REVIEW

Review of thermal infrared polarimetry,part 2: experiment
Nathan Hagen *Utsunomiya University, Department of Optical Engineering, Utsunomiya, Japan

Abstract. After the discussion on thermal polarization theory from part 1 of this review, we
now review practical methods for experimentally measuring infrared polarization properties.
Starting with a model for thermal emission from inhomogeneous media, we discuss the complexities of paints and how to determine the ideal thickness of paints used for blackbody simulators.
Another commonly used inhomogeneous material is anodized aluminum, and we provide anextensive discussion of its fascinating structure and its optical properties in the thermal infrared.
Theoretical analysis and experimental measurements show how the peculiar properties of alumina in the longwave infrared region combine to create a material that has a surprisingly highemissivity, for optically smooth sapphire and highly inhomogeneous anodize-coated aluminum.
To illustrate features of thermal polarization theory given in part 1 of this review, we also present
a series of infrared polarization images, and demonstrate the use of a convenient reference source
for thermal polarization testing. © 2022 Society of Photo-Optical Instrumentation Engineers (SPIE)[DOI: 10.1117/1.OE.61.8.080901]

Keywords: infrared; polarization; emissivity; blackbody; Kirchhoff’s law; paint; anodization;
alumina.
Paper 20220229V received Mar. 8, 2022; accepted for publication Aug. 9, 2022; published
online Aug. 26, 2022.

1 Introduction
Part 1 of this review focused on the theory needed to understand polarization behavior in thethermal infrared, with a particular emphasis on the physics underlying thermal emission.1 In thispart, we cover thermal polarization measurements, and particularly focus on how we can interpret measurements in situations where we cannot control or accurately quantify many of thevariables involved in a measurement. This is a common problem for outdoor measurements,
or when measuring surfaces with unknown optical properties. Whereas textbook examples
of measurements are often limited to well-controlled situations that are only available in a lab,the discussion that follows aims to show how to interpret measurements of things such as the
optical and thermal behavior of a paint layer and its metal substrate, how they interact when
exposed to sunlight or night sky, and how their behavior changes depending on the thicknessof the paint coating. Moreover, in outdoor environments, we often do not know the background
spectrum of the light being reflected from a surface. As a result, such measurements can involvea bit of detective work, combining thinking about the underlying physics with building approximate thermal models for the materials, to make sense of measurements.
The discussion that follows starts with practical techniques to obtain the reflectivity andemissivity. Section 3 then describes how paints behave in the thermal infrared region, and how
one can use this information to decide on the ideal coating thickness for a blackbody simulator
using high-emissivity paint. The discussion of different types of paints and paint coatings brings
together material that is difficult to find in the research literature, yet is helpful for considering
measurements of car bodies, building exteriors, and coated objects.
Another common complicated material found in almost every lab is anodized aluminum.
Section 4 describes the structure of these coatings, how they are created, and the reason for
their surprisingly high emissivity. While the behavior of these anodize coatings is “obvious”*Address all correspondence to Nathan Hagen, nh@hagenlab.org

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August 2022 • Vol. 61(8)Hagen: Review of thermal infrared polarimetry, part 2: experimentin hindsight, we show that they perform optically much the same as a pure unstructured slab
made of alumina (amorphous sapphire) glass.
Although the radiance from paints and anodize coatings turns out to have little polarization
content, other situations show significant polarization, and so Sec. 5 reviews the special
requirements of polarimetric data and how to obtain the Stokes parameters with a rotating wire
grid polarizer. We then show an easily constructed reference source for thermal polarimetric
imaging—a painted light bulb—and how to make use of it in laboratory measurements. Finally,
we present a collection of outdoor polarization images taken in both the midwave infrared(MWIR) and longwave infrared (LWIR), to show quantitatively the magnitude of polarimetricsignatures found in the thermal regime.

2 Combined Radiance from Emission and Reflection
In most outdoor environments, thermal contrast is driven primarily by two sources: warming
sunlight and cooling sky. After dawn, sunlight begins to warm up surfaces that it touches, at
a rate faster than the surrounding air. For objects exposed to sunlight, the surface temperatureis driven by the amount of sunlight that it absorbs versus the rate at which the surface transfers
heat to its surroundings via conduction, convection, and radiation. For objects that remain in theshade, or which equilibrate to the local air temperature (as plants do using transpiration), thermal
contrast remains small.
In the MWIR and LWIR measurement windows (3 to 5 μm and 8 to 12 μm, respectively),
thermal photons radiated by surfaces into a cloudless sky have a high chance of escaping into
space. Because a cloudless sky also has low thermal emission, this allows sky-facing surfaces tocool down in proportion to the solid angle of clear sky visible to them. Though outer space has aneffective temperature of only 3 K, atmospheric transmission in the window regions is not 100%so the night sky never gets as cold as that, but can reach −100°C for wavelengths near 10 μm,
at the center of the LWIR window, when viewing through dry air.
Because the night cooling process is dominated by radiative cooling whereas the morning
warming process is dominated by sunlight absorption, objects generally warm up in the morning
faster than they cool down at night. These two processes drive the development of thermal contrast between objects in the outdoors, and consequently the production of thermal polarization
signatures.
Figure 1 shows the radiance reaching a thermal infrared camera, where the at-sensor radianceis a sum of the object surface’s self-emission Lobj ¼ ϵLbb ðT obj Þ and the reflected radiance fromthe background, ρLbkg
Lmeas;m ¼ ϵobj;m Lbb ðT obj Þ þ ρobj;m Lbkg;m ;EQ-TARGET;temp:intralink-;e001;116;307(1)Fig. 1 The measurement geometry, showing the object emission (in red) and background reflection (in blue) components of thermal radiance detected by the camera. The thermal contrast is
ΔT ¼ T obj − T bkg , and the radiance contrast is ΔL ¼ Lobj − Lbkg .
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August 2022 • Vol. 61(8)Hagen: Review of thermal infrared polarimetry, part 2: experimentfor polarization m ∈ fs; pg. Each of the quantities here also depends on the wavelength λ andthe direction of emission/reflection θ 0 , but explicitly showing these dependencies makes theexpressions unwieldy, so we leave them implied.
Light from the background passes through the intervening atmosphere before reaching theobject surface, and this generally causes absorption of the object’s radiance, as well as pathradiance emission by the air. Using Kirchhoff’s law to equate the path emission with pathabsorption, ϵpath ¼ 1 − τpath , we define Lbkg as
Lbkg;m ¼ τpath ½εbkg;m Lbb ðT bkg Þ þ ð1 − τpath ÞLbb ðT path Þ :EQ-TARGET;temp:intralink-;e002;116;651(2)

If the atmospheric absorption is small enough to be neglected (τpath ¼ 1), such as when the
optical path is short, then substituting Eq. (2) into Eq. (1) and writing ρobj;m ¼ 1 − ϵobj;mgives
Lmeas;m ¼ ϵobj;m Lbb ðT obj Þ þ ð1 − ϵobj;m ÞLbkg;m ¼ ϵobj;m ΔL þ Lbkg ðT bkg Þ ;EQ-TARGET;temp:intralink-;e003;116;577(3)

for radiance contrast ΔL ¼ Lbb ðT obj Þ − Lbkg .
When ρLbkg ≫ ϵobj Lobj , the reflected radiance dominates over surface emission, as when theobject is much cooler than the background, or when the object emissivity is much smaller than
the reflectivity (e.g., polished metals). When ϵobj Lobj ≫ ρLbkg , surface emission dominates overreflection, as when the object is much hotter than the reflected background. This is a common
situation when viewing warm objects that have a high emissivity or when the reflectedbackground is very cold (e.g., a cloudless sky).
One of the consequences of Eq. (3) is that, as Tyo et al.2 demonstrated, there will be nopolarimetric signature when the surface and the reflected background are in radiometricequilibrium, where ΔL ¼ 0.

