1. Introduction

Micro-Fourier Transform Infrared Spectroscopy (Micro-FTIR) is used to measure broadband infrared response (reflectance and or transmission) at micron length scales to deduce local material properties. This technique is frequently used for investigating intrinsic material properties such as in the study of highly correlated phase transitions at their fundamental length scales [1,2] or deciphering chemical composition of microscopic samples [3]. Alternatively, devices that involve infrared remote sensing, could require a small-area infrared probe to evaluate future device performance such as in bolometers [4], imaging arrays [5], superconducting nanowire single photon detectors (SNSPD’s) [6], high Q infrared micro resonators [7] or metamaterial arrays [8]. The signal to noise ratio (SNR) is often a major limitation for achievable resolution in Micro-FTIR and is attributable to low emission power from commonly used broadband thermal sources. In addition, diffraction at infrared wavelengths is also a major limiting factor in the spatial resolution that can be achieved. The SNR limitation is exacerbated if one wants to measure the response of low-reflection materials, such as for diffuse reflectors. Coatings made from this class of materials, which we refer to as hyper-black, have numerous high-impact applications such as in absorbers for solar power conversion [9], previously mentioned detectors [10], stealth coatings [11], or tailorable frequency-selective surfaces [12,13]. Direct absorption measurements such as a direct calorimetric measurement, photoacoustic [14] or photothermal [15] spectroscopies could be implemented but would require a suite of infrared lasers covering the mid-infrared to obtain wavelength dependent spectra. Instead of this approach, for hyper-black materials, the results of reflection experiments can be used to derive absorptance by assuming zero transmission (R + A = 1), where A is absorptance and R is reflectance. One of the benefits of performing reflectance measurements is that broadband thermal sources can be used, which greatly reduces cost and experimental complexity. Measuring infrared absorption of diffuse materials assists in optimizing device or material performance, calibration of devices such as in detector performance for radiometry, or in uncovering fundamental absorption/scattering mechanisms.

Traditionally, reflection of diffuse samples at infrared wavelengths belongs in the category of diffuse-reflectance infrared Fourier spectroscopy (DRIFTS) measurements [16]. The most complete DRIFTS measurement would be quantifying the bidirectional reflection distribution function (BRDF), which represents completely the reflection for arbitrary incident and reflection angles [17]. Unfortunately, BRDF measurements on small samples are typically constrained to laser or plasma light sources and are not feasible with thermal infrared sources due to the vanishingly small SNR. The next best DRIFTS measurement is the directional-hemispherical reflectance (DHR), which is defined as an incident field with one incident angle (commonly near-normal to the surface) and measurement of all reflected radiation in the upper hemisphere [18]. A DHR measurement can be done using an integrating sphere but is limited by the sample size it can measure. Typically, lateral dimensions greater than 25 mm are used. For smaller samples, a biconical arrangement DRIFTS measurement is traditionally used such as in a Praying Mantis type FTIR accessory [19]. Biconical reflectance is defined as an incident field with a given solid angle ( and a reflected/scattered field with solid angle ($\omega^{\prime}$) [18]. In the Praying Mantis accessory, two large off-axis ellipsoidal mirrors are used to focus and collect the reflected light while simultaneously being able to discriminate between specular and diffuse components with a resolving spatial resolution of approximately 3 mm [19]. The increase in spatial resolution (or decrease in allowable sample size) for this setup (3 mm) over the integrating sphere (25 mm) is offset by the reduction in detected solid angle. However, for next generation materials and devices, the length scales of interest are shrinking to sub-mm, and so one needs a micro-DRIFTS measurement, which means incorporating micro-FTIR techniques [20]. Micro-FTIR is a type of biconical reflectance that can boast high spatial resolution, sometimes approaching diffraction-limited because of the high numerical aperture (NA) of the focusing and collection optics. The real challenge for incorporating this technique for studying small area, highly diffuse samples is attaining sufficient spatial resolution and SNR. In addition, since we want to evaluate the DHR, being able to connect a biconical measurement to a DHR is also an important consideration. In this work we demonstrate a bespoke micro-DRIFTS reflectance setup using low-cost commercial off the shelf components, for studying highly diffuse samples in the wavelength range of (2 µm - 18 µm). We demonstrate the capabilities of our system by measuring the reflectance of hyper-black vertically aligned carbon nanotubes (VACNT) on a test sample and on prototype VACNT detectors. An uncertainty budget is established, and our measured data is connected to a preliminary DHR with further discussion about how to improve this connection.

