Compressive Broad-Band Hyperspectral Sum Frequency

As a proof-of-principle, this system performed molecule-specific imaging of a .... far fewer samples than required by the Shannon–Nyquist sampling t...
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Compressive Broad-Band Hyperspectral Sum Frequency Generation Microscopy to Study Functionalized Surfaces Desheng Zheng,† Liyang Lu,‡ Yun Li,‡ Kevin F. Kelly,*,‡ and Steven Baldelli*,† †

Department of Chemistry, University of Houston, Houston, Texas 77204-5003, United States Department of Electrical and Computer Engineering, Rice University, Houston, Texas 77005, United States

‡

S Supporting Information *

ABSTRACT: A broad-band sum frequency generation microscope has been developed for the study of molecular monolayers on surfaces. Because sum frequency generation is a vibrational spectroscopy based on a second-order optical process, it is uniquely sensitive to detecting a molecule’s vibrational fingerprints specifically at interfaces. In this microscope, a structured illumination beam generated by a spatial light modulator is used to irradiate the sample with a series of sparsifying pseudorandom patterns. The spectra associated with each pattern are then input into a reconstruction algorithm to compressively recover the full hyperspectral image cube. As a proof-of-principle, this system performed molecule-specific imaging of a microcontact-printed selfassembled monolayer of alkanethiolate on copper. This hyperspectral compressive imaging effectively recovered both spatial and spectral surface features with compression greater than 80%, meaning more than a 5-fold decrease in acquisition time compared to traditional methods.

T

is surface-sensitive and molecule-specific because the signal depends largely on the vibrational resonances of interface adsorbed monolayers. Most microscopic methods use contrast methods that are not intrinsic to the sample, but label-free methods allow for inherent knowledge of sample heterogeneity via the chemical functionality distribution. Chemical contrast provides knowledge on the sample properties to explain their performance that is not possible with nonimaging average analysis or secondary indirect methods of microscopy. For surface studies, the probe method is ideally surface-specific for in situ analysis, and SFG microscopy for surface studies fulfills this requirement. Lately, compressive sensing (CS) has been implemented as a novel means of sampling in a narrow-band SFG imaging microscope.6 There are several features that make CS a unique and beneficial technique for SFG imaging. First, CS can be used to recover certain signals and images from fewer samples or measurements than required by Nyquist−Shannon’s theorem and thus has the potential to increase the imaging speed (a major motivation for the development of this technique) while maintaining the image quality.7−12 Second, each measurement maintains high signal at the sensor because each measurement samples half of the image (compared to raster scanning), generally improving the sensitivity and signal-to-noise ratio (SNR) (see SI Figure S2 for a comparison of the raster scan

he study of interfaces is a difficult endeavor for multiple reasons, not the least being the chemical and structural complexity that exists on most natural surfaces.1 Surface science plays an important role in many disciplines including chemistry, physics, biology, materials engineering, and environmental science, where reliable characterization of surfaces and interfaces is indispensable. These systems typically present domains with various chemical properties such as hydrophobic/ hydrophilic, crystalline/amorphous, polar/nonpolar, and so on. Accordingly, many tools for surface analysis with either high spatial or spectral resolution have been developed over the years to characterize these domains, but most are limited by a variety of factors in their actual application. For example, electron scattering and diffraction, photoelectron emission, Auger spectroscopy, and mass spectroscopy can only be operated in a vacuum.2 Scanning probe methods have unprecedented spatial resolution but rarely chemical specificity. Optical spectroscopic techniques can generally be applied to any interface accessible to light, but they generally do not have enough surface specificity and sensitivity and can therefore be used only if the signal contributed by the bulk can be suppressed. Recently, several laser techniques have been developed for imaging surfaces, including the so-called superresolution techniques based on fluorescence2 and spectroscopy.3,4 Optical second-order sum frequency generation (SFG) imaging is an exciting new microscopy technique for studying surfaces and interfaces with spatial resolution based primarily on chemical functional groups.5 The advantage of SFG is that it © 2016 American Chemical Society

