restoration and spectral recovery of mid-infrared chemical images

Restoration and Spectral Recovery of Mid-Infrared Chemical ImagesEric 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 apowerful technique for label-free chemical imaging that has supplied importantchemical information about heterogeneous samples for many problems acrossa variety of disciplines. State-of-the-art synchrotron based infrared (IR)microspectrometers can yield high-resolution images, but are truly diffractionlimited for only a small spectral range. Furthermore, a fundamental trade-offexists between the number of pixels, acquisition time and the signal-to-noiseratio, limiting the applicability of the technique. The recently commissionedinfrared 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 sampleplane and detector. Noise-free wavelength-dependent theoretical PSFs are deconvoluted from images generated from narrowbandwidths (4 cm−1) over the entire mid-infrared range (4000−900 cm−1). The stack of restored images is used to reconstructthe spectra. Restored images of metallic test samples with features that are 2.5 μm and smaller are clearly improved incomparison to the raw data images for frequencies above 2000 cm−1. Importantly, these spatial image restoration methods alsowork for samples with vibrational bands in the recorded mid-IR fingerprint region (900−1800 cm−1). Improved signal-to-noisespectra are reconstructed from the restored images as demonstrated for a mixture of spherical polystyrene beads in apolyurethane matrix. Finally, a freshly thawed retina tissue section is used to demonstrate the success of deconvolution achievablewith a heterogeneous, irregularly shaped, biologically relevant sample with distinguishing spectroscopic features across the entiremid-IR spectral range.

Chemical imaging encompasses methods that revealspatially resolved chemistry via a wide variety of probes,

detection schemes (raster scanning, multichannel, or parallelchannel detection) and for many different length scales (mm tonm). A particular class of chemical imaging experiments usesphoton probes to excite natural vibrational signatures of distinctfunctional groups for chemical specificity in combination withmicroscopy approaches for submicrometer to micrometer scaleresolution.1 Such methods can detect a wide range of chemistryfor minimally prepared samples. The applications of thesetechniques span many disciplines including life sciences,2−8 artconservation,9,10 geology,11,12 and materials science.13,14 Someof these modalities have the potential to provide detailedchemical information of evolving systems at a microscopicscale. Direct measurements of mid-infrared active vibrationswith wavelengths in the range of 2−10 μm reach a fundamentalspatial resolution limit of 1−5 μm that is wavelength dependentand diffraction limited. Typically, a resolution limit is definedby the well-known Rayleigh criterion (d = 1.22 λ/NA, where dis the distance between two objects at the sample plane, λ is thewavelength, and NA is the numerical aperture of the objective)for conventional imaging systems with unobstructed lenses. Forthe case of Schwarzchild objectives used in IR optics, noanalogous closed-form expression exists due to the obstructed

geometry of the lens; however, the PSF of such an imagingsystem was recently derived from first principles by Davis etal.15 Near field techniques16 detect specific distributions of IRabsorbing materials within micrometers of surfaces with spatialresolution well below the diffraction limit, yet require longacquisition times because of raster scanning, while penetrationdepths are not clearly defined. Raman-based techniques such asRaman spectromicroscopy,17 coherent antistokes Raman spec-troscopy (CARS),17 and stimulated Raman scattering (SRS)microscopy18 can achieve higher spatial resolution thancomplementary IR imaging. However, longer times are requiredfor the Raman-based measurements to cover a full spatial areaand spectral range similar to the measurements presented inthis paper. They are, depending on the experimental setup,raster scanned to cover a sample area and/or wavelengthscanned to span the entire fundamental vibrational spectrum.The advance in IR spectrochemical imaging described hereinpermits acquisition of spatially uncontaminated, restoredabsorbance spectra across the mid-IR bandwidth at submi-

Received: April 30, 2012Accepted: June 25, 2012Published: June 25, 2012

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© 2012 American Chemical Society 6173 dx.doi.org/10.1021/ac301080h | Anal. Chem. 2012, 84, 6173−6180