2.1 Practical Methods of Measuring Reflectivity and Emissivity
In the thermal infrared, it is very difficult to obtain surfaces that are completely dark. Everymeasurement of a surface is therefore a composite of the surface’s self-glow and the backgroundreflected from the object. As a result, one must exploit reference samples to a much larger extent
than is necessary in the visible spectrum. For example, while we may wish to measure the reflectivity ρobj of a surface, the radiance received by the camera depends on multiple unknowns.
However, if the object emissive radiance can be ignored (such as when the measurement object
is much colder than the reflected background), then we can use a blackbody as background taken
at two different temperatures T 1 and T 2 . When we subtract then subtract the two measurments,
we obtain
Lobj;1 − Lobj;2 ¼ ρobj ½Lbb;bkg ðT 1 Þ − Lbb;bkg ðT 2 Þ ;EQ-TARGET;temp:intralink-;e004;116;273(4)in which we obtain the reflectivity asρobj ¼

EQ-TARGET;temp:intralink-;e005;116;225

Lobj;1 − Lobj;2;
Lbb;bkg ðT 1 Þ − Lbb;bkg ðT 2 Þ(5)where Lobj is a radiance measured by the camera, and Lbb is the blackbody radiance source.
Unfortunately, this by itself is not a practical approach for outdoor measurements.
If we can ignore the reflected signal and work with only the emissive radiance, then anotherapproach is possible. For this, we insert into the scene an opaque reference sample of known
temperature T ref and emissivity ϵref , and take the ratio of the radiance from the object and theradiance from the reference

EQ-TARGET;temp:intralink-;e006;116;104

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Lobj ðλÞ qðλÞϵobj ðλÞ Lbb ðλ; T obj Þ¼;
Lref ðλÞ qðλÞ ϵref ðλÞ Lbb ðλ; T ref Þ
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where qðλÞ represents the responsivity of the optics and detector, as well as influence of themeasurement geometry. In the outdoors, these can be difficult to estimate accurately, but becauseqðλÞ can be arranged to be approximately the same for both “obj” and “ref,” we rewrite this asϵobj ðλÞ ¼

EQ-TARGET;temp:intralink-;e007;116;699

Lobj ðλÞ Lbb ðλ; T ref Þε ðλÞ ;
Lref ðλÞ Lbb ðλ; T obj Þ ref(7)from which we obtain the emissivity estimate. This too is not yet a practical approach since
we have had to ignore the reflected radiance.
For a general situation, in which the reflected and emitted radiances are significant, we needto combine the two above. If we measure the detected radiances from the object and the reference, at two different temperatures T 1 and T 2 , we subtract the two measurements and then takethe ratio between the object and reference radiances. For a detected radiance from the object,
Lobj ðλ; TÞ ¼ qðλÞ½ϵobj ðλÞLbb ðλ; TÞ þ ρobj Lbkg ðλÞ ;EQ-TARGET;temp:intralink-;e008;116;581(8)

we use the shorthand Lobj;1 ¼ Lobj ðλ; T 1 Þ and ΔLobj ¼ Lobj;2 − Lobj;1 to write
ΔLobj ¼ qðλÞϵobj ðλÞ½Lbb;2 − Lbb;1  ;EQ-TARGET;temp:intralink-;e009;116;536(9)where the background radiance terms have dropped out. Next, we do the same thing for thereference measurements and then take the ratio

EQ-TARGET;temp:intralink-;e010;116;480

ΔLobj ϵobj ðλÞ½Lbb ðλ; T obj;2 Þ − Lbb ðλ; T obj;1 Þ;¼
ϵref ðλÞ½Lbb ðλ; T ref;2 Þ − Lbb ðλ; T ref;1 Þ
ΔLref

(10)

so the emissivity is obtained asϵobj ðλÞ ¼

EQ-TARGET;temp:intralink-;e011;116;423

ΔLobj
ΔLref




Lbb;ref;2 − Lbb;ref;1ϵ ðλÞ:
Lbb;obj;2 − Lbb;obj;1 ref(11)

In the lucky circumstance where one can ensure that the temperatures T 1 and T 2 are the same
temperatures for both the object and the reference, then this simplifies to


ΔLobj
ϵobj ðλÞ ¼(12)ϵ ðλÞ:
ΔLref refEQ-TARGET;temp:intralink-;e012;116;352

One should also keep in mind that the approach shown here gives the emissivity at the particular angle of view at which the measurements were taken. Any change in the view angle, thesurface angle, or the background light distribution will require another set of measurements for ϵunder the new conditions.3 The derivation leading to Eqs. (11) and (12) also assumes a specularreflecting surface. For nonspecular reflecting surfaces and nonuniform backgrounds, a fully
four-dimensional representation of the incident and reflected light fields becomes necessary.4,53 Paint Coatings
Paint consists of a binder (such as a resin or polymer-based oil) mixed with a diluent (such as
water or an organic solvent), a colorant (such as pigment particles or dye), an opacifier (such as
TiO2 particles), and other additives. For example, a varnish is considered as a pigment-free paintand an ink is considered as a paint with minimal binder. Because paints are often formed as acolloidal suspension of soluble and insoluble materials, light passing through a paint coating
layer will experience the coating as a material with inhomogeneous optical properties.
Though one can model the light propagation at the microscale, using Monte Carlo methods andoptical models of the various constituents in the paint, this requires considerable work to set up
and implement. A more practical approach is to model the paint as a scattering medium withuniform properties of n, k, and scattering coefficient σ that are in some sense an average over theproperties of the material mixture.
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August 2022 • Vol. 61(8)Hagen: Review of thermal infrared polarimetry, part 2: experimentFig. 2 The hemispherical-average emissivity ϵ as a function of paint coating layer thickness, forvarious paint optical properties ðn; k ; sÞ.