2. Experiment

Our experimental investigation is based on a commercial FTIR operated with an internal globar thermal source and potassium bromide (KBr) beam splitter. Using an output port from our FTIR, transition optics can be moved to guide the output of the spectrometer into our homebuilt micro-reflectance setup (see Fig. 1). A pair of 75.4 mm diameter off-axis parabolic (OAP) mirrors resize the beam down to 21 mm, with 151.6 mm and 75.4 mm focal lengths respectively. The shared focus of these mirrors acts as a field stop and sets the spot size on the sample. The collimated output of the second OAP mirror passes through a 0.5 mm thick, 30 mm diameter germanium beam splitter and on to a 38.1 mm diameter, 20.32 mm focal length OAP mirror which illuminates the sample and collects the back reflected light. Ge was chosen as our beam splitter, because of the low absorption in the 2 μm–18 μm band of the infrared and the small thickness availability. The small thickness increases transmission and allows the first backside reflection to overlap sufficiently with the reflected beam from the sample. Overall, this overlap increases the detected signal by approximately 25% which improves our measured SNR. For our thickness of germanium and incident wavelength, interference fringes appear with a separation on the order of 10s of nanometers in the mid-infrared. Since our measurements have coarse spectral resolution, interference fringes due to the beam splitter are not visibly present in measured single channel reflectance. Any phase difference between the sample and reference spectrum that occurs from interference in the beam splitter, will be largely canceled through normalizing. At the short wavelength range of our measurements ($\lambda \sim 2$ μm) we expect contributions from the beam splitter to appear in the single channel spectrum, although we are unable to resolve them because of our low SNR. For our focusing optics, the more common Schwarzschild-type objective was not chosen because of the obscurations that are present in those optics, which can reduce the detected signal by upwards of 50%. For samples with low reflection, signal is at a premium and worth the potential reduction in achievable resolution. The sample is mounted to a 25 mm diameter magnetic disc which can be magnetically coupled to a housing carriage which is attached to a three-dimensional translation stage. The three-dimensional stage is then mounted to an automated 1-dimensional stage which can translate between the sample, a reference, and a thermal camera. The reflectance measurements in this setup are made relative to a well-known specular reference such as gold or polished silicon. Our reference selection depends on single channel signal of the sample; for instance, if there is a relatively high signal on a vertically aligned carbon nanotube (VACNT) sample, then translating to a gold reference could saturate the detector, and therefore we would use a silicon reference. We found silicon to be a sufficiently low reflector. To reduce reflection further one could used optical grade potassium bromide (KBr), or potassium chloride (KCl), although care needs to be taken as these materials are hygroscopic and the reflectance could either change with time or be modified by a protective coating. The reference is mounted on a kinematic mount, which is mounted on the 1-dimensional stage. As mentioned, a thermal camera, sensitive between 7 μm–14 μm was used for spot profiling to ensure correct size and shape (see results section). The reflected beam from the sample or reference is recollimated and sent back towards the Germanium beam splitter and is refocused onto a final pinhole via a final pair of 38.1 mm diameter, 50.8 mm focal length OAP mirrors. The pinhole is used to filter any diffracted light reflections from the sample surface and clearly define the field of view on the detector. After this pinhole, the field is focused onto a small area (0.25 mm x 0.25 mm) liquid-nitrogen cooled

 

Fig. 1. Schematic of the micro-DRIFTS setup. A broadband thermal source is coupled through a Michelson Morley type interferometer. The output of the interferometer is directed into the micro-DRIFTS setup which is described element by element in the main text.