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crometer pixel spacing. Data acquisition is rapid (<1 min for asample area of 50 × 50 μm2), even with the requisite spatialoversampling to achieve spatial resolution at the diffractionlimit across the entire spectral range. To realize the fullpotential of infrared spectrochemical imaging, computationalimage enhancement methods are applied to achieve optimalspatial resolution while still preserving spectral integrity. Aprerequisite for the implementation of such methods is that theentire raw data set be collected at the diffraction limit withsufficient spatial oversampling and high quality signal-to-noisecharacteristics.Efforts to achieve diffraction-limited resolution for infrared

imaging have historically been limited by the photon flux fromthermal sources. One approach is to use bright, stable,broadband synchrotron sources to illuminate a single elementdetector,19,20 where the illuminated area is determined by auser-defined aperture and the sample is raster scanned throughthe high flux synchrotron beam. In this method, data iscollected at the diffraction limit for at least part of the mid-infrared range. This approach has been used for a wide range ofapplications.21−27 The smallest practical aperture used to date is3 × 3 μm2, but standard applications use sizes of ≥5 × 5 μm2.Other developments have focused on microscopes equippedwith multielement (also known as focal plane array, FPA)infrared detectors, enabling parallel detection capability whencoupled to thermal source FTIR microscopes.28−30 Recently,the two methods, a synchrotron source and a commercialmicroscope equipped with a multielement detector31−33 (96 ×96 pixel FPA), were combined at the Synchrotron RadiationCenter in Madison, WI. This novel beamline, infraredenvironmental imaging (IRENI), extracts twelve infraredbeams to concurrently and homogeneously illuminate thesample plane with widefield illumination, exploiting the FPA torapidly collect a full array of spectra. In this way, the effectivegeometric pixelization at the detector defines the spatialsampling. The microscope optic has been chosen such thateach pixel at the detector represents an effective geometricalsample area of 0.54 × 0.54 μm2, which is less than half theshortest wavelength in the entire bandwidth (2.5−10 μm).Importantly, this oversampling meets the Stelzer criterion,34

which requires that, when imaging a point-like aperture at thesample plane, at least 8 pixels need to be illuminated across thefwhm of the central peak in the image for the wavelength ofinterest. The aperture for this test is similar in size to thesmallest wavelength in the spectral range. With this sufficientoversampling of the data, it has now become practical to applycomputational techniques to further improve the quality of IR“hyperspectral” data sets through removal of the blurringcreated by imaging at the diffraction limit.The point spread function (PSF) of an optical imaging

system provides a measure of diffraction effects, chromaticaberrations and other factors that distort the object beingimaged. The relationships between an observed image, the trueform of the object being imaged and the PSF that representsthe optical response of the system to a point light source aredescribed within the degradation model of image formation.Mathematically, these three quantities are related by theconvolution operation

= *I I PSFmeas true (1)

where * denotes convolution. If the PSF for a given opticalsystem is known, one can remove the blurring because ofdiffraction effects from the measured images, to restore images

with enhanced resolution and contrast. In this paper, weprovide a detailed analysis of the wavelength-dependent PSFfor the 74× Schwarzschild objective, with numerical aperture(NA) of 0.65. The PSF of the Bruker Hyperion 3000 IRmicroscope for the experiments described here is dominated bythis 74× objective. In addition, several examples of restoredimages that were obtained through application of thedeconvolution algorithm are presented. Starting with datacollected from IRENI, images at every wavelength in the mid-IR spectral bandwidth can be restored, substantially reducingthe diffraction effects and improving image contrast. Mostimportantly, we show for the first time that restored imagesover the broad Mid-IR bandwidth can be used to reconstructspectra that retain all the chemical information.

■ METHODS

The new mid-IR beamline, IRENI, extracting 320 hor. × 25vert. mrads2 from a synchrotron bending magnet, has beendeveloped29−31 to homogeneously illuminate a commercial IRmicroscope equipped with an IR sensitive focal plane array.IRENI is coupled to a Bruker Vertex 70 FTIR spectrometerfollowed by a Bruker Hyperion 3000 IR microscope, allowingfor high-speed acquisition of chemical images over the entiremid-IR spectral range. (Further details can be found in SI andrefs 27−29.). Several test samples were used to evaluate thePSF, diffraction effects in raw data sets, and the effect ofdeconvolution. The instrument PSF was measured using a 2μm pinhole. USAF targets provided a measure of diffractioneffects and resolution obtainable with deconvolution. PS/PUhybrid polymers were used as a test of the spectralreconstructions of deconvoluted images, and finally a retinatissue sample was used as an application to a real biologicalsystem. (Further details on samples and sample preparation canbe found in Supporting Information).