Paints come in a wide variety of materials, so that the exact theoretical models are generally
not very useful except as a guide to the overall behavior. Speaking in broad terms, we can saythat most paint binders (especially for paints used for visible-light purposes and not speciallydesigned for particular infrared properties) are formed with materials that have a relatively hightransmittance in the LWIR region.6,7 Most inorganic pigments found in paints have strong, broad
absorption bands in the LWIR, with carbonates having absorption bands centered near 7 μm,
silicates near 9 μm, and oxides between 9 and 30 μm.8 Organic pigments show strong, sharp
absorption bands principally between 6 and 11 μm. Metallic pigments generally exhibit a lower
wavelength dependence, and generally reduce the emissivity of a paint.
Painters generally consider a typical paint coating thickness for interior walls of building(using a brush or roller) to be about 50 μm. Paints applied by spray application tend to havelower concentration of solids and higher concentration of solvents, so that a paint coating appliedwith a spray can achieve thicknesses as low as 2 μm.9 For industrial coatings such as used on
automobile exteriors, multiple paint layers (e.g., primer, base, and enamel) are common, so thatthe total coating thickness of >200 μm is not unusual. As a result of the high absorbance of dyes
and pigments mixed with the paints, these coatings often produce a high emissivity (ϵ > 0.9) atthese standard thicknesses.6
Using the Kubelka–Munk model of light propagation in scattering media (from section 9 ofpart 1 in this review), we can estimate the effect that internal scattering has on the reflection andemission properties of a given paint coating in the longwave infrared. Figure 2 shows the estimatedemissivity as a function of coating thickness, using equation (59) from part 1 of this review, for aset of paint coating layer properties ðn; k; sÞ, where s ¼ ση. We can see that in the regime simulated here, of refractive index 1.40 < n < 1.52, absorption coefficient 0.009 < k < 0.46, and scattering coefficient s ¼ 8 mm−1 , that the absorption coefficient range plays the largest role inaffecting changes in emissivity. With these parameters, we find that the critical thickness of thecoating layer is bc ¼ 5, 23, and 114 μm when k ¼ 0.009, 0.1, and 0.46, respectively.

3.1 Choosing the Ideal Paint Thickness for a Blackbody Simulator
In a laboratory setting, it is common to paint aluminum or copper parts with a high-emissivity
matte paint to create a blackbody simulator for the purposes of calibration and creating welldefined thermal sources. Two examples are shown in Fig. 3, of a painted shutter intended forcamera calibration, and a painted kitchen pot placed on a heater stove. The paint used here is
Krylon 1602 ultraflat black paint. Surprisingly, the painted kitchen pot is actually one of the mostversatile and reliable thermal sources that the author has used, having a larger thermal mass andlarger area than commercial blackbody sources do, while also allowing a means of quickly
changing the temperature by replacing the water inside.
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(a)

(b)

Fig. 3 Two blackbody simulators commonly used in laboratory infrared imaging: (a) a metal
shutter and (b) a heated kitchen pot, each coated with a high-emissivity paint.

When constructing these blackbody simulators out of painted metal surfaces, we select metals having high conductivity so that the metal surface is maintained at more-or-less the same
temperature as the heat source. (In the case of the kitchen pot, the heat source is the water in thepot.) Next, it is useful to know how thick the paint coating should be. A coating that is too thickwill create a thermal insulation barrier against the heat source, so that the coating surface will besignificantly cooler than the heat bath, because it is radiating into the cooler ambient air, and isalso cooled by air convection currents. A thick paint coating will also make the blackbody simulator susceptible to changes in temperature due to turbulent air currents and changing external
heat sources. In contrast, a coating that is too thin will have a reduced emissivity, because themetal substrate will be close enough to the surface to influence the emissivity value. Thus, acoating should be as thick as it needs to be—the critical thickness bc —but no more.
Unfortunately, the many differences among paint types means that it is very difficult tospecify bc except in broad terms. In Fig. 2, we see three models of paint layers, for which bc
varies from 5 μm—close to the minimum thickness at which a paint layer can be applied—to
225 μm, which is a rather thick coating. Sharma et al.10 recommend an optimal paint coating
thickness of 50 to 60 μm for high-emissivity paints. While one can use a paint thickness gauge toachieve the desired thickness, in practice the difference among paints means that it is necessary
to measure each paint experimentally to determine bc . Though this is not difficult, a ready shortcut is available. In the author’s experience, the transmittance of the Krylon 1602 black paint in
the visible spectrum is actually not far from the transmittance in the LWIR region, so that one canjudge the correct thickness by painting a transparent sample such as an acrylic plate and placea bright light source behind the sample. Once the fully dried paint layer is opaque enough thatthe light source is no longer visible, the paint layer is also close to bc for LWIR light. Using thesame paint techniques to achieve an equivalent thickness on the metal part is a simple matter ofpractice and care.
One question that arises for painted-metal blackbody simulator sources is how these can beconsidered blackbodies if the paint layer, being a thermal insulator, produces a thermal gradient
between the substrate and the surface. If we compare the paint coating to a blackbody of equivalent surface temperature, then the paint will be unfairly biased and we might obtain ϵ > 1
because the warmer inner layers of the paint will be emitting more light than they should beunder an isothermal assumption. Of course, when we make the blackbody, we can compensate
for this by calibrating the simulator to drive the metal to a slightly lower temperature, but clearly
this is an expediency. As long as the correction is small enough, however, the blackbody
simulators remain useful sources to have in the lab.
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Section 7.2 in part 1 of this review dealt with this issue and simulated the case for paintcoatings, concluding that for high-emissivity paints the isothermal requirement can be ignoredin the LWIR regime. For low-emissivity paints, however, it is possible to have modest deviations
from the expected emissivity limits when comparing emission with a blackbody at the object’s
surface temperature. In the MWIR regime, however, where the absorption of the paint basebecomes small, there is a much higher likelihood of seeing a significant boost to apparent emissivity (M > 0) when heating the surface from behind, and when the paint contains few particulate absorbers (such as for a clear coat).