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Mercury Cadmium Telluride detector. The entire system is enclosed in an opaque acrylic box that serves both the purpose of limiting stray background light and as a container for nitrogen gas. The nitrogen air suppresses atmospheric absorbances in the near- and mid-infrared which is critical for performing reflectance measurements in the infrared. The interior of the box is wrapped in aluminum foil with the intent of dropping the emissivity of the enclosure to create a uniform background and reduce coupling the optics to background variations due to changes in room temperature. To align the samples with the focused IR light, a visible laser is aligned colinear with the IR beam path via a flip beam splitter. The visible light illuminates the samples and can be seen via a high-resolution visible camera for precise alignment of samples via a 3-axis translation stage. Two Lyot stops were used after each of our pinholes. The Lyot stop blocks some of the flare from the edges of the pinhole which improves our spot quality on the sample and our MCT detector.

Throughout this paper the system’s ability to measure a biconical reflectance is demonstrated on VACNTs. VACNTs are one of the darkest materials known with reflectance not exceeding 1% across the visible through much of the infrared [21]. The main reason for their low biconical reflectance is their nearly Lambertian reflectance properties and high absorption. VACNTs also lack sharp absorption features in the MIR which precludes the need for high spectral resolution which would otherwise greatly reduce our SNR [22]. NIST has demonstrated expertise in the fabrication of VACNT-based devices [21], and they are thus the perfect material for us to characterize our system. Throughout this paper spectral resolutions between $16\; \textrm{cm}^{-1} \le \Delta \nu \le 64\; \textrm{cm}^{-1}$ were used, where $\Delta\nu$ is bandwidth in wavenumbers, which are sufficient for producing smooth high SNR reflection curves for our VACNTs. Spectral resolution is reported in terms of wavenumber as opposed to wavelength simply because it remains a constant for the whole spectrum. In principle high spectral resolution measurements ($\Delta\nu \le 4\; \text{cm}^{-1}$) can be performed, but that would require at least an order of magnitude increase in acquisition time. The specific resolution chosen is determined by the SNR, which depends on the pinhole sizes used for a particular sample and how reflective a VACNT sample is. Throughout the results section, pinholes sizes (notation from Fig. 1(a)) used and spectral resolution for all measurements are presented. Reflectance modeling of our VACNTs and diffuse materials in general is not reported on in this work because it is outside of the scope of what we are trying to demonstrate.

3. Results

To characterize the performance of our optical setup, the shape and size of the focused field on the sample was determined. To do this, a commercial infrared camera, sensitive between 7 µm – 14 µm was useded, and the P₁ diameter (Fig. 1) was varied. We placed the thermal camera on the same stage as the sample, and then minimized the spot size on the camera via a translation stage (translation was along the optical axis). We took it as a reasonable assumption that when measuring reflectance, the maximum reflected signal on the detector corresponds to the minimum spot size on the sample which is what was captured by the thermal camera. The thermal images as a function of P₁ diameter are shown in Fig. 2(a). An approximately gaussian beam profile is obtained for P₁ diameter $\le$1 mm and a central maximum for smaller P₁ diameter can be identified as the Airy disc of the spot. The Airy disk can be identified as the white circular portion of the beam profiles in Fig. 2(a). Once the P₁ diameter is reduced beyond 300 $\mu$m, further reductions have a diminishing effect on the spot size. From the spot images in Fig. 2(a), we can visually approximate the diameter of the central maximum for a P₁ diameter = 0.3 mm as roughly 100 µm. There is a distinction between the spot sizes presented in Fig. 2, and the detected resolution, which is described later in the results section. Our relatively poor etendue source has a large divergence angle which in conjunction with diffraction from small P₁ diameters are our limiting factors in further minimizing our spot sizes. Improvements to the thermal source could improve the quality of focusing, but for the purposes of this work, these spot sizes were sufficient.

