great circle of the sphere, asshown in Fig. 2. There also is a detector port, withits center located along the normal to the great circle.The white Hg:Cd:Te   MCT   detector Dewar locatedon the port can be seen mounted on the top of thesphere in Figs. 1 and 2. The detector’s field of viewis centered on the same normal and corresponds tothebottomregionofthesphere. Thesampleandthereference ports are located symmetrically with re-spect to the entrance port and can be seen in theforeground of Fig. 1   the sample port has a KRS-5sample mounted on it  . The exact location of thesample and the reference ports is in general deter-mined by the angle of incidence for which the reflec-tance and the transmittance are to be determined. An arrangement of ports could, in principle, be set upfor any angle of incidence from approximately 2° to28°andfrom32°to75°,dependingontheinput-beamgeometry of the source   or spectrophotometer  . Forthis sphere, port locations have been selected for 8°,which is close to normal incidence, yet for which noportion of the  f   5   6° half-angle   input beam will bereflected back onto itself.   For incidence angles inthe neighborhood of 30°, a variation of the designwouldberequiredsothatthereflectedbeamfromthesample port does not hit the reference port and vice versa  . Theentranceportisofsufficientsize  3.3-cmdiameter   to accept the entire input beam, and thesample and the reference ports are also sized  2.22-cm diameter   to accept the entire beam   at thefocus, in a focused geometry  . All the ports are cir-cular in shape, with the sphere’s inside and outsidesurfaces forming a knife edge at the port edge wherethey meet. In this sphere, as seen in Fig. 2, themeasurement of reflectance is designed for an inci-dence angle of 8°   in general   ; the sample and thereference ports are located at 16°   in general   2  and   16°   in general   2  , respectively, measuredfrom the center of the sphere and with respect to thelinethroughthespherecenterandthespherewall  at Fig. 1. Photograph of the integrating sphere for absolute IR spec-traltransmittanceandreflectance. TheHg:Cd:Te  MCT  detectorDewar   white   is mounted on the top of the sphere. We view theback side of the sphere that includes reference   empty   and sample  with a KRS-5 window   ports. A pair of rotation stages under-neath the sphere is used to move the sphere into positions for bothreflectance and transmittance measurements. 1 July 2001    Vol. 40, No. 19    APPLIED OPTICS 3197  a point directly opposite the entrance port  . Bafflesseparating the detector port and the detector field-of- view region from the sample and the reference portsare shown in Fig. 2. The baffles are critical to thesphere performance for characterization of diffusesamples, 8 but do not play a significant role for thespecular-sample case.The arrangement of the ports described above re-sults in the regions of the sphere wall illuminated bythe specularly reflected or transmitted light and thereferencebeambeingcenteredonthesamegreatcircleas the entrance, sample, and reference ports. In ad-dition, the regions are symmetrically positionedaround the entrance port. The reflected or the trans-mitted light also will be incident at the same angle onthese regions. As a result, the reflected or the trans-mitted light will have throughput to the detector thatis nearly identical. The procedure for orienting thesphere for the reflectance, transmittance, and refer-ence measurements is described in Section 3. 3. Sphere Mounting and Manipulation Hardware Thesampleandthereferencemounts,apairofwhichcan be seen on the sphere in Fig. 1, are constructed tohold the sample against and centered on the sampleport from outside of the sphere. During spheremovement,theholderspreventthesamplefrommov-ing or shifting relative to the sample port. This isdone in such a way as to leave the back of the samplefree and open, so that the beam centered on the sam-ple can proceed through it   for a transparent sample  withoutobstruction. Thisisrequiredforperforming either transmittance or reflectance measurements ontransparent samples. This arrangement can also beused to check thin-film mirrors for optical opacity.The integrating-sphere system includes two motor-izedrotationstagesstackedontopofeachother. Thestagesaremountedwiththeiraxesofrotationparallelto each other. The rotation axes of the stages areidentified in Fig. 3. Stage 1 has its axis of rotationoriented parallel to the normal of the great circleformed by the entrance-, sample-, and detector-portcenters, as well as passing through the edge of thiscircle. This base stage remains fixed to the opticaltable. Its rotation axis is perpendicular to the inputbeam and passes through the beam-focus position.Stage 2 is mounted on the rotation table of the basestage so that its axis of rotation is located a distance Fig. 2. Diagram of sphere interior and arrangement of its elements. Input and reflected beams are shown for a specular sample in thereflectance measurement geometry. The sample and the reference specular regions of the sphere wall are the first to be illuminated inthe sample and the reference measurements, respectively. The baffles are positioned for measurement of diffuse samples and are notcritical for specular sample measurement. 