4 Anodized Aluminum Coatings
Aluminum parts used in manufacturing are often anodized rather than painted, because anodize
coatings are generally much stronger than paint, and adhere better to the metal, making them lessprone to damage from aging and wear. In optomechanics, anodize coatings are almost always
given a black coloring to reduce stray light, though matte paint actually does a better job at thisthan the anodize coatings can. Although anodize coatings may also more brittle than paint coatings, making them more susceptible to cracking from thermal stress, the hard layer provides
good protection against wear and corrosion. However, it is not clear what role the anodizing
plays for thermal infrared systems. Thermal infrared optics also use black-anodized aluminum
mounts, but it is not clear from the literature whether this is simply a matter of habit among optics
manufacturers, or whether the anodizing provides a useful role in reducing unwanted thermal
gradients.
Aluminum metal naturally forms a thin layer of amorphous oxide film (alumina) on its surface when exposed to air.11 Although this 2 to 4 nm natural Al2 O3 coating is quite hard, it isgenerally too thin to protect the underlying metal against damage. As a result, many manufacturers apply an electrolytic processes to increase the oxide layer thickness, creating either a uniform “barrier” oxide layer or a porous anodize layer.
Nonporous “barrier oxides” are grown in electrolytic solutions in which the aluminum oxide
is chemically neutral, while porous oxide coatings are grown within an acidic electrolyte bath—typically sulfuric acid in the case of aluminum—in which the alumina is partially dissolved. Fora barrier oxide coating, when an electrical current is applied to the aluminum substrate throughthe electrolyte, the electric field causes the negatively charged oxide ions to move inward to reactwith aluminum at the metal-oxide interface.12 This causes a migration of aluminum atoms out
from the substrate while also pushing the oxide layer deeper into the substrate. The positively
charged aluminum ions pulled out from the substrate are attracted to the interface between theoxide coating and the electrolyte, allowing the oxide layer to thicken. For a barrier (i.e., nonporous) oxide, the final thickness of the oxide layer depends on the applied voltage, producing
about 1.1 nm thickness per volt.13 A 100 V process thus generates a barrier oxide thickness of
110 nm, which is much thicker than the original natural oxide layer of 2 to 4 nm.
Although the growth of porous oxide films follows a very similar electrochemical process,they can be formed at much lower voltages by placing the metal inside an acidic solution—
typically sulfuric acid in the case of aluminum. Because the aluminum oxide is partially soluble
in the acid bath, the surface layer partially dissolves and develops pores.14,15 As the anodization
proceeds, the pores allow the oxides to continue migrating deeper into the metal substrate than ispossible with a barrier oxide, so that the process grows a thick porous layer of aluminum oxide
directly out of the aluminum substrate. The size of the pores and rate of oxide layer growth arecontrolled through the acid concentration, applied voltage, temperature, and aluminum alloy
type (for example, see Fig. 4). Typical commercial aluminum anodize may have thicknesses
ranging from 2 to 25 μm, with typical pore diameters of 30 nm spaced 100 nm apart.17,18
In precision engineering, a common practical rule followed by designers is that during anodization the aluminium oxide grows equal amounts into the surface as out from the surface, as
shown in Fig. 5. By this rule, an anodize layer will increase the original part dimensions on eachsurface by half the oxide layer thickness.19 Precise measurements, however, have shown that theactual growth is typically closer to 1.4—that is, the anodization expands the part dimensions
by 40% of the thickness of the oxide layer (rather than the 50% given by the common rule).16
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(a)

(c)

(b)

100 nmFig. 4 (a)–(c) Field-emisson scanning electron microscopy top view images of anodized aluminum formed at voltages ranging from 20 to 160 V in different acid solutions, showing the change inpore diameter with process conditions. Adapted with permission from Ref. 16.

Fig. 5 Cutaway view of the anodize film structure as it develops: (1) the aluminum base metal(dark gray), (2) develops pores of aluminum oxide (light gray) that extend down into the metal
and up above the original surface layer. (3) The pores grow over time, after which the metal
is removed from the acid bath. (4) The metal is dipped into a bath of dye (with the dye particles
shown here as small spheres), which collects inside the pores. (5) The metal is sealed, producing
a layer of boehmite (medium gray) at the outer surface that closes the pores.

Li et al.16 noticed, however, that this growth value can vary considerably with the anodization
process used.
At the end of the first anodization step, bare anodized aluminum appears like the unpolishedmetal, but slightly whitened in color (step 3 in Fig. 5). Because the porous coating is composedof Al2 O3 , the aluminum now has a very hard surface that is no longer brittle, as it is now muchthicker. However, at this point so far it retains most of its natural metallic color. The process ofadding color to an anodize can occur simultaneously with the anodization process by addingcolorants into the acidic solution. Or, color can be added after completion of the anodize bydipping the anodized metal in one or more warm dye solutions (cobalt acetate and ammonium
sulfide are common dyes). This is step 4 in Fig. 5. Whether colored during anodization or after,
the coloring process is followed by inserting the metal into either a hot water bath, or into aroom-temperature nickel acetate solution, to “seal” the surface (step 5 in Fig. 5).20,21 (The nickel
acetate C4 H14 NiO8 acts as a catalyst for the formation of boehmite.) Most sources describe thissealing process as producing a layer of boehmite (γ − AlOðOHÞÞ at the outermost surface of thesample, causing the outermost layer of aluminum oxide to expand. This forces the pores to close,
and prevents the enclosed dye from escaping.22 Hu et al.,20 however, show measurements implying that the boehmite also coats the interior walls of the pores. In the end, the resulting seal iseffective enough that the colorants enclosed by the anodize layer do not outgas even when
exposed to vacuum.10 Finally, while most of the dyes used for coloring anodized aluminum aresusceptible to fading on exposure to strong UV and blue light, a few dyes can retain their color
even after extended exposure.
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August 2022 • Vol. 61(8)Hagen: Review of thermal infrared polarimetry, part 2: experimentFig. 6 Measured emissivity of anodized aluminum at normal incidence at λ ¼ 10 μm, with datataken from Refs. 10, 23, and 24.

Figure 6 shows the normal-angle measurements of anodized aluminum emissivity at
λ ¼ 10μm, as a function of the anodize layer thickness, obtained from three publishedsources.10,23,24 The Kohara and Sharma measurements in Fig. 6 use a standard anodize coating,while the Brannon measurements use a hard (low-temperature) anodize coating. In each case,from a base polished aluminum emissivity of 0.05, the anodization layer increases ϵ to 0.15 with
only 1 μm thickness, 0.45 with 2 μm thickness. From the collected measurements, we can seethat the anodize films reach ϵ ¼ 0.91 at critical thicknesses of bc ¼ 15, 25, and 50 μm, respectively, for the Kohara, Sharma, and Brannon data. The Brannon and Kohara data are for anundyed anodize coating, while the Sharma data contain measurements for both undyed andblack-dyed anodize. Adding the black dye appears to have increased the emissivity of the coatingslightly when the coating is thin, but the dye does not seem to affect the emissivity value forlayers above the critical thickness. The larger critical thickness value obtained by Brannon may
be a result of the use of a hard anodize process, but may also be due to other differences in theanodize process used.
A final concern is that once the porous anodize oxide layer is sealed, the various sealing
methods form a thin layer of boehmite on the outer surface of the coating. Emissivity dataon boehmite are quite difficult to find, but Kollie et al.25 presented measurements of boehmite
films, giving ϵ from 0.91 to 0.93. Because this value is quite close to the value of the anodize
coating itself, it seems that the boehmite layer is unlikely to change the overall emissivity
by much.