Received: March 3, 2016 Accepted: April 26, 2016 Published: April 28, 2016 1781

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The Journal of Physical Chemistry Letters and CS image).11 Third, the use of a high-speed optical modulator and CS reconstruction algorithms means that it is compatible with other broad-band SFG spectrometers.13 Here, we describe the development of a SFG microscope based on CS and broad-band SFG generation, broad-band hyperspectral CS-SFG. Spatial resolution is accomplished by structured illumination and sparsity-based algorithms that allow for reconstructing the broad-band SFG signal into spectrally resolved image slices. To demonstrate its utility, this system is used to study microcontact-printed self-assembled monolayers on a metal surface. The basic operation of the CS-SFG microscope is that the image of the surface is obtained not by the use of direct image acquisition on a charge coupled device (CCD) camera or by raster scanning a focused laser beam across the surface but rather by using a spatially structured probe beam and reconstructing the surface pattern after a number of spatiospectral acquisitions. For this, the imaging CCD has been replaced by the digital micromirror device (DMD) to create a structured visible probe beam. In addition, the use of broad-band IR provides a broad-band SFG output that is spectrally resolved using a spectrograph/CCD array. Each setting on the DMD creates a pseudorandom spatially variable beam generating the SFG spectrum from those selected regions; thus, each pattern is associated with a unique spectral distribution from the surface. From this data, a hyperspectral cube is formed and is used to reconstruct the unknown surface pattern with chemical contrast. This method allows for faster and efficient sampling of heterogeneous surfaces by use of CS techniques and a structured illumination optical scheme, as will be demonstrated here. SFG as a surface spectroscopy technique was developed nearly 30 years ago and as a surface microscopy in 1999 by Florsheimer and co-workers.14−16 The typical surface SFG experiment involves the overlap of two laser beamsone visible and one infraredon the sample surface to generate the sum frequency beam (Figure 1). The nonlinear optical interaction results in a signal in the visible portion of the spectrum that reflects infrared chemical signal but can be acquired by silicon-based optical detectors. SFG imaging is well-suited for imaging purposes because it uses laser light and the coherent nature of the SFG signal to allow for easier

manipulation in the imaging optics and detection system. Further, because the SFG signal is primarily due to the vibrational spectrum of the monolayer, the image contrast contains local chemical information on the surface. In addition, the SFG signal vanishes in a centrosymmetric medium and thus, unlike linear spectroscopy, can be uniquely sensitive to the noncentrosymmetric environment of the interface.17 The SFG signal is given by the general form of eq 1. Equations 2 and 3 show that there are several mechanisms that can provide contrast in the SFG image.5,17 In this study the chemical selectivity through the vibrational spectrum is used for contrast. (2) ISFG = |χeff : EvisE IR |2

(1)

χ(2) eff ,

The effective susceptibility, contains two major contributions, a resonant term and a nonresonant term, such that (2) (2) (2) χeff = χres + χNR

(2)

χ(2) res ,

The resonant term, in this case is mostly due to the molecular monolayer, octadecanethiolate (ODT) on Cu, where the latter is the major contribution to χ(2) NR. The susceptibility is expressed as the orientational averaged hyperpolarizability, χ(2) = N⟨β(2)⟩, where N is the number of molecules. The hyperpolarizability is usually given as the following equation αRamanμIR β (2) = ωQ − ωIR − ΓQ (3) α and μ are the Raman polarizability and IR transition moments, respectively, showing that the SFG and the images in SFG microscopy are chemically sensitive. In comparison to traditional SFG microscopes,5,14,18−23 a compressive imaging one was developed around a signal processing technique for efficiently acquiring and reconstructing a sparse or compressible signal, by finding solutions to underdetermined linear systems. If there are conditions of sparsity of the signal in a particular basis and it is acquired by incoherent measurements, then it satisfies the restricted isometric property and the recovery of an image from far fewer samples than required by the Shannon−Nyquist sampling theorem is possible.24 Previously, CS has been used in a narrow-band SFG imaging microscope based on a single detecting element.6 In this study, the system is expanded into a compressive hyperspectral imaging one with an improved reconstruction algorithm that exploits the three-dimensional sparsity of the acquired data. Additional details are provided in the SI. The realization of compressive broad-band SFG microscopy as sketched in Figure 1 relies on three key elements in the design: an optical modulator (in this case the DMD), the imaging optics (including a diffraction grating), and a spectrograph with multiple detector elements (CCD). A structured illumination beam (515 nm) that incoherently samples the surface through the use of permuted Walsh− Hadamard patterns was displayed on a spatial light modulator, which in this case was the Texas Instruments DMD. Examples of these patterns are embedded on the right side of the optical schematic shown in Figure 1. The patterns are pseudorandom with half of the mirrors on and half off. The patterns are projected onto the surface and overlapped with the infrared beam (uniform profile); thus, the total SFG signal only originates from the on areas of the structured beam. The SFG signal is then spectrally resolved in the spectrograph, and an

