quantitative infrared directional- hemispherical diffuse

Methods for quantitative infrared directional-hemispherical and diffuse reflectancemeasurements using an FTIR anda commercial integrating sphereTHOMAS A. BLAKE,1,* TIMOTHY J. JOHNSON,1 RUSSELL G. TONKYN,1 BRENDA M. FORLAND,1,2

TANYA L. MYERS,1 CAROLYN S. BRAUER,1 YIN-FONG SU,1 BRUCE E. BERNACKI,1

LEONARD HANSSEN,3 AND GERARDO GONZALEZ4

1Pacific Northwest National Laboratory, 902 Battelle Blvd., Richland, Washington 99354, USA2Current address: Red Rocks Community College, 13300 West 6th Avenue, Lakewood, Colorado 80228, USA3Optical Technology Division, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, USA4Alecam FTIR Services and Consulting, The Woodlands, Texas 77381, USA*Corresponding author: [email protected]

Received 27 September 2017; revised 7 December 2017; accepted 7 December 2017; posted 13 December 2017 (Doc. ID 307361); published 17 January 2018

We have developed methods to measure the directional-hemispherical (ρ) and diffuse (ρd ) reflectances of pow-ders, liquids, and disks of powders and solid materials using a commercially available, matte gold-coated inte-grating sphere and Fourier transform infrared spectrometer. To determine how well the sphere and protocolsproduce quantitative reflectance data, measurements were made of three diffuse and two specular standards pre-pared by the National Institute of Standards and Technology (NIST), LabSphere Infragold and Spectralon stan-dards, hand-loaded sulfur and talc powder samples, and water. Relative to the NIST measurements of the NISTstandards, our directional hemispherical reflectance values are within �4% for four of the standards and within�7% for a low reflectance diffuse standard. For the three diffuse reflectance NIST standards, our diffuse reflec-tance values are within �5% of the NIST values. For the two specular NIST standards, our diffuse reflectancevalues are an order of magnitude larger than those of NIST, pointing to a systematic error in the manner in whichdiffuse reflectance measurements are made for specular samples using our methods and sphere. Sources ofuncertainty are discussed in the paper. © 2018 Optical Society of America

OCIS codes: (120.3150) Integrating spheres; (120.4800) Optical standards and testing; (120.5700) Reflection; (120.6200)

Spectrometers and spectroscopic instrumentation; (300.6300) Spectroscopy, Fourier transforms; (300.6340) Spectroscopy,

infrared.

https://doi.org/10.1364/AO.57.000432

1. INTRODUCTION

The use of longwave infrared (IR) hyperspectral imaging of ter-restrial and extraterrestrial targets to determine geological com-position and surface temperature has increased many-fold overthe past three decades [1–8]. With the advent of both compactsensor designs and low noise-equivalent ΔT focal plane arraydetectors, the sensing of environmental (geological and vegeta-tion) and manmade materials from satellites, aircraft, fencelines, and handheld contact sensors has become possibleand, in many cases, routine [9–15]. In addition to sensordevelopment, great progress has been made in data analysis(preprocessing, anomaly detection, target identification, etc.)[16,17] and in building laboratory spectral databases used

for material identification (wavelength dependence of spectralfeatures) and surface temperature measurement (i.e., absoluteemissivity as a function of wavelength) [18–20].

For geological materials, for example, spectral databases havebeen populated using either of two methods: the first usesan integrating sphere to measure the materials’ directional-hemispherical reflectance (DHR or ρ) spectrum and then usesKirchhoff ’s law, ε � 1 − ρ, to calculate the emissivity, ε [18].For brevity, in this paper we will use “DHR” to mean“directional-hemispherical reflectance.”

Alternatively, the emissivity of the materials in the databasecan be measured directly by placing each on a temperature-regulated plate and using a conical mirror to direct the emitted

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longwave light from the sample into a spectrometer [19].Twenty years ago, Salisbury et al. demonstrated [21,22] thatthe two laboratory techniques produce equivalent emissivity re-sults for the majority of geological materials that they studied,both as powders and as disks. The majority of databases usedfor disentangling field data are populated with DHR data. TheNASA/Jet Propulsion Laboratory ASTER Spectral Librarydatabase [18], for example, consists of reflectance data of miner-als, rocks, vegetation, soils, manmade materials, snow, water, ice,etc. Additionally, Christensen and co-workers have developed alongwave infrared (5 μm–45 μm) emission spectral database ofrocks and rock-forming minerals in support of several thermalmapping missions to Mars [19]. Reflectance databases used foranalysis of specific classes of materials, such as industrial processchemicals, explosives, etc. tend to be more limited, impromptu,and not widely distributed [12–14]. Given the growing interest inthis field, we present here a practical guide for the use of a com-mercial integrating sphere and Fourier transform spectrometer forquantitative DHR and diffuse-(ρd ) reflectance measurements ofsolids and powders in the infrared (1.3 μm–16.7 μm). We haverequired from the outset a horizontally oriented sample cup, sothat a cover window for the powders would not be needed. Thisalso provides for easy sample exchange and avoids étalons andother spectral artifacts associated with either internal or externalwindow reflections [23].

Notations, terminology, and definitions used here followthose summarized by Hanssen and Snail in their comprehen-sive review paper [24] on integrating spheres used for reflec-tance measurements in the infrared and near-infrared. Inthat paper, they point out that the sphere wall coatings, detec-tors, and standards for the infrared are not as developed as thoseof their ultraviolet, visible, and near-infrared counterparts.They also go on to describe several absolute measurement tech-niques for making integrating sphere measurements in the in-frared, including the technique used by the National Instituteof Standards and Technology (NIST, USA) to measure DHRspectra of the five standards presented in this paper. In a pre-liminary study at the Pacific Northwest National Laboratory(PNNL), [25] we reported DHR and diffuse reflectance mea-surements of three NIST reflectance standards, andLabSphere’s Infragold [26] and Spectralon materials, and con-cluded that good agreement between our measurements andcalibration or reported values for these materials could beachieved. Subsequently, measurements have been made usingour sphere and spectrometer that have allowed us to expandthe number of standards and samples measured, properly scalethe measured DHR and diffuse reflectance spectra with respectto an appropriate NIST standard, provide an uncertaintybudget for the resulting reflectance spectra, and better under-stand the sources of these uncertainties. The results of thesemeasurements on five NIST reflectance standard materials,as well as Infragold, Spectralon, sulfur, talc, and water are pre-sented here. Comparisons among our measurement results,NIST standards’ calibrated values, and published results (whereavailable) for the other materials are presented, and from these,estimates of random and systematic measurement uncertaintiesare given. Corrections to the results to account for anomalies inthe sphere design, or the protocol used, are discussed.

2. EXPERIMENTAL

A. InstrumentationThe infrared DHR and diffuse reflectance measurementsreported here utilized the same setup as previously reported,[25] which consists of a commercial integrating sphere(Bruker model A 562-G, hereafter referred to as “the Brukersphere”) and Fourier transform infrared spectrometer (Brukermodel IFS 66S) configured to operate in the mid-infrared usinga 1500 K silicon carbide light source, germanium-coated,potassium bromide beamsplitter, 10 mm aperture, and f ∕4.5optics [27]. The instrument resolution was set to 4.0 cm−1. ACooley-Tukey fast Fourier transform using a Blackman-Harrisapodization function and Mertz phase correction, at 8 cm−1

phase resolution was used to transform the interferograms tospectral space (cm−1). The transformed data were savedbetween 600 cm−1 and 7500 cm−1. Bruker’s OPUS software(version 5.5) was used to run the spectrometer and also tocollect and display the data. Further details of the operationof the FTIR spectrometer are given elsewhere [27]. In mostcases, 2048 double-sided interferograms were averaged for boththe reference and sample single-channel spectra. The integrat-ing sphere was mounted in the sample compartment separatedfrom the interferometer by a thin, wedged KCl window.However, no window is used over the sample. While thiscan potentially lead to sphere contamination, it avoids certainartifacts such as reflections, étalons, etc. The interferometer andintegrating sphere interior were under dry nitrogen purge; thedoor to the sample compartment was, however, left open forthese measurements. When the single-channel sample andreference spectra were ratioed, many of the water and CO2

spectral features were removed, and most—though not all—remaining features were removed using an atmosphericcompensation routine in the OPUS software.