 

Fig. 2. (a) Thermal images of our spot-on sample from figure 1 with varying P₁ diameters. For decreasing P₁ diameter size, spot size decreases as expected, in addition the size and intensity distributions more closely resemble a gaussian profile. (b) 100% line for P₁=1000 µm, P₂=500 µm on a typical VACNT sample with ${\Delta }\nu $ = 64 cm^-1. From the 100 % lines we are able to bound our SNR uncertainties. Our uncertainty budget is further presented in Table 1. (c) Single channel spectra of a silicon reference, and typical VACNT sample for P₁ = 1000 µm, P₂ = 500 µm and ${\Delta }\nu = 64\; c{m^{ - 1}}$. Background (Bg) selection is traced through the baseline in the measured range as discussed in the results section.

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Table 1. Uncertainty for reflectance measurements. Uncertainties are generalized since they can vary slightly between different samples and system configurations. The total relative standard uncertainty is evaluated by adding the square of the individual components (x_i) and then taking the square root of this sum [25].

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To characterize our SNR, 100% lines were used. The 100% line is two successive measurements with identical experimental parameters, divided by each other [19]. For infinite SNR, the value of the 100% would be exactly 100%, but in reality, the values will deviate from 100%, and this deviation can be used to determine the overall SNR. The absolute deviations from 100% form the bounds for our measurement uncertainty due to the SNR of our measurement. For the presented system, the SNR depends on numerous parameters which include the pinhole diameters (see Fig. 1), sample reflectance, spectral resolution, throughput, and measurement time. An example 100% line with P₁ = 1000 µm and P₂= 500 µm diameters on a standard VACNT sample with spectral resolution of $\Delta\nu = 64\; \text{cm}^{-1}$is plotted in Fig. 2(b).

The extremely low VACNT reflectance is approaching the noise floor for the system. Therefore, it is important to account for the background when measuring the reflectance of VACNTS or any other very low reflectance material. To account for the background in our results, measurements extended outside of our detectable range (λ< 2 µm, λ > 20 µm) and a background value was selected that intersects through the signal in these ranges (see Fig. 2(c)). The low transmission of our Germanium beamsplitter and ZnSe window on our detector from (λ< 2 µm, λ > 20 µm), coupled with the low flux of our source and reflectance in these wavelength ranges, we expect the measured intensity from the VACNT’s in these ranges to be below the noise of our detector. Since the detected background is from the enclosure and not being modulated by the FTIR reference mirror, we expect the background contribution to be additive and spectrally flat. Therefore the signal in these wavelength ranges (λ< 2 µm, λ > 20 µm) provides a good approximation of the background signal of our reflectance measurements. With the background selected, the normalized biconical reflectance is then the following

To characterize the spatial resolution that we could achieve with sufficient SNR to measure VACNTs, a test sample was fabricated and patterned with a series of incrementally small square and circular areas of VACNTs on a silicon substrate (Fig. 3(a)) [19 µm - 26 µm range of heights]. An equivalent test sample with the same shapes and sizes but with a 300 nm layer of gold as opposed to VACNTs (Fig. 3(b)) was also fabricated. Using these samples, measurements could be taken on decreasingly small areas of VACNTs with the expectation that the reflectance should be nearly constant. An increase in reflectance indicated overfilling the sample and detection of the higher reflecting substrate near the edges of the sample. Figure 3(c) shows the reflectance results on circular samples of VACNTs of varying heights from 1 mm diameter down to 100 µm. The 2 mm diameter VACNT patch reflectance has been omitted from Fig. 3(c) because of nonuniform VACNT growth across the reference sample. The substrate could be visibly seen in the center of the 2 mm VACNT patch, and therefore the measured reflectance was much higher than for a typical VACNT sample. From Fig. 3(c), good relative agreement from 1 mm down to 250 µm diameter can be seen with deviations at 100 µm. The deviation can be attributed to overfilling and being unable to resolve this spatial resolution. In addition, oscillations with varying phase and amplitude are seen in all but the 100 µm sample reflectance. These oscillations can be attributed to interference between the VACNT/substrate interface with the VACNT surface reflections. The phase and amplitude of the interference depends on the optical thickness of sample $({n_{smp}} \times \textrm{thickness})\; $ where ${n_{smp}}$ is refractive index of the sample and surface roughness. We can define the constructive and destructive interference conditions for a smooth surface as