4.1 Reflectivity Measurements on Anodized Aluminum Parts
To explore how the porous structure of anodize layers and the colorants sealed inside them affectthe optical properties in the thermal infrared, we measured the reflectivity of two smooth flat
anodized surfaces, from two widely adopted optomechanics manufacturers (Thorlabs BA2/M
and OptoSigma CAAN-25LSEE). Choosing smooth samples minimizes the effect of diffuse
reflection on the reflectivity measurements. The results of the experimental measurements, takenwith a LWIR microbolometer camera (FLIR A35), are shown as dots in Fig. 7, from which we fit
polynomial curves. Because it was difficult to control the background source radiance for measurements taken at smaller angles of incidence (<30 deg), the data at these angles is less reliable(as indicated in the figure using unfilled circles for those data points), and these points were
given less weight in the fitting. The figure also shows a curve drawn in red representing thetheoretical reflectivity curve for Al2 O3 averaged over the 8 to 12 μm wavelength region.
The results of Fig. 7 show that the measured reflectivity of the anodized materials closely
corresponds to the theoretical curve for alumina in the LWIR. We can conclude, therefore, thatthe porous structure and the enclosed dyes play almost no role in the optical behavior of thematerials at these wavelengths. It seems likely that the process of sealing the pores has created
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August 2022 • Vol. 61(8)Hagen: Review of thermal infrared polarimetry, part 2: experimentFig. 7 The experimentally measured reflectivity as a function of angle of incidence. The curves
show polynomial fits to the two anodized samples overlaid with the theoretical reflectivity curve for
Al2 O3 averaged across the 8 to 12 μm region.

an external layer of amorphous alumina (or perhaps boehmite) that is sufficiently thick to shield
the underlying pores and colorants from affecting the external optical properties. Figure 7
also shows that anodized surfaces have a surprisingly high emissivity at angles near normal
incidence—a result that corresponds closely to the data in Fig. 6.
Although the laboratory measurements for Fig. 7 used a rotating wire-grid polarizer in frontof the camera to collect the linear polarization state distribution, at none of the measured angles
of incidence did the degree of linear polarization (DOLP) exceed 1%, even at grazing angles. Partof the reason for the low DOLP is likely that the reflectivity is already so low that both s andp reflections from the surface will be close in magnitude.

5 Thermal Polarimetry Requires Radiometric Calibration
Thermal imaging data typically come in three types: raw digital counts, temperature units, andradiance units. Temperature units are the most intuitive, but they are unfortunately incompatible
with the Stokes vectors, which require the data to be proportional to the at-sensor radiance.
While digital counts are proportional to radiance, they are almost always offset by an unknown
bias that causes error when calculating quantities related to the degree of polarization (DOP).
To illustrate this point, if can measure the light passed by a polarizer at angles 0 deg, 45 deg,
90 deg, and 135 deg, the four intensities (in digital counts and ignoring noise) are given as26,27
g1 ¼ kL0 þ B;

(13)

g2 ¼ kL45 þ B;

(14)

g3 ¼ kL90 þ B;

(15)

g4 ¼ kL135 þ B;

(16)

EQ-TARGET;temp:intralink-;e013;116;307

EQ-TARGET;temp:intralink-;e014;116;264

EQ-TARGET;temp:intralink-;e015;116;242

EQ-TARGET;temp:intralink-;e016;116;220

for bias value B and unknown constant k. The linear Stokes vector is defined as

EQ-TARGET;temp:intralink-;e017;116;198

s0
s1
s2

!

01
¼@

2 ðL0 þ L45 þ L90 þ L135 Þ

L0 − L90
L45 − L135

1
A;

(17)

so that we can try to take our four measurements gi with the polarizer to estimate the Stokes
vector as
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0

1

@

EQ-TARGET;temp:intralink-;e018;116;735

01
ks0 þ 2B
A ¼ @ ks1 A :ks2

1ðg þ g2 þ g3 þ g4 Þ
B2 1C

g1 − g3
g2 − g4(18)

Whereas the bias B drops out of the estimates for s1 and s2 , so that these two are estimatedaccurately despite the bias, the error remains in s0 . Because the DOLP is calculated from the
Stokes vector elements aspﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ
s21 þ s22
DOLP ¼;(19)
s0
EQ-TARGET;temp:intralink-;e019;116;643

dividing by s0 propagates this error into the DOLP result. If B is uncorrected and positive, theestimated DOLP will be too small; if B is negative, then the estimated DOLP will be too large.
The same issue occurs when calculating the normalized Stokes parameters s~ 1 ¼ s1 ∕s0 ands̃2 ¼ s2 ∕s0 . As a result, it is necessary to correct for the bias when working with data in raw
digital counts. The bias-corrected digital counts are equivalent to relative radiance units.
The Stokes parameters themselves can be given in absolute radiance units L or relative radiance units kL (with unknown k). When calculating the normalized Stokes parameters or the
DOLP, however, the unknown factor drops out of the equations so that the two become identical.
Equation (3) holds for both p- and s-polarizations. If we detect the two polarization states
independently, then we write the polarization contrast C as
C¼

EQ-TARGET;temp:intralink-;e020;116;477

Lp − Ls;
Lp þ Ls(20)

where DOLP is related to the contrast as DOLP ¼ jCj. Another polarimetric parameter that
we will have use of below is the angle of linear polarization (AOLP), which is defined as 
1s
AOLP ¼ arctan 2 :
(21)
2
s1
EQ-TARGET;temp:intralink-;e021;116;408

It is widely known that smooth surfaces produce polarized reflection and emission, so thatman-made objects tend to produce more highly polarized light than natural objects do. And thisis especially true in the thermal infrared, because the ratio between the surface roughness and thewavelength is reduced by a factor of 20 in going from visible (∼0.5 μm) to LWIR (∼10 μm)
wavelengths. Surfaces that are optically rough in the visible can often become optically smoothin the LWIR. Even rough road surfaces, such as asphalt and concrete, show significant polarizedreflection properties at 10 μm wavelengths.28 Nevertheless, researchers used to visible-lightpolarimetry often experience surprise upon first encountering the extremely low DOP one typically encounters in the thermal infrared. This low DOP is a direct consequence of the complementarity of the emissivity and reflectivity, which tend to cancel one another, and of the fact thatthe temperatures we usually encounter are a small ΔT (e.g., 10 K) on top of a large baseline
temperature T 0 (e.g., 300 K). From a radiance standpoint, the temperature contrast we experiencein common thermal scenes is small (often ∼10%) in comparison with the contrast between lightand dark in the visible spectrum that we often experience with our eyes (often a factor of
10 or more).
Figure 8 shows an example of reflection of an unpolarized cold object (T bkg ¼ 20°C) from awarm surface of silica glass (T obj ¼ 40°C), at angles of incidence θ ¼ 0 deg, 30 deg, 45 deg, and60 deg. At θ ¼ 0 deg, the p- and s-polarization spectra coincide, but separate as the incidence
angle increases. Thus we see that the polarization contrast for the sum Lmeas of reflected andemitted light is increasing with angle. We can also see that because the p- and s-polarizationreflectivities are equal for silica glass at about 8.5 μm, the polarization contrast at this wavelength is zero for all angles. Thus, as implied by Eq. (3), we see that when the radiance contrast
between the surface and the background reflected from it is small, the polarization-dependencein ϵobj has little effect.
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(a)

(b)

(c)

(d)

Fig. 8 The p- and s-polarized radiance spectra (solid and dashed curves, respectively) of a SiO2
glass surface: (a) for T obj ¼ 40°C, reflecting a background blackbody at T bkg ¼ 20°C, for angles ofincidence θ ¼ 0 deg, 30 deg, 45 deg, and 60 deg. Each arrow indicates the direction of increasing
angle; (b) the polarization contrast CðθÞ for the data shown in panel (a). (c) The radiance spectra
for an angle of incidence of θ ¼ 30 deg, for increasing amounts of thermal contrast ΔT ¼ 0°C,
15°C, 30°C, 60°C, and 120°C; (d) the polarization contrast CðΔT Þ for the data shown in panel (c).