The Bruker sphere has an inner diameter of 7.5 cm with anominally matte gold interior surface that displays some specu-lar characteristics [28]. A schematic of the sphere is shown inFig. 1. A vertical plane located at the center of the sphere bisectsa 2.0 cm diameter entrance port where light from the interfer-ometer enters the sphere. A small flip mirror is positioned in-side the sphere, so that light entering the sphere can be directeddownward to a 1.9 cm diameter sample port in the bottom ofthe sphere, back out the entrance port, upward to a 3.2 cmdiameter specular exclusion port in the top half of the sphere,or to any point on the sphere wall along an arc joining the cen-ters of these three ports. The mirror, sample port, and specularexclusion port are all bisected by the aforementioned verticalplane. Light from the spectrometer comes to a focus at the flipmirror. The specular exclusion port is large enough to accountfor the beam divergence of the spectrometer’s f ∕4.5 optics.The centers of the sample and specular exclusion ports arein the same vertical plane as the entrance port. The 1 cm diam-eter detector port is bisected by a horizontal plane that includesthe center of the sphere and is centered on the sphere wallopposite the flip mirror handle (see below). The detector isa 2 mm × 2 mm, 60 deg field-of-view, liquid-nitrogen-cooledHgCdTe (MCT). Two diffuse gold-coated baffles (not shownin Fig. 1) are positioned near the detector port to prevent first-bounce light from either the bottom sample port or the specular

Research Article Vol. 57, No. 3 / January 20 2018 / Applied Optics 433

exclusion port from reaching the detector. A loose-fitting capwhose inward-facing, matte gold surface has the same curvatureas the sphere is used to cover the specular exclusion port whenneeded for DHR measurements. The flip mirror is connectedto the exterior of the sphere by a thin axle, which is connectedto a lever arm so that the mirror can be flipped from the “up”position pointing at the specular exclusion port to the “down”position pointing at the sample port. Two spacers are used todelimit the travel of the lever, and these are adjusted to centerthe light in the top and bottom ports. With the mirror pointingdown, the angle between the incident light on the sample sur-face and the surface normal is 14.8 deg. The detector and itspreamplifier are bolted to the sphere, and the entire unit, inturn, is bolted to a three-point kinematic baseplate that sitsin the sample compartment. The sample or sample cup ispressed tightly against the bottom of the sphere, thus helpingto avoid artificially low reflectance values that can arise fromoptical sample standoff, even from distances <1 mm [29–31].

The radiance, L, inside the sphere, when illuminated byinfrared light from the interferometer, is given by [32]

L � ΦπAs

·ρ

1 − ρ�1 − f � ; (1)

where Φ is the incident power, which is 0.036 W, as measuredwith a calibrated pyrometer (model E6, Eppley Laboratory,Inc.), As is the sphere’s surface area, 1.767 × 10−2 m2, ρ isthe reflectance of the matte gold surface of the sphere, assumedto be 0.95 here, and f is the exchange fraction, which is theratio of the surface area of the open ports to the sphere’s totalsurface area. When the cap is in the specular exclusion port,f � 0.0227 and L � 8.7 W∕�m2 sr� and with the cap re-moved f � 0.0677 and L � 5.4 W∕�m2 sr�. The second

term on the right side of Eq. (1), which is referred to asthe sphere multiplier, scales the radiance of the sphere due tomultiple reflections as a function of sphere reflectance and portfraction. The incident power, radiance, and reflectances arefunctions of wavenumber (cm−1). Based on measurements, abetter estimate of the matte gold reflectance for the Brukersphere is given in the Discussion section.

For comparison, visible near-infrared (VNIR) spectra wererecorded for some of these materials using a dispersive spec-trometer (Cary 5000) and pre-formed polytetrafluoroethylene(PTFE)-lined integrating sphere from LabSphere (DRA-2500).A detailed description of the VNIR measurements is given in[23]. For the VNIR sphere, the samples are held vertically, anda cover window is used to hold powdered samples in the samplecup. There is spectral overlap (ca. 1.4 μm–2.3 μm) between theVNIR system and the present infrared system, which is used forcomparison purposes.

B. MethodsAlignment of the sphere is critical, especially the positioning ofthe input light’s focus from the interferometer onto the Brukersphere’s flip mirror, to obtain the quantitative reflectance valuesgiven here. Selecting a point on the sphere wall that is baffledfrom the detector’s field of view, and using the same spot forboth DHR and diffuse reflectance reference measurements arealso important considerations. The procedures used to recordDHR and diffuse reflectance measurements have been reportedearlier [25]. Here, we provide more thorough descriptions ofthe methods used. In order to obtain quantitative reflectancevalues, a reference spectrum relative to matte gold is required.For this study, we have chosen the position where the bottomedge of the light spot, as directed by the flip mirror, is approx-imately 1 cm above the bottom sample port on the wall of thesphere as our point for the reference measurements for bothDHR and diffuse reflectance spectra. The sample is in the sam-ple port when the reference measurement is made. A spacer isplaced between the mirror lever and a mechanical stop on theside of the sphere to reproducibly position the mirror at thisreference point. With the light directed to this reference spoton the sphere wall, the baffle on the wall of the sphere betweenthe sample port and the detector port is positioned to blockmost of the first-bounce light from this reference position fromreaching the detector. (An alternate reference position for theDHR spectra is to point the IR beam at the cap in the specularexclusion port. This approach gives DHR values comparable tothe ones reported here, certainly within the expanded uncer-tainties.) For the DHR measurements reported here (seeFig. 1), the sample is in the bottom port, and the diffuse golddome cap is in the specular exclusion port. The flip mirrordirects the light from the entrance port to the reference pointto record the reference spectrum (V reference) and toward thesample to record the sample spectrum (V sample). The two spec-tra are ratioed, ρ � V sample∕V reference, and scaled to a calibratedstandard, viz. [24,28]:

ρsample-scaled �Vsample∕Vsample-reference

Vstandard∕Vstandard-reference

� ρstandard; (2)

where (V sample∕V sample-reference) and (V standard∕V standard-reference)are measurements made using the Bruker sphere of the sample,

Fig. 1. Schematic of the A 562-G integrating sphere used by PNNLfor the work presented here. The sample, reference, entrance, and de-tector ports are shown. The flip mirror is left of center. The light bafflesare not shown. Dashed line with an arrow indicates the path of thelight directed to the reference spot on the sphere wall. Cap in thespecular exclusion port is removed for diffuse reflectance measure-ments; it is kept in place for DHR measurements. The figure isreproduced, in part, from the A 562-G operating manual, BrukerOptics, Inc.


and its reference measurement, and a standard, and its referencemeasurement, from, for example, NIST. ρstandard is the reflec-tance spectrum of the standard as measured by the issuer of thestandard (NIST).

To measure the diffuse reflectance (see Fig. 1), first the cap isremoved from the specular exclusion port. Next, with the sam-ple in the bottom sample port, the reference spectrum is re-corded with the light directed to the reference point on thesphere wall, and the sample spectrum is recorded with the lightdirected onto the sample. The two spectra are then ratioed asρd � V sample∕V reference. The amount of light exiting the specu-lar exclusion port is dependent on the bidirectional reflectiondistribution function (BRDF) and the solid angle interceptedby the port. The sphere used by NIST [24,33–35] to measuretheir standards, for example, has smaller port sizes, and it letsless light out during diffuse measurements. For a sample with aspecular lobe in its BRDF, a NIST measurement will give largerdiffuse reflectance values compared with a diffuse measurementof the same sample using the Bruker sphere. Consequently, weuse the DHR standard values as measured by NIST and theDHR values of the standard as measured by PNNL to scalethe PNNL diffuse reflectance measurement using Eq. (2).

C. MaterialsFive reflectance standards were purchased from NIST(Gaithersburg, MD, USA) in the fall of 2009 [25]. The stan-dards are not official NIST standard reference materials butwere prepared and calibrated by NIST researchers as part ofa multi-laboratory reflectance study [36]. Of the five25 mm diameter disks, two are specular (PN/S25A02: highlyreflecting electroplated gold on a polished copper substrate andPN/S25B02: medium reflecting, polished, high-density siliconcarbide [25]), and three are diffuse (PN/D25A02: highly re-flecting electroplated gold on nickel on arc-sprayed aluminumon a machined brass substrate, [25] PN/D25D02: medium-reflecting Krylon silver paint on arc-sprayed aluminum on amachined brass substrate, and PN/D25C02: low-reflectingNextel black paint on a machined brass substrate [25]).NIST calibration data from 555 cm−1 to 10;000 cm−1 are pro-vided for each of these standards, which include a DHR spec-trum, ρ, the diffuse spectrum, ρd , specular spectrum, ρs, andthe specularity spectrum, defined as ρs∕ρ, where ρ � ρs � ρd[36]. Each of these spectra has an associated NIST expandeduncertainty (coverage factor k � 2, level of confidence 95%)[37]. The D25X02 standards were recalibrated in 2014, andthe S25X02 standards were recalibrated in 2015.

