Article pubs.acs.org/ac
Restoration and Spectral Recovery of Mid-Infrared Chemical Images Eric C. Mattson,† Michael J. Nasse,†,‡,∥ Margaret Rak,§ Kathleen M. Gough,§ and Carol J. Hirschmugl*,† †
Department of Physics, University of Wisconsin, Milwaukee, Wisconsin 53211, United States Synchrotron Radiation Center, University of Wisconsin, Wisconsin 53589, United States § Department of Chemistry, University of Manitoba, Winnipeg, Canada, R3T 2N2 ‡
S Supporting Information *
ABSTRACT: Fourier transform infrared (FTIR) microspectroscopy is a powerful technique for label-free chemical imaging that has supplied important chemical information about heterogeneous samples for many problems across a variety of disciplines. State-of-the-art synchrotron based infrared (IR) microspectrometers can yield high-resolution images, but are truly diffraction limited for only a small spectral range. Furthermore, a fundamental trade-off exists between the number of pixels, acquisition time and the signal-to-noise ratio, limiting the applicability of the technique. The recently commissioned infrared synchrotron beamline, infrared environmental imaging (IRENI), overcomes this trade off and delivers 4096-pixel diffraction limited IR images with high signal-to-noise ratio in under a minute. The spatial oversampling for all mid-IR wavelengths makes the IRENI data ideal for spatial image restoration techniques. Here, we measured and fitted wavelength-dependent point-spread-functions (PSFs) at IRENI for a 74× objective between the sample plane and detector. Noise-free wavelength-dependent theoretical PSFs are deconvoluted from images generated from narrow bandwidths (4 cm−1) over the entire mid-infrared range (4000−900 cm−1). The stack of restored images is used to reconstruct the spectra. Restored images of metallic test samples with features that are 2.5 μm and smaller are clearly improved in comparison to the raw data images for frequencies above 2000 cm−1. Importantly, these spatial image restoration methods also work for samples with vibrational bands in the recorded mid-IR fingerprint region (900−1800 cm−1). Improved signal-to-noise spectra are reconstructed from the restored images as demonstrated for a mixture of spherical polystyrene beads in a polyurethane matrix. Finally, a freshly thawed retina tissue section is used to demonstrate the success of deconvolution achievable with a heterogeneous, irregularly shaped, biologically relevant sample with distinguishing spectroscopic features across the entire mid-IR spectral range.
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geometry of the lens; however, the PSF of such an imaging system was recently derived from first principles by Davis et al.15 Near field techniques16 detect specific distributions of IR absorbing materials within micrometers of surfaces with spatial resolution well below the diffraction limit, yet require long acquisition times because of raster scanning, while penetration depths are not clearly defined. Raman-based techniques such as Raman spectromicroscopy,17 coherent antistokes Raman spectroscopy (CARS),17 and stimulated Raman scattering (SRS) microscopy18 can achieve higher spatial resolution than complementary IR imaging. However, longer times are required for the Raman-based measurements to cover a full spatial area and spectral range similar to the measurements presented in this paper. They are, depending on the experimental setup, raster scanned to cover a sample area and/or wavelength scanned to span the entire fundamental vibrational spectrum. The advance in IR spectrochemical imaging described herein permits acquisition of spatially uncontaminated, restored absorbance spectra across the mid-IR bandwidth at submi-
hemical imaging encompasses methods that reveal spatially resolved chemistry via a wide variety of probes, detection schemes (raster scanning, multichannel, or parallel channel detection) and for many different length scales (mm to nm). A particular class of chemical imaging experiments uses photon probes to excite natural vibrational signatures of distinct functional groups for chemical specificity in combination with microscopy approaches for submicrometer to micrometer scale resolution.1 Such methods can detect a wide range of chemistry for minimally prepared samples. The applications of these techniques span many disciplines including life sciences,2−8 art conservation,9,10 geology,11,12 and materials science.13,14 Some of these modalities have the potential to provide detailed chemical information of evolving systems at a microscopic scale. Direct measurements of mid-infrared active vibrations with wavelengths in the range of 2−10 μm reach a fundamental spatial resolution limit of 1−5 μm that is wavelength dependent and diffraction limited. Typically, a resolution limit is defined by the well-known Rayleigh criterion (d = 1.22 λ/NA, where d is the distance between two objects at the sample plane, λ is the wavelength, and NA is the numerical aperture of the objective) for conventional imaging systems with unobstructed lenses. For the case of Schwarzchild objectives used in IR optics, no analogous closed-form expression exists due to the obstructed © 2012 American Chemical Society
Received: April 30, 2012 Accepted: June 25, 2012 Published: June 25, 2012 6173
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with enhanced resolution and contrast. In this paper, we provide a detailed analysis of the wavelength-dependent PSF for the 74× Schwarzschild objective, with numerical aperture (NA) of 0.65. The PSF of the Bruker Hyperion 3000 IR microscope for the experiments described here is dominated by this 74× objective. In addition, several examples of restored images that were obtained through application of the deconvolution algorithm are presented. Starting with data collected from IRENI, images at every wavelength in the midIR spectral bandwidth can be restored, substantially reducing the diffraction effects and improving image contrast. Most importantly, we show for the first time that restored images over the broad Mid-IR bandwidth can be used to reconstruct spectra that retain all the chemical information.