Figure 1. Schematic diagram of the broad-band CS-SFG microscope. G1 and G2 are the plane ruled reflectance gratings; M1−M8 are protected silver mirrors; TL represent the tube lens; L1−L3 are the lenses; Obj is the long working distance objective lens; RL1 and RL2 are the 1:1 relay lenses; RDL is the reference diode laser; and DMD is the digital mirror device. The one pattern−one spectrum relationship is specified on the right side. 1782

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Figure 2. Characterization of the CS-SFG microscope. (a) Spectral bandwidth of the picosecond visible beam; (b) spectral bandwidth of the femtosecond IR beam; (c) spatial resolution along the x- axis; (d) spatial resolution along the y-axis; (e) view field of the microscope under a 5× objective lens.

laser beam (RDL) through the visible optics; then, using a flip mirror (Thorlabs) in front of the DMD (FM2), this reference beam is directed to a CCD camera placed precisely in the image plane position equivalent to the DMD (Figure 1). Last, the SFG signal exits the sample at an angle of −40° and is collected by the relay lens. This lens partially compensates for beam movement during the SFG wavelength scans and keeps the beam collection efficient for launching into the spectrograph. The SFG signal beam is reduced in diameter and NA matched to the Acton Research spectrograph (sp i2500, grating 1800 g/mm). SFG spectra are collected on the liquid-nitrogencooled CCD (Pylon Roper Scientific). The spectral resolution, bandwidth, spatial resolution, and FOV are demonstrated in Figure 2. The spectrum from each pattern is recorded by the liquidnitrogen-cooled CCD when triggered by the DMD. In these experiments, the exposure time of the CCD was set at 1 s/ frame; the illumination time was set to 1.07 s. The extra 70 μs of illumination time of the DMD was to ensure that the CCD could be chronologically triggered by the DMD. Patterns consisting of a 128 × 128 element permuted Walsh−Hadamard matrix in 3 × 3 micromirror groupings were loaded to the DMD memory via Java code; these settings along with a 10× microscope objective in this system achieved a resolution of 8 μm per pixel. Cosmic ray spikes in the spectra were removed by a preprocessing median filter. Each spectrum was additionally processed by a wavelet denoising procedure. From these measured spectra, images were reconstructed by the 3DTV algorithm25 at each wavenumber in the SFG spectrum. The system used to validate the utility of this new instrument was a microcontact-printed ODT monolayer on a Cu substrate. The patterns were created by wetting a patterned PDMS (polydimethylsiloxane, donated by Dow-Corning) stamp with octadecanethiol solution (∼5 mM in ethanol) for several seconds and subsequently blowing dry with nitrogen gas. The stripe-possessing stamp was then pressed to the Cu film for up to 15 min.26−28 The Cu substrates were prepared by vacuum evaporation of ∼2 nm Ti onto a Si(100) wafer and then

SFG spectrum corresponding to the specific pattern is recorded. Many patterns/SFG spectra are acquired and used for the image reconstruction.6 Broad-band SFG is based on picosecond visible (515 nm) pulses and femtosecond infrared pulses derived from a light conversion (Pharos) Yb:KGW based system with a fundamental wavelength of 1030 nm and 180 fs pulse duration running at a repetition rate of 5 kHz. A portion of the output of this laser is sent to an optical parametric generator/amplifier (Orpheus) and a difference frequency generator (Lyra) with output from 1000 to 4000 cm−1 for the infrared beam. The remaining Pharos output is sent to the SHBC (second harmonic bandwidth compressor) and generates a 515 nm beam with a 2−3 ps pulse and 8 cm−1 bandwidth. Beam properties are shown in Figure 2. The infrared and visible beams are intensity-, timing-, and polarization-controlled and overlapped onto the sample surface, as shown in Figure 1. Unlike the earlier CS-SFG work,6 in this newer system, the compressive optical modulation has been moved from between the sample and the detector to the laser illumination source, minimizing optical losses at the DMD, which results in a nearly 10-fold improvement in the SNR. The heart of the broad-band CS-SFG hardware is the DMD. This optical modulator is comprised of ∼800 000 micromirrors each 13.6 × 13.6 μm2 in an array of 768 × 1024 mirrors. To produce the structured illumination beam on the surface, the DMD is placed at an image plane of the microscope and then reduced by a Mitutoyo 10× objective (NA = 0.28) to the grating plane, G2 (Figure 1). The 515 nm beam is reflected at the first-order angle by the diffraction grating, which matches the image plane of the surface for a 515 nm beam at a +60° angle of incidence. The plane of the grating is effectively imaged onto the sample surface by a 1:1 relay lens (Edmund Scientific, NA = 0.124). The broad-band infrared beam is overlapped with the visible beam at an angle of −60° to maximize the SFG signal. The resulting field-of-view (FOV) is ∼700 μm in diameter. The microscope alignment and focus are maintained by directing a counterpropagating 515 nm diode 1783

