Downhole FT-MIR Spectrometer Using Perfect Metasurface Absorber

Realization of “Fourier transform infrared (FT-IR) on a chip” holds the potential of a disruptive technology for downhole chemical analysis within the oil and gas industry. One of the critical obstacles to downhole integration though has been the cooling requirements of conventional technologies. Here, we report the design and numerical analysis of an uncooled miniaturized Fourier transform mid-infrared (FT-MIR) spectrometer compatible with downhole thermal environments, enabled by a broadband mid-infrared metasurface detector/source combination derived from a geometric inversion of a set of conformal mapping contours. The metasurface is numerically found to exhibit a near-zero index metamaterial (NZIM) behavior with absorption characterized by surface plasmon resonances confined to the ultrathin ( $\lambda $ /300) metasurface plane, making the absorption properties of the microbolometer design much less sensitive to the remaining support structure than in typical designs. This feature allows the metasurface to be integrated on a single VO2 substrate operated at elevated downhole temperatures that coincide with the metal–insulator transition region. Within this transition region, the VO2 material exhibits enhanced thermometric properties, enabling an uncooled microbolometer design with predicted maximum detectivity ${D}^{*} = 1.5\times {10}^{{10}}\,\,\text {cm} \sqrt {\text {Hz}}/\text {W}$ and noise equivalent difference temperature (NEDT) of 1 mK at a modulation frequency of 500 Hz. These parameters approach entry-level lab FT-MIR spectrometers and could represent a significant step in deploying mid-infrared spectroscopy into oilfield downhole logging applications.

more benign, at less than 125 • C and 100 MPa, but packaging constraints are even more stringent with sensors much less than a few centimeters in diameter needed. Accordingly, downhole applications have not been compatible with the cryogenic cooling systems characteristic of laboratory-grade detectors, as well as the thermal management issues created by conventional blackbody infrared sources.
To migrate spectroscopic technology downhole, a major change in the design approach for detectors and sources will be required. An important component may involve the development of electromagnetic metamaterials specifically tailored for downhole applications and high-temperature environmental conditions. The subset comprised of electromagnetic metasurfaces offers interesting properties that may be leveraged as the building blocks for enhanced absorption/emission devices at high temperatures. Metasurfaces function on the principle that surface plasmons can be created at the interface between metal and dielectric media. With certain designs of the metasurface geometry, surface plasmons can make it possible to manipulate the electromagnetic radiation at the subdiffraction scale and increase local intensities by orders of magnitude [4], [5], through strong local field confinement near the surfaces of This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/ the metal metasurface. Certain geometries of the metasurface can take advantage of this phenomenon to develop broadband perfect absorption. The local field intensities near the metasurface act to confine the absorption mechanism to the ultrathin metasurface plane and can be leveraged to make the absorption properties of a metasurface-based microbolometer design less dependent on the material properties of the remaining materials in the laminate. This feature is potentially important for high-temperature applications. Designs may be envisioned that integrate a metasurface absorber with a common thermometric substrate material, for example, VO 2 , that exhibits a metal-insulator transition (MIT) region where the thermometric material transitions from an insulator to an electrically conductive metal. For undoped VO 2 , within the transition region, the thermometric properties improve by more than an order of magnitude with a commensurate enhancement in detectivity characteristics. A conceptual approach integrates a perfect metasurface absorber (PMA) with a single VO 2 material thermometric substrate in a microbolometer design that is temperature controlled to 60 • C, within the MIT region. The application of temperature control on the detector cavity then conceptually would provide detectivity compatible with conventional cryogenic technologies, a key aspect of realizing downhole spectroscopy.