A LabSphere 2-in. square Infragold standard (UIRT-094-020, AS-02792-020) was purchased (November 2013) as amid-infrared standard. There are no reflectance calibration datafor this particular standard. LabSphere lists DHR values forInfragold between 1.0 μm and 2.5 μm in 0.05 μm steps[38]. Using spectral values between 2.5 μm and 13 μm froma LabSphere-calibrated Infragold standard produced in 2001,together with the aforementioned near (NIR) and shortwaveinfrared (SWIR) values, we produced a composite referencespectrum that approximates the original calibration. LabSphereaffirms that it has been making Infragold in the same mannerfor decades and that the calibration values are persistent.LabSphere 99% (SRS-99-020, AS01161-060) reflecting

Spectralon standard that is calibrated in the visible andnear-infrared to 2.5 μm was also measured. A DHR calibrationspectrum was supplied with this standard, but a diffuse reflec-tance spectrum was not available.

To measure the reflectance of liquid water and the loosepowder materials, the samples were placed in machined alumi-num sample cups. The cups have an outside diameter of3.0 cm, an outside height of 1.1 cm, an inside diameter of2.5 cm, and an inside depth of 0.9 cm for a sample volumeof 4.4 cm3. The cups are sufficiently deep that infrared lightdoes not penetrate to the bottom when filled with a sample.Deionized water was used for reflectance measurements. Thesulfur (purity >99.5%) was procured from Aldrich (part #84638-1KG, CAS # 7704-34-9). The sulfur was used withoutfurther purification but does show evidence of a hydrocarbonimpurity and adsorbed water in its reflectance spectrum. Thetalc was procured from Aldrich (part # 243604-500G, CAS #14807-96-6). The powder samples were prepared for the infra-red measurements by weighing out the powder for eachcup, placing it into the cup and smoothing the surface withthe blade of a spatula, so that the surface is uniform, and thenre-weighing the cup.

D. Measurement UncertaintiesTo estimate the uncertainties in the PNNL reflectance mea-surements, we made multiple measurements of the standardsand materials to determine the random measurement uncer-tainties (Type A) and used an optical ray tracing program tomake estimates of systematic uncertainties originating fromthe sphere design and measurement protocols (Type B).These uncertainties were then combined in quadrature witha coverage factor of k � 2 to give an expanded uncertaintyas given for the NIST uncertainty described above [37].

For each material examined here, at least six sets of DHRand diffuse reflectance spectra were measured and, unless statedotherwise, each reflectance spectrum consists of a ratio of 2048sample scans to 2048 reference scans. Six different samples wereprepared for each of the “loose” compounds: hand-loaded sul-fur and talc, and water. The solid disk standards from eitherNIST or LabSphere were placed in the bottom sample portof the sphere and rotated to six different positions, 60 deg apartto provide six different “samples.” Average DHR and averagediffuse reflectance spectra were calculated from the six samplesfor each material. Also, DHR and diffuse reflectance standarddeviation spectra are calculated from the averaged reflectancespectra. These spectra give a measure of the sample-to-samplerandom uncertainty.

To determine the systematic uncertainties in our reflectancemeasurements from both the sphere and the methods used tomake those measurements, a 3D CAD drawing from Bruker ofthe integrating sphere was used in conjunction with an opticalengineering software program (TracePro) to ray trace lightmoving through the sphere. To keep the calculations tractable,the sphere and sample surfaces were assumed to have aLambertian BRDF with 97% reflectance. One million parallel,monochromatic starting light rays were introduced into thesphere through the entrance port. The radiance reaching thedetector for a DHR measurement is determined for the sphereconfigured, as it is used compared to an idealized sphere. So, for


example, the radiance reaching the detector when the incidentlight is directed toward a curved sample within a sphere withflat specular port edges is simulated and compared with theradiance reaching the detector when the incident light isdirected to a curved sample within a sphere that has knife edgeports. A fractional change between these two radiances is cal-culated, and this is used as the fractional uncertainty introducedby the flat specular port edges. Similar calculations are per-formed to determine the fractional uncertainties introducedby flat samples and combined detector field of view and baffleposition. The process is repeated with the sphere configured fordiffuse reflectance measurements. Modeling of the sphere witha specular sample shows that reflected light in the sphere doesnot significantly interact with the port edges. Consequently, thefractional uncertainty for the port edges is set to zero for specu-lar samples. The other fractional uncertainties remain the sameas the diffuse sample case. The fractional uncertainty related tothe baseline drift of the FTIR is estimated to be 0.002. Thefractional uncertainties are summarized in Table 1.

The expanded uncertainty at wavenumber bin i, δRexp�i�, iscalculated from

δRexp�i� � k��μ1R�i��2 � �μ2R�i��2

� �μ3R�i��2��μ4R�i��2 � σrndm�i�2�1∕2; (3)

where k � 2 is the coverage factor for a 95% confidence level,μj are the Type B fractional uncertainties, R�i� is the measuredDHR or diffuse reflectance, and σrndm�i� is the random sample-to-sample standard deviation. The DHR and diffuse reflectanceexpanded uncertainties are plotted with their respectivereflectances for each material in Fig. 2 through Fig. 9 [37].

For those sample reflectance spectra scaled using Eq. (2), theuncertainty associated with the standard used for scaling mustbe taken into account. To do this, the propagation formulagiven in Eq. (4) is used:

δRss � Rss

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi�δRsu

Rsu

�2

��δRstdPNNL

RstdPNNL

�2

��δRstd

Rstd

�2

s; (4)

where Rss is scaled reflectance of the sample, Rsu is the unscaledreflectance of the sample as measured using the Bruker sphere,RstdPNNL is the reflectance of the standard as measured byPNNL using the Bruker sphere, and Rstd is the reflectance

of the standard as measured by the issuer of the standard(NIST, for example). The δRi are the expanded uncertaintiesas given in Eq. (3). All these values are functions of wavenum-ber (cm−1).

A NIST traceable polystyrene film on a KBr window (NISTStandard Reference Material 1921) was used to regularly checkthe wavenumber scale of the FTIR. For each measured trans-mission spectrum of the film, the wavenumber positions of adozen spectral features are compared with those in NIST 1921,and a root mean square of the differences is calculated. Theaverage RMS difference is 0.25 cm−1.

3. RESULTS

A. NIST StandardsMeasurement results for NIST standards D25A02 and S25A02are shown in Figs. 2 and 3, respectively. In these figures, weshow the PNNL ρ and ρd spectra as the uncorrectedV sample∕V reference data.

In the upper panel of Fig. 2 are shown, on an expandedscale, our DHR (blue) and diffuse (green) reflectance spectraof the NIST diffuse gold reflectance standard, D25A02[25]. The expanded uncertainties of the PNNL ρ and ρd spec-tra are shown in the bottom panel. The NIST ρ (black) and ρd(red) spectra, which were recorded in June 2014, are also shownin the upper panel and the NIST expanded uncertainties [37]are also shown in the lower panel. The NIST DHR and diffusespectra for this material are coincident with one anotherindicating a highly Lambertian material [36,39]. The PNNLDHR and diffuse spectra are not coincident for much ofthe wavenumber range shown, pointing out an important dis-tinction between the NIST and PNNL data sets. The NIST

Table 1. Fractional Uncertainties Used for CalculatingSystematic Uncertainties When Using the Bruker Spherefor DHR and Diffuse Reflectance Measurementsa

Source of SystematicUncertainty

DHRConfiguration

DiffuseConfiguration

Knife edges/flat specularport edges

0.0294 0.0135

Curved sample/flat sample 0.0020 0.00106Detector FOV and baffleposition

0.0078 0.0155

FTIR baseline drift 0.0020 0.0020aFractional uncertainties for the sphere are calculated from ray trace

simulations of the Bruker integrating sphere assuming a Lambertian wallinterior and Lambertian sample surface both with R � 0.97. For specularsamples, the fractional uncertainty associated with knife edges and portedges is assumed to be zero.