6 Painted Tungsten Bulb for a Thermal Polarimetry Reference Source
To validate polarization measurements, it is important to have a trustworthy reference source
against which one can check the results. One useful idea put forward by Bowers et al.29 is
to use a large sphere heated to a high temperature and coated with a high-emissivity material.
For this, they used a 45-cm diameter hollow brass sphere, painted with high-emissivity paint(n~ ¼ 1.6 þ i0.1), with a heater placed inside the sphere. Although this reference source should
not be difficult to make, it is also not something that one can get off-the shelf. Similarly, Kudenov
et al.30 used a 125-mm diameter sphere of obsidian glass. In this case, the sphere was heated byimmersion in warm water before being dried and placed for imaging. While this too is a usefulreference object, it is not as easily obtained, and not as convenient as we might like.
A similar style of reference source that is readily obtained is a spherical tungsten light bulb.
This kind of bulb is a reasonable approximation to a true sphere, inherently contains a heater
element, and achieves impressively high temperatures. An example set of images of this kind of
bulb is shown in Fig. 9. From the images, one can immediately see that the glass of the bulb isactually diathermous, so that the internal tungsten element saturates the image. While glass is anabsorbing material in the MWIR range, the bulb glass is evidently too thin to absorb enough of
the infrared light. As a result, it is necessary to paint the bulb to increase its opacity. Not only
does this increase the surface emissivity, but it also helps increase the surface temperature by
absorbing the bulk of the light emitted by the bulb.
Figure 10 shows the same bulb after applying a black paint. As mentioned in Sec. 3.1, one
should apply paint as thinly as possible, but sufficiently thick to fully obscure the substrate. In
Fig. 10, we can see that the filament is no longer saturating the MWIR camera, but it is nevertheless still visible as the brightest feature in the data. Thus, the paint layer is a little bit too thin.
The visible camera image also shows that the black paint does not entirely obscure the visiblespectrum light underneath, and so the visible image can be used as a rough guide to the behavior
in the thermal infrared as well. Note that the integration time used in Fig. 9 is longer than thatused in Fig. 10 due to the hotter bulb surface of the latter.
One concern with applying black paint to a bulb is that the paint should be designed for hightemperature use. Ordinary paints will likely start to burn after extended use of more than couple
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August 2022 • Vol. 61(8)Hagen: Review of thermal infrared polarimetry, part 2: experimentFig. 9 MWIR polarization images of an unpainted tungsten lamp with a spherical bulb. The s 0
image is given in units of digital counts, with bias term removed.

Fig. 10 MWIR polarization images of a tungsten lamp with a spherical bulb painted with blackheat-resistant paint. The s 0 image is given in units of digital counts, with bias term removed.
The black arrows in the AOLP figure indicate the AOLP direction at the edge of the sphere.

of minutes. In addition, anyone who might want to give this a try should exercise caution. The
bulb glass is not designed for temperatures this high, and is also not designed for the additional
mechanical constriction forced on it by the paint coating. As a result, there is some risk that the
bulb may shatter. This has not yet occurred in any of my own experiments, but it remains a safetyconcern.
Taking advantage of the painted spherical bulb as a reference source, we use the data ofFig. 10 to check our polarization results. We expect emission to be predominantly p-polarized,
so that the angle of polarization will follow the angle of the radius extended from the center of thesphere, with respect to horizontal. Tracing the data along a circle just inside the edge of thereference sphere image gives the AOLP data shown in Fig. 11. Most of the measured AOLP
data fall within 5 deg of the ideal polarization angle. The relatively low DOLP of 0.05 is partly
due to the roughness of the matte paint surface. (Most high-temperature paints are matte type.)
Although we expect the pattern of polarization emission from the sphere to give constant AOLP
along radii extending from the center, we can see that the center of the AOLP image showsdeviations from this pattern. It seems likely that polarization emission from the filament is
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August 2022 • Vol. 61(8)Hagen: Review of thermal infrared polarimetry, part 2: experimentFig. 11 The AOLP (red curve) and DOLP (blue curve) traced along the circle at the edge of thereference sphere shown in Fig. 10. The slanted gray line shows the ideal polarization angle.

mixing with the bulb surface emission to produce the observed pattern, because the DOLP image
clearly shows that the filament is blurred on transmission through the bulb glass and paint.
Finally, in Fig. 12, we show the image of the spherical reference source reflected from a basinof chilled water (∼5°C). The experiment layout viewed from the side shows that the reflection
angle for this setup is roughly 69 deg—somewhat beyond the pseudo-Brewster angle of 53 deg.
This is different from the previously stated pseudo-Brewster angle of 50.6 deg because figure 4
in part 1 of this review gives the reflectivity at 10 μm, while the camera used here measures in
the MWIR (3 to 5 μm). This angle is still sufficient to generate a strong polarization signature.

Fig. 12 (Top) The experiment layout, viewed from the side, for measuring the polarization imageof the spherical bulb reference source reflected from a basin of chilled water. To the right one cansee the wiregrid polarizer and camera lens. (Bottom rows) MWIR polarization images of theblack-painted bulb of Fig. 10 seen in reflection from 5°C water, near the pseudo-Brewster angle.
Because the water reflection induces a large polarization for objects with such a large thermal
contrast, the radial polarization signature seen in Fig. 10 is no longer apparent. The s 0 image
is given in units of digital counts, with bias term removed. The concentric circular pattern apparent
in the AOLP image is residual calibration error, due to the reflection off the rotating polarizer in frontof the camera.
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In this case, the rotating AOLP around the edge of the sphere is no longer apparent. Instead, we
see only the dominating uniform linear polarization signature due to the water surface reflection.
Due to the strong thermal contrast between the reference source and the water, the DOLP
achieves a value of about 0.26 over most of the bulb image. Outside of the bulb image, the
DOLP generally stays below 0.01 due to the small thermal contrast between the water surface
and the reflected room walls.
In the images of Fig. 12, we can also see the image of the tungsten filament inside the bulb
reflected from the water. Due to the very large thermal contrast between the filament and thewater, we find that the DOLP reaches up to 0.68 for those pixels covering the filament. The
pattern of concentric circles surrounding the image of the bulb is due to the linear polarizer.
Although the camera’s calibration attempted to compensate for the polarizer’s effect, the compensation was incomplete, leaving this residual pattern.