■ COMPUTATIONAL METHOD

For the IR imaging community, it has long been a goal toperform spatial and spectral deconvolution of hyperspectralcubes. However, to perform spatial deconvolution properly, anappropriate characterization of the PSF of the optical imagingsystem must be performed and implemented. In doing this, wemust account for the fact that the PSF is intrinsicallywavelength-dependent, yet we need to apply it to the broadmid-IR wavelength range (2.5−10 μm, for IRENI). Otherapproaches to deconvolution of IR hyperspectral data sets37

have applied the well-known methods of Fourier Self-Deconvolution (FSD) to the spectral domain as well as thespatial domain. These methods, implemented in commercialsoftware packages, deconvolute Lorentzian lineshapes from thespectra, as well as from the two-dimensional images in thehyperspectral cube. The fundamental difference in the methodwe present here is that our work has focused on deconvolving aPSF which truly represents the response of the imaging systemto a point light source and thus correctly describes themechanism of image formation. No deconvolution is applied inthe spectral domain. Rather, a two-dimensional restorationmethod is applied to an IR image at every wavelength which isthen scaled as described below. Then these images arereassembled into a hyperspectral cube, from which we extractthe reconstructed spectra.

Analytical Chemistry Article

dx.doi.org/10.1021/ac301080h | Anal. Chem. 2012, 84, 6173−61806174

Fourier Filtering Approach and Scaling. By employingthe convolution theorem, (1) may be inverted and the solutionfor the deconvoluted image may be expressed as

= =− −⎡⎣⎢

⎤⎦⎥

⎡⎣⎢

⎤⎦⎥I

I IFT

FT( )FT(PSF)

FTFT( )

OTFtrue1 meas 1 meas

(2)

The term in the denominator is the Fourier transform of thePSF or the optical transfer function (OTF). While this problemis commonly encountered in Fourier analysis, the directsolution for the true image becomes intractable because theOTF approaches zero at high spatial frequencies. Stablesolutions to such inverse problems are routinely obtained byapplying a low-pass filter to the data. In practice, these filtersallow all spatial frequencies below a certain threshold, abovewhich the OTF becomes zero, to contribute to thereconstructed image. The filter is brought continuously tozero by a smoothly varying function, so that spatial frequenciesat which the OTF is nearly zero are not included in thereconstructed image. We have employed this Fourier inversionapproach to image deblurring in this work; however, there arecertain inherent drawbacks to this method. For example, thereis a loss of high spatial frequency information, which isdetermined by the high-frequency content in the PSF.Furthermore, the use of discrete FTs can cause oscillatory“ringing” artifacts near physical boundaries and discontinuitiesof objects. Despite its drawbacks, this method has distinctadvantages over other methods: it is robust and computation-ally inexpensive. In contrast, more sophisticated methods whichimplement an iterative, variational or statistical approach aresubject to long computation times and user subjectivity;however, they do not employ a low-pass filter and therefore donot involve an inherent loss in high spatial frequencycomponents in the image.For the present work, the restored image was recovered by

Fourier Inversion, as described in eq 2; here, an image refers tothe as-collected spatial transmission distribution at a singlewavelength. To avoid ringing artifacts at the image boundaries,the image was placed in an array with the original image in thecenter and additional images on each side reflected about thecommon edge before applying the FT . This effectivelyprovides a boundary condition for the original data such thatthe data is mirrored at the boundaries (“reflexive” boundaryconditions38). A Hanning apodization kernel of the followingform was applied to the Fourier data:

π=

<

+−−

< <

>

⎧

⎨⎪⎪⎪

⎩⎪⎪⎪

⎡⎣⎢⎢

⎛⎝⎜

⎞⎠⎟⎤⎦⎥⎥H k

k k

k kk k

k k k

k k

( )

1

12

1 cos( )

0

min

min

max minmin max

max

(3)

Here k is the radial coordinate in the Fourier domain, kmax is thecutoff frequency, where the OTF approaches zero, and kmin isan effective smoothing parameter. The Hanning function isequal to 1 for all frequencies less than kmin and is equal to 0 forfrequencies greater than kmax. At frequencies between kmin andkmax, the filter smoothly approaches zero by using a functionwith a sinusoidal dependence. Ringing artifacts associated withdiscontinuities in the image are mitigated by smoothlyapproaching zero. We choose kmin to optimize image sharpnessand suppress edge-ringing artifacts that could arise from the