Many on-chip spectrometer designs proposed are dispersive designs, which use gratings or microresonators to separate certain wavelengths of broadband light in a spectral range and direct each wavelength individually to a detector. Dispersive designs suffer from inherent signal-to-noise ratio (SNR) penalties due to spreading the input light beam over many spectral channels and are not preferred for downhole spectral chemical analysis applications. Nondispersive instruments, such as FT-IR spectrometers, do not separate out the individual wavelengths of the broadband light source and as a result retain what is called the multiplex advantage with a significantly higher SNR. Conventional FT-IR spectrometers utilize this nondispersive approach in an optical design incorporating moveable mirrors to generate an optical path length (OPL) difference providing an interferogram that can be processed by Fourier transform (FT) techniques into a spectrum of intensity versus wavelength. Several on-chip FT-IR interferometer designs have been proposed and demonstrated that focus principally outside the wavelength regime (<7 μm) of the bandwidth of interest for downhole analysis [3]. Some onchip FT-IR interferometers have been proposed, which rely on thermo-optic or electrooptic modulation to change the OPL in a waveguide, such as described by Zheng et al. [6] using a tunable micro-ring resonator filter or Souza et al. [7] using a thermo-optic nonlinearity and dispersion correction. The very small refractive index modifications produced by these modulation effects, however, were reported to result in large device footprints with spectral resolution in tens of cm −1 in wavenumber, less than ideal for downhole chemical spectroscopy applications where 10-cm −1 resolution would be preferred for discrimination of the various elements and compounds of interest. Kita et al. [8] recently proposed an on-chip concept that utilizes a digital FT (dFT) interferometer, which acquires high-resolution spectra via time-domain modulation of a reconfigurable Mach-Zehnder interferometer with the multiplex advantage. Noise suppression is accomplished through the adaptation of machine learning regularization techniques for spectrum reconstruction. Their design for a 64-channel dFT interferometer has approximately 17 × 20 mm 2 in footprint, and the machine learning techniques provided on the order of 1-cm −1 resolution in a narrow bandwidth between 1.55 and 1.57 μm. For downhole chemical spectroscopy, a broad bandwidth range, including the mid-IR, would be preferred due to important hydrocarbon molecular resonances found here.
The data from a production logging sensor suite are typically related to estimating water, oil, and gas volume fractions and rely on a priori knowledge or assumption of many fluid constituent properties. Direct measurement of the wellbore fluid composition from chemical spectroscopy would enhance the data value and allow other types of analyses such as in situ SARA quantification. For downhole application, the preferred approach would utilize FT mid-infrared (FT-MIR) spectroscopy due to the high modulation frequencies that could be achieved to support real-time fluid properties measurement. However, the challenge confronting realization of this concept for in situ downhole application remains in the limitations of the state of the art in infrared detector technologies and blackbody radiation sources. Fundamentally, these limitations derive from poor detectivities at the modulation frequencies and elevated temperatures associated with downhole logging environments, and the thermal management implications of integrating a full spectrum blackbody radiation source into a sensor suite at downhole temperatures. Conventional FT-MIR systems that offer the needed detectivity at sample rates rapid enough to be of interest for real-time analysis are based on superconductivity and/or actively cooled detector technologies that typically operate over a narrow bandwidth of the IR spectrum and in conjunction rely upon full spectrum blackbody radiation sources that would create problems with downhole thermal management.
To enable an FT-MIR concept for in situ downhole logging, a completely different type of detector/source technology is needed that: 1) requires no active cooling in order to achieve the detectivity, which would support real-time analysis sample rates; 2) operates over the full MIR bandwidth of interest for discrimination of reservoir chemicals; and 3) develops a minimal thermal footprint compatible with the constraints of downhole logging operations. This type of technology would fall well outside the capabilities of the current state of the art for uncooled detector technologies and infrared sources but could well be adaptable to novel approaches such as electromagnetic metamaterials. In the following, we describe a miniaturized FT-MIR spectrometer, which leverages the perfect absorbtion properties of a near-zero index metasurface to achieve significant progress toward this goal for downhole application.

II. METHODOLOGY
The described miniature downhole spectrometer is built upon a PMA for the uncooled microbolometer detector and thermal infrared source. A previous work [10] described how a broadband electromagnetic absorption could be achieved from a metamaterial built upon complex subcellular geometries derived from geometric inversion of a Rhodonea conformal mapping set of contours. A similar approach is used here based on a geometric inversion of the canonical tangent circles' conformal mapping contours leading also to a metamaterial with near-zero index metamaterial (NZIM) behavior and broad perfect absorption bandwidth. In our experience, only these two base conformal mapping geometries have led to a geometric inversion with the NZIM perfect absorption properties. This absorption mechanism is confined to the ultrathin metasurface and makes the absorption properties of the detector relatively independent of the material properties of the remaining materials that may comprise the microbolometer. This unusual feature is significant for integration into downhole systems. It now allows integration of the PMA with a common thermometric material layer, undoped VO 2 , that exhibits an MIT region, that is to say, in the region where the thermometric material is transitioning from an insulator to an electrically conductive metal. For a thermometric material such as undoped VO 2 , in this MIT state, the thermometric properties improve significantly from room temperature. Our approach is based on integration of the PMA in a microbolometer construction with a single VO 2 material thermometric layer temperature controlled to 60 • C resulting in about 50× enhancement in the thermometric properties compared to room temperature. With elevated temperature control, detectivity performances are expected that conventionally require decreasing the cavity temperature to cryogenic conditions (<−200 • C).
The metasurface geometry is based on geometric inversion of the canonical tangent circles' conformal mapping contours defined by the relations, which transform the Cartesian coordinate space to a new virtual domain described by (see [9]) The geometric inversion of these conformal contours is developed usingx which gives a new set of nonconformal contours that in effect "invert" the original tangent circles' geometry from inside out. A graphical illustration of the geometric inversion process from the original tangent circles' conformal contours transformed to the inverted contours and eventually to a metasurface geometry is shown in Fig. 1. The details of the subcell of the metasurface geometry are shown in the bottom right of Fig. 1. The inverted domain effectively presents a set of continuously distributed contours that can be tailored for a design to accommodate the specific geometric constraints of the application to be addressed. The 12-fold symmetry of the base geometric inversion in Fig. 1(b) is reduced to the eightfold symmetry in the physical metasurface design shown in Fig. 1(c) in order to achieve the number of resonators intended for each subcell. In this particular design, we begin with a seed pattern of six nearly evenly distributed radially spaced contours containing seven nearly evenly spaced angular resonators along the outermost contour. The number of resonators along each of the radially spaced contours is decreased proportionately with the radial distance of the contour from the center of the cell, in order to create a staggered angular alignment of resonators between successive contours. This seeding scheme may be only one of many approaches that can be implemented successfully with this inverted geometry to achieve broadband perfect absorption. The resulting geometry creates a 2-D array of electromagnetic resonators in the metasurface, which manipulates electromagnetic waves within a subwavelength distance between the resonators, each also smaller than the wavelength scale. In a conventional optical element, phase control is based on continuous phase accumulation through light propagation, while here, the resonators in the metasurface introduce an abrupt phase change upon interaction with the electromagnetic waves. In this manner, the metasurface modulates incoming radiation in both amplitude and phase within a total thickness much smaller than the wavelength. This phenomenon is enabled by the generation of multiple gap plasmon resonance modes in the metasurface leading to the superposition of a nearly continuous series of perfect absorption resonances with an expansion of the high absorption bandwidth.

III. EFFECTIVE EM PROPERTIES
Several methods have been investigated for the determination of effective electromagnetic properties of metamaterials [23], [24], [25], [26], [27], with conventional approaches utilizing retrieval of a set of scattering parameters (S-parameters) from a unit cell by plane wave simulations or tests. The S-parameters approach derives from transmission-line theory based on transmitted and reflected voltage waves. For high-frequency problems, voltage is not a well-defined variable making it necessary to define the S-parameters in terms of the electric field. In the formulation of the S-parameters retrieval approach, it is assumed that all ports are connected to matched loads or excitations, that is, there is no reflection directly onto any port from the far field. Consequently, in our simulations, both input Port 1 and output Port 2 are bounded by 3-D perfectly matched layers (PMLs). For a 2 port scattering simulation, the S matrix is defined as (5) in which S 11 is the reflection coefficient at Port 1, S 21 is the transmission coefficient due to wave propagation from Port 1 to Port 2, S 12 is the transmission coefficient due to wave propagation from Port 2 to Port 1, and S 22 is the reflection coefficient at Port 2. Here, the metasurface simulations for effective properties do not include a reflecting perfect electrical conductor (PEC) ground plane, and the complete matrix of scattering parameters can be retrieved from a single simulation with a plane wave propagating from Port 1 to Port 2 to extract the parameters S 11 , S 21 . The time average power reflection/transmission coefficients are obtained as |S ij | 2 . The scattering parameters retrieval was conducted with a 3-D finite-element analysis of the inverted tangent circles' elemental cell using the commercially available Comsol 1 MultiPhysics 5.6 finite-element analysis software package. The simulation model consisted of a 3-D periodic waveguide geometry integrating the metasurface pattern centrally located between input and output ports, as shown in Fig. 2. The metasurface pattern is modeled with a surface transition boundary condition of 27 nm thickness on the surface of a 3-D thermometric layer of 135-nm-thick VO 2 material suspended in the vacuum waveguide. For the microbolometer infrared absorption simulations, the metasurface pattern is modeled on the surface of the 3-D thermometric layer of 135-nm-thick VO 2 material and with a 500-nm spaced PEC boundary 1 Trademarked. condition. The metasurface material is modeled as gold with a frequency-dependent electrical permittivity Drude model [11] of the form where ω p = 2.164 × 10 15 Hz is the plasma frequency and γ = 16.68 × 10 12 Hz is the electromagnetic damping frequency. The VO 2 material was modeled with constant properties of relative permittivity r = 10, relative permeability μ r = 1, and electrical conductivity σ = 2881 S/m corresponding to material properties within the MIT region at 60 • C. The cross section of the waveguide coincides with the thermometric layer dimensions. The remainder of the waveguide has the properties of free space (vacuum). The waveguide is excited with an incident transverse magnetic (TM) wave from Port 1 according to H y = e jkx e jky (8) where k = ω/c is the wavenumber in free space at the electromagnetic frequency ω and c is the speed of light in vacuum. Port 2 is located symmetrically about the substrate surface from Port 1. The waveguide boundaries perpendicular to the x and y coordinate directions have Floquet periodic boundary conditions that account for the plane wave interaction with periodic structure. The simulation results for retrieved scattering parameters of the metasurface are shown in the spectrum plot of Fig. 3(a). For the metasurface in the absence of the reflecting ground plane, the scattering parameters for forward/backward propagation are identical due to symmetry. The effective properties calculations were made using a conventional retrieval process [12] slightly modified for the selection of the phase complex root [10], which considers the case made by Markel [13] that material passivity fully constrains the imaginary part of permittivity to be positive but does not preclude negativity in the imaginary part of permeability. In this analysis, no cyclic branching from the root with m = 0 was found over the frequency range considered up to 2500 cm −1 with this inverted conformal mapping geometry.
The resulting refractive index spectra calculated for the inverted geometry metasurface are shown in Fig. 3(b) with both real and imaginary components varying closely about zero over the wavenumber range of interest (500-2000 cm −1 ). The corresponding electrical permittivity and magnetic permeability spectra shown in Fig. 3(c) and (d) similarly indicate near-zero effective electromagnetic properties with both real and imaginary parts varying closely to zero over the range of interest. For the metasurface having no reflective ground plane, the absorption spectrum can be calculated using The resulting absorption spectrum in Fig. 4 for the metasurface on VO 2 substrate (no PEC ground plane) indicates a maximum absorption of 99.88% at 767 cm −1 (13 μm) with a 90% absorption bandwidth in the range between 600 and 1534 cm −1 and 112% full-width at half-maximum (FWHM) centered about 1218 cm −1 . In this bandwidth, the inverted tangent circles' metasurface geometry is ultrathin at a small fraction (λ/300) of the center frequency incident wavelength. The imaginary components of the effective parameters spectra shown in Fig. 3 indicate that the metasurface is a very low loss effective medium over this high absorption bandwidth, contrary to conventional assumption that intrinsically high loss media are necessary to develop high absorptivity in thin layers. This suggests that the absorption phenomena found here for the inverted metasurface geometry are related to surface plasmon resonances, and predominantly, the losses develop from surface plasmon scattering and the absorption mechanism is confined strongly within the metasurface plane [4], [31], [32], [33], [34], [35].
The electromagnetic response of the metasurface/substrate (no PEC ground plane) for the perfect absorption resonance at 767 cm −1 is shown in the plots of Fig. 5. The loss mechanism for the metasurface/substrate is strictly resistive and is shown in the current density plot of Fig. 5(a) and the associated surface power dissipation plot in Fig. 5(b). The regions of highest power dissipation appear to correspond generally to the central symmetry lines of each of the eight subcell geometric patterns.
The effects of deviation of the incident plane wave orientation from the surface normal were analyzed to understand the sensitivity of the metasurface absorption to detector mounting orientation relative to the field of view. The absorption spectra corresponding to varying incidence angles between 0 • and 45 • from normal for TM waves are shown in Fig. 6. The comparison of absorption spectra indicates a significant enhancement of the near-perfect absorption bandwidth as the incidence angle approaches 30 • deviation from normal, particularly over the short wavelength range approaching 2000 cm −1 . The broadest 90% absorption bandwidth is seen at a 30 • incidence Fig. 6. Microbolometer absorption spectra for varying TM incidence angle θ relative to surface normal. Metasurface is gold at 27 nm thickness and thermometric substrate is VO 2 at 135 nm thickness, with a reflective ground plane spaced 500 nm from substrate back surface. Fig. 7. Microbolometer absorption spectra for varying TE incidence angle θ relative to surface normal. Metasurface configuration matches that for the TM incidence spectra.
angle, ranging between 600 and 1540 cm −1 with a 114% FWHM centered about 836 cm −1 . The broadest absorption bandwidth is exhibited at 15 • incidence angle with consistently >75% absorption for wavenumbers above 500 cm −1 . The absorption spectra corresponding to varying incidence angles between 0 • and 45 • from normal for TE waves are shown in Fig. 7. Comparison with the TM incidence results indicates only moderate difference primarily in reduction of the high absorption bandwidth at 15 • and 30 • oblique angles with a moderate increase in bandwidth for normal incidence and 45 • oblique angle. This is consistent with the symmetry of the base unit cell geometry.

IV. MICROBOLOMETER PERFORMANCE
The microbolometer detector design involves a micromachined bridge structure suspended over a readout integrated circuit (ROIC) substrate in which the gold metasurface geometry is imprinted on a single thermometric layer of VO 2 material, as shown in Fig. 8. The design avoids the typical support layers characteristic of conventional devices and is made possible due to the low mass loading from the ultrathin gold metasurface layer. For a 135-nm VO 2 thermometric layer thickness and 27-nm gold metasurface thickness with 35% areal fill factor, the resultant mass loading on the microbolometer develops a maximum bending stress of 7 kPa/g in the VO 2 thermometric layer. The tensile strength of the VO 2 material is σ ult = 172 MPa translating into an ultimate shock capability >24 000 g, well in excess of the expected worst case shock loads that could be experienced downhole in a production logging environment (<100 g). Thus, the single thermometric layer provides more than adequate structural support when integrated with this ultrathin metasurface for the expected downhole vibration and shock environments.
The normalized detectivity is dependent on the electrical resistivity and thermal coefficient of resistance of the thermometric VO 2 layer, while the noise equivalent difference temperature (NEDT) is dependent on its specific carrier density. The trends of the electrical resistivity and temperature coefficient of resistance properties of VO 2 films with temperature were measured by Takami et al. [18] and are shown in Fig. 9, which clearly illustrates the MIT. For undoped VO 2 film, the data in Fig. 9(a) indicate a resistivity at 60 • C of approximately 3.5 × 10 −2 ·cm. The electron density of VO 2 has been calculated based on theoretical considerations by Pergament et al. [22] as approximately 4 × 10 18 /cm 3 . Using these material properties for the VO 2 thermometric layer and the Comsol Multiphysics simulation results for the metasurface absorptivity, the performance anticipated from the microbolometer may be estimated using well-known formulas found in the literature [28], [29], [30]. Using the procedure as described in [10] indicates a microbolometer maximum detectivity D * of 1.5 × 10 10 cm (Hz) 1/2 /W at 333 K and NEDT of 1 mK. The results are based on 175-μA bias current, which creates a latent resistive temperature rise of 2.3 K in the microbolometer.
The direct comparison in Fig. 10 includes the detectivity spectrum of the metasurface detector at 500-Hz modulation frequency superimposed onto the spectra for various   [19]) operated at the noted temperatures. The modulation frequency for all detectors is 1000 Hz, except for the state-of-the-art uncooled thermistor bolometers at 10 Hz and the metasurface detector at 500 Hz.
commercially available infrared detector technologies operated at the noted temperatures and over the wavenumber range from 5000 to 250 cm −1 . The superimposed metasurface microbolometer spectrum indicates detectivity comparable to the performance conventionally associated with state-of-theart cryogenically cooled detectors. Consequently, this level of detection would represent a disruptive technology for uncooled microbolometers in consideration of the comparison with such as a photon detection-based Ge:Cu cooled to 4.2 K. The details of the metasurface detector design are summarized in Table I.

V. INFRARED SOURCE PERFORMANCE
The principle on which conventional infrared sources operate is based on emittance over the classical blackbody radiation spectrum. The radiation spectrum from these types of emitters is generally concentrated in the visible and near-infrared wavelength ranges. For mid-infrared spectroscopy applications in downhole chemical analysis, we are interested in the electromagnetic wavelength range 5-20 μm (2000-500 cm −1 ) so that the predominant portion of the radiation from these type sources lies outside this bandwidth below 5 μm wavelength and would represent a heat load limiting the downhole integration of such devices. In illustration, consider the blackbody radiation spectrum shown in Fig. 11(a) corresponding to a radiating blackbody at 900 K. The spectrum shows that the energy radiated in the wavelength range below 5 μm (2000 cm −1 ) is significant in relation to the energy in the wavelength range beyond 5 μm, in fact comprising almost 60% of the total radiation. This is one of the practical obstacles confronting micro-electromechanical system (MEMS) scale miniaturization of spectroscopy instruments downhole, as thermal management options are severely limited in logging tools due to the extreme wellbore temperatures and miniature volumetric constraints. Here, we leverage the unusual properties of the inverted geometry metasurface perfect absorber to create a bandwidth-limited infrared source that circumvents this problem.
From Kirchoff's law, we understand that, for an arbitrary body emitting and absorbing thermal radiation in thermodynamic equilibrium, the absorptivity and emissivity are equivalent. Thus, the bandwidth-limited perfect absorptivity characteristics of the metasurface translate into bandwidthlimited perfect emissivity characteristics as well. This concept is shown in the plot of Fig. 11(a) depicting a comparison of the emissivity of the copper metasurface cells imprinted onto a Si 3 N 4 substrate controlled to 900 K and the natural blackbody radiation spectrum at the same temperature. The comparison in the figure indicates that the bulk of the waste heat problem is eliminated by the bandwidth-limited emissivity of the metasurface array, with the electromagnetic radiation concentrated within the wavenumber range 2000-500 cm −1 (5-20 μm) being of specific interest for the downhole chemical analysis application, as highlighted in the crude oil absorption spectra shown in Fig. 11(b). The emissivity characteristics for the metasurface thermal source were determined using an electromagnetic simulation model similar to the previous one described for absorption properties of the metasurface microbolometer. Due to the high operational temperature of the emitter metasurface, it was determined that copper would make a more suitable material selection for the emitter than the gold material utilized in the detector design. As the optical bench cavity will be maintained under hard vacuum conditions, the risk of oxidation of the metasurface is not considered high for typical logging job durations. However, this material selection may need to be revisited if problems do occur as the sensor development progresses. The metasurface copper material is modeled with an electrical permittivity that is frequency dependent following a Drude model [11] with a simple hyperbolic temperature dependence of the form [see (10)], as shown at the bottom of the page, where ω p = 2.118 × 10 15 Hz is the plasma frequency, γ = 23.09 × 10 12 Hz is the electromagnetic damping frequency, and α = 4.29 × 10 −3 1/ • C is the copper resistivity temperature coefficient with respect to ambient conditions at temperature T 0 . For the emittance analysis, the metasurface pattern is modeled as an imprint on 500-nm Si 3 N 4 with the back surface of the substrate modeled as a PEC boundary condition, the laminate suspended in the vacuum waveguide.
The intrinsic bandwidth limited radiation of the metasurface infrared source is coincident with important chemical spectra of downhole hydrocarbons as shown in the spectra overlay plot of Fig. 11(b) from experimental data by Aske et al. [1]. The spectra in Fig. 11(b) show the differences between crudes of different SARA fractions and emphasize the high distinctions that exist in the lower wavenumber range below 1400 cm −1 in which the metasurface absorptivity remains generally above 95%. The metasurface array infrared source module is comprised of: 1) a metasurface radiation source; 2) an off-axis-parabolic (OAP) folding mirror; and 3) an optical tube that houses the two optical components and creates the knife-edge baffle diameter of the incidence beam onto the OAP mirror-1. The details of the metasurface infrared source array are shown in Fig. 12(a) and the details of the emitter heating filament design are shown in Fig. 12(b). The target temperature of the source array is maintained by controlling the electrical current in the heating filament through a pulsewidth-modulation scheme on the electrical voltage across the resistive filament. The array support functions as thermal isolation with a nominal leakage of 690 mW at 900 K to the optical bench with temperature controlled to 333 K (60 • C). This leakage can be directly absorbed using a 1 × 2 array of a commercial off-the-shelf Peltier device capable of maintaining a bidirectional 40 • C temperature differential under 0.8 W heat load, using 1.5 W supply power. For downhole wireline logging operations, this is a minimal power requirement, and 40 • C bidirectional temperature differential is compatible with the target application involving environmental conditions of 40 • C-100 • C with an optical bench control temperature of 60 • C. VI. DOWNHOLE FT-MIR SPECTROMETER Decreasing the size of existing laboratory-grade FT-MIR spectroscopic instruments is one of the major prerequisites to migrating this technology to remote sensing applications such as downhole production logging systems. For downhole applications, an equally critical criterion for adaptation is high-temperature capability, which is in direct conflict with many of the fundamental technologies used in conventional mid-infrared spectrometry devices. To address the problem of migrating laboratory mid-infrared spectrometry downhole, the current state of the art faces several critical challenges to downhole application: 1) development of spectroscopy at elevated temperature without the need for cryogenically cooled detector technologies; 2) miniaturization of infrared source and interferometer assembly to a scale amenable with integration into downhole logging instrument platforms; and 3) spectral resolution λ sufficient for discrimination of various chemicals that may be encountered downhole in wellbore fluids. The more significant of these challenges could be uncooled MIR spectroscopy at downhole elevated temperatures because current technologies have limited detectivity in the longer wavelengths unless assisted with active cooling.
In laboratory-grade benchtop mid-infrared spectrometers, one of the more common design approaches is the use of a Michelson-type interferometer combined with FT postprocessing. The operation of this type of spectroscope is based on separating an incident beam of radiation into two beams by means of a beamsplitter, whereupon a path length difference between the separated beams is introduced by antisymmetric movement of both of two reflecting elements. This path length difference creates an interference between the recombined beams at the beamsplitter, resulting in a change in the intensity of the output beam as a function of the relative path length difference. This interference mechanism is called an interferometer. The intensity of the interferogram can be monitored as a function of path difference (i.e., relative displacement between the reflecting elements) using an appropriate detector. The Fourier transformation techniques can then be applied to the raw interferogram data to convert the spectra from the relative displacement domain to a radiation wavelength domain, and this can then be used to analyze the absorption spectra characteristics and subsequently the chemical composition of the sample. We use a similar design approach here in developing a miniaturized downhole spectroscopic probe of the Michelson type.
A set of graphical views for the proposed downhole FT-MIR spectroscopic probe design is shown in Fig. 13. The probe assembly includes the miniaturized optical train and MEMS-based Michelson-type interferometer, the attenuated total reflection (ATR) prism for fluid sample sensing, a flowthrough shroud to protect the prism sample interface from potential large debris impact, pressure housing, and pressure feedthrough multipin connector. The probe pressure housing maximum outer diameter is 22.5 mm, which is compatible with integration into a sensor array-type configuration for highly deviated and lateral wellbore logging applications.
The first-order optical train design is determined using a simple 2-D analysis of the probe center plane ray bundle. The 2-D geometric analysis approach does not consider multi-reflection scattering from the baffle tube and in general any 3-D effects on the ray bundle during propagation through the optical train. An objective in the analyses was to estimate whether the beam path could feasibly be confined within a 2-cm probe diameter as well as roughly assess the emitted source intensity onto the detector. The mechanical configuration integrates the uncooled metasurface microbolometer with an MEMS-based interferometer, Ge ATR optical prism, and metasurface thermal infrared source. The thermal infrared source is comprised of a 3 × 3 array of metasurface cells each 150 μm in diameter. The source radiation is directed along an optically black tube with the output aperture directed onto the first OAP mirror being defined by a single knife-edge baffle. The ATR prism receives the folded OAP-1 beam bundle and uses a stepped thickness to produce three reflections of approximately ∅1.4 mm over a 5-mm length fluid sampling interface, with the goal to constrain the total ATR prism length to less than 15 mm. The ATR prism output beam is directed to a subsequent two-mirror fold-focus/fold-focus assembly (OAP-2 and OAP-3) and then output onto the ZnSe 50/50 beamsplitter. Here, the beam divides into two orthogonal paths of equal transmission: path-1 is created by a 50% reflection onto the moveable mirror MM1 and path-2 is created by a 50% transmission onto moveable mirror MM2. Each moveable mirror reflects the individual beams back onto the beamsplitter, with path-1 having a 50% transmission and path-2 having a 50% reflection finally onto the metasurface detector. The uncooled microbolometer detector is comprised of a 2 × 2 array of metasurface cells of the same geometry as the thermal infrared source cells. The two beams recombine on the metasurface detector with a footprint formed by two eccentric circles as shown in Fig. 14, fitting within an oval-shaped envelope 0.184 × 0.228 mm. Due to the eccentricity of the two beams, the detector spot pattern is comprised of a nonuniform intensity central double crescent with 150% net intensity signal and two single-crescent sidelobes with 75% net intensity each. The central double-crescent and the two single-crescent sidelobes have approximately equal areas. This results in about 54% of the detector spot pattern area having 150% net relative intensity (˜1000 mW/cm 2 ), and the remainder comprised in the sidelobes with 75% net relative intensity. A graphical summary of the spectrometer design is shown in Fig. 15(a) for a set of midplane emittance points on the infrared metasurface source, with the gut-ray coordinates, beam diameter variation, and intensity throughput for the two moveable mirror paths shown in the tabular listing in Fig. 15(b).
The MEMS interferometer utilizes a pair of on-chip electrostatic actuators that drive movable micromirrors through a displacement amplification mechanism. The conventional obstacle to sufficient spectral resolution for downhole chemical discrimination in an MEMS device derives from the fundamental limit in interferometric spectroscopy whereby the resolution λ is inversely proportional to the amplitude of the interferometer mirrors motion. The conventional spectral  resolution limitations encountered in interferometric miniaturization are overcome in this invention by a displacement amplification mechanism with about 9.4:1 translation of actuator motion to the moveable mirror element. The interferometer accepts the ray bundle from the optical train with the interface to the wellbore fluids and is comprised of two moveable mirror assemblies, a 50/50 infrared beamsplitter, and the metasurface detector array. A graphical illustration of the MEMS interferometer mechanism is shown in the plan views of Fig. 16(a) and (b).
Each moveable mirror is controlled by an individual electrostatic comb-drive actuator and displacement amplification mechanism, as shown in Fig. 16(b). The displacement amplification mechanism is created through the combination of a symmetric fulcrum about the actuator axis and three serpentine geometry moment release flexures. The comb-drive actuator imparts motion Act on the actuator central axis, which activates the fulcrum lever about the constraint points "F" resulting in an amplification of this motion at the moveable mirror. The three pairs of serpentine flexures are designed to function as quasi-perfect hinge joints at each location. The degree of departure from the perfect hinge moment release degrades the mirror/actuator amplification ratio. For the idealized case in which the three pairs of flexures could be replaced by perfect ball joints, the amplification ratio would be approximately 10:1, whereas in the practical design case involving the quasi-perfect serpentine flexures, the amplification ratio is 9.4:1 due to the incomplete release of the moment. To increase the voltage limit at which the comb-drive experiences lateral instability, a sway stabilization flexure mechanism is integrated at the extreme location from the amplification mechanism. A graphical illustration of the moveable mirror motion due to the amplification mechanism is shown in Fig. 16(c). The illustration in Fig. 16(c) indicates the electrostatic actuator displacement of 27 μm is increased to 256 μm by the action of the amplification mechanism. This amplification of the electrostatic actuator displacement at the two moveable mirrors creates an interferometric spectral resolution of 10 cm −1 over the mid-IR spectral range up to 2000 cm −1 . The maximum quasi-static stress developed in the moveable assembly flexures during actuation is approximately 350 MPa, well within the single-crystal silicon material infinite life fatigue strength [21]. The moveable assembly has a fundamental resonance frequency mode at 198 Hz in the actuation direction and 465 Hz in the lateral direction. These fundamental resonance frequencies lie within the major downhole random vibration spectra that are concentrated below 1 kHz and will be susceptible to excitation. The lateral response is of critical interest due to the potential that vibrational excursions violate the minimum finger gap for lateral voltage stability. For a 110-μm finger gap and ±550-V maximum potential, the allowable lateral dynamic displacement is ±17 μm, indicating a 15-Grms effective dynamic load capacity, which exceeds wireline random vibration requirements typically less than 10 Grms. The moveable mirror scan frequency is 2.4 Hz, which is not a significant excitation source for the moveable assembly having 198-Hz resonance frequency.
For in situ downhole chemical analysis applications, a sample rate on the order of once every second should be acceptable. For the theoretical 10-cm −1 resolution predicted for the design and 500-Hz modulation frequency, 2.4 Hz is the limiting sample rate over the spectral range up to 2000 cm −1 . This limited number of interferogram sweeps/sample should provide an acceptable measurement for the downhole applications considering the low noise characteristics of the microbolometer, requiring verification in subsequent phases.

VII. CONCLUSION
In this article, we report the design of a miniaturized FT-MIR spectroscopic instrument compatible with downhole application. The spectrometer design leverages the perfect absorption properties of an electromagnetic metasurface design formed from a set of inverted conformal contours of the canonical tangent circles' conformal mapping. The PMA behaves as an NZIM having intrinsic multiple coupled absorption resonances that combine to form broadband infrared absorption characteristics. Scattering parameter retrieval simulations indicate that the metasurface absorbs between 80% and 100% of incident infrared radiation in the range 1667-567 cm −1 (6.0-17.6 μm), with a 114% FWHM bandwidth on the 837cm −1 (12 μm) center wavelength. An uncooled microbolometer design is described, which uses the metasurface geometry on a single vanadium dioxide (VO 2 ) thermometric substrate leading to an infrared detector with perfect absorption properties coincident with important chemical spectra of downhole hydrocarbons. Figure-of-merit analyses for the uncooled microbolometer result in predicted maximum detectivity D * = 1.5 × 10 1 0 cm(Hz) 1/2 /W and NEDT of 1 mK at a modulation frequency of 500 Hz. The spectrometer design packages within a 23-mm-diameter envelope compatible with many downhole sensor suite requirements and was numerically evaluated to allow up to 2.4-Hz sample rate logging data. These design parameters indicate that the concept could be viable for downhole application of in situ FT-MIR spectroscopy.