7 Collection of Infrared Stokes Vector Imagery of Outdoor Scenes
To demonstrate thermal polarization behavior in the outdoors, Fig. 13 shows a suburban scene ofa row of houses illuminated by direct sunlight against a background of blue sky. This data wascaptured with a FLIR A35 LWIR microbolometer thermal camera, with an image size of
320 × 256 pixels, 25 μm pixel size, 12 bit analog to digital converter (ADC), 50 mK noiseequivalent temperature difference (NETD), and an f∕1.25 lens. The polarization data wereobtained by rotating a wiregrid polarizer, made of aluminum wires deposited on a Germanium
substrate, and rotated to azimuth angles of 0 deg, 45 deg, 90 deg, and 135 deg. The s1 and s2
images were obtained as in Eq. (17), then divided by s0 for normalization. Although the s0 image
was calibrated to units proportional to radiance for the purposes of obtaining the Stokes
parameters, for purposes of display, the data in Fig. 13 were converted back to radiometric temperature for clarity of discussion, and also to provide an example of the radiometric temperatureof the sky.
The solar panel roofing in Fig. 13 is warmed by sunlight, while reflecting a cold background(blue sky). This setup roughly corresponds to the values used in Fig. 8. Because the sky in theseimages is seen close to the horizon, it is not as cold as when viewed at zenith angle. If we estimate
the slant angle of the roof with respect to the line of sight as roughly 30 deg, and that the solar
panels are covered with silica glass, then this situation would correspond to the data shown in

Fig. 13 LWIR polarization images of a row of houses with solar panel roofing. The s 0 radianceimage has been converted to temperature units. Due to residual registration errors, object edges in
the image contain spurious polarization signatures.
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August 2022 • Vol. 61(8)Hagen: Review of thermal infrared polarimetry, part 2: experimentFig. 14 MWIR polarization images for a car, where the reflected background is primarily blue sky.
(The visible and MWIR images were taken at different times.) The faint concentric circles visible in
the polarization images are residual calibration errors, due to the reflection off the rotating polarizerin front of the camera.

Fig. 8(d), with the polarization signature averaged across the LWIR band (8 to 12 μm). Solarpanels are generally covered with tempered glass, which may have a different reflectance spectrum from pure silica glass, and may or may not be antireflection coated. However, if the solar
panel glass is equivalent to silica, we can infer that the thermal contrast between the glass and thereflected background (blue sky) was likely >40°C.
Although the grass and trees in Fig. 13 reflect sky polarization just as the roof panels do, theirtemperature is lower, due to their transpiration, and their surfaces are also less smooth. In addition, the small size of each leaf means that each pixel in the image contains a range of leaf angles,
so that the measured polarization is a sum over a semirandom set of orientation angles. The result
is a negligible polarization signature.
The next example (Fig. 14) shows the polarization image of a car, captured with a FLIR
x6900sc MWIR InSb thermal camera, with an image size of 640 × 512 pixels, 25 μm pixel size,
14 bit ADC, 20 mK NETD, and an f∕2.5 lens. In Fig. 14, the reflected background is once again
blue sky, providing a strong thermal contrast for the car body warmed in the sun. Because thereflected background itself is unpolarized, one can use the AOLP defined in Eq. (21) to infer theorientation angle of the surface with respect to the line of sight.
Even under the favorable circumstances of Fig. 14, we can see that the DOP never surpasses
0.1. Although the car windshield, warmed up in the sunlight, is much warmer than the sky background, the radiance contrast is smaller than one might expect because of the 300 K offset to all
natural temperatures we experience around us. Though something like 40°C may seem a large
thermal contrast, the polarization signature is based to a radiance contrast which would be from,say, a 300 K object and a 340 K object. In terms of temperatures, this is only a 13% difference.
For radiances, the ratio will be somewhat larger than this due to the nonlinear relationship.
Note that the faint pattern of concentric rings visible in the polarization images of Fig. 14
appears to be caused by ghost reflections from different surfaces of the camera lens and from theinside surface of the wiregrid polarizer.

8 Conclusion
Although an earlier review of imaging polarimetry suggested that typical polarimetric signaturesin the MWIR and LWIR can be as high as 20% to 25%,31 my own experience is that typicalnatural signatures (i.e., outside the lab) generally do not extend beyond 10% except in unusual
circumstances.32 The low DOP for most phenomena in the thermal infrared is likely why the field
has so far not seen widespread use. Though the polarization signature is useful for applications,
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the low DOP means that measurements suffer from a low signal-to-noise ratio except in thosecircumstances where one can ensure a large thermal contrast between the object under test andthe background being reflected from the object. Such circumstances where thermal polarimetry
could benefit measurements may be the detection of objects in deep shade or at night, and themeasurement of surface orientations from the resulting polarization. In the open ocean, this could
potentially include the measurement of wave surfaces at night, if the skies remain clear enough toprovide sufficient thermal contrast with the water surface.
As Shaw33 indicated with respect to thermal polarization measurements containing waterreflection, the partial cancellation of reflection and emission polarization is generally more
severe in the MWIR than the LWIR, making it more difficult to do emission polarization workin the midwave. In contrast, the MWIR has the advantage that it can work with reflected sunlight,
providing with an extremely strong light source for use in reflection polarization that is only
available to LWIR measurement through the sunlight’s heating of the imaged surface.
In the discussion already noted, we found that blackbody simulators using high-emissivity
paints can maintain optimal performance using paint coatings on the order of 20 μm thick. Thiscan be difficult to measure, but one can apply the same painting procedure to a sample that istransparent in the visible spectrum and increase the paint coating until a bright visible lightsource no longer transmits through the coating. This is a simple rule that can be applied in any
laboratory.
We also found that, after anodization, an aluminum surface achieves a surprisingly highemissivity of ϵ ≈ 0.91. This is useful in infrared optomechanics, as it helps to homogenize thermal gradients within systems, and gives one reason why the use of anodized aluminum parts is
ubiquitous in the field. The discussion also showed that anodize coatings demonstrate a surprisingly complex inhomogeneous structure. Though this makes it difficult to create an accurate
optical model of the surface, the fine structure does not seem to have much effect on the opticalproperties of the material in the thermal infrared. That is, one can treat a dyed anodize coating
simply as a slab of amorphous alumina.
The laboratory and outdoor polarization measurements that we presented in Secs. 6 and 7 use
only linear polarization states. Though it is possible to generate circular polarization states in thethermal infrared, theoretical considerations tell us that we can expect the degree of circularpolarization to be quite small in almost all natural circumstances. However, though circularly
polarized emission has not been demonstrated for natural surfaces, it has been shown to exist for
nonreciprocal media34 and structured chiral media.35,36 For those readers interested in exploring
circular states in the thermal regime, there are zero- and low-order quarter-wave plates andhalf-wave plates that are commercially available for MWIR and LWIR ranges. Most waveplates
operating in the MWIR use MgF2 , while LWIR waveplates are generally made of cadmium
thiogallate (CdGa2 S4 ), cadmium sulfide (CdS), or cadmium selenide (CdSE). There are even
achromatic waveplates made of CdS and CdSE waveplate doublets.
Finally, we can also add that many of the nonthermal phenomena exhibited in infrared emission polarization apply directly to fluorescence emission phenomena as well. As a result, polarization measurement can be used for the separation of fluorescent emission from reflection.37,38

Acknowledgments
The author is grateful to Photron Inc. for allowing use of their FLIR x6900sc InSb camera in the
MWIR polarimetry experiments. The author would also like to thank Shuhei Shibata for help
conducting the FLIR A35 LWIR polarimetry experiments. A portion of this research was funded
by a grant from Denso Corp., and by JSPS KAKENHI (Grant No. JP 20K04516).