discrete FT. Universally acceptable values for the parameterskmax and kmin were determined empirically over a wide spectralrange using a four-step process. First, a phantom test image wasblurred by the known PSF. Second, the deconvolution routinewas applied with different kmin and kmax values and the optimalchoices for the two parameters were inferred based on thefidelity of the resulting images. Third, the second step wasrepeated for images spanning the entire mid-IR spectral rangeto establish variation of the parameters as a function ofwavelength. Fourth, a polynomial curve was fitted to thewavelength-dependent kmin and kmax values. The latter dependonly on the PSF, and are thus generally applicable to allspectrochemical data sets.Importantly, because of the normalization convention used

for the PSFs, the resulting images will have arbitrary absorptionintensity scales. Since it is important to recover meaningfulspectra from the deconvoluted hyperspectral cube of data, wecompensate for the arbitrary scaling for each deconvolutedimage. To find the correct scaling we required that the zero-frequency component in the FT of the original anddeconvoluted images at a given wavelength be equal. Wethen required that the total transmitted light reaching thedetector be equal for both the original and deconvolutedimages. In practice this latter correction was a smallcontribution to the results. This scaling leads to high-quality,faithful, and chemically meaningful spectra. Further details onthe implementation of this process can be found in SupportingInformation.

■ RESULTS AND DISCUSSION

Instrumental Resolution and Schwarzschild PSF. Adimensionless point source, when imaged on a length scalesimilar to the probing wavelength, is distorted into a shape withfinite dimension. The distortion in the intensity distributionobtained when imaging a dimensionless point source yields thePSF of the imaging system. The PSF thus quantifies how theinstrument distorts the characteristics of the true object in theimage formation process. This effective distortion is evident inthe comparison of IR and visible images of group 7 elementsfrom a USAF resolving test chart (Figure 1A, B, respectively).As can be seen from the visible image, the elements of the charthave sharp rectangular features that are blurred in the IR image.While the rectangular elements are still resolved in the IRimage, the edges and intensity distribution appears fuzzy.The PSF for the Schwarzschild optic used in IR microscopes

differs from that of a conventional microscope objective due togeometrical differences of the lens. Schwarzschild opticsgenerally consist of a pair of concave/convex metallic mirrors;in the case of the 74× of interest here, the optic consists of twoparabolic mirrors of different diameters, offset from oneanother (Figure 1C−D). The primary concave mirror (larger,with hole in the center) collects the focused beam originating atthe sample plane. The smaller, secondary convex mirror ispositioned close to the focus of the concave mirror. Thus, thesmaller mirror collects the radiation and focuses the beam sothat it exits through the hole in the primary concave mirror.This secondary mirror also creates a small obscuration,preventing a cone of light from reaching the primary concavemirror. Thus wave propagation through the Schwarzschildobjective may be crudely modeled by plane wave transmissionthrough an annular aperture. The far-field diffraction pattern ofan annulus at the image plane is described by the equation:39



θε

= −⎛⎝⎜

⎞⎠⎟I I

J x

x

J x

x( )

2 ( ) 2 ( )0

1 12

(4)

where J1 is the Bessel function of order 1, ε is the ratio of theouter radius of the primary mirror (r2, in Figure 1C) to theradius of the obscuring secondary mirror (r1 in Figure 1D). Thevalue x = kr2 sin θ is a dimensionless quantity, where k is thewavevector, r2 is the outer radius of the primary mirror oraperture in the annulus model, and θ is the angular position atthe image plane with respect to the central axis of theSchwarzschild objective. Since this objective is a three-dimensional object, and the obscuration due to the secondarymirror is not coplanar with the image plane, there are smalldeviations from this ideal theory that are wavelength depend-ent. They are absorbed into an “effective r1 ” as describedbelow.In practice, when characterizing the wavelength-dependence

of the PSF, d and r2 are fixed to their known physicaldimensions, and the trend for the effective size of theobscuration (effective r1) is obtained by fitting the measureddata to a function describing an annular diffraction pattern overa range of wavelengths. Deviations from the ideal annulusmodel, such as the optical path differences introduced from thecurvature of the primary optic, are absorbed into the effectiveobscuring mirror radius (effective r1) in the annular model. Theobscuring mirror amplifies the intensity of the diffractionmaxima in the PSF, while narrowing the central maximum ascompared to the conventional Airy function.40 In Figure 2, weshow center profiles of the measured PSFs for a 74× objectivelens on the Bruker Hyperion IR microscope, as observed atthree different wavelengths. (See Supporting Information forfurther 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 theappropriate Hanning apodization kernels overlaid. As can beseen from the image, the spatial frequencies in which the OTF

has appreciable intensity correspond to the Hanning filter beingequal to one. The filter then smoothly approaches zero in thevicinity of the frequencies for which the OTF approaches zero.