crometer pixel spacing. Data acquisition is rapid ( k max ⎩ (3)
Here k is the radial coordinate in the Fourier domain, kmax is the cutoff frequency, where the OTF approaches zero, and kmin is an effective smoothing parameter. The Hanning function is equal to 1 for all frequencies less than kmin and is equal to 0 for frequencies greater than kmax. At frequencies between kmin and kmax, the filter smoothly approaches zero by using a function with a sinusoidal dependence. Ringing artifacts associated with discontinuities in the image are mitigated by smoothly approaching zero. We choose kmin to optimize image sharpness and suppress edge-ringing artifacts that could arise from the 6175
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Figure 1. Images of a USAF resolving test chart showing group 7, element 4−6, and diagrams of a Schwarzchild objective. (A) IR image at 3000 cm−1. (B) Visible Image. (C) Three-dimensional schematic of objective (top) and condenser (bottom) Schwarzschild optics used at IRENI. (D) Schematic diagram showing cross-section of a cylindrically symmetric Schwarzschild optic. Optical rays that enter the objective at different radial positions at the annulus plane travel different optical paths, two such rays are shown here as red and blue lines. The annular model described in the text requires parameters r1 and r2 (the inner and outer radii of the annulus) and d, the distance from the annulus plane to image plane, as marked. 2 ⎛ 2J (x) 2εJ1(x) ⎞ 1 ⎟ I (θ ) = I 0 ⎜ − x ⎠ ⎝ x
Figure 2. PSFs for the 74× objective lens within the Hyperion 3000 IR microscope. Center profiles through measured PSFs at 3500, 3000, and 2500 cm−1 are overlaid with simulated curves resulting from the fitting results.
(4)
where J1 is the Bessel function of order 1, ε is the ratio of the outer radius of the primary mirror (r2, in Figure 1C) to the radius of the obscuring secondary mirror (r1 in Figure 1D). The value x = kr2 sin θ is a dimensionless quantity, where k is the wavevector, r2 is the outer radius of the primary mirror or aperture in the annulus model, and θ is the angular position at the image plane with respect to the central axis of the Schwarzschild objective. Since this objective is a threedimensional object, and the obscuration due to the secondary mirror is not coplanar with the image plane, there are small deviations from this ideal theory that are wavelength dependent. They are absorbed into an “effective r1 ” as described below. In practice, when characterizing the wavelength-dependence of the PSF, d and r2 are fixed to their known physical dimensions, and the trend for the effective size of the obscuration (effective r1) is obtained by fitting the measured data to a function describing an annular diffraction pattern over a range of wavelengths. Deviations from the ideal annulus model, such as the optical path differences introduced from the curvature of the primary optic, are absorbed into the effective obscuring mirror radius (effective r1) in the annular model. The obscuring mirror amplifies the intensity of the diffraction maxima in the PSF, while narrowing the central maximum as compared to the conventional Airy function.40 In Figure 2, we show center profiles of the measured PSFs for a 74× objective lens on the Bruker Hyperion IR microscope, as observed at three different wavelengths. (See Supporting Information for further details on measured PSFs and PSF curve fitting.) The OTF of the measured PSF is shown in Supporting Information Figure S2 for 2 different wavelengths with the appropriate Hanning apodization kernels overlaid. As can be seen from the image, the spatial frequencies in which the OTF
has appreciable intensity correspond to the Hanning filter being equal to one. The filter then smoothly approaches zero in the vicinity of the frequencies for which the OTF approaches zero. Effect of Restoration on Spatial Resolution. Fundamental resolution limits in IR microscopy are clearly observed in IR images of test objects with features at or beyond the diffraction limit, and have been explored extensively.35,40 In Figure 3A and C, images representing the raw IR absorbance of the 3-bar USAF targets for groups 8−9 (256−645 cycles/mm) are shown for two different wavelengths: 2.63 (3800 cm−1) and 3.70 μm (2700 cm −1), respectively (reproduced from Supporting Information Figure 3, reference 32). Images in Figure 3B and D show the patterns from A and C after deconvolution with measurement-based PSFs. Vertical and horizontal line profiles from the marked regions are respectively shown, to the left and below Figure 3A,C and D, to demonstrate the improvement in contrast and resolution following application of our deconvolution algorithm to these single wavelength IR images. The pairs of dashed lines in the profiles in Figure 3 contrast range of 26.4%, corresponding to the Rayleigh resolution limit. Analysis of the line profiles indicates that this imaging system exceeds the theoretical Rayleigh resolution (2.47 and 3.48 μm for A and C, respectively, since the 1.74 μm pattern is clearly resolved (contrast = 30.7%) in (A), as is the 1.95 μm pattern (contrast = 29.1%) in C, while the 1.55 μm pattern in A is almost resolved (contrast = 23.8%). The resolution improvement upon deconvolution with the instrument’s PSF is clearly apparent in the images and in the line profiles. The contrast of the patterns with a width of 1.38 μm increases from 14.1% (unresolved) in A to 30.9% (resolved) in B, and from 13.7% (unresolved) in C to 40.2% (resolved) in D, respectively. 6176