 

Fig. 3. (a) VACNT test sample on single side polished Silicon substrate with varying-sized square and circular patches with VACNT heights approximately 20 µm. The lateral dimension and diameter for each row of square and circle are equivalent. The dimensions corresponding to the numbering in the figure are the following for row 1 (2 mm), row 2 (1 mm), row 3 (0.5 mm), row 4 (0.25 mm), row 5 (0.1 mm). (b) Equivalent to (a) but with gold patches with heights approximately 20 nm. (c) Micro-DRFITS on circular VACNT patches from (a) from 1 mm diameter down to 0.1 mm diameter with measured thickness. Large circles are locations of calculated maxima and minima from equations 2 and 3, with the ${n_{sample}}\; $ used, specified in the legend for each patch. The pinholes of the data sets are the following, P₁ = 500 µm, P₂ = 200 µm for D=1 mm, 0.5 mm, 0.25 mm at ${\Delta }\nu = 16\; c{m^{ - 1}}$ and P₁=200 µm,P₂=150 µm for D=0.1 mm with ${\Delta }\nu = 64\; c{m^{ - 1}}$. (d) Calculation of the fractional power incident (β) on the 100-um diameter gold circular patch in (b) based on equation 2 with P₁ = 200 µm,P₂ = 150 µm for D=0.1 mm and ${\Delta }\nu = 64\; c{m^{ - 1}}$. Atmospheric absorbance has been masked at ∼ 4.5 µm.

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To further improve our spatial resolution estimate, the following formulation of the measured reflectance was used

Sources of uncertainty have been tabulated for these measurements and are presented in Table 1. By far the dominant source of uncertainty is the SNR of the measurement which is expected since we are measuring hyper-black diffuse media. The SNR uncertainty is presented as an approximate range since it depends on the sample in question and spectral resolution desired. Although the noise is Gaussian distributed, the way we are defining SNR uncertainty is from the 100% line (Fig. 2(b)) which assigns a relative standard uncertainty that belongs to a rectangular distribution. The next largest source of error is the focus alignment, which is an estimate for the focus alignment. Focus alignment is how well the incident field is focused on the sample surface. For a specular or less-diffuse sample, one can maximize the measured intensity, but with VACNTS which have near-zero reflected intensity this is not possible. To determine the uncertainty introduced by how well the VACNT surface is focused, measurements were repeated on a VACNT sample with a realignment between measurements, it was found that measurements were within 5%. Other sources of uncertainty are the alignment of the reference and the true reflectance value of the reference. The angle of reference surface is not necessarily identical to the samples since they are on different mounts. It was found that if two well-characterized specular samples (gold and silicon) were used, they can be measured within 2.5% of their expected value. As previously discussed, there is some ambiguity on how the background is chosen, the uncertainty in this selection is obtained by looking at the peak-to-peak intensity in the single channel VACNT spectra (see Fig. 2(c)) outside of our measurement range. Smaller contributions are the temporal stability of the employed globar source and atmospheric absorbances not being completely removed by the N₂ purge.