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The Journal of Physical Chemistry Letters deposition of 100 ± 5 nm of Cu metal at a rate of 1.5 ± 0.5 Å/ s. The Cu surface formed a thin oxide once exposed to the atmosphere, onto which the ODT molecules self-assembled. These samples were investigated in the microscope under ambient conditions at room temperature. The regions where the PDMS stripes on the stamp contact the Cu substrate were assumed to deposit approximately one monolayer of ODT; the regions in between the striped pattern on the Cu where the stamp did not make contact remained uncovered and thus lacked the molecular signature of ODT. In Figure 2a,b, the spectral range and resolution of the SFG spectrometer are shown. The fwhm of the infrared defines a spectral range of approximately 130 cm−1. In broad-band SFG, the spectral resolution is determined by the visible beam.29 The SHBC generates 515 nm light from the femtosecond output of the Pharos through second harmonic generation in KTP crystals with a spectral width of 8 cm−1. Also displayed are the spatial and spectral properties of the CS-SFG microscope and spectrometer as characterized in this configuration. The resolution quality of the structured illumination has been measured directly using the 1951 USAF resolution test chart. The 515 nm beam is reflected from the target with 128 × 128 single micromirrors and CS reconstructed to give the images in Figure 2c,d. Because SFG is configured in an oblique geometry, the resolution is different in the x and y directions,30 and two perpendicular line scans are acquired for the group 7 elements in the target (see Figure 2c,d). The line spacing in the target in the x- and y-dimensions are 2.193 and 3.906 μm, respectively, and are well-resolved. The view field is influenced by the beam profile, shrinkage ratio, and wavefront distortion at the sample plane where the SFG signal is generated. Here, the view field has been measured based on the gold-coated silicon wafer with patterned holes 50 μm in diameter, as in Figure 2e. The green curve demonstrates the final CS-SFG image with a FOV of ∼700 μm diameter. The capability of imaging with the chemical contrast for a defined molecular monolayer sample is shown in Figure 3. The SFG signal in this sample has two contributions, a resonant signal from the ODT monolayer and a nonresonant signal from the Cu substrate, as given by eq 2. The nonresonant signal follows a Gaussian-like profile across the wavelength range (see Figure 2b) of this sample, while the ODT monolayer displays the distinct peaks of vibrational resonances. This spectrum/ image was acquired with the IR centered at 2900 cm−1, and the spectrum is not normalized to the Gaussian-like IR band of 130 cm−1 (see Figure 2b); however, this does not affect the qualitative use of these images for chemical analysis. The peaks at 2860, 2875, and 2935 cm−1 are assigned to CH2(sym), CH3(sym), and CH3(sym, FR), respectively.31 The arrows in the spectra correspond to the images in the lower part of Figure 3 and demonstrate that the major contribution to the image contrast is the vibrational spectrum of the ODT SAM. For these slices of the hyperspectral data cube, 100% of the measurements were used. For example, image j displays high contrast in response with CH3 groups of ODT and bright areas of the image. However, analysis at image h shows inverted contrast from that of the resonant peaks; at this wavenumber, 2910 cm−1, Cu is the major contribution to the signal (Figure 3; the blue curve is above the red curve). Other peaks in the spectra also display this image contrast mechanism, that is, images f−j show a bright image for CH3, bright from the Cu region, (off-resonance of ODT, 2920 cm−1), and then bright again for the CH3 peak at 2935 cm−1. The SFG signal intensity

Figure 3. Typical spectra of ODT and Cu taken from adjacent areas. The red curve is extracted from the ODT stamped region (e); the blue line is nonresonant signal from the Cu area (h). The reconstructed images by 3DTV (a−l) are from the corresponding spectrum position as in the top panel.

is the sum of each resonant and nonresonant susceptibility squared (eq 1); this leads to cross terms that interfere depending on the relative phase of the terms (eq 2).32 Thus, off-resonance, such as at 2920 cm−1, the Cu signal is more intense than ODT and appears brighter in the image, that is, the location where ODT is not patterned. This main spectroscopic contribution (eq 3) to the image contrast means that the broad-band CS-SFG microscope is sensitive to chemical image analysis of a single molecular layer on any surface or interface.5,33 The images and spectra in Figure 4 further demonstrate the capabilities of the CS-SFG microscope. Images in Figure 4 show the effect of compression on the image, where Figure 4a− f shows 95, 50, 25, 12.5, 6.25, and 3% of the measurement patterns used to reconstruct each image, corresponding to a range of 5% compression up to 97%. The accompanying image slices presented in Figure 4 are reconstructed from measurements at the CH3(sym) peak position. Clearly, the contrast in the images changes as the compression increases. Each image is shown with its corresponding SFG spectrum extracted from a 16 × 16 μm2 region of ODT (red) and the Cu substrate (blue). The pattern is still apparent at better than 5:1 compression, and the spectra of both Cu and ODT remain relatively pure. However, increased compression results in loss of spectral image quality; this is a well-known effect of CS. In this relatively low pixel image (128 × 128), compression is expected to be limited to approximately 90%. The normalized mean square error (NMSE) is a useful quantitative measure of the image quality under the various compression conditions. Figure 5b shows the NMSE for the three compression methods in this study. These consider the 1784

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Figure 4. Compressed 3DTV reconstruction of the images and spectra. (a−f) Reconstructed images with 95% measurement patterns used down to 3%. The corresponding SFG spectra extracted from the 16 × 16 μm2 ROI of ODT and Cu, respectively. Image shown at 2875 cm−1. ROI squares in the image are not to scale.

Figure 5. (a) Comparison slices from the hyperspectral data cube for the f band vibration reconstructed using 3DTV,35,36 D-AMP,25 and TVAL3,37 at compression ratios of 2:1 and 4:1, respectively. (b) NMSE plot for the three reconstruction methods used in (a).

and displays a decrease in the SNR as the compression increases. It is interesting to note the effect of the reconstruction method on the compression level and image quality. Figure 5 demonstrates the reconstructions of a single-band image at the band-f vibrational peak at a 2935 cm−1 wavelength, denoted in Figure 3, as performed for 2:1 and 4:1 compression by three different sparsity minimizing algorithms: 3DTV,36 D-AMP, and TVAL3. The TVAL3 algorithm is optimized for images37 and exploits only the sparsity in 2D spatial gradients of the image, disregarding information from adjacent spectral bands. In high noise measurements, reconstructions with TVAL3 degrade

100% 3DTV as the ground truth image. From the graph, the error becomes higher for greater compression. The NMSE values increase faster as the compression is increased above 80%. This is interpreted as providing at least a 5:1 compression ratio for this data set. Also plotted in Figure 5b is the NSME for BM3D-AMP (D-AMP) and TVAL3. While D-AMP shows similar NMSE values, the reconstructed image shows significant distortion. 3DTV appears to be the best method for reconstruction of these data sets. It is noteworthy that DAMP maintains relatively good NMSE values, while the image itself is noticeably distorted.34 Another effective evaluation of image quality is with peak SNR. This plot is shown in Figure S3 1785

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Membrane Proteins in Lipid Bilayers. J. Am. Chem. Soc. 2013, 135, 18292−18295. (5) Cimatu, K.; Baldelli, S. Chemical Microscopy of Surfaces by Sum Frequency Generation Imaging. J. Phys. Chem. C 2009, 113, 16575− 16588. (6) Cai, X. J.; Hu, B.; Sun, T.; Kelly, K. F.; Baldelli, S. Sum Frequency Generation Spectroscopy-Compressive Sensing Microscopy. J. Chem. Phys. 2011, 135, 194202. (7) Howland, G. A.; Lum, D. J.; Ware, M. R.; Howell, J. C. Photon Counting Compressive Depth Mapping. Opt. Express 2013, 21, 23822−23837. (8) Baraniuk, R. G. Compressive Sensing. IEEE Signal Process. Mag. 2007, 24, 118−120. (9) Candès, E. J. Compressive Sampling. International Congress of Mathematics (Madrid, Spin) 2007, 3, 1433−1452. (10) Donoho, D. L. Compressed Sensing. IEEE Trans. Inf. Theory 2006, 52, 1289−1306. (11) Duarte, M. F.; Davenport, M. A.; Takhar, D.; Laska, J. N.; Sun, T.; Kelly, K. F.; Baraniuk, R. G. Single-Pixel Imaging via Compressive Sampling. IEEE Signal Process. Mag. 2008, 25 (2), 83−91. (12) Studer, V.; Bobin, J.; Chahid, M.; Moussavi, H. S.; Candès, E. J.; Dahan, M. Compressive Fluorescence Microscopy for Biological and Hyperspectral Imaging. Proc. Natl. Acad. Sci. U. S. A. 2011, 109, E1679−E1687. (13) Richter, L. J.; Petralli-Mallow, T. P.; Stephenson, J. C. Vibrationally