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Figure 3. Transmission images of a high-resolution 1951 USAF test target. Panels A and B show unprocessed images in transmittance at a wavelengths of 2.63 μm (3800 cm−1) and 3.70 μm (2700 cm−1), respectively. Panels C and D show the same patterns after deconvolution with the measurement-based PSFs (see text). Intensity profiles extracted along the dashed lines in A−D are shown: green = original and blue = deconvoluted. White scale bar in a: 10 μm. This figure has been reproduced with permission from ref 32. Copyright 2011 Nature Publishing Group. Please see Supporting Information Figure 3.
Effect of Restoration on Localization of Chemical Signatures of Heterogeneous Polymers. Naturally, the effects of blurring due to sampling beyond the diffraction limit are manifested in the spectra and in spectrochemical images, as illustrated in the analysis of a chemical image of the PS/PU mixed sample, Figure 4. Closely spaced 5.9 μm spheres, as well as smaller 1 and 2 μm spheres throughout the field of view (schematic in Figure 4), were imaged by integrating each spectrum over a PS-specific CH stretching band (3007−3041 cm−1 with same baseline), to reveal the location of PS in the PU matrix (Figure 4A). The PS absorption signal observed near the interface of the two central beads should be smaller than the absorption signal observed at the centers of the beads, since the optical path length traversed is predominantly through PU, and the path length of PS is much smaller near the interface. Similarly, the optical path length through the PU should be reduced at the top of a bead, yet nearly equal amounts of PS are detected all across the interface of the two beads. Figure 4B shows the C−H stretching region of spectra taken along the line connecting the two spheres. Reference spectra of PS and PU are shown below as red and black, respectively. In the spectra along the line joining the two spheres, there is very little variation in the intensity of the PS-specific bands. Figure 4C, which shows the variation in the intensity of the PS band at 3026 cm−1, indicates that this value is nearly constant along the line. This is in contrast to the expectation that the PS signal should be strongest immediately on top of the spheres, and much weaker in between them. In addition, the intensity of the PU-specific band at 2960 cm−1 remains nearly constant along
the line as well. These data demonstrate how imaging at the diffraction limit produces IR spectra contaminated with signals from neighboring pixels, and concomitantly blurred images. We applied our deconvolution algorithm to the chemical image for every wavelength in this data set, and reassembled the deconvoluted images in a hyperspectral cube to thus produce a reconstructed spectrum for every pixel. Reconstructed spectra are compared to original spectra from the same positions in Figure 4D−E, taken from the PU background and on top of a PS bead, respectively. The reconstructed spectra follow the unprocessed spectra closely, maintain all spectral features and show that the deconvolution process does not introduce additional artifacts. The baseline fringes come from multiple reflections in the PU film. Figure 4F shows an image generated from the restored data set integrated over the same spectral range as that used in Figure 4A for comparison. Enhanced contrast and a reduction of blurring are immediately obvious, particularly evident at the interface of the two beads. Smaller 1 and 2 μm beads scattered throughout the field of view become more apparent. Figure 4G shows the reconstructed spectra taken from the sample pixels used to generate the spectral stack in Figure 4B. While in the original data the absorbance signatures in the spectra from every point along the line contain very similar absorption strengths (Figure 4C, green), much stronger variation is observed in the restored data set. These spectra more accurately reflect the expected absorption strengths for PS and PU function groups across the interface of the two beads. Moving from the left bead to the center of the interface, one observes that the absorption strength detected 6177