Effect of Restoration on Spatial Resolution. Funda-mental resolution limits in IR microscopy are clearly observedin IR images of test objects with features at or beyond thediffraction limit, and have been explored extensively.35,40 InFigure 3A and C, images representing the raw IR absorbance ofthe 3-bar USAF targets for groups 8−9 (256−645 cycles/mm)are shown for two different wavelengths: 2.63 (3800 cm−1) and3.70 μm (2700 cm−1), respectively (reproduced fromSupporting Information Figure 3, reference 32). Images inFigure 3B and D show the patterns from A and C afterdeconvolution with measurement-based PSFs. Vertical andhorizontal line profiles from the marked regions are respectivelyshown, to the left and below Figure 3A,C and D, todemonstrate the improvement in contrast and resolutionfollowing application of our deconvolution algorithm to thesesingle wavelength IR images. The pairs of dashed lines in theprofiles in Figure 3 contrast range of 26.4%, corresponding tothe Rayleigh resolution limit. Analysis of the line profilesindicates that this imaging system exceeds the theoreticalRayleigh 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 upondeconvolution with the instrument’s PSF is clearly apparentin the images and in the line profiles. The contrast of thepatterns 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.

Figure 1. Images of a USAF resolving test chart showing group 7,element 4−6, and diagrams of a Schwarzchild objective. (A) IR imageat 3000 cm−1. (B) Visible Image. (C) Three-dimensional schematic ofobjective (top) and condenser (bottom) Schwarzschild optics used atIRENI. (D) Schematic diagram showing cross-section of a cylindricallysymmetric Schwarzschild optic. Optical rays that enter the objective atdifferent radial positions at the annulus plane travel different opticalpaths, two such rays are shown here as red and blue lines. The annularmodel described in the text requires parameters r1 and r2 (the innerand outer radii of the annulus) and d, the distance from the annulusplane to image plane, as marked.

Figure 2. PSFs for the 74× objective lens within the Hyperion 3000 IRmicroscope. Center profiles through measured PSFs at 3500, 3000,and 2500 cm−1 are overlaid with simulated curves resulting from thefitting results.



Effect of Restoration on Localization of ChemicalSignatures of Heterogeneous Polymers. Naturally, theeffects of blurring due to sampling beyond the diffraction limitare manifested in the spectra and in spectrochemical images, asillustrated in the analysis of a chemical image of the PS/PUmixed sample, Figure 4. Closely spaced 5.9 μm spheres, as wellas smaller 1 and 2 μm spheres throughout the field of view(schematic in Figure 4), were imaged by integrating eachspectrum over a PS-specific CH stretching band (3007−3041cm−1 with same baseline), to reveal the location of PS in thePU matrix (Figure 4A). The PS absorption signal observed nearthe interface of the two central beads should be smaller thanthe absorption signal observed at the centers of the beads, sincethe 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 bereduced at the top of a bead, yet nearly equal amounts of PS aredetected all across the interface of the two beads. Figure 4Bshows the C−H stretching region of spectra taken along theline connecting the two spheres. Reference spectra of PS andPU are shown below as red and black, respectively. In thespectra along the line joining the two spheres, there is very littlevariation in the intensity of the PS-specific bands. Figure 4C,which shows the variation in the intensity of the PS band at3026 cm−1, indicates that this value is nearly constant along theline. This is in contrast to the expectation that the PS signalshould be strongest immediately on top of the spheres, andmuch weaker in between them. In addition, the intensity of thePU-specific band at 2960 cm−1 remains nearly constant along

the line as well. These data demonstrate how imaging at thediffraction limit produces IR spectra contaminated with signalsfrom neighboring pixels, and concomitantly blurred images.We applied our deconvolution algorithm to the chemical