With the system characterized, a more relevant reflectance measurement on a microbolometer detector was performed. We tested a prototype VACNT microbolometer for the future Libera NASA mission (see Fig. 4(a)) being built to be a replacement for the Cloud and the Earth’s Radiant Energy System (CERES), an Earth radiance measurement satellite [26]. The detectors are relatively small (∼ 1 mm lateral dimension, see Fig. 4(b)) and since Libera is being designed for use as a replacement for CERES, the detectors are sensing from visible out to 100 µm wavelengths. Characterizing the infrared properties of the detector is important to optimize both performance and measurement accuracy. Our measurement is not an SI-traceable calibration, but it provides the first measured reflectance on this new type of detector and assists in experimental optimization of VACNT growth parameters that could be compared to larger samples having rigorous calibration. Figure 4(c) shows reflectance spectra measured from multiple prototype detectors for the Libera mission, all with different growth parameters. The growth parameters can change the packing density of the VACNTs, surface morphology and their heights, (which could lead to changes in reflectance). The simplest VACNT parameter to extract post-growth is height, therefore only the height of each prototype VACNT detector is displayed in the legend of Fig. 4(c). A clear correlation in increasing VACNT height to decreasing reflectance is observed. The reduction in reflectance with increasing thickness comes with returning to the assumption of very low transmission, or A ≈ (1-R). Under this assumption, it is known that the absorptance depends on material thickness [27],therefore the reflectance should also follow the same dependence . Similar to the reflectance measured in Fig. 2(c), interference fringes are present for shorter VACNTs. A major difference between the test sample used in the measurements shown in Fig. 2(c), and the Libera protype is the difference in reflectance from the substrate. The Libera detectors are grown on a thin silicon nitride (SiN) membrane (n = 1.04, k = 1.33 @ $\lambda = 10\; \mathrm{\mu}\textrm{m}$ [28], which has a much different refractive index to Silicon (n = 3.42, k = 7.6E-5 @ $\lambda = 10\; \mathrm{\mu}\textrm{m}$ [28]). In addition, on the backside of the SiN membranes are platinum meanders that are used for temperature sensing in the bolometers. It has also been shown that VACNTs grown on different substrates can have different optical properties [29]. Given the difference in substrates, it is not surprising that Libera mission detector prototypes with similar VACNT heights to our test sample (19 µm - 26 µm) exhibit qualitatively different interference fringes. These measurements qualitatively demonstrate what height the VACNTs need to be on the detectors to have sufficiently low reflectance over the wavelengths of interest. For a better quantitative understanding of our measurements, an accurate reflectance model is required, but is outside of the scope of this manuscript to present.

 

Fig. 4. (a) Image of front (upper) and backside (lower) of prototype detectors for the Libera mission. These detectors are bolometer type detectors, coated with (VACNTs) which act as the absorbing element. (b) Dimensions of the VACNT absorber from (a). (c) Micro-DRIFTS measurements from setup in figure 1 for multiple s prototype detectors with varying growth parameters. Reflectance measurements were performed with an P₁=1000 µm, P₂=500 µm and ${\Delta }\nu = 64\; c{m^{ - 1}}$. The heights of the VACNTs for different prototypes are labeled for each trace in the (c). A clear reduction in reflectance and interference fringes is observed for increasing VACNT height.

