Departments of Bioengineering, Mechanical Science and Engineering, Electrical and Computer Engineering, Beckman Institute for Advanced Science and Technology, University of Illinois Cancer Center University of Illinois at Urbana-Champaign, Urbana, IL 61801
Find articles by Rohit BhargavaRohit Bhargava, Departments of Bioengineering, Mechanical Science and Engineering, Electrical and Computer Engineering, Beckman Institute for Advanced Science and Technology, University of Illinois Cancer Center University of Illinois at Urbana-Champaign, Urbana, IL 61801;
Rohit Bhargava: ude.sionilli@bxr The publisher's final edited version of this article is available at Appl SpectroscInfrared (IR) spectroscopic imaging seemingly matured as a technology in the mid-2000s, with commercially successful instrumentation and reports in numerous applications. Recent developments, however, have transformed our understanding of the recorded data, provided capability for new instrumentation, and greatly enhanced the ability to extract more useful information in less time. These developments are summarized here in three broad areas— data recording, interpretation of recorded data, and information extraction—and their critical review is employed to project emerging trends. Overall, the convergence of selected components from hardware, theory, algorithms, and applications is one trend. Instead of similar, general-purpose instrumentation, another trend is likely to be diverse and application-targeted designs of instrumentation driven by emerging component technologies. The recent renaissance in both fundamental science and instrumentation will likely spur investigations at the confluence of conventional spectroscopic analyses and optical physics for improved data interpretation. While chemometrics has dominated data processing, a trend will likely lie in the development of signal processing algorithms to optimally extract spectral and spatial information prior to conventional chemometric analyses. Finally, the sum of these recent advances is likely to provide unprecedented capability in measurement and scientific insight, which will present new opportunities for the applied spectroscopist.
Index Headings: Infrared spectroscopic imaging, Fourier transform infrared spectroscopy, FT-IR imaging, Infrared microspectroscopy, Mapping, Focal plane arrays, FPA, Discrete frequency IR imaging, Quantum cascade lasers, QCL, Synchrotron, Chemical imaging, Scalar wave theory, Electromagnetic theory, Compressive sensing, Reconstruction, Noise reduction
The combination of infrared (IR) vibrational spectroscopy and optical microscopy has been the subject of many studies and the analytical approach has been employed in thousands of applications for many decades. The recent evolution of the field can be found in periodic reviews 1–3 and compilations. 4–7 While there are approaches in which optical microscopy can provide structural detail and point measurements of spectra provide chemical information, 8 the two measurements are commonly performed today such that IR absorption provides the contrast mechanism for the entire field of view of the optical image. 9 The underlying concept for obtaining spatially resolved spectroscopic data is to localize the interacting volume of a sample with propagating light such that data can be recorded and interpreted and information extracted from the targeted area. These three areas of spectrometry—data recording, interpretation, and information retrieval—form the core of the science of IR microspectroscopy. Applications to particular problems, using a combination of specific techniques in the three areas, are covered in other recent reviews. 10–16 Here, we focus on the science of IR microspectrometry, especially on recent developments that can potentially transform imaging spectroscopy in the future.
Fourier transform infrared spectroscopic imaging, which is most commonly referred to as FT-IR imaging, combines an interferometer, IR microscope, and array detector ( Fig. 1 ). 33 Data is recorded by spectral multiplexing in time using the interferometer and simultaneously by a large number of detectors (multichannel advantage). The genesis of this instrumentation can be traced to the availability of focal plane array (FPA) detectors with extended wavelength sensitivity, 34 non-microscopy imaging attempts, 35 and the use of filter-based imaging. 36,37 From the initial, relatively crude, step-scan systems with attendant issues of sub-optimal data recording, 38,39 instrumentation has now evolved into rapid-scan systems 40,41 with improved detector electronics and fast signal processing. Step-scan imaging, similar to bulk step-scan spectroscopy, would still be useful for time-resolved FT-IR imaging 42 but has only been reported in a few studies. 43–45 Though imaging instrumentation is commercially available, no major conceptual innovations have occurred over the past 8 to 10 years in the available systems. To some extent, this is a sign of mature component technology. While some advances can be foreseen, such as detectors with improved speed and larger formats, the approach to imaging is largely the same as a decade ago. As argued later in this article, this stagnation is also a product of a lack of theoretical and fundamental understanding that can guide further development. The stagnation has also spurred a look elsewhere for competing technologies and alternate approaches that address specific shortcomings of present-day instrumentation.
(A) Typical layout of a Fourier transform infrared (FT-IR) spectrometer. Instrumentation is usually general purpose, with transmission and reflection sampling configurations in the same system (only the transmission path is shown here), dual detectors enabling both point mapping and imaging technology, as well as external interferometer and computer to acquire and process data [figure by Kevin Yeh]. (B) Conceptually, the optical path proceeds from a source to a spectrometer, microscope, sample, and to the detector. The computer serves to operate the spectrometer and process signals from the detector into information. (C) The ongoing evolution of technology will make computing and control central to imaging. The source/spectrometer combination will essentially function as a known and controlled light source. Information about the sample and microscope configuration will be fed to the computer and used to process signals from the detector via new theory and algorithms as described in this article. The quality of information extracted, as a consequence, will be considerably improved.
In a competing approach, which we term discrete frequency IR (DF-IR) imaging, data may be recorded at single frequencies of limited bandwidths without extensive spectral multiplexing in time. A frequency sweep, as for example with gratings, has long been out of favor for spectrometry due to the Fellgett and Jacquinot advantages offered by interferometry. Filters and gratings, nevertheless, have been used sporadically. While these attempts were useful for sampling a single frequency or a few bandwidth regions, they did not gain much favor for spectroscopy over appreciable spectral bandwidths. As opposed to bulk measurements, however, spatially resolved measurements are actually more favorable for these alternate forms of spectral recording. The throughput and multiplexing advantage can be recovered somewhat by relaxing slit width as lower spectral resolutions are typically required in imaging condensed matter while simultaneous recording with a multichannel focal plane array (FPA) detector alleviates the multiplexing advantage to some extent. While the use of gratings permits the recording of smaller bandwidths of data, instrumentation in other spectral regions 46 has typically focused on specific applications requiring compact size, robust performance, and speed. These advantages are typically not the driving requirements for mid-IR microscopy systems, though they can potentially be used in this spectral region as well. The reduction in bandwidth can be continued to the level of recoding a single spectral resolution element at a time. Towards this end, there are two major emerging trends. In the first, lasers are becoming more available and practical for the mid-IR region. Quantum cascade laser (QCL) technology, 47 in particular, is maturing and transitioning from academic to commercial success. The second trend is the increasing integration of powerful computers in spectroscopy. This trend will enable the extraction of significantly higher quality information, even from poorer quality recorded data. Spatial deconvolution, noise rejection, and other signal-processing approaches can potentially provide solutions that displace the need for sophisticated hardware. We examine these trends next and discuss progress in the context of recent advances.
The globar has long been the source of choice for both IR spectrometry and imaging due to its broadband emission, sufficiency of light for most conventional applications, simplicity, robustness, and low cost. The output of a globar is matched well to the detector characteristics of modern single-element detectors and electronics such that photon flux is not a limitation for the vast majority of bulk measurements. For imaging, due to the need for focusing and uniform distribution of light over a large area, the flux per detector element is significantly smaller and requires longer observation times. At the same time, the miniaturized detector and electronics in an FPA are noisier. Hence, imaging data are inherently noisier than their corresponding single-point measurements. 48 Interestingly, quantitative analyses of the expected signal-to-noise ratio (SNR) indicate that an increased SNR can be realized with miniaturized detectors—if the same flux can be maintained. 49 Hence, a higher flux source is likely to prove beneficial for imaging.
Compared to thermal sources, a synchrotron provides high-brightness radiation that is particularly relevant for microscopy and imaging. 50–54 A summary of the properties of synchrotrons and their applications for microscopy is available, 55 and hence, we only focus on the features relevant for imaging. Details of recent developments and description of a major improvement in performance are available in a recent review. 56 The emitted beam from a synchrotron is of high brightness, collimated, and of a small size. While this property was excellent for point microscopy in which light from a larger diameter would anyway be rejected, it was not very effective for wide-field imaging. There were reports of coupling a focal plane array to synchrotrons 57,58 and the notion of improved data quality was proposed. A major recent advance was the combination of multiple beams to provide a bright, wide beam source that could be coupled into an interferometer. 59 While SNR improvement was a major outcome, the work has changed IR imaging in a more fundamental manner. The resolution of any IR imaging system is limited by the diffraction limit and the numerical aperture (NA) of the objective. As demonstrated in the above study and shown theoretically (discussed further in this article in the Microscopy section), 60 the sample size imaged per pixel was not optimized. Commercial instruments typically image ∼5 μm per pixel in order to ensure a sufficient SNR from the weak thermal source. Using a synchrotron source with the same setup alleviates the lack of throughput and enables smaller pixel sizes at the sample plane to be recorded. The resulting image quality clearly demonstrated the utility of the synchrotron source in providing diffraction-limited images for the first time. The quality of images was so dramatically different that these are dubbed “high-definition” (HD) images to distinguish them from the previous state-of-the-art. The study also highlighted the need to develop new sources and detectors and exposed the lack of rigorous considerations in the design of most instruments. A new set of synchrotron-based high-performing microscopes will probably result given the development of new beamlines that is currently underway and the convincing demonstration of HD imaging. The obvious drawback of this approach for applied spectroscopists is that synchrotron sources for IR imaging have limited availability due to their cost, size, and accessibility. Free electron lasers, 61 another source using accelerated particles but using an undulator to achieve optical amplification, can generate an output with a much higher spectral brightness and coherence than a synchrotron. Used sporadically for microscopy of practical systems, 62 their application for IR microscopy is even more limited than that of synchrotrons. These are perhaps better suited for fundamental spectroscopic studies, 63 therapeutic use, 64 or near-field nano-scopy 65,66 approaches. In summary, no major advances in the technology of sources are anticipated but changes are likely forthcoming in the manner in which these sources are used, for example, for HD imaging.
A new approach to spectrometry was described involving an FPA detector in which a conventional grating arrangement was used to disperse light and individual pixels in the array were employed to record a single resolution element region ( Fig. 2 , left). 67 The spectrometer is termed planar array infrared (PA-IR) spectrograph. While the genesis of the PA-IR approach is both in the use of gratings and single-element detectors that preceded FT-IR spectroscopy as well as in the use of multichannel detection 68 in ultrafast spectroscopy or nanoscale mapping, 69 the approach has significant additional implications for microscopy and imaging. The approach is flexible as different bandwidths can be selected depending on the optical and array arrangements 70 as well as very high fidelity in terms of speed 71 and sensitivity. 72 The spectrometer inherently involves multiplexing due to the multi-channel detection, and elimination of a narrow slit results in improved SNR. The flux is very efficiently utilized, enabling measurements even in aqueous solutions. 73 Since there are no moving parts for recording a specific (though, limited) bandwidth, data acquisition can be rapid and is limited only by the integration times (∼10 μs) of the detector. The frame rate of the detector determines the temporal interval between spectral acquisitions (∼ 1 ms), making the rate of spectral acquisition quite comparable to the fastest FT-IR imaging systems. With the inevitable future availability of FPA detectors with faster electronics and larger sizes, ∼100 μs spectral acquisition is likely going to become possible and larger bandwidths may be accessible. The limited bandwidth problem of this approach can be overcome by using multiple pixel rows available in the FPA. Configurations have been proposed to illuminate the FPA with two or more separate and independent spectral bandwidths. Perhaps the greatest advantage of this technology lies in its ability to perform real-time background corrections by obtaining sample and background single beams from the same FPA image, virtually eliminating the effects of water vapor or source fluctuations. Despite these advantages, however, the use of this approach for imaging has not been actively pursued.
Hybrid spatial–spectral data recording is possible using a grating or a prism-based spectrograph coupled to a microscope. (Left) Experimental arrangement of components in the PA-IR spectrograph. (Middle) Spectra acquired (across a row) using a prism-based spectrograph. The detector image of Parylene can be used to extract spectra (right) that change with the optical parameters of the system. Spectra recorded at slit width settings of (a) 46, (b) 64, (c) 108, and (d) 153 lm with the sodium chloride single-pass prism spectrograph. (e) The CH stretching and fingerprint regions of the FT-IR spectrum were acquired at 22 and 14 cm −1 resolution, respectively. [Figure at left reproduced with permission from Ref. 67 , copyright Society for Applied Spectroscopy. Figures in the center and to the right reproduced with permission from Ref. 75 , copyright Society for Applied Spectroscopy.]
In principle, using an aperture and systematically translating the sample to collect spectra permits mapping of the sample in a manner comparable to point mapping. A similar concept has been implemented, though using prisms, 74 for point-mapping measurements. 75 The spatial area-defining aperture of the microscope at the sample plane also served as the entrance slit to the spectrograph and light is dispersed both along the column (spatial information) as well as across the row (spectral information) of the detector array ( Fig. 2 , middle). Prisms require a more complicated setup to provide the higher resolution typically afforded by grating-based systems but, for a particular array, the spectral coverage can be higher. Since FPA detectors are two dimensional, it also is possible to spectroscopically and spatially map the sample at the same time. A hybrid imaging approach has been proposed 76,77 in which one dimension of the FPA is used for spectral recording while the other is used for spatial resolution. The line-scan approach to mapping, however, has not yet been extended to raster the sample. This could prove to be an exciting development for some applications. Recorded spectra compared very favorably with those from an FT-IR spectrometer ( Fig. 2 , right) and can be seen to depend strongly on the optical setup (slit width). Because the slit width would also be coupled to the spatial resolution, spectral and spatial resolution would be correlated in any mapping system using this architecture. Hence, considerable thought and optimization may be needed to design a flexible system that can provide both excellent spectral and spatial resolution. Given the ability to perform high fidelity spectroscopy, real-time corrections, and other advantages enumerated above, it should be possible to obtain data of very high quality using an appropriately designed instrument. Given the coupling between spectral and spatial domains as well as challenges in accessing vibrational modes over large bandwidths, hybrid mapping or point microscopy systems would likely only be useful for moderate performance applications where cost, robustness, and simplicity are significant considerations.
A practical benefit of a microscope based on PA-IR spectrometers would be in the rapid examination of small regions of exceptionally small signals, e.g., mapping of monolayers, an ability that is not easily available in FT-IR microscopes. The most exciting result, however, is probably the ability to provide exceptionally low levels of noise. The peak-to-peak noise level of the baseline in absorption spectra acquired in tens of minutes was reported to be of the level of 10 −5 . Combined with the spatial localization of microscopy, the SNR could potentially provide the capability to image domains, inclusions, or impurities at the sub-picogram level or lower in minutes. The sensitivity, speed, and robustness of such a microscope could potentially be useful for real-time quality control or forensics, for example, but no applications have been reported in those directions. While not explicitly stated or analyzed theoretically in the above works, there is a fundamental concept of significant value in using the PA-IR system for imaging. Interferometry has been so ingrained into the body of knowledge for decades that it has become synonymous with multiplexing. Multiplexing can also occur in the spatial domain. In the non-imaging version of the PA-IR setup, spectra from different spatial regions were simply averaged to provide an average “bulk” spectrum while a multichannel detection advantage was obtained using different pixels to record data. Thus, the spectral acquisition was multiplexed in both the spatial regions of the sample as well as the spatial extent of the detector. While Fellgett's advantage 78 in temporal/spectral multiplexing is often cited as a major competitive advantage of interferometry, this spatial multiplexing confers an advantage of similar magnitude, though arising from different considerations. Hence, we argue that the long-accepted belief in the general utility of the Fellgett advantage for spectroscopy should be re-examined in the context of imaging, as discussed in the next section.
The multiplex advantage has played a central role in the evolution of instrumentation in the mid-IR. Briefly, in an interferometer, all frequencies in the bandpass of the optical system are acquired all the time. Hence, as opposed to sequentially measuring each spectral resolution element individually, an N-fold higher signal is measured N times. Comparisons of interferometric methods with other methods often rely on the assumption that the entire spectrum of large bandwidth has to be measured, that the finite dynamic range of the detector does not play into the theoretical advantage, and that a high spectral resolution is required. A complete discussion of the relative merits of interferometric versus other approaches is in preparation; 79 here, the most important considerations are summarized. The first pertinent aspect is the sheer size of the data. As opposed to N spectral data points in a single spectrum, there are Nx and Ny spatial resolution elements as well. Hence, the total data points that are to be measured is N × Nx × Ny in an imaging experiment. For the purposes of acquisition, which is limited by detector readout speed, and for recording and analyzing the fewest data needed, in the interest of conserving time and resources, it may not be necessary to record the entire spectrum. For many applications, such as imaging biological tissues, 80 it may be beneficial to record only specific spectral bands of interest. A second pertinent issue is the one of limited performance of available array detectors, mainly their electronics and dynamic range. Interferometry encodes the intensity of the source such that that there is a massive signal recorded around zero optical retardation. The spectral SNR of the single beam is approximately equal to the SNR of the centerburst divided by √N. In a conventional spectrometer, the speed of the interferometer can be increased for large signals and signal averaging can be extensive, thereby reducing detector noise contributions in a given acquisition time. With FPA systems, the readout time of the detector is fixed, whereas the integration time for signal acquisition can be tailored to best fit the centerburst signal into the dynamic range of the ADC. Methods such as gain ranging, 81 staggered step-scan, 82 rapid scanning, interferometer modulation, 83 and detector aperture matching 84 have been proposed around this limitation but have not been able to address the limited dynamic range problem. Further, the full range is not utilized for fear of saturating the detector and some range is lost to thermal background. Since the globar bandwidth used in interferometry is large, N is typically 512–2048 points and the SNR for one scan at each pixel is no more than 250:1. Typically, studies report 100:1 85 and uncooled detectors 86 would report SNR of 10:1. While small detectors provide impressive SNRs, 5 spatial coverage suffers dramatically. Practitioners today have to tolerate the reduced multichannel advantage to gain high SNR, for example, for biomedical applications, or sacrifice SNR to gain imaging speed, for example, for kinetics experiments. 87
An alternative approach to overcome these difficulties encountered with FT-IR imaging has been recently proposed. 88 In this approach, a spectrally narrow-band beam is provided to the microscope and a spectral image at a specific frequency is recorded directly. Hence, high SNR can be achieved rapidly by averaging a small spectral range instead of spectrally scanning a large bandwidth. Since the recording of spectral elements is decoupled from recording the entire bandwidth (the FT-IR case), this approach is termed DF-IR spectroscopy ( Fig. 3 ). The approach would ideally, first, greatly simplify instrumentation while providing performance at least comparable to an FT-IR spectrometer in terms of recording spectral elements of interest, resolution, and data recording speed. Second, it would make instrumentation more robust by replacing the sensitive interferometer with a simple moving part or solid-state lasers. The ability to selectively acquire data at a few or all wavelengths and to do so in random access is the obvious advantage of this approach. The same advantages are available using lasers. There are different approaches to lasers that are now becoming more prominent for the mid-IR spectral region. We divide spectroscopy candidates into two major groups based on the components and output of the laser system. The first group includes lasers in which mid-IR radiation is directly generated and available, including QCLs and lead-salt or CO2 lasers. The second group is based on frequency conversion, using well-established sources from other spectral regions, for example, using optical parametric generation in nonlinear crystals. While the DF-IR term was first introduced with respect to filters, the idea is essentially the same using lasers. Hence, we use the term to imply the general embodiment of imaging where selective and individually addressable wavelengths can be employed for imaging. In general, throughput in a laser system will be higher than filter-based systems, as will be cost and complexity.
(A) Essentials of the FT-IR and (B) DF-IR Setup. A broadband source (C) is encoded and decoded by FT-acquisition using (D) interferograms. (E) A small number of filters are used in DF mode to measure the informative spectral sections.
A second advantage of DF-IR approaches addresses the dynamic range problem directly. In DF-IR measurements, the dynamic range is simply filled by a narrowband signal and the single-beam SNR can be 1000:1 (cooled FPA) or 100:1 (uncooled FPA). The ability to use uncooled arrays is perhaps the most exciting aspect of DF-IR approaches. Uncooled FPAs are cheaper and have much larger formats than cooled arrays. Hence, coverage can be enhanced and more time can be spent averaging signal to improve SNR. Uncooled FPAs are also becoming increasingly available in larger formats, though only at near-video-rate readouts due to technological and market limitations, and are likely to be used for spectroscopy only in this format. Further, the ADC can be filled by integrating the signal for varying times for each spectral element. Hence, we can obtain uniform SNR (or by design, enhanced SNR at any frequency) simply by software control. This potential, though not implemented in any reports thus far, will also mean that the conventional notions of SNR will need to be reconsidered. In DF-IR spectroscopic imaging, SNR can be tailored for different elements of the spectrum such that SNR in absorbance, rather than baseline noise as obtained in interferometry, is constant across the spectrum. In summary, the DF-IR approach has the potential to be simpler, robust, and cheaper, as well as being superior to FT-IR imaging in some cases. We emphasize that these analyses do not imply that DF-IR is superior to FT-IR imaging in all cases. If the entire spectrum is required at high resolution, the detector is of large dynamic range and low noise, the source is exceptionally weak (emission spectra), or there are noise frequencies that can be filtered, then FT-IR imaging will be distinctly superior. DF-IR imaging will likely evolve for very specific uses, also providing additional opportunity to optimize performance and lower costs. In particular, its use is likely to be popular where a few spectral features provide all the information of interest, 89 for example, in tissue typing. 90
The possibility raised above points to a trend in which the source, spectrometer, and analysis need to be controlled and to be in sync with one another. This is not only required but can potentially provide improved performance. Efforts to maximize performance, however, also usually restrict the range of studies that one particular implementation can address. To become more generally applicable, optical arrangements for DF-IR systems would have to be flexible and configurable; implying again the use of software for optimization and control significantly more than presently implemented.
The critical technology for DF-IR imaging is obviously the “source”, which integrates a source of light at different wavelengths as well as a means to separate multiple frequencies into individual narrowband ones. The distinction from interferometric methods is that the source–spectrometer combination provides the opportunity to select a single narrowband illumination at one time, while the distinction from grating based methods is that the intensity at frequencies is unrelated to a single grating frequency that has been optimized. Three major classes of such sources are available and are worth following as the DF-IR approach becomes more prevalent. Technology for sources and software approaches are discussed in the next section.
In IR imaging, a microscope is coupled to a spectrometer. Hence, for both DF-IR and FT-IR imaging, the microscope, sample mounting, and beam steering components are the same. The source of light and the spectrometer are the only differences. The effects of microscopy optics and sample are discussed in subsequent sections; here we examine the source– spectrometer component. The use of filters allows recording of spectral data directly using narrow linewidths. There are two major impediments to this ideal. The first is conceptual in that it is not simple to design narrowband filters of multiple bandpass (resolution) appropriate for spectroscopy. The second is practical in that conventional processes such as mechanical ruling used to manufacture gratings are far too slow and, consequently, too expensive to mass produce sets of filters. There are other minor concerns such as how an optical design would incorporate tens to hundreds of filters that may be needed. Recent renaissance in optical sciences provides technology that is capable of providing filters with characteristics sufficient for use in spectroscopy in the form of so-called guided-mode resonance filters (GMRF). 91 Mass production of the filters is enabled by recent advances in nanofabrication technology, optical modeling, and use of unconventional materials for manufacture. For effective application in IR spectroscopy, the set of filters should provide high reflection efficiency over a narrow wavelength range for all spectral resolution elements. The resolution achieved must be the same as common FT-IR settings (4 to 16 cm −1 ). A set of filters should also be capable of spanning a large wavelength range (e.g., 3950 cm −1 , the sampling cut-off for under-sampled FT-IR spectroscopy to 950 cm −1 , the FPA cut-off). The materials and fabrication challenges to achieve these conditions are quite significant and, until recently, only wide (∼100 cm −1 ) band filters had been reported in the mid-IR. The efficient production of these filters and design of ones with tailored characteristics are likely to remain topics for research. Hence, we examine the concept behind these filters, their testing, and review the state of the art in the next few paragraphs.
Since their discovery more than a century ago 92 and as described in recent analyses, 93–96 anomalies in periodically modulated structures have attracted much attention for spectral selectivity. Resonant anomalies, 97,98 termed guided-mode resonance (GMR), in waveguide-gratings result from structures with a sub-wavelength modulation in refractive index along one dimension. Designed structures can be used to function as filters that produce complete exchange of energy between forward- and backward-propagating diffracted waves. More importantly, for spectroscopy applications, it was shown that smooth line shapes and arbitrarily narrow linewidths could be obtained. 99 GMR arises from the introduced periodicity that allows phase-matching of externally incident radiation into modes that can be re-radiated into free-space. They are often referred to as “leaky eigenmodes” of the structures as these modes possess finite lifetimes within such structures. GMRFs store energy at the resonance wavelength, which is manifested in optical near fields that interact with the device itself as well as with the external environment. For normal incidence illumination, the response of the GMRF is coupled to the second-order Bragg condition and therefore the spectral location of peak reflection can be given by:
where λ is the resonant wavelength, neff is the effective index, and Λ is the modulation period. 100
The effective index is a weighted average of the refractive indices of the materials in which the standing wave generated at resonance is supported. Hence, structures to provide large numbers of resonant wavelengths needed for spectroscopy can be readily tailored by changing geometric parameters (modulation period). There were successful examples 101 of making such structures for ultraviolet (UV), visible, and near-infrared (NIR) wavelengths and the first example for mid-IR wavelengths was also recently reported. 91 Although modeling and simulation of these structures required additional details and accounting for dispersion in the materials used, actual fabrication and unproven manufacturing in the mid-IR were impediments that needed to be overcome. The primary challenge is that materials of the structure need to have little or no absorption at the resonant wavelength in order to maintain near 100% reflection efficiency. We have selected plasma-enhanced chemical vapor deposited (PE-CVD) silicon nitride (SiN) and fumed silica dielectrics specifically for their low mid-IR absorption and have produced highly efficient reflectance spectra. Since there are a large number of frequencies, a secondary challenge is to ensure both an efficient fabrication and use of these filters. A “filter wheel” has been developed using a single wafer to address both needs. One positive aspect of fabricating filters for mid-IR wavelengths is that the device period, which must be less than one-half the resonant wavelength, increases as wavelength increases according to Eq. 1. A device designed to measure the CH stretching mode, for example, is resonant at λ ∼ 3.45 μm and requires a period of Λ = 2.1 μm, which dictates that the size of etched features will be 1.1 μm. Features of this size are well within the dimensions of routine contact photolithography using conventional photoresists and chrome exposure masks. Hence, mass fabrication is possible and can be very cost effective. We have obtained filter parameters that can provide narrow linewidths at usual FT-IR resolutions. Filters with these characteristics were fabricated and demonstrate performance as per theory. These filters can be demonstrated in principle but have not been used for imaging spectroscopy due to fabrication and interfacing challenges at this time. This technology is in its earliest stages but the economic argument is compelling. Advances in modern fabrication and the wide availability of electronics manufacturing can be leveraged to provide fairly inexpensive spectrally resolved sources for microscopy. This aspect is likely to sustain interest in developing low-cost filters.
A typical GMRF and its use for mid-IR imaging is shown in Fig. 4 . The filter ( Fig. 4A ) is conceptualized to comprise a low refractive index substrate (soda lime glass, n = 1.5) upon which a thin film of high refractive dielectric material (silicon nitride, n = 1.975) is deposited. A one-dimensional linear grating pattern upon the dielectric material is realized by photolithography and a reactive ion etch process is used to etch grooves partially into its surface ( Fig. 4B ). With theory-guided selection of the material refractive index parameters, dielectric layer thickness, and grating depth, the device structure performs the function of a highly efficient reflectance filter. At the resonant wavelength, the structure achieves high reflection efficiency for a narrow bandpass and other wavelengths are transmitted. They are eventually absorbed by the thick soda glass. A rigorous coupled wave analysis 102 (RCWA) computer code was written for simulations of these structures and used to predict the reflection efficiency as a function of wavelength, that were subsequently validated in individual filters ( Fig. 4C ), though important differences between the predicted and observed performance could be seen. A number of filters could be co-housed on the same substrate ( Fig. 4D ), which is incorporated into an optical arrangement for both testing against an FT-IR spectrometer as well as for use in a microscopy system ( Fig. 4E ). A narrowband absorbance image obtained using the filters demonstrates that imaging is possible ( Fig. 4F ). Any frequency can, hence, be addressed rapidly and randomly by turning the wheel from software control.
Components and results from DF-IR imaging. (A) Schematic of a designed filter. (B) Characterization of the designed filter by microscopy and atomic force microscopy shows the ability to fabricate structures as per design and their uniformity. (C) The imperfect prediction and fabrication capabilities at this early stage, however, do present challenges in translating the narrowband predicted performance (for example, on the left) to actual filter performance (right). (D) Tens of filters can be placed on a single substrate and fabricated together on the same optical path using the concept of a filter wheel. (E) Schematic of setup for characterization of the filter, spectroscopy or for comparison with FT-IR imaging. (F) An absorbance image from an unoptimized system showing the antisymmetric CH stretching band absorbance of an SU-8 sample. The image size is approximately 500 μm × 500 μm. White levels indicate a higher beam attenuation and gray/black levels indicate little to no attenuation.
While the DF-IR approach enabled by GMRFs is an exciting avenue, many challenges remain. Filters have been designed and tested and important insights obtained into their design. However, the filter–optical setup is not optimized. Even in theory and simulations, smaller refinements need to be incorporated. For example, the refractive indices and dispersion due to small absorption within the fabrication materials are likely causes of the variance; hence, characterization and prediction of these properties is needed. The efficiency and FWHM of any filter depend both on the optical alignment as well as properties of the underlying materials. While the filters themselves can be fabricated and coupled to a globar source, great care must be taken in alignment. Alignment concerns can likely be resolved with the same dynamic approaches as used in an interferometer but beam collimation (restricted with an aperture similar to that in an FT-IR spectrometer) and its effect on spectra need to be studied. Spectra from the filter wheel show higher noise compared to a conventional single-element spectrometer, which is several thousand fold larger in area and lower resolution due to the broad spectral bandwidth. Hence, further optimization is needed for routine spectroscopy. As with all frequency selection methods via coherent processes, polarization is introduced into the beam. An alternative to GMRFs might be to use a conventional grating/slit monochromator, where serial adjustment of the monochromator slit position illuminates the sample one wavelength at a time. While such a method would suffice in principle, the GMRF approach has a number of advantages. By using the described approach, efficiency at all wavenumbers can be optimized, frequencies are individually selectable, ruling cost is much lower, and large wavelength regions can be covered in a single part (filter wheel). The fundamental limitation of a globar in terms of flux remains. For filters, the use of an aperture and polarizer further decreases total available intensity. Hence, the need for higher intensity sources is not addressed and actually becomes more acute in using filters. Tunable lasers are an obvious choice and two routes, discussed next, stand out in their potential for IR imaging.
Quantum cascade lasers (QCLs) 103,104 are a class of unipolar lasers based on inter-sub-band transitions in a semiconductor heterostructure. Most common embodiments involve using InGaAs/AlInAs/InP composites 105 that are active at wavelengths longer than ∼3 μm. The most effective approach in this direction is emerging in the form of an external cavity (EC) QCL. A grating is coupled to a free-running semiconductor laser to select a specific band and tune the entire device into a single-band source. The setup consists of three components: the gain element (QCL chip), collimating mirrors, and grating. 106 In principle, the setup is similar to the combination of a grating-based spectrometer and source. The major advantage, however, is that exceptionally narrowband light of unprecedented intensity can be obtained. QCLs function at room temperature, 107 the source is compact, and, in principle, it can become fairly inexpensive after further development. Lasers have been widely used for spectroscopic analyses 108 for a number of years and, similarly, various studies have used QCLs for IR spectroscopy 109–113 as well as microscopy and imaging. 114,115 The most widely reported studies in spectroscopy have been focused on using the narrow-band properties and high intensity of the QCL to profile specific species, aqueous environments 116–118 or the integrated and compact instrumentation 119,120 that may be developed for specific experimental configurations 121 or applications. 122–124 The technology has made rapid progress, specifically in spectral properties and power. 125
A large effort in the QCL-related fields has been in the modeling, measurements, and optical properties of these devices. Imaging and microscopy instruments as well as applications have lagged significantly. Since their initial demonstration more than 15 years ago, 47 the technology has matured and there are several commercial vendors offering QCL systems. Though realized around the same time, the maturation of IR imaging technology has been considerably faster, given the long history of IR microscopy. It is curious that combining the two technologies has received limited attention. The first factor in this lack of progress may be the limited spectral range, high cost, and restricted availability of stable, packaged QCL sources that are usable. The second is more fundamental. While QCL manufacturing technology is making rapid progress in developing broadband output devices appropriate for spectroscopy, turning them into viable sources for microscopy will likely require substantial further work on the part of spectroscopy and imaging scientists. Based on preliminary experiments thus far, a QCL cannot simply be integrated into existing microscopes in the manner that FPAs were integrated into single-point IR mapping microscopes. Though the single point-to-FPA detector transition required opening the apertures and changes in software, the beam size, spectroscopy, noise characteristics of the spectrometer, and optical performance of the microscope were not changed. These would all have to be reconsidered in using a QCL source. We illustrate one aspect from our work 126 in Fig. 5 . The coupling of the laser to a microscope required beam expansion, reduction of spatial coherence, and new optical elements for illumination. Without these measures, coherence makes data interpretation difficult; even with this design, illumination and recording are not trivial. The beam intensity and size, as well as its polarization, coherence, and narrowband emission all present significantly new challenges that are discussed and would require a careful analysis of the performance of an integrated system and a likely re-design of existing microscopy systems to be of significant value. An excellent recent example of integrating the unique advantages of this technology in designing instruments is available in the near-field microscopy arena, 127 while new opportunities may lie in photoacoustic spectroscopy applications. 128 The challenge for spectroscopists would be to integrate the new sources with a better understanding of their potential and of the implications of the limited-wavelength, coherence, and polarization for spectroscopic imaging. The challenge for QCL device manufacturers obviously lies in extending the wavelength coverage, providing compact and integrated sources with seamless transition between wavelengths, and high beam stability. Complementary sources to cover shorter wavelengths (
USAF 1951 optical resolution target absorption images (cycle 3, elements 5 and 6) as acquired by three different instruments. As opposed to chrome-on-glass targets, these samples were designed to be a cross-linked photolithographic polymer (SU-8) on polished barium fluoride substrates. Top row: QCL + bolometer system without diffuser plate. Middle row: QCL + bolometer system with rotating diffuser plate. Bottom row: commercial FT-IR instrument. [Reproduced with permission from Ref. 126 , copyright American Chemical Society.]
While QCLs produce mid-IR light directly, the considerable advances in powerful sources in other spectral regions as well as photonic fibers can also be leveraged using frequency conversion. 129,130 A complete discussion of these sources and their potential for imaging is beyond the scope of this article but compilation of the fundamentals of several potential technologies 131 and recent advances are available. 132 The development of appropriate materials such as periodically poled lithium niobate (LiNbO3) and the emergence of NIR sources have been most crucial to the development of tunable mid-IR sources by optical parametric generation (OPG). Advances in materials processing, microfabrication technology, and understanding of these systems has led to other candidates and materials for frequency conversion. Specific examples of successful technologies are using, for example, GaAs, 133 which promises to considerably extend the capability of this approach. The most successful example of application is in coupling with a sub-micron scanning sensor 134 and the commercial translation to nanoscale imaging, 135,136 demonstrating that a system built from these sources may also be viable for microspectroscopy.
An excellent example of the potential of this approach is demonstrated in the coupling of an OPG-based system with a conventional IR microscope and FPA. 137 The flux allowed the acquisition of images with sufficient SNR in ∼1 μs of acquisition, thereby considerably reducing the contributions from thermal background radiation and providing new opportunities for noise rejection. The primary limitations at present are the relatively coarse spectral resolutions attainable (∼10 cm −1 ) that cannot be arbitrarily changed, pulse-to-pulse stability, and complexity of the setup. Though pulses may be spectrally broader, spectroscopy can be performed by spacing the tuned peak wavenumber closer to provide a quasi-resolution that is comparable to those typically used for condensed-phase imaging. Further, in principle, computation can be used to recover the true spectrum at higher resolution using signal processing techniques. The sources will likely imply shot-noise-limited performance, though such an analysis has not been reported for imaging systems. Though the capability to image across the entire mid-IR bandwidth exists with OPG-based systems, a source with consistent spectral performance over the range is difficult to achieve in practical terms. Alternative materials with new crystals, for example, cadmium selenide (with an idler tuning range of 1160–850 cm −1 ), are becoming available. A comparison of IR imaging with a laser and thermal source has not been reported in terms of spectral or spatial performance, though spectra were found to be in reasonable agreement in qualitative terms. 137 In addition to the optical and performance issues discussed for QCLs, cost is an additional factor in these systems. While the compact packaging and ability to use the same material for a variety of applications and wavelengths exists for QCLs, indirect production of mid-IR light inherently requires a larger capital cost and complexity of instrumentation for phase matching. In the opinion of the author, the rapid development of QCLs and their relative simplicity will eventually lead to their adoption over other laser technologies.
As seen in the discussion of the previous section, there is significant value in acquiring only a limited set of data. The obvious trade-off is that the spectral range and resolution of acquired data would also be limited. This tradeoff can be mitigated to some extent by the use of modern computational power and algorithms. Computational approaches to spectral reconstruction are an emerging area in which fewer data are acquired than would be dictated by classical sampling considerations and the deficiency in data quantity can be compensated by estimation algorithms. The estimation algorithms at one extreme can be completely blinded to spectroscopic details and use signal processing approaches that, essentially, operate to optimize entropy. Methods at the other extreme perform reconstructions of full spectral detail using a knowledgebase, either of expected spectra for the problem or a general understanding of spectral features, to predict missing details in the data. Applications in data reconstruction have also been reported for temporal measurements an interpolation sense, for example, to obtain time-resolved measurements with better accuracy. 138 The reconstruction approach has also been proposed 139 as an alternative to recovering SNR and circumventing some limitations of classical FT-IR approaches in some cases. An important conclusion was that reconstructions are relatively noise free. While not explicitly stated in the study, the important implication for imaging measurements (in which sensitivity is often limited by SNR) can be that the inaccuracy in reconstruction may be smaller than the noise for rapidly acquired data. Hence, it may actually be advantageous to acquire a smaller set of spectral points at high SNR and reconstruct the entire dataset rather than acquiring the entire data set at some low SNR. A demonstration of this possibility has not been reported.
Reconstruction approaches have been reported in spectroscopy but have not been extensively applied; their application to imaging data can provide significant benefit. In most cases, data are spectrally sparse, data acquisition times are long, and storage requirements are vast. At the same time, much is known about specific applications, for example, using the data to determine tissue types. 140 In one study, 141 a representation for IR absorption spectra was developed using a learned dictionary ( Fig. 6 , top row). A sparse representation of this dictionary is used as prior knowledge in regularizing the compressed sensing inverse problem. The reduced measurement during acquisition was modeled as a process of interferogram truncation, providing a benefit for data acquisition in terms of a reduced set of data as well as the centerburst to enhance the SNR at the cost of the sharper spectral components. The model was implemented using low-pass filtering and down-sampling in the spectral domain as dictated by the measurement process. Spectra could be obtained that closely resembled the spectra acquired without truncation ( Fig. 6 , middle row). In any reconstruction, there is no doubt that signal is lost and an estimate of the true signal is obtained. The critical measure of success then becomes whether the task at hand is accomplished. The developed approach was tested in its ability to predict cell types in a number of tissue samples and the results were compared to those obtained with full data acquisition. Hence, a number of tissues, which contained multiple cell types and were drawn from different patients reflecting the natural variance expected in the task, were used as a test bed. A down-sample factor of four was found to be adequate for accurate tissue classification and matched the performance of the data dacquire at full resolution. The method also provided an improvement in the SNR of the reconstructed signal, though the effect of this improvement on enhancing classification accuracy 142 was not evaluated. The work was important in demonstrating that data storage and acquisition times in FT-IR imaging can be significantly reduced while preserving data quality by employing compressed sensing. Spatial correlation and spatial–spectral correlations may similarly be useful in specific cases. Approaches such as the one reported are likely to evolve with increasing sophistication.
Reconstruction of data from a small number of spectral measurements. (Top) The basis of the approach relies on reconstructing spectra from a representation of the data as a combination of sparsely measured data, parameters from a dictionary of known samples, and correlation coefficients. (Middle, left) Different parameters of the process result in reconstructed spectra (dashed lines) that may be lower resolution or closer to the recorded data (solid line). (Bottom, left) Gray colors indicate different cell types deduced from IR data measured at full resolution while the same information is sought from a reconstructed data set (bottom, right).
These studies represent a significant untapped area of inquiry in IR imaging, especially with the emergence of DF-IR approaches. Spectral reconstructions from a smaller measured set and strategies for sparse acquisition are likely to become more prominent. We strongly emphasize that there is a difference between recording spectroscopic imaging data and estimating it via reconstruction approaches, however. While the former can offer the greatest confidence, the latter offer speed. Care must be exercised in evaluating the relative merits of the approaches and claims must be tempered accordingly. It is not correct to assume, given the excellent quality and speed of reconstruction with modern computers and advanced algorithms, that one is superior to another. When the outcome of the imaging study relies on conclusions to be drawn from the data but the data itself are of limited interest, reconstruction approaches are especially relevant, for example, in rapid tissue or polymer identification when the range of possible solutions is limited. In general, reconstruction methods are ideally suited for repeated imaging of similar samples in which rigorous validation of the approach can be conducted to optimize both the parameters of reconstruction as well as determine the optimal results. This topic engenders another direction that is likely to evolve for imaging in the convergence of signal processing, theory, and spectral reconstruction with details of the experiment, as seen in some areas of spectroscopy. 143 Computation, as used thus far, not only represents a necessity for imaging data analysis but can potentially tie together emerging instrumentation, theory, sensing, and analysis.
While we have hitherto focused on describing spectral recording approaches, the other aspect of IR imaging lies in the optics of image formation. While several studies in IR microscopy and imaging have used predictions from optical microscopy, a complete model of the IR microscope was not available until recently. 144 A model for light propagation in an imaging instrument is important to both the understanding of image quality as well as to the rational design of improved instruments that optimize quality. Theoretical models for instrumentation, based on ray (geometric) optics, have been proposed to describe IR microscopy for many years. Most efforts concentrated on the angular dependence of data related to focusing and corrections to measurements such as dichroicratios. 145 Similarly, other methods of understanding spectral dependence on sampling geometry in conventional spectroscopy have often focused on molecular properties in thin films or at interfaces. 146 It must be recalled that sample path lengths as well as microscopic features are often at the scale of the wavelength of light; hence, frameworks based on geometric (ray) optics that have been largely used in spectroscopy until now are inadequate in the investigation of effects associated with light–matter interaction. Full electromagnetic models capture all of the physics of image formation but are also significantly complex. They are most useful when a precise prediction of a combination of specific microscopy optics–sample is desired. For many other purposes, a simpler model suffices, especially to understand the effects of the optics of the microscope on the recorded data. The first attempt in this direction recently reported, 144 in the author's opinion, the simplest approach to microscopy that incorporates all the phenomena of interest, forgoing full electromagnetic modeling in favor of the conceptually simpler and computationally easier model based on scalar wave theory. We capture the major aspects of this theory in the next section. While details of the theory are described in the original publication, the salient features and critical equations are captured here in a simplified notation for comparison with other studies and for the sake of completeness.
In the scalar wave theory model, the electric field at every plane in the microscope is explicitly calculated. For simplicity, consider a monochromatic component of the field with a wavenumber ῡ, and complex amplitude U. Since the spectral frequencies in any measurement are independent, the approach can simply be extended to the entire bandwidth of the instrument. The field, in any spatial plane for any wavenumber, is expressed as a superposition of plane waves described by functions of the form U(f) expi2π[f.r +fz(f) z]> where f = (fx, fy) and r = (rx, ry) are the two-dimensional frequency and spatial coordinate vectors, respectively, in Cartesian coordinates. The function fz is defined such that |f| 2 +fz(f) 2 = ῡ 2 , implying that the individual plane waves satisfy the Helmoltz equation. 147 The microscopy system is assumed to be linear; hence, summation of individual plane waves can be employed to reconstruct the field and all linear transformations of the field. For each plane wave constituting the field, the amplitude determines its quantitative contribution and the phase determines its relative position. Both the amplitude and phase are necessary and sufficient for a complete description of the field. Subsequently, a plane wave decomposition can be achieved via the two-dimensional Fourier transform. Each plane wave constituting the field has a specific direction, or “angle” of propagation, and therefore the plane wave decomposition described above also describes the “angular spectrum” of the field. Complete description of light propagation, hence, consists of the related contributions of the three spatial coordinates, spectral wavenumber as well as individual amplitudes and phases describing the angular spectrum. The term “spatial frequency” is also used to describe f and this arises from the spatial Fourier transform interpretation of the fields.
In the most general sense, the goal of modeling an IR imaging instrument is to relate the field at the detector UD(f) to the sample S(f) via a function, or an operator A(f1, f2). The operator incorporates the details of the specific instrument. Formally, the relation between the detector field, the sample, and the instrument is described using the equation
UD(f2) = ∫d 2 f1A(f1, f2)S(f1)The operator A(f1, f2) can be decomposed into constituent operators pertaining to various aspects of light propagation in air, through substrates and samples as well as optical components, as follows. The propagation of the field U1(f) in a plane to the field U2(f) in a plane at a distance d in free space is given by the equation
U2(f2) = ∫d 2 f1Kd(f1, f2)U1(f1)where the operator Kd(f1, f2) is defined as
Kd(f1, f2) = δ(f1 − f2)e i2πfz(f1)dThe operator for the interferometer can be described in terms of a pair of propagation operators as
Id1,d2(f1, f2) = ½[Kd1(f1, f2) + Kd2(f1, f2)]The Schwarzschild optic can be modeled as a Fresnel lens, which imparts a quadratic phase factor to the incident field, and is described by the operator
G C ( r 1 , r 2 ) = δ ( r 1 − r 2 ) Q C ( r 1 ) e − i π υ ¯ r 1 2 / L fwhere Lf is the focal length of the Schwarzschild and QC(r) is a pupil function
Q a b ( r ) = < 1 a < r < b 0 elseThe quadratic phase factor converts each plane wave incident on the Schwarzs-child optic into a spherical wave converging on its focal plane. The phase relation between incident plane waves and the imparted quadratic phase determines the final image position and size. Combining propagation operators and the lens functions allows us to construct an operator relating the scalar field in the image plane of the lens to the field in the object plane. If the object plane is at a distance d1 from the lens and the image plane is at a distance d2, then the relation between the object plane field U0(f) and the image plane field U1(f) is
U 1 ( f ) = Q υ NA in υ NA out ( f ) U 0 ( − M C f )where MC = d2/d1 is the magnification of the system. The above expression is for a Schwarzschild focusing light on to a sample (i.e., the “condenser”). The corresponding expression for the collector Schwarzschild (focusing lens) is
U 1 ( f ) = Q υ NA in υ NA out ( M C f ) U 0 ( − M C f )The imaging system consists of the condenser, C1, the focusing lens, C2, and the detector collection lens, CD. The interaction of the incident field, U1(f), with a thin sample, S(f), resulting in the field U2(f) can simply be described as a product in the spatial domain or, equivalently, a convolution in spatial frequency as
U2(f2) = ∫d 2 f1U1(f2 − f1)S(f1)The field at the source is assumed to be Uz0(f). Light from the source passes through the interferometer, is focused on the sample, and is propagated via the microscope to the detector. Combining the operators described above allows us to construct an expression relating the sample, S(f), the instrument parameters, and the detector field, UzD(f), as follows:
U z D ( f ) = 1 2 Q C D ( f ) Q C 2 ( − M C f ) × ∫ d 2 f 1 Q C 1 ( − f 1 M C 1 ) × < 1 + exp [ i 2 π f z ( f 1 ) ( 2 d 2 − 2 d 1 ) ] >× U z 0 ( f 1 ) S ( f 1 M C 1 + M C 2 M C D f )
This equation describes an IR imaging system, based on an interferometer in this case, under the scalar wave model. The same formalism may be extended to DF-IR systems as well to account for the effect of different spatial frequencies of features in the sample. While details on the validation and use of the model are available elsewhere, 144 a crucial result is highlighted here.
The model was used to predict the behavior of two different optical arrangements as well as to obtain insights into the performance of imaging systems: a high numerical aperture (NA) system (74×, NA = 0.65) and a commercially available low NA system (15×, NA = 0.5) in terms of imaging a standard chrome-on-glass USAF target. Data from optical microscopy were used to simulate the object and simulations were compared with experiments ( Fig. 7 ). The major conclusion was that the higher NA provided higher quality images, as expected, but that the sampling frequency at the detector was the limiting factor in the performance of current imaging systems. The correct pixel size for sampling the image without loss of detail was shown to be ∼40× smaller than previously believed. To date, there is one report of an HD imaging instrument with a globar source 144 and one report of an application. 148 An optimal pixel size, which balances the throughput, which determines spectral data quality, with small pixels, which determines spatial image quality, was determined at the highest usable wavenumber in most spectra to be ∼1.1 μm. This is approximately twofold larger than that reported for a synchrotron HD imaging system 59 because of a careful optimization of throughput, maximum wavenumber, and the needs of the tissue system. As opposed to studies of HD spectroscopic imaging with a synchrotron in which there is sufficient flux to over-sample the spatial domain, the use of a globar for HD imaging requires maximizing throughput for the highest desired resolution. The two studies illustrate the success as well as the need to carefully understand the requirements, trade-offs, and performance using system modeling to make intelligent spectrometer design decisions.
(A) The original object consists of a set of bars of sizes with transmittance indicated to the left. Absorbance images from simulations (at 3950 cm −1 ) are shown for the focusing Schwarzschild with a (B) NA = 0.65, (F) NA = 0.50, and (G) NA = 0.50. The effective sample pixel size at the detector in (B) and (F) is 1.1 μm, whereas the pixel size in (G) is 5.5 μm. Measured absorbance images (also at 3950 cm −1 ) are shown with configurations (C) NA = 0.65, pixel size = 1.1 μm and (H) NA = 0.50, pixel size = 5.5 μm. (D), (E), (I), and (J) show magnified regions from corresponding images. [Reproduced with permission from Ref. 144 , copyright Society for Applied Spectroscopy.]
Given the improvement in image quality, there is immense interest in the optical setup and use of this configuration. The decreased pixel size, however, results in a substantial loss in throughput and the SNR of the resulting data is poor. Synchrotrons and DF-IR sources may well be the answer as a hardware solution. A signal-processing approach to reducing noise (see section on noise reduction later in this article) can also be implemented. Ultimately, the choice between conventional and HD imaging will be determined by the necessity of HD imaging or of high spectral SNR. Spatial averaging could be a compromise in some cases and other methods that could potentially be useful have been previously discussed. 149 Currently, almost all commercial instruments routinely provide approximately the same optical setup (0.5 NA, 15× objective). The demonstration of HD imaging has already spurred a number of different instrument configurations. While the diversity in image quality using different lenses is obvious, the spatial and spectral domains are intimately related in the recorded data and changing the lens changes the quality and content of the recorded data. A more complete theory is needed to understand this convolution of optics, sample structure, and recorded data. A framework for this approach is discussed in the next section.
Infrared microscopy and imaging have long been considered to be simple adjuncts to optical microscopy. The recorded data are usually considered to be a simple extension of the IR spectroscopy of bulk materials, with the additional trivial consideration that data are selectively obtained from specific points on the sample. Other than reflecting species concentration, the spatial structure of the sample was not thought to play a major role in the recorded data. The first major hint that there may be additional considerations arose almost at the same time FT-IR imaging with a focal plane array was first reported. 150 It is only during the past three years, however, that the full import of structure–spectra relationships has been quantitatively explored by significant advances in theory and a number of experimental studies. It is now widely recognized that there are differences in the data recorded from a bulk measurement and a microscopic measurement, as there are between homogeneous and heterogeneous samples in a microscope. These differences arise from light focusing at the point of interaction with the sample as well as from the microstructure of samples on the scale of the wavelength. Recent work has provided a framework to understand these effects as a function of spatial and spectral properties of the sample.
In this section, we focus on discussing the forward problem, i.e., predicting the spectra recorded from a sample in a microscope. In particular, it is interesting to understand how spectra from heterogeneous materials in a microscope differ from those that would have been recorded from the bulk of the same material using conventional spectroscopy. These differences are often termed to be errors, distortions, or artifacts. We would emphasize here that these terms should not be used. There is ample understanding, from the theory summarized below and form confirmatory experimental evidence, to indicate that the spectral dependence on optical configuration and sample microstructure is deterministic and reliably reproducible. Hence, there are no errors or artifacts that arise from light–matter interactions and it would not be correct to term them as such. Rigorous electromagnetic models analyzing the interaction of light with heterogeneous samples have quantitatively predicted recorded spectra as a function of experimental parameters, clearly indicating that a deeper understanding of the recorded data is sorely needed. In fact, IR microscopy is an unusually rich area of investigation in the general realm of microscopy because the spectral diversity and unique light–matter interactions in the mid-IR spectral range give rise to interesting theoretical questions and instrument-design tradeoffs. We divide further discussion to summarize the framework for predicting the spectral response of homogeneous materials, which indicate the effects of focusing, as well as heterogeneous materials, which additionally describe the effect of scattering at interfaces and light transport within the sample structure. Details of the theory are described in the original publications. Here, we reproduce the critical equations, for parallelism with other studies and for the sake of completeness.
A rigorous electromagnetic model to describe light–sample interaction and its effect on recorded data has been reported. 151 Just as for the scalar wave theory case, the sample is assumed to be a linear system consisting of multiple layers of varying (complex) refractive indices. This conceptual position allows a simplification of the general problem of light–sample interaction into understanding light transport between pairs of homogeneous layers. The approach is general in that it can isolate heterogeneity within layers, allowing for the extension of the same framework to heterogeneous samples. The electromagnetic field can be described as consisting of a linear combination of plane waves, each of which satisfy Maxwell's equations at the boundaries as the entire system is linear. Hence, the studies employ the same approach as the scalar wave framework in this case and analyze the response of the system to a single plane wave first. The total response of the system to illumination would then be the sum of each of these individual plane wave responses.
Let the electric, E, and magnetic, H, fields at a position, r, = (x, y, z) T be represented by their complex amplitudes and the permittivity and permeability of free space be denoted by ε0 and μ0, respectively. Let the real and imaginary parts of the refractive index of a single layer be denoted by n(ῡ) and k(ῡ), respectively. For homogeneous layers, the electric and magnetic fields can be written as