image for every wavelength in this data set, and reassembled thedeconvoluted images in a hyperspectral cube to thus produce areconstructed spectrum for every pixel. Reconstructed spectraare compared to original spectra from the same positions inFigure 4D−E, taken from the PU background and on top of aPS bead, respectively. The reconstructed spectra follow theunprocessed spectra closely, maintain all spectral features andshow that the deconvolution process does not introduceadditional artifacts. The baseline fringes come from multiplereflections in the PU film. Figure 4F shows an image generatedfrom the restored data set integrated over the same spectralrange as that used in Figure 4A for comparison. Enhancedcontrast and a reduction of blurring are immediately obvious,particularly evident at the interface of the two beads. Smaller 1and 2 μm beads scattered throughout the field of view becomemore apparent. Figure 4G shows the reconstructed spectrataken from the sample pixels used to generate the spectral stackin Figure 4B. While in the original data the absorbancesignatures in the spectra from every point along the line containvery similar absorption strengths (Figure 4C, green), muchstronger variation is observed in the restored data set. Thesespectra more accurately reflect the expected absorptionstrengths for PS and PU function groups across the interfaceof the two beads. Moving from the left bead to the center of theinterface, one observes that the absorption strength detected

Figure 3. Transmission images of a high-resolution 1951 USAF test target. Panels A and B show unprocessed images in transmittance at awavelengths 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 themeasurement-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 seeSupporting Information Figure 3.



from the PS decreases as expected, while the absorptionstrength from the PU is smaller directly at the center of thebead, and gradually increases near the center of the interface.Figure 4C compares the absorption strength of the PS band at3026 cm−1 as a function of position along the indicated line forboth the original and restored data. The changes in PSabsorption along the line are clearly resolved in thedeconvoluted data, whereas little change is observed in theraw data. Thus, the improvements in spatial resolution areobservable not only in the deconvoluted images, but also in thefaithfulness of the resulting spectra.Restoration of Chemical Images of Biological Tissue.

The PS/PU composite sample provides a clear and effectivedemonstration of the power of the restoration algorithm;however, much of the material imaged with FTIR isheterogeneous and components are distributed in irregularpatterns. For example, the retina, a biological tissue that iscomposed of several highly distinct layers, presents an excellentreal-world test case for evaluating improvements in resolution.In a recent paper, we reported the high-resolution IRENIimages of mouse retina tissue.36 The deconvolution algorithmhas now been applied to data from that study. The visualsignaling pathway through the retina includes three main typesof neurons: photoreceptors (containing the rods or cones),bipolar cells and ganglion cells, connected approximately end toend. Images and data, before and after deconvolution, areshown for the region that includes the photoreceptor nucleusand outer plexiform layers (Figure 5).The nucleus layer is composed of the nuclear bodies of

photoreceptor neurons, while the outer plexiform layer iscomposed of dendrites and synapses. The former layer is

therefore rich in nucleic acids while the latter, composedprimarily of cell membranes, are rich in phospholipids. TypicalIRENI spectra extracted from well within each region areshown in Figure 5A. The CH stretch peak intensities are muchgreater in the plexiform layer; the polyunsaturated fatty acid(PUFA) peak at 3012 cm−1 and the phospoholipid carbonylpeak at 1740 cm−1 are also considerably elevated relative to thesame bands in the nuclear layer. Distinguishing spectral featuresof the photoreceptor nucleus layer include the appearance of asmall peak at 1712 cm−1, associated with nucleic acids, anddecreased intensity in all phospholipid bands. The photoimageof a near-by section, nuclei stained deep blue with hematoxylin,(Figure 5B) may be compared to the spectrochemical false-color images for the area inside the white box, created from theintensity of the 1712 cm−1 nucleic acid peak, before and afterthe deconvolution process (Figure 5C and D, respectively). Ineach case, the image processing allows one to distinguishbetween the layers, but, prior to deconvolution, the sharpdemarcation between nuclei and axons is blurred by poorspatial resolution.To show the improvement in spectral purity, a stack of 25

spectra spanning the transition region was extracted from theoriginal and restored data sets (Figure 5C and D, white line).Baseline-corrected areas of several biomarker peaks weremeasured and plotted (Figure 5E and F). Plots of the intensityof peaks corresponding to distinct tissue constituents (markedin 5A) that vary between the two morphological layers showthat the transition is sharper and stronger in each case,following deconvolution (solid lines) compared to the originaldata (dashed lines). The deconvolution algorithm is thus

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 areclearly 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 oforiginal and reconstructed spectra from the PU background (D) and from one of the PS beads (E). (B,G) Stacked spectra taken along the black linein 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 Ball show a very similar PS/PU mixture (compare reference spectra on the bottom), the reconstructed spectra in G clearly exhibit the PS−PU−PStransition demonstrating the spatial resolution enhancement in the spectra achieved with the deconvolution algorithm.



successful in increasing the spatial resolution and spectrochem-ical contrast of IRENI images.This demonstration has important implications for the value

of this restoration process. Many biochemical and biomedicalstudies are focused on changes at the cellular and subcellularlevel. The deblurring capability offered by this deconvolutionmethod represents a significant practical step forward, retainingthe true chemical information through achieving the best spatialand chemical contrast from the raw data.