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We have demonstrated biconical reflectance on diffuse reflectors having a diameter as small as 140 µm or area of 0.015 mm², and on a physical device in the Libera mission prototype detectors. The reflectance that we have measured includes the specular component of reflection. We could in principle omit the specular component by rotating the sample, if we wanted to discriminate between diffuse and specular components. Although the DHR is the more relevant quantity to completely describe the reflectance for a diffuse material, it is in principle possible to upshift our reflectance to a DHR by reasonably assuming a normal incidence ($\theta_{inc} = 0$) Lambertian BRDF [30] and by knowing our effective numerical aperture (NA). The effective NA is the maximum reflected/scattered angle from our sample that reaches the detector and is not necessarily the same as the NA of the collection mirror. For our system this depends both on the collection mirror, which itself has a high NA, the acceptance diameter of the beam splitter, and divergence angle of collimated light from the reflection from the sample. The effective numerical aperture can be estimated using geometrical optics for the reflectance data presented in Fig. 4(c). The acceptance diameter of the Ge BS (D_BS) is 21.2 mm, this is since the BS is at a 45 degree angle relative to the beam path, and has a diameter of 30 mm. From etendue conservation, we can estimate the beam divergence of the reflected field from the sample which is collimated and returned to the BS as $\theta_{div} = \frac{r_{beam}}{f}$, where r_beam is the radius of the incident focused spot, f is the focal length of the mirror and $\theta_{div}$ is the divergence angle of the collimated reflected field which is traveling back towards the BS. Using the experimental focused spot diameter (D = 500 µm, Fig. 2(a) with P₁ = 1 mm) and focal length of the collimating mirror (f = 20.3 mm), the beam divergence of our collimated field can be approximated as $\theta_{div}$= 12 mrad. Using $\theta_{div}$, we can then estimate what beam diameter (D_accepted) would fall within D_BS after propagating from the collection mirror back towards the BS (distance of 352 mm). We estimate D_accepted to be 12.8 mm. With D_accepted, we can then calculate the effective NA = $\sin \left( {{{\tan }^{ - 1}}\left( {\frac{{\frac{{{D_{accepted}}}}{2}}}{f}} \right)} \right)$ and finally arrive at an effective NA = 0.3 for our system, which corresponds to a half angle of 17.5°. This approximation does not include the effects of diffraction which will become more pronounced as the P₁ aperture gets reduced in diameter. Based on the NA of only the mirror (0.68), the estimated value indicates that the diameter of the beam splitter and beam divergence are the main limiting factors in the detected solid angle. It ultimately does not matter what reflected angle from the sample is detected, only that there is a reasonable estimate for what that value is, because upshifting the biconical reflectance curve to a DHR will need to occur regardless of what the effective NA is. Using this approach, an upshift factor ($\gamma $) can be calculated by integrating the Lambertian BRDF (constant albedo) over our projected solid angle and dividing it by the same integrand integrated over the entire upper hemisphere.

In Eq. (6), $\phi \; \textrm{and}\; \theta $ are the azimuthal and polar angle respectively, $\rho $ is the albedo of the sample and is assumed constant. $NA'$ is the effective NA of our system as discussed above, the estimated value is 0.3. Using Eq. (6) and the calculated effective NA, $\gamma $ is 0.09. With $\gamma $ we can then upshift our reflectance by calculating $\frac{1}{\gamma }R = {R_{THR}}$. The correction in Eq. (6) serves as a first-order approximation to a DHR from the measured reflectance reported. To improve the connection to DHR one could improve the understanding of the VACNT BRDF or be able discriminate between specular and diffuse reflections.

4. Conclusions

We have developed a micro-DRIFTS measurement system capable of measuring hyper-black diffuse materials in the wavelength range between 2 µm and 18 µm with 140 µm spatial resolution. The system was demonstrated on microscopic VACNT patches and on a prototype VACNT-based microbolometer. We have also tentatively connected our measured results to a DHR. Improvements could be made to the achievable spatial resolution and ability to connect to a DHR. To boost spatial resolution, one option is to use a smaller, hotter thermal source that could provide better etendue, thus allowing better re-imaging and spatial resolutions. Another improvement is to switch to the canonically used high-NA Schwarzschild-type objective; based on these measurements, we estimate there would be sufficient SNR. To improve our connection to a DHR we could in the future employ a more sophisticated BRDF model that incorporates both a frequency-dependent specular and diffuse component, such as a Cook-Torrance type model [30]. This could be an interesting approach to obtain a $\gamma $ as a function of wavelength, since it is possible that the specular contribution in the reflectance is beginning to increase in this wavelength regime. Another potential approach would be to measure the BRDF explicitly using a goniometer and laser. With these measured BRDFs we could then accurately calculate the DHR reflectance and then anchor our broadband measurements through these tie points. The system and approaches presented here create a foundation to stimulate development of additional, more sophisticated infrared characterization and optimization methods for diffuse materials and devices having small area.