References
1. N. Hagen et al., “Review of thermal infrared polarimetry, I: theory,” Opt. Eng. 61, 070902(2022).
2. J. S. Tyo et al., “The effects of thermal equilibrium and contrast in LWIR polarimetricimages,” Opt. Express 15, 15161–15167 (2007).
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August 2022 • Vol. 61(8)Hagen: Review of thermal infrared polarimetry, part 2: experiment

3. B. Bartlett et al., “Spectro-polarimetric BRDF determination of objects using in-scene
calibration materials for polarimetric imagers,” Proc. SPIE 7461, 74610T (2009).
4. W. C. Snyder and Z. Wan, “BRDF models to predict spectral reflectance and emissivity inthe thermal infrared,” IEEE Trans. Geosci. Remote Sens. 36, 214–225 (1998).
5. I. G. E. Renhorn, T. Hallberg, and G. D. Boreman, “Efficient polarimetric BRDF model,”Opt. Express 23, 31253–31273 (2015).
6. J. R. Aronson, “Modeling the infrared reflectance and emittance of paints and coatings,”
U.S. Army Research Office, 17451.1-0 (1982).
7. B. P. Sandford, “IR reflectance of aircraft paints,” Phillips Laboratory, USAF, PL-TR-942313 (1985).
8. L. V. Wake and R. F. Brady, “Formulating infrared coatings for defence applications,”
DSTO Materials Research Laboratory, MRL-RR-1-93 (1993).
9. W. D. McKelvey, P. B. Zimmer, and R. J. H. Lin, “Solar-selective paint coating development,” U. S. Department of Energy, DOE/CS/34287-T1 (1979).
10. A. K. Sharma et al., “Anodizing and inorganic black coloring of aluminum alloys for space
applications,” Metal Finish. 95(12), 14–18 (1997).
11. N. F. Mott, “Oxidation of metals and the formation of protective films,” Nature 145,
996–1000 (1940).
12. J. E. Houser and K. R. Hebert, “The role of viscous flow of oxide in the growth ofself-ordered porous anodic alumina films,” Nat. Mater. 8, 415–420 (2009).
13. R. S. Alwitt, “Anodizing,” in Electrochemistry Encyclopedia, Electrochemical Society(2002).
14. J. P. O’Sullivan and G. C. Wood, “The morphology and mechanism of formation of porous
anodic films on aluminum,” Proc. R. Soc. Lond. A 317, 511–543 (1970).
15. C. A. Grubbs, “Anodizing of aluminum,” Metal Finish. 97(12), 476–487 (1997).
16. A. P. Li et al., “Hexagonal pore arrays with a 50–420 nm interpore distance formed by
self-organization in anodic alumina,” J. App. Phys. 84, 6023–6026 (1998).
17. F. Keller, M. S. Hunter, and D. L. Robinson, “Structural features of oxide coatings on
aluminum,” J. Electrochem. Soc. 100, 411–419 (1953).
18. P. Wade and C. Preedy, “Fujihokka: a high-emissivity approach to aluminum anodizing,”
Metal Finish. 101(12), 8–13 (2003).
19. S. Liu et al., “Fast anodization fabrication of AAO and barrier perforation process on ITO
glass,” Nanoscale Res. Lett. 9, 159–166 (2014).
20. N. Hu et al., “Effect of sealing on the morphology of anodized aluminum oxide,” Corrosion
Sci. 97, 17–24 (2015).
21. S. U. Ofoegbu, F. A. Fernandes, and A. B. Pereira, “The sealing step in aluminum anodizing: a focus on sustainable strategies for enhancing both energy efficiency and corrosion
resistance,” Coatings 10, 226–280 (2020).
22. C. J. Donahue and J. A. Exline, “Anodizing and coloring aluminum alloys,” J. Chem. Educ.
91, 711–715 (2014).
23. R. R. Brannon, Jr. and R. J. Goldstein, “Emittance of oxide layers on a metal substrate,”
J. Heat Transfer 92, 257–263 (1970).
24. S. Kohara and Y. Niimi, “Infrared radiation properties of anodized aluminum,” Mater. Sci.
Forum 217, 1623–1628 (1996).
25. T. G. Kollie, T. D. Radcliff, and F. J. Weaver, “Emittance of boehmite and alumina films on
6061 aluminum alloy between 295 and 773K,” J. Heat Transfer 113, 185–189 (1991).
26. E. F. Zalewski, “Radiometry and photometry,” in Handbook of Optics,M. Bass, Ed., Vol. 2,
2nd ed., Chap. 24, McGraw-Hill (1995).
27. J. R. Schott et al., “Thermal infrared radiometric calibration of the entire Landsat 4, 5, and 7
archive (1982–2010),” Remote Sens. Environ. 122, 41–49 (2012).
28. U. P. Oppenheim and Y. Feiner, “Polarization of the reflectivity of paints and other roughsurfaces in the infrared,” Appl. Opt. 34, 1664–1671 (1995).
29. D. L. Bowers et al., “Unpolarized calibration and nonuniformity correction for long-wave
infrared microgrid imaging polarimeters,” Opt. Eng. 47, 046403 (2008).
30. M. W. Kudenov, J. L. Pezzaniti, and G. R. Gerhart, “Microbolometer-infrared imaging
Stokes polarimeter,” Opt. Eng. 48(6), 063201 (2009).
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31. J. S. Tyo et al., “Review of passive imaging polarimetry for remote sensing applications,”
Appl. Opt. 45(22), 5453–5469 (2006).
32. S. H. Sposato et al., “Two long-wave infrared spectral polarimeters for use in understanding
polarization phenomenology,” Opt. Eng. 41, 1055–1064 (2002).
33. J. A. Shaw, “Degree of linear polarization in spectral radiances from water-viewing infrared
radiometers,” Appl. Opt. 38, 3157–3165 (1999).
34. Y. Wang et al., “Broadband circularly polarized thermal radiation from magnetic Weyl
semimetals,” Opt. Mater. Exp. 11, 3880–3895 (2021).
35. J. Ginn et al., “Polarized infrared emission using frequency selective surfaces,” Opt. Express
18, 4557–4563 (2010).
36. C. Khandekar and Z. Jacob, “Circularly polarized thermal radiation from nonequilibrium
coupled antennas,” Phys. Rev. App. 12, 14053–14064 (2019).
37. O. Sandus, “A review of emission polarization,” Appl. Opt. 4, 1634–1642 (1965).
38. S. Ahmed et al., “Separation of fluorescence and elastic scattering from algae in seawaterusing polarization discrimination,” Opt. Commun. 235, 23–30 (2004).
Nathan Hagen: Biography is not available.

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