Fig. 2. DHR (blue) and diffuse (green) PNNL uncorrected reflec-tance spectra of NIST D25A02 standard. The standard is an electro-plated gold on nickel on arc-sprayed aluminum on machined brasssubstrate. The PNNL spectra were recorded with the disk in six differ-ent positions; for each position, 2048 scans were co-added. Data fromthe six positions were averaged (upper plot); the expanded uncertain-ties are shown in the lower plot. The NIST DHR and diffuse reflec-tance measurements of this standard are shown as the black and redtraces, respectively. The NIST uncertainties—DHR and diffuse—lieon top of one another.


and PNNL data were collected using different spheres and tech-niques, and these differences, which are described in Section 4,can lead, in some cases, to a divergence in reflectance values.

In both the PNNL and NIST spectra, weak organic featuresnear 2900 cm−1—probably due to the solvent used in makingthe standard—are visible, and broad, adsorbed water featuresnear 1600 cm−1 and 3400 cm−1 are also visible. The PNNLdiffuse spectrum is not as level as that of the DHR, and thereappears to be a pivot point at 1850 cm−1 at which the diffusespectrum slopes away below the DHR at higher wavenumbers.The steep increase in the PNNL-measured DHR and diffusereflectance below about 1200 cm−1 and that the diffuse crossesover the DHR in this wavenumber range indicates that theD25A02 is more Lambertian in this spectral region thanthe sphere wall material, which is used as the reference (seethe Discussion section). Diffuse materials, with respect to theirreflectance spectra, appear to be less diffuse with increasingwavelength [36].

As with the D25A02, both the D25C02 [25] and theD25D02 exhibit small organic and adsorbed water featuresin their reflectance spectra. In contrast with D25A02 andD25D02, whose average PNNL DHR values are within theuncertainty range of the average NIST DHR values (roughly3%), the PNNL D25C02 [25] is slightly out of theNIST uncertainty range. Nonetheless, the comparisons be-tween the PNNL and NIST DHR (shown in Table 2) are quitegood considering that no correction or scaling has been madefor the reflectance properties of the Bruker sphere wall. In termsof percent change, the average PNNL diffuse reflectances forD25A02 and D25D02 are below their NIST values by1.93% and 4.9%, respectively, but the average PNNL diffusereflectance for D25C02 is above that of the NIST value by 4%.As will be described below (see the Discussion section), theD25A02 and the D25D02 have specular lobes that escape fromthe Bruker sphere to a greater extent than from the NISTsphere during diffuse reflectance measurements. The BRDFof the D25C02 is flat.

Spectra of the NIST specular reflectance standard, S25A02,shown in Fig. 3, are flat across the infrared. Similarly, theS25B02 standard [25] is spectrally flat above 2000 cm−1.The NIST-PNNL DHR agreement for the two specularstandards is very good with percent changes of 1.1% and 3.3%for S25A02 and S25B02, respectively, and absolute differencesof ρ � ∼0.01 reflectance units (see Table 2). Although thePNNL diffuse reflectances for these two standards haveρd < 0.01, they are approximately an order of magnitude largerthan those of the NIST spectra. This discrepancy is explainedin the Discussion section.

B. Gold StandardsLabSphere’s Infragold is a commonly used diffuse infraredreflector with a DHR reflectance of about 0.94 from the far-infrared through the SWIR. Our preliminary DHR and diffusereflectance measurements for a 2 0 0 × 2 0 0 square of the materialwere presented in [25]. In that work, we made several DHRand diffuse reflectance measurements along one side of thesquare and then rotated the square 180 deg and made moremeasurements on the side opposite the previous measurements.We noted that there was little difference in the DHR spectra forthe two orientations of the square, but there was a statisticallysignificant difference between the diffuse reflectance spectra.This result points to an anisotropy in the BRDF of Infragoldwhen light is incident at 14.8 deg. Here, we have scaled the

Fig. 3. DHR (blue) and diffuse (green) PNNL reflectance spectraof NIST S25A02 standard. The standard is electroplated gold on pol-ished copper substrate. The PNNL spectra were recorded with the diskin six different positions; for each position, 2048 scans were co-added.Data from the six positions were averaged (upper plot); the expandeduncertainties are shown in the lower plot. The NIST DHR and diffusereflectance measurements of this standard are shown in black and redtraces, respectively.

Table 2. Average DHR and Diffuse Reflectance and Percent Change Between PNNL and NIST Measurement of the FiveNIST Standardsa

Sample Standard Type ρ(PNNL) ρ(NIST) %Δρb ρd (PNNL) ρd (NIST) %Δρb Dc(PNNL)

D25A02 Diffuse 0.971(59) 0.985(28) −1.42 0.965(40) 0.984(28) −1.93 0.993(74)D25C02 Diffuse 0.0344(23) 0.0324(13) 6.17 0.034(2) 0.0323(12) 4.02 0.975(75)D25D02 Diffuse 0.863(53) 0.844(24) 2.25 0.792(35) 0.831(24) −4.9 0.917(69)S25A02 Specular 0.999(17) 0.988(3) 1.11 0.0072(6) 0.0006(4) 1100 0.0072(6)S25B02 Specular 0.1859(30) 0.180(1) 3.28 0.0059(6) 0.0006(5) 880 0.033(3)

aAverages calculated between 1000 cm−1 and 7000 cm−1. The values in parenthesis after the reflectances are the two standard deviation (k � 2 coverage factor)expanded uncertainties.

bPercent change, %Δρ � f�ρPNNL − ρNIST�∕ρNISTg × 100%.cThe diffuseness spectrum is defined as D � ρd∕ρ and measured by the Bruker sphere. D is averaged between 1000 cm−1 and 7000 cm−1 to give the values shown.


Infragold results using the NIST D25A02 standard. The DHRand diffuse reflectance spectra are shown in Fig. 4 along withthe expanded uncertainties and LabSphere’s DHR referencespectrum. Measurements made on the “left” side of the squareare labeled as 1, 2, 3, and 7 and those made on the “right” side

as 4, 5, and 6. The scaled average (averaged between 1000 cm−1

and 7000 cm−1) DHR for samples 4, 5, and 6 is 0.956(87), andfor samples 1, 2, 3, and 7 is 0.954(87); the DHR average fromLabSphere is 0.943 [38] (see Table 3). The values in parenthe-sis after the reflectances are the two standard deviation (k � 2coverage factor) expanded uncertainties. The percent changebetween the average PNNL DHR values and the LabSphereDHR reflectance are 1.38% and 1.17% for the 4, 5, 6 and1, 2, 3, 7 samples, respectively. The agreement between thescaled PNNL infrared measurements and the LabSphere refer-ence is thus very good. The scaled average diffuse reflectance forsamples 4, 5, and 6 is 0.944(74), and for samples 1, 2, 3, and 7is 0.935(74) (see Table 3). Unfortunately, there are no cali-brated diffuse reflectance spectra to which we can compareour results. The calculated diffuseness spectrum, defined asD � ρd∕ρ and averaged between 1000 cm−1 and 7000 cm−1,is 0.987(119) for samples 4, 5, and 6 and 0.980(121) for sam-ples 1, 2, 3, and 7 (See Table 3). The diffuseness, D, is analo-gous to the “haze factor,” b, used in visible transmission orfenestration measurements [40,41]. Shepherd reported a specu-lar reflectance component for Infragold that increases across theinfrared from ∼2% at 2 μm to ∼5% at 12 μm [42,43].

To determine if moving the sample increases the sample-to-sample standard deviation, six sets of DHR and diffuse re-flectance spectra were measured for the Infragold with thesquare fixed in one position on the “right” side (see above)for all the measurements. The results were again scaled usingthe NIST D25A02 standard. The average scaled DHR is 0.957(87), and the scaled diffuse reflectance is 0.949(74) and D �0.992�120� for this set of measurements (see Table 3). Theaverages for the DHR and diffuse reflectance and the expandeduncertainties are nearly identical to those for the spectra(samples 4, 5, 6) shown in Fig. 4, so moving the sample doesnot appear to increase variability. The LabSphere Infragold

Fig. 4. DHR and diffuse reflectance spectra of 2 0 0 × 2 0 0 LabSphereInfragold square, part # UIRT-94-020 are shown in the plot.Reflectance measurements were made with the Infragold square in thebottom sample port. Four sets of measurements, samples 1, 2, 3, and 7weremade from the “left” side of the square. The squarewas then turned180 deg and three sets ofmeasurements weremade from the “right” sideof the square, samples 4, 5, 6. For each position, 2048 scans wererecorded for DHR and diffuse reflectance measurements. The left sidemeasurements were averaged, as were the right side measurements. Thespectra were scaled using the NIST D25A02 standard. The expandeduncertainties are shown in the lower panel. The LabSphere DHRInfragold reference data are shown in the blue trace.

Table 3. Average Scaled DHR and Diffuse Reflectance Values for Infragold, Bruker Diffuse Gold, Spectralon 99%Reflectance Standard, Hand-Loaded Sulfur, Hand-Loaded Talc, and Watera

Sample ρ(PNNL) ρ(Calib.) %Δρb ρd (PNNL) Dc(PNNL)

Infragold (Right, 4, 5, 6)d 0.956(87) 0.943 1.38 0.944(74) 0.987(119)d

Infragold (Left, 1, 2, 3, 7)d 0.954(87) 0.943 1.17 0.935(74) 0.980(121)d

Infragold (Right, fixed)d 0.957(87) 0.943 1.48 0.949(74) 0.992(120)d

Infragold (VNIR)e 0.958 0.941 1.81 0.952 0.993d

Bruker Goldd 1.007(91) – – 0.914(60) 0.909(112)d

Spectralon 99% f 0.961(88) 0.972 1.13 0.961(63) 0.998(113)g

Sulfur (Hand-Loaded)d 0.969(88) – – 0.967(65) 0.998(113)d

Sulfur (VNIR)h 0.964 – – 0.946 0.982h

Talci 0.882(80) – – 0.887(58) 0.994(112)c

Talc (VNIR)i 0.856 0.841 0.982i

Waterj 0.0232(7) 0.0216 7.41 0.005(4) 0.23(80) j

aAverage DHR values for calibration spectra, where available, and percent change with the PNNL results are given. Calculated diffuseness values are also given. Thevalues in parenthesis after the reflectances are the two standard deviation (k � 2 coverage factor) expanded uncertainties.

bPercent change, %Δρ � f�ρPNNL − ρcalib�∕ρcalibg × 100%.cThe diffuseness spectrum is defined as D � ρd∕ρ and measured by the Bruker sphere. D is averaged over the wavenumber ranges noted to give the values shown.dAveraged between 1000 cm−1 and 7000 cm−1.eAveraged between 5000 cm−1 and 9000 cm−1.fAveraged between 4000 cm−1 and 7000 cm−1.gAveraged between 1500 cm−1 and 7000 cm−1.hAveraged between 5000 cm−1 and 7500 cm−1.iAveraged between 5000 cm−1 and 7000 cm−1.jAveraged between 1000 cm−1 and 5000 cm−1.


reference data and the DHR and diffuse VNIR reflectancespectra of the same standard were measured using our dispersivespectrometer and PTFE integrating sphere. For the VNIRresults, three different sets of measurements were made, eachtime the Infragold square was rotated 120 deg. No discernibledifference was observed for the spectra in the three differentpositions, and the spectra were averaged. The PNNL VNIRmeasurement of the Infragold square’s DHR and diffusereflectance values are 0.958 and 0.952, respectively, givingD � 0.993, averaged between 5000 cm−1 and 9000 cm−1.

The scaled and unscaled DHR and diffuse reflectance spec-tra of a flat, diffuse gold plug are shown in Fig. 5. The plug issold with the Bruker sphere and fits in the bottom sample port.Using Eq. (2), the data were scaled using the NIST D25A02standard. Scaling pushes the DHR and diffuse reflectances upabout 0.02 reflectance units throughout much of the mid-andshort-wave infrared. The scaled DHR is 1.007(91), averagedbetween 1000 cm−1 and 7000 cm−1, suggesting a slight over-estimate in the scaling factor, and the scaled diffuse reflectanceis 0.914(60) with the average of the diffuseness spectrum at0.909(112), as seen in Table 3. The finish on the flat, mattegold plug is highly reflective but is far less Lambertian(D � 0.909) than Infragold (D � 0.987�119�) [28].C. SpectralonOur DHR and diffuse infrared reflectance spectra for a 99%reflecting disk of Spectralon (LabSphere) are shown inFig. 6 [25]. A calibration DHR spectrum that came with thedisk is plotted as the green trace in this figure. Spectralon is auseful and convenient Lambertian reflecting material in the vis-ible and near-infrared wavelength regions, but strong absorp-tions begin in the mid-infrared and extend into the far-infrared

[23,31]. The NIST D25A02 standard was used to scale thereflectance spectra shown in Fig. 6. The figure shows both thescaled and unscaled spectra. Because of the highly Lambertiannature of Spectralon, the DHR and diffuse reflectance spectraare nearly coincident. The diffuseness spectrum, D, averagedbetween 1500 cm−1 and 7000 cm−1, is 0.998(113). The aver-age DHR for the LabSphere calibration between 4000 cm−1

and 7000 cm−1 is 0.972, and the PNNL scaled DHR for thismaterial averaged over the same range is 0.961(88) with arelative percent change between the two of 1.13%. The scaleddiffuse reflectance is 0.961(63) over the same range (seeTable 3) [38,42,43].

We observed that there is a slight anisotropy in the specularfraction on the surface of the Spectralon disk: as we rotated thedisk to different positions in the sample port the spread be-tween the DHR and the diffuse in the shortwave infraredwould increase to 1% (maximum) for several positions andthen begin to grow closer until the DHR and diffuse spectrawere lying on top of one another. By noting the position with anotch on the side of the Spectralon disk, we noticed that thepositions where the DHR and diffuse spectra merged and sep-arated were repeatable as the standard was rotated in the sampleport. Furthermore, the disk is not entirely flat: one half of thedisk’s surface slopes down approximately 0.4 mm with respectto the other. This may explain the slight difference indirectional–hemispherical and diffuse reflectance of the disk,as it is rotated in the sample port.

Fig. 5. DHR and diffuse reflectance spectra of the Bruker flat dif-fuse gold plug. Ten sets of reflectance measurements were made withthe plug in the bottom sample port. For each set, 256 scans were re-corded for the DHR and diffuse measurements. All sets were averagedto give the spectra shown in the upper plot. The spectra were scaledusing the NIST D25A02 standard. Both the scaled and unscaled spec-tra are shown. The expanded uncertainties are shown in the lowerpanel.

Fig. 6. DHR and diffuse reflectance spectra of the LabSphereSpectralon 99% standard are shown in the plot. Six sets of reflectancemeasurements were made with the standard in the bottom sampleport. The standard was rotated 60 deg for each new set of measure-ments. For each set, 2048 scans were co-added for the DHR and 2048scans were co-added for the diffuse reflectance measurements. All setswere averaged to give the unscaled spectra shown in the upper plot: theblue trace is the unscaled DHR spectrum and the purple trace is theunscaled diffuse reflectance spectrum. The spectra were scaled usingthe NIST D25A02 standard: the black trace is the scaled DHRspectrum and the red trace is the scaled diffuse reflectance spectrum.The expanded uncertainties are shown in the lower plot. The greentrace is the LabSphere DHR calibration spectrum that came withthe standard.


D. SulfurThe average DHR and diffuse reflectance spectra of the hand-loaded sulfur samples are shown in Fig. 7. The average packingdensity of the sulfur in the cups was 0.78�3� g∕cm3, and themean sulfur particle size was 40(26) μm as determined byoptical microscopy [44]. The DHR (black trace) and diffusereflectance (red trace) were scaled using the NIST D25A02standard. As with the Spectralon 99% reflectance standard,the DHR and diffuse reflectance spectra are nearly coincidentacross the entire infrared, with D � 0.998�113� averaged from1000 cm−1 to 7000 cm−1 (see Table 3). As noted previously,[44] the infrared reflectance measurements for sulfur show anearly perfect Lambertian behavior for the hand-loadedmaterial, but pellets of sulfur made with a die and hydraulicpress (pellet density 1.79�7) g∕cm3) have a significant specularcomponent.