■ CONCLUSIONWe have successfully demonstrated that diffraction-limitedspectrochemical imaging can be achieved through thecombination of a uniquely designed multibeam synchrotron-based spectrochemical imaging system and Fourier-baseddeconvolution algorithms with well-defined PSFs. Applicationof this method to images from one hyperspectral data set, forseveral different wavelengths, demonstrates the new capability

to significantly counteract diffraction-induced blurring. Thisrepresents a significant advancement toward improving thespatial resolution of IR spectrochemical images. Deconvolutionof the PSF from measured data sets, over the entire spectralbandwidth, enables faithful reconstruction of spectra at eachpixel, from which contamination from neighboring regions ofthe sample has been significantly reduced. Samples withfeatures between 0.5 to 6 μm in diameter, on the order ofinfrared wavelengths, provide a stringent test for the effects ofdeconvolution. Application to a spectrochemical image ofretina, a real-world biological sample, demonstrates thepotential for subcellular spatial resolution with biochemicallysignificant spatial contrast. This successful demonstration,restoring hyperspectral cubes of data in the spatial domainand recovering high quality spectral information, shows that wehave an accurate model for the PSFs as a function ofwavelength for Schwarzschild objectives employed for highspatial resolution wide-field mid-infrared imaging. While thisFT based approach is appropriate for the experimental data setsshown here, and can therefore be directly applied to many datasets, undoubtedly, some hyperspectral cubes of data will haveproperties that may require more sophisticated approaches forimage restoration. Such future developments can build uponthe foundation presented here.

■ ASSOCIATED CONTENT

*S Supporting InformationSample preparation and details, additional information on PSFmeasurements and curve fitting deconvolution, and transferfunctions and apodization kernals. This material is available freeof charge via the Internet at http://pubs.acs.org

■ AUTHOR INFORMATION

Corresponding Author*E-mail: [email protected].

Present Address∥Karlsruhe Institute of Technology, Institute for PhotonSources and Synchrotron Radiation, Hermann-von-HelmholtzPlatz 1, 76344 Eggenstein-Leopoldshafen, Germany.

NotesThe authors declare no competing financial interest.

■ ACKNOWLEDGMENTSThe authors are grateful for the feedback provided by SarahPatch, Rohit Bhargava and Brynmor Davis. Sample preparationby Karl Stuen from the University of Wisconsin, Madison, ofthe PU films with PS beads, and from Ben Albensi fromDepartment of Pharmacology and Therapeutics, Faculty ofMedicine, University of Manitoba, and Principal Investigator,Division of Neurodegenerative Disorders, St. Boniface HospitalResearch Centre, Winnipeg, Manitoba, of the retina sample isalso acknowledged. This work has been done with supportfrom a National Science Foundation (NSF) Major ResearchInstrumentation grant (DMR-0619759) and also NSF Chem-istry (CHE-1112433). Research on retina was supported bygrants from the Canadian Institutes of Health Research, theManitoba Health Research Council, and NSERC Canada. Thisresearch is based upon work performed at the SynchrotronRadiation Center. The SRC is funded by the University ofWisconsin-Madison and the University of Wisconsin-Milwau-kee.

Figure 5. Deconvolution of IRENI data resolves biological details. (A)Representative single-pixel IRENI spectra of the photoreceptornucleus layer (red) and outer plexiform layer (blue) from mouseretina. (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 imagescreated by integrating the area of the nucleic acid peak at 1712 cm−1

for (C) the original IRENI FTIR-FPA data and (D) data afterhyperspectral deconvolution (red = high, yellow-green = medium, blue= low spectral intensity, scale bar = 5 μm). White lines in C and Ddenote the exact locations of the stack of spectra extracted from the 25pixels for analysis. (E, F) Peak areas for region-specific marker peaks,plotted from data in each stack.



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restoration and spectral recovery of mid-infrared chemical images

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