3198 APPLIED OPTICS    Vol. 40, No. 19    1 July 2001  away from the base-stage axis exactly equal to thesphere radius. The integrating sphere is mounted tothe rotation table of stage 2 so that the stage’s axis of rotation is along the sphere axis that includes the cen-ter of the detector port and the sphere center.The function of base stage 1 is to vary the angle of incidenceoftheinputbeamonthespheresurfaceandto switch between reflectance and transmittancemeasurement geometries. The function of stage 2 isto select upon which port, the entrance, the sample,or the reference port, the beam will be incident. 4. Measurement Geometry and Method forReflectance and Transmittance The arrangement of the input beam and the integrat-ingsphereforabsolutetransmittanceandreflectancemeasurements is shown in Fig. 3. The sample re-flectancemeasurementsetupisshowninFig.3  a   aswell as in Fig. 2  , the reference measurement in Fig.3  c  , and the sample transmittance measurement inFig. 3  e  . In each diagram, the rotation required forreaching the following diagram is shown as a curvedarrow around the appropriate rotation axis. In thereflectance measurement geometry of Fig. 3  a  , theinputbeampassesfromthespectrometerthroughthesphere entrance port and onto the sample surfacefacing the sphere. This is the typical reflectance ge-ometry for directional-hemispherical sample reflec-tance in most sphere systems. The only differencein Fig. 3  a   is the empty reference port   as opposed toone occupied with a standard for a relative measure-ment  . Onreflectionoffthesample,thebeamtrans- verses the sphere and is incident upon a region wedenote as the sample specular region   see Fig. 2  .From this point, the reflected flux is distributedthroughout the sphere in an even fashion because of the Lambertian coating and the integrating nature of the sphere. In Fig. 3  a   a clockwise rotation aboutaxis1turnsthebackofthesampletothebeaminFig.3  b  . An additional clockwise rotation about axis 2places the   empty   reference port at the input beamfocus in Fig. 3  c  , where it continues on to strike thesphere wall at the reference specular region   labeledin Fig. 2  , producing the reference measurement. Another counterclockwise rotation about axis 2 re-sults in Fig. 3  d  , a repeat of Fig. 3  b  . A final coun-terclockwise rotation about axis 1 positions thesphere in Fig. 3  e   for the transmittance measure-ment, with the same angle of incidence as that of Fig.3  a  onthesampleandincidenceregiononthespherewall   the sample specular region  .The somewhat unusual geometry for the referencemeasurement   Fig. 3  c   is chosen in order to achievethe highest degree of symmetry between the reflec-tanceandthereferencemeasurements. Thesampleand the reference specular regions are symmetricallylocated on either side of the entrance port. Becauseof the symmetry of the sphere design, the throughputis nearly equal for these two regions. Because theonly other difference between the sample reflectanceand reference measurements is the initial reflectionoff the sample, the ratio of sample reflectance andreferencemeasurementsisequaltotheabsolutesam-ple reflectance   for specular samples  . Varioussources of error, including the difference in the sam-ple and the reference specular region throughputs,can be included in the expanded measurement un-certainty or can be corrected for.Theratioofthesamplereflectancemeasurementof Fig. 3  a   to the reference measurement of Fig. 3  c   isequal to the absolute sample reflectance   for specularsamples  . The ratio of the transmittance measure-mentofFig.3  e  tothereferencemeasurementofFig.3  c  isequaltotheabsolutesampletransmittance  forspecular samples  .The absolute absorptance is indirectly obtainedwhen the sum of the absolute reflectance and trans-mittance is subtracted from unity. Kirchoff’s lawapplies because the reflectance and the transmit-tance measurements are made under identical con-ditions of geometry and wavelength  s  . The inputbeam is incident upon opposite surfaces of a sample Fig. 3. Sphere measurement geometries for reflectance andtransmittanceandrotationstepsusedtoorientthesphereforeach  a  reflectancemeasurementgeometry,  c  referencemeasurement,and   e   transmittance measurement geometry.   b   and   d   areintermediate steps. Two rotation stages, stage 1 centered at theinput-beam focus and sphere wall and stage 2 centered at thesphere center, are used to change geometries. 1 July 2001    Vol. 40, No. 19    APPLIED OPTICS 3199
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