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Figure 4. Original and deconvoluted hyperspectral data from 1.0, 2.1, and 5.9 μm diameter PS beads dispersed in a 10 μm thick PU film. (A) unprocessed and (F) deconvoluted absorbance images integrated over the PS peak at 3020 cm−1 (aromatic CH stretch). Three 5.9 μm PS beads are clearly visible, the weaker signal in the background stems from several 1.0, 2.1 μm PS beads, some of which are out of focus. (D, E) Comparison of original and reconstructed spectra from the PU background (D) and from one of the PS beads (E). (B,G) Stacked spectra taken along the black line in A, between the centers of the 5.9 μm PS beads, illustrating the effect of the reconstruction process on the spectra. While the original spectra in B all show a very similar PS/PU mixture (compare reference spectra on the bottom), the reconstructed spectra in G clearly exhibit the PS−PU−PS transition demonstrating the spatial resolution enhancement in the spectra achieved with the deconvolution algorithm.
therefore rich in nucleic acids while the latter, composed primarily of cell membranes, are rich in phospholipids. Typical IRENI spectra extracted from well within each region are shown in Figure 5A. The CH stretch peak intensities are much greater in the plexiform layer; the polyunsaturated fatty acid (PUFA) peak at 3012 cm−1 and the phospoholipid carbonyl peak at 1740 cm−1 are also considerably elevated relative to the same bands in the nuclear layer. Distinguishing spectral features of the photoreceptor nucleus layer include the appearance of a small peak at 1712 cm−1, associated with nucleic acids, and decreased intensity in all phospholipid bands. The photoimage of a near-by section, nuclei stained deep blue with hematoxylin, (Figure 5B) may be compared to the spectrochemical falsecolor images for the area inside the white box, created from the intensity of the 1712 cm−1 nucleic acid peak, before and after the deconvolution process (Figure 5C and D, respectively). In each case, the image processing allows one to distinguish between the layers, but, prior to deconvolution, the sharp demarcation between nuclei and axons is blurred by poor spatial resolution. To show the improvement in spectral purity, a stack of 25 spectra spanning the transition region was extracted from the original and restored data sets (Figure 5C and D, white line). Baseline-corrected areas of several biomarker peaks were measured and plotted (Figure 5E and F). Plots of the intensity of peaks corresponding to distinct tissue constituents (marked in 5A) that vary between the two morphological layers show that the transition is sharper and stronger in each case, following deconvolution (solid lines) compared to the original data (dashed lines). The deconvolution algorithm is thus
from the PS decreases as expected, while the absorption strength from the PU is smaller directly at the center of the bead, and gradually increases near the center of the interface. Figure 4C compares the absorption strength of the PS band at 3026 cm−1 as a function of position along the indicated line for both the original and restored data. The changes in PS absorption along the line are clearly resolved in the deconvoluted data, whereas little change is observed in the raw data. Thus, the improvements in spatial resolution are observable not only in the deconvoluted images, but also in the faithfulness of the resulting spectra. Restoration of Chemical Images of Biological Tissue. The PS/PU composite sample provides a clear and effective demonstration of the power of the restoration algorithm; however, much of the material imaged with FTIR is heterogeneous and components are distributed in irregular patterns. For example, the retina, a biological tissue that is composed of several highly distinct layers, presents an excellent real-world test case for evaluating improvements in resolution. In a recent paper, we reported the high-resolution IRENI images of mouse retina tissue.36 The deconvolution algorithm has now been applied to data from that study. The visual signaling pathway through the retina includes three main types of neurons: photoreceptors (containing the rods or cones), bipolar cells and ganglion cells, connected approximately end to end. Images and data, before and after deconvolution, are shown for the region that includes the photoreceptor nucleus and outer plexiform layers (Figure 5). The nucleus layer is composed of the nuclear bodies of photoreceptor neurons, while the outer plexiform layer is composed of dendrites and synapses. The former layer is 6178