To our knowledge there is no definitive sulfur reflectancereference spectrum. Nash examined sulfur from different sup-pliers using an FTIR and a biconical reflectance accessory [45].He states that those samples were powders with particle sizesless than 100 μm and that these were lightly packed, thoughhe does not give a specific packing density. In the1430 cm−1–5000 cm−1 region, his observed reflectances forhis various sulfur samples are all ∼0.90 referenced to a pieceof 600-grit sandpaper that had been gold coated. BecauseNash’s interest was in examining reference reflectance materialsfor CO2 lasers operating at about 10.6 μm, he notes that hissulfur reflectances at 938 cm−1, which is at a dip in the reflec-tance corresponding to the v1 � v5 sulfur combination band,

range between 0.54 and 0.63 [45]. Egan and Hilgeman [46]examined the DHR reflectance of sulfur powder using an in-tegrating sphere, though they do not specify a reference surface,and report an average reflectance of 0.94 between 900 cm−1

and 3300 cm−1; the resolution of their spectrograph was suffi-ciently low (R � λ∕Δλ � 33) that no sharp features were ob-served. Our average DHR reflectance for the hand-loadedsulfur in the short to midwave infrared is 0.95, and at the localminimum at 938 cm−1 the reflectance is 0.60, so our reflec-tance values are consistent with previous results. Also shownin Fig. 7 are our VNIR DHR (blue trace) and diffuse reflec-tance (green trace) spectra of sulfur powder [23]. These spectraoverlap with the infrared measurements between 5000 cm−1

and 7500 cm−1. Because the sample in the VNIR sphere is heldvertically, a quartz window must be used to hold the sample inplace, and, while the specular nature of the window has beencorrected for [23], the sulfur powder, pressing against the win-dow, may introduce effects that make the material slightly morespecular than the hand-loaded powder samples used for theinfrared measurements described here. In the overlap region,the infrared DHR spectrum is, on average, about 0.52% abovethe VNIR spectrum, and the infrared diffuse reflectance spec-trum is 3.4% above that of the VNIR. Overall, the agreementbetween the two methods is very good, lending further cre-dence to the hardware and protocols used for the infraredmeasurements. Such good agreement between IR and VNIRmeasurements (<3%) for PTFE have also been reported byTsai et al. [47].

E. TalcTalc is a common phyllosilicate that is chemically stable, and, ifkept dry in a desiccator box when not in use, can be used as areference material for infrared integrating sphere performance.The average DHR and diffuse reflectance spectra for six hand-loaded samples are shown in Fig. 8. The talc DHR (black trace)and diffuse reflectance (red trace) were scaled using the NISTD25A02 standard. The average packing density for thesesamples is 0.73�3� g∕cm3, and the particle size is less than10 μm. Between 5000 cm−1 and 7000 cm−1 (i.e., betweenthe talc v4 �OH stretch and OH stretch overtone), the aver-age DHR is 0.882(80), the average diffuse reflectance is 0.887(58) and D � 0.994�112� (see Table 3). The VNIR measure-ment of the DHR (blue trace) and the diffuse reflectance (greentrace) of a talc powder sample held behind a glass window arealso shown in Fig. 8.

F. WaterIn the past, researchers have used water as a specular, lowreflectivity standard [21]. To examine its suitability for this pur-pose, the DHR and diffuse spectra of six deionized sampleswere recorded at 23°C and the results plotted in Fig. 9. TheNIST S25B02 reflectance standard was used to scale the data;both the scaled and unscaled spectra are shown in the plot. Thescaled diffuse spectrum is essentially flat across the entire infra-red with an average reflectance of 0.005(4) in the 1000 cm−1 to5000 cm−1 range. Over the same range, the average scaledDHR is 0.0232(7). As expected, the spectrum shows twomajor absorptions at 1600 cm−1 and 3200 cm−1. As a refer-ence, we calculated the bidirectional reflectance spectrum of

Fig. 7. DHR and diffuse infrared reflectance spectra of six differenthand-loaded sulfur samples. The average packing density of the sulfuris 0.78 g∕cm3. For each sample, 2048 scans were recorded for DHRand diffuse measurements. All sets were averaged to give the spectrashown in the upper plot. Black (DHR) and red (diffuse) traces havebeen scaled using the NIST D25A02 standard. The expanded uncer-tainties are shown in the lower panel. The blue and green traces are theDHR and diffuse reflectance visible/near-infrared (VNIR) measure-ments of sulfur in which the sulfur was packed into a sample cupand a glass cover was placed over the sulfur in the cup. The VNIRmeasurements were made using a Cary 5000 grating spectrographand LabSphere DRA-2500 PTFE integrating sphere.


water (green trace) using Fresnel’s equations and the n and kvalues for water (27°C) given in [48]. We use an angle of in-cidence of 14.8 deg and assume unpolarized light is incident

upon the water’s surface. The calculated curve has an averagereflectance over the 1000 cm−1–5000 cm−1 range of 0.0216.In terms of percent change, the measured DHR is 7.41%higher than that of the calculated bidirectional reflectance.Unfortunately, Downing and Williams do not present theirraw reflectance data in their paper [48] and do not provideuncertainties for their n and k values, so it is not possible todetermine if our values lie within their error bars.

4. DISCUSSION

The integrating sphere we have used for producing the resultsreported here is convenient to use, fits easily into most FTIRsample compartments, and, as demonstrated, yields good quan-titative DHR and diffuse reflectance values. We emphasize thatthese results were achieved only after careful alignment and useof the sphere. Comparing the absolute differences between theaverage PNNL DHR and NIST DHR measurement resultsgiven in Table 2, we see that these differences are <0.02 re-flectance units in all cases, corresponding to a percent changeagreement for the PNNL values to within 4% of the NISTvalues except for the low diffuse reflecting standard D25C02.Comparing the percent changes between the PNNL and NISTaverage diffuse reflectance results, we see that the PNNL valuesare within 5% for the diffuse standards. The measuredPNNL diffuse reflectances for the specular standards S25A02and S25B02 are an order of magnitude larger than the NISTvalues for these standards. For the Bruker sphere with a specularsample in the sample port, the specular exclusion port cap re-moved, and the infrared light directed to the sample, our raytracing results show that no reflected light reaches the detector.When we examine the sample channel data for this arrange-ment for both S25A02 and S25B02, we see that the signalsare indeed small, though non-zero. The reference channel sig-nals are considerably larger than those of the sample channel,though, on the interferometer’s A/D scale, still less than one.For S25A02 at 2125 cm−1, for example, the ratio of the sampleand reference signals is 0.00011∕0.0211 � 0.0052. An alter-nate method for measuring the diffuse reflectance of specularsamples will have to be found.

Using a comparison sphere, Shepherd gives results for a lim-ited number of materials: Infragold, a silver mirror, and a sand-blasted copper disk [42]. The Newport Corp. specular silvermirror exhibits a DHR reflectance spectrum close to 1.0 acrossthe infrared, which is in agreement with the manufacturer’sspecification, and a diffuse spectrum close to zero, as expected.For Infragold, Shepard measures a DHR of 0.94 and diffusereflectance of 0.91 at 4 μm, and these values drop at longerwavelengths: ρ � 0.93 and ρd � 0.89 at 8 μm. Shepherd’sDHR values are thus similar to ours; however, he has lowerdiffuse reflectance values leading him to emphatically concludethat Infragold is not Lambertian. Shepherd’s sandblasted cop-per disk does appear to be far more Lambertian across the infra-red from 2 μm to 12 μm, with ρ � ρd � 0.84 at 8 μm, thoughdetails on how the disk was prepared were not given [42].

Due to the paucity of diffuse reflectance data for many ofthese materials, we have made some qualitative comparisonsbetween our diffuse reflectance measurements and those madeby others using the same or similar materials. Our Cary VNIR

Fig. 9. DHR and diffuse reflectance spectra of six different deionizedwater samples, 23°C, averaged. For each sample, 2048 scans were re-corded for the DHR (blue) and diffuse (pink) unscaled measurements.All sets were averaged to give the spectra shown in the upper plot. Thescaled DHR (black) and diffuse (red) reflectance measurements werescaled using the NIST S25B02 standard. The expanded uncertaintiesare shown in the lower plot. The green trace is a calculated DHRreflectance spectrum using the n and k values from [48].

Fig. 8. DHR and diffuse infrared reflectance spectra of six differenthand-loaded talc samples. The average packing density of the talc is0.73 g∕cm3. For each sample, 2048 scans were recorded for DHR anddiffuse measurements. All sets were averaged to give the spectra shownin the upper plot. The black (DHR) and red (diffuse) traces have beenscaled using the NIST D25A02 standard. The expanded uncertaintiesare shown in the lower panel. Blue and green traces are the DHR anddiffuse reflectance visible/near-infrared (VNIR) measurements of talcin which the talc was packed into a sample cup and a glass cover wasplaced over the talc in the cup. The VNIR measurements were madeusing a Cary 5000 grating spectrograph and LabSphere DRA-2500PTFE integrating sphere.


spectrometer and LabSphere DRA-2500 integrating sphere al-low us to make some comparison measurements. However, our1 0 0 diameter NIST standards and the Bruker diffuse gold plugare too small to fit properly in the sample port of the VNIRintegrating sphere, and it would be preferable to make compar-isons without the intervening window over the powder samplesin the VNIR measurements. For the Infragold, the Cary 5000/DRA-2500 measurements show a near-perfect Lambertian ρ �0.958 and ρd � 0.952 at θi � 8°, D � 0.993 in the SWIRwithout a cover window over the standard, and for the infraredmeasurements of the same standard ρ � 0.957�87� andρd � 0.949�49� at θi � 14.8°,D � 0.992�120�. These valuesare for the fixed position Infragold measurements and afterscaling using the D25A02 standard.

Balling reports [43] BRDF values at wavelengths 544 nm,632.8 nm, and 3.39 μm for Infragold, Spectralon, and theNIST DxxA, DxxC, and DxxD materials. He describes the ex-tent, if present, of any spectral lobing for these materials over arange of incident angles. From his BRDF values, he calculatesthe DHR for these materials, and these calculated values agreewell with our measured DHR values at 3.39 μm [25].

It was of interest to find that the Bruker diffuse gold plugthat comes with the integrating sphere has a significant specularcomponent (ca. 9%, see Fig. 5). Both the DHR and diffusereflectance curves for this material are spectrally flat acrossthe infrared, and the DHR average is 1.007(91) after scalingto the D25A02 NIST standard. If we assume that the spherewall was prepared in the same manner as the surface of the plug,and, because we are referencing our spectra to the sphere wallbefore scaling, this high value is not surprising. With the flipmirror pointing at the wall reference spot, and the diffuse goldplug in the bottom sample port, we have measured the detectorsignal ratio without and with the cap in the specular exclusionport. From Eq. (1), we can calculate the ratio as

V w∕o

V w� 1 − ρ�1 − f w�

1 − ρ�1 − f w∕o�; (5)

where f w � 0.0227 and f w∕o � 0.0677 are the exchange frac-tions with and without the cap in the specular exclusion port[32]. A sphere wall reflectance value of approximately ρ � 0.98best replicates the measured signal ratio.

Again, we are not familiar with how the Bruker sphere’s sur-face is prepared, but it appears both visually, and from the re-sults in Table 3, that the Bruker matte gold is not as porous asthe LabSphere Infragold. The less Lambertian (more specular)nature of the Bruker sphere’s surface (D of 0.909 versus 0.990)has consequences on the performance of the sphere. Koehl andForcht [28] pointed out that essentially all IR spheres havegold-coated surfaces of some sort. As a sphere surface materialbecomes more porous, it becomes more Lambertian; conse-quently, the reflectivity, ρ, generally drops, particularly inthe longwave IR. Increasing the smoothness of the surfacegenerally increases ρ, but, as Hanssen [49] demonstrated, theincreased specularity of a non-Lambertian surface leads to ar-tifacts in the reflectance values, particularly for dark sampleswhose reflectivities differ greatly from those of the referencematerial. Reflectance measurements are thus not only sample

and reference dependent but contain dependencies on spheredesign and coatings as well.

In addition to the sulfur reflectance results of Nash [45]discussed above, Haner and Menzies [50] have measured thein-plane reflectance of two preparations of sulfur at10.6 μm. In one sample, a cast of sublimed sulfur was preparedby making a slurry of the sulfur with acetone and allowing thisto dry in the sample cup; in the other, dry sublimed sulfur wasloaded and pressed in the sample cup; the packing densities forthese preparations are not given. Using a CO2 laser to illumi-nate the surface of the sulfur samples, they observed a sharpretro-reflection at the angle of incidence, and, while the slurrypreparation showed a near-perfect Lambertian reflectance spec-trum over a wide sweep of reflection angles, the pressed sulfursample showed a distinct specular reflection peak. Oppenheimand Feiner [51] repeated the Haner and Menzies experiment in1994 using only the sulfur/acetone slurry preparation and ob-served that sulfur “is probably the most Lambertian surface inthe IR.” Assuming that the hydrocarbon impurities can be re-moved and the sulfur dried, this statement is certainly true atwavelengths shorter than 5 μm, though working with sulfurpowder can be inconvenient. Our infrared results, after scalingwith the NIST D25A02 standard, show the DHR and diffusereflectance traces nearly coincident in the shortwave-infraredand well into the mid-infrared and longwave-infrared, as seenin Fig. 7. Our VNIR reflectance spectra for sulfur powder, alsoshown in Fig. 7, show similar reflectance values with the infra-red measurements; however, the VNIR results have a small sep-aration between the DHR and diffuse reflectance traces. Thisdifference could be a residual effect not removed when we cor-rected for the specular reflectance from the glass sample cover,or possibly the sulfur is being slightly compressed by the glasswindow as discussed above.

Finally, the water’s DHR spectrum leaves some doubt as toits usefulness as a reflectance standard. As expected, the diffusereflectance spectrum is essentially flat and near zero across theinfrared. (The deionized water was carefully pipetted intothe sample cups; we did not observe a meniscus on its surface.The nitrogen purge was turned off during the water reflectancemeasurements.) We observe as much as a 30% change in someregions of the infrared between our measured DHR curve andthe reflectance curve calculated using the indices of refractionfrom the paper by Downing and Williams [48]. They do notprovide estimates of their random or systematic sources ofuncertainty in their n and k values that were fit to severalabsorption and reflection data sets. Because our measurementof the more convenient NIST D25C02 standard, which has asimilar average reflectance to that of water, gives agreementwithin 0.002 reflectance units (6%) of the NIST referencespectrum, we will use this as a reference for low reflectancevalues until the water reflectance/absorbance spectrum in theinfrared is better understood.

Though the PNNL measurements of the five NIST stan-dards compare well with the NIST measurements, there areclearly some significant differences in the appearance of thePNNL and NIST data. The variability in the percent changesbetween the PNNL and NIST measurements of the DHR anddiffuse reflectances of the different standards show that a simple


scaling factor cannot account for the differences. There are sys-tematic differences in the way PNNL and NIST make theirmeasurements. NIST uses the absolute reflectance method de-veloped by Hanssen [24,33,39] and a sphere that is symmet-rical with respect to the geometry of the sample and referencemeasurements. The NIST sphere does not use an internal mir-ror to steer light to the ports; rather light from the interferom-eter is steered external to the sphere. In contrast, the sample andreference measurement geometries of the Bruker sphere are notsymmetric, and the sphere has an internal steering mirror that isa minor source of light loss. When making reflectance measure-ments with a sphere, one is ratioing results from two differentgeometries, and open ports can lead to loss of hemisphericallydistributed light from the sample and the reference point on thewall in the case of the Bruker sphere. The amount of light lostthrough the ports for the sample and reference measurements isaffected by differences in measurement geometries and any dif-ference in the BRDF of the sample and reference [33,39]. Adirect example of the effect of this is the apparent crossoverof the DHR and diffuse curves in Fig. 2. This is at least partiallydue to the fact that D25A02 is likely more Lambertian (flatBRDF) than that of the integrating sphere wall. The wave-length dependence is what one would expect: at longer wave-lengths, a diffuse surface begins to appear more specular.

To obtain the diffuse reflectance, the specularly reflectedlight needs to be removed. In the case of the Bruker sphere,this is done by removing the cap in the specular exclusion port.To obtain a reference measurement without changing thesphere throughput, the internal mirror is rotated to the refer-ence position, and the two spectra are ratioed. The effects of thesphere geometry under these circumstances can be understoodfrom Figs. 10 and 11. In the Bruker sphere, reflected light isdirectly lost in three locations: the specular exclusion port, the

entrance port and the input mirror, which will reflect samplescattered light back through the entrance port. In the case of anideal sphere coating, and a sample that has perfectly specularand diffuse components, the entire specular component ofthe sample is removed, and the fractional loss of the diffuselyscattered light is the same for both sample and sphere wall refer-ence. In the case of a realistic sample BRDF and a realisticsphere coating BRDF, the situation is more complex, as dem-onstrated in the figures. For the DHR measurement, light isonly lost directly through the entrance port and mirror. Inthe ideal case for sample and wall BRDF, the specular and dif-fuse components are measured together, and the reference pro-vides the proper throughput correction. However, with realisticBRDFs as shown, the relative correction may be different, re-sulting in an error that may show up as an effective negativespecular component, when subtracting the diffuse reflectancefrom the DHR.

It is important to note that, because the specular exclusionport of the Bruker sphere subtends a larger solid angle (23.5 degfull apex angle, 0.132 sr) than the specular exclusion port ofthe NIST sphere does (12.7 deg full apex angle; 0.0385 sr), thediffuse reflectance spectrum of a sample, as measured by theBruker sphere, will always be equal to or smaller than that mea-sured by the NIST sphere, depending on the BRDF of the sam-ple. For a perfectly Lambertian sample, the two spheres shouldgive, after the aforementioned corrections are made, equal dif-fuse reflectance values. But, as the sample becomes more specu-lar, the Bruker sphere will let more specular light out and willconsequently give a smaller diffuse reflectance spectrum (andhence smallerD value) than that measured by the NIST sphere.Whenever comparing diffuse reflectance results from twodifferent integrating spheres, the geometry of the specularexclusion port must be taken into account.

Fig. 10. Light loss plot for the Bruker sphere measurement samplegeometry is shown. The bidirectional reflection distribution function(BRDF) of a typical diffuse sample at 10.6 μm is shown, and regions oflight loss are shown with solid vertical lines. The horizontal axisrepresents the angle of reflected light relative to the sample’s surfacenormal. The range of angles associated with regions of light loss isestimated from the schematic shown in Fig. 1. The horizontal lineand vertical shaded region represent ideal diffuse and specular compo-nents, respectively. This plot is a 2D cross-section of the actual3D case.

Fig. 11. Light loss plot for the Bruker sphere measurement referencegeometry is shown. The BRDF for a typical diffuse gold interior spherewall at 10.6 μm is shown, and regions of light loss are shown with solidvertical lines. The horizontal axis is incidence angle with respect to thereference’s (sphere wall) surface normal. The angles associated with eachport loss are estimated from the schematic shown in Fig. 1. Below thehorizontal line (1∕π) light loss is from diffusely reflected light, andabove the horizontal line light loss is from specularly reflected light.This plot represents a 2D cross-section of the actual 3D case.


These concepts are illustrated in Figs. 10–12. In Fig. 10 weshow a plot of one slice of the BRDF (log y axis) of a typicaldiffuse sample at 10.6 μm. The horizontal line representsan idealized Lambertian reflector. The x axis is the angle withrespect to sample surface normal, and the angular extents of thevarious ports are marked off as horizontal lines on the plot. Thepositions of these lines have been estimated from the schematicin Fig. 1. The cap in the specular exclusion port, in this exam-ple, has been removed. Figure 10 represents the sample mea-surement geometry; Fig. 11 represents the reference geometrywhere the BRDF of a typical diffuse gold sphere lining has beenplotted. The differences in the specularly reflected light in thetwo plots would have to be accounted for to properly calculatethe diffuse reflectance spectrum, or in the case where the cap isin place, the DHR spectrum.

The NIST absolute reflectance measurement geometries areshown in Fig. 12 [24,33,39]. The sample diffuse measurementgeometry with regions of light loss are shown with solid lines,and the sample DHR geometry light loss is shown with dashedlines and an italic label. These are overlaid with an exampleBRDF and compared to ideal diffuse and specular BRDFs.In the case of the NIST sphere, there is no specular port orinternal mirror. (There is an empty reference port, but thereis a baffle, which prevents sample reflected light being lostthrough it.) [39] The only lost light is through the entranceport. The diffuse reflectance is obtained by using a compensat-ing wedge between the sample and sample port, which resultsin normal incidence on the sample and consequently results inthe loss of the specularly reflected light. The DHR measure-ment is made without the wedge and has 8 deg incident light.Figure 12 shows the sample measurement case for the DHR

and diffuse reflectance cases. The reference measurementgeometry is unchanged in both cases. See [33] for further de-tails. In NIST’s case, the “specular reflectance” is determined bythe difference in light lost from the two measurements, whichboth use the sample and hence the same—or quite similar—BRDFs at the 0 deg incidence versus 8 deg incidence measure-ment geometries. For the diffuse measurement, an 8 deg wedgeis used between the sample and the sample port edge that re-sults in normal incidence on the sample. In NIST’s method, thetwo results are subtracted to obtain the specular component,with minor corrections [39]. Reference measurements are per-formed for both 0 deg and 8 deg angle of incidence measure-ments and are ratioed with the sample measurements to obtainreflectance values. However, the reference measurement geom-etry does not change and hence does not play any role in thespecular/diffuse separation.

5. CONCLUSION

We have demonstrated that a commercial integrating sphereand Fourier transform spectrometer can, with the proper align-ment and measurement procedures, be used to record DHRand diffuse reflectance spectra in the infrared and give quanti-tative results when compared with calibration standards. Theparticular sphere used here allows for measurement of powdersamples in a horizontal port in the bottom of the sphere[52,53]. Expanded uncertainties have also been determinedfor the measurements with coverage factor k � 2 [37].Comparing measured results for a set of NIST and commoninfrared reflectance reference materials shows that we can ob-tain good DHR values compared with reference spectra with-out corrections. For our measurement of the DHR of the fourNIST reflectance standards with ρ > 0.18, our values for thosestandards are about 4% relative to the NIST DHR values,and for the one standard with ρ < 0.18 our value is about7% relative to the NIST DHR data for that one standard.For our measurement of the diffuse reflectance of the fiveNIST reflectance standards, the percent change for the diffusestandards is 5% compared with the NIST diffuse reflectancevalues, and for the specular standards the diffuse reflectances,ρd , (all ≤ 0.01 reflectance units) are about an order of magni-tude larger than the NIST calibration spectra for these stan-dards. Discrepancies between the PNNL and NIST resultshave been discussed in terms of the differences in measurementgeometries, BRDFs of the sample and reference surfaces, andlight lost through ports in the sphere. Ray tracing of Brukersphere has been conducted to determine absolute uncertaintiesfor the PNNL reflectance measurements.

Using the reflectance values and their uncertainties for theNIST standards given in Table 2, we can examine how well thePNNL and NIST DHR and diffuse reflectance fall within theircombined uncertainty ranges. By taking the difference betweenthe PNNL and NIST reflectance value for each standard,and adding their uncertainties, we can see that most of thedifferences fall within their combined uncertainty. The excep-tions are the S25A02 diffuse reflectance measurement and theS25B02 DHR and diffuse reflectance measurements.

A scaling method was described to allow direct comparisonof the reflectance spectra of other materials with one of the

Fig. 12. Light loss for the NIST absolute reflectance measurementgeometries is shown. For the sample geometry, regions of light loss areshown with solid lines; for the reference geometry, regions of light lossare shown with dashed lines and an italic label. These are overlaid withan example sample BRDF and compared to ideal diffuse and specularBRDFs. Here the “specular component” is the difference in light lostfrom the two geometries, which both use the sample (and hence thesame—or quite similar—BRDFs—0 deg incidence versus 8 deg inci-dence). The reference measurements are made in the same way forboth 0 deg and 8 deg incidence measurements and are only usedto correct for any extremely small changes in throughput or driftin going from the 0 deg and 8 deg incidence measurements.


NIST standards. The scaled DHR spectra of Infragold and99% reflecting Spectralon as measured using our sphere andmethod gives an agreement within 2% of the calibrationspectra provided by LabSphere. Our DHR results for sulfurpowder and water also agree well with literature values, thoughthe provenance of these literature values makes it difficult tomake quantitative comparisons.

Funding. U. S. Department of Energy, National NuclearSecurity Administration (NNSA), Defense NuclearNonproliferation; United States Department of Energy bythe Battelle Memorial Institute (DE-AC05-76RLO 1830).

Acknowledgment. The authors would like to thankDrs. Michael Juette and Arno Simon of Bruker Optics, Inc. forvaluable discussions regarding the use of the Bruker A562-Gintegrating sphere. Support was provided by the Department ofEnergy’s National Nuclear Security Administration, DefenseNuclear Nonproliferation and Dr. Victoria Franques. Theauthors would also like to thank Dr. Steven Sharpe ofthe Pacific Northwest National Laboratory for his support.The Pacific Northwest National Laboratory is operated forthe United States Department of Energy by the BattelleMemorial Institute.

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