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to significantly counteract diffraction-induced blurring. This represents a significant advancement toward improving the spatial resolution of IR spectrochemical images. Deconvolution of the PSF from measured data sets, over the entire spectral bandwidth, enables faithful reconstruction of spectra at each pixel, from which contamination from neighboring regions of the sample has been significantly reduced. Samples with features between 0.5 to 6 μm in diameter, on the order of infrared wavelengths, provide a stringent test for the effects of deconvolution. Application to a spectrochemical image of retina, a real-world biological sample, demonstrates the potential for subcellular spatial resolution with biochemically significant spatial contrast. This successful demonstration, restoring hyperspectral cubes of data in the spatial domain and recovering high quality spectral information, shows that we have an accurate model for the PSFs as a function of wavelength for Schwarzschild objectives employed for high spatial resolution wide-field mid-infrared imaging. While this FT based approach is appropriate for the experimental data sets shown here, and can therefore be directly applied to many data sets, undoubtedly, some hyperspectral cubes of data will have properties that may require more sophisticated approaches for image restoration. Such future developments can build upon the foundation presented here.
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ASSOCIATED CONTENT
S Supporting Information *
Sample preparation and details, additional information on PSF measurements and curve fitting deconvolution, and transfer functions and apodization kernals. This material is available free of charge via the Internet at http://pubs.acs.org
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Figure 5. Deconvolution of IRENI data resolves biological details. (A) Representative single-pixel IRENI spectra of the photoreceptor nucleus layer (red) and outer plexiform layer (blue) from mouse retina. (B) Photomicrograph of a hematoxylin-stained serial section. The white box indicates the approximate location of the IRENI images (scale bar = 50 μm). (C and D) False-color spectrochemical images created by integrating the area of the nucleic acid peak at 1712 cm−1 for (C) the original IRENI FTIR-FPA data and (D) data after hyperspectral deconvolution (red = high, yellow-green = medium, blue = low spectral intensity, scale bar = 5 μm). White lines in C and D denote the exact locations of the stack of spectra extracted from the 25 pixels for analysis. (E, F) Peak areas for region-specific marker peaks, plotted from data in each stack.
AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Present Address ∥
Karlsruhe Institute of Technology, Institute for Photon Sources and Synchrotron Radiation, Hermann-von-Helmholtz Platz 1, 76344 Eggenstein-Leopoldshafen, Germany.
Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS The authors are grateful for the feedback provided by Sarah Patch, Rohit Bhargava and Brynmor Davis. Sample preparation by Karl Stuen from the University of Wisconsin, Madison, of the PU films with PS beads, and from Ben Albensi from Department of Pharmacology and Therapeutics, Faculty of Medicine, University of Manitoba, and Principal Investigator, Division of Neurodegenerative Disorders, St. Boniface Hospital Research Centre, Winnipeg, Manitoba, of the retina sample is also acknowledged. This work has been done with support from a National Science Foundation (NSF) Major Research Instrumentation grant (DMR-0619759) and also NSF Chemistry (CHE-1112433). Research on retina was supported by grants from the Canadian Institutes of Health Research, the Manitoba Health Research Council, and NSERC Canada. This research is based upon work performed at the Synchrotron Radiation Center. The SRC is funded by the University of Wisconsin-Madison and the University of Wisconsin-Milwaukee.
successful in increasing the spatial resolution and spectrochemical contrast of IRENI images. This demonstration has important implications for the value of this restoration process. Many biochemical and biomedical studies are focused on changes at the cellular and subcellular level. The deblurring capability offered by this deconvolution method represents a significant practical step forward, retaining the true chemical information through achieving the best spatial and chemical contrast from the raw data.
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CONCLUSION We have successfully demonstrated that diffraction-limited spectrochemical imaging can be achieved through the combination of a uniquely designed multibeam synchrotronbased spectrochemical imaging system and Fourier-based deconvolution algorithms with well-defined PSFs. Application of this method to images from one hyperspectral data set, for several different wavelengths, demonstrates the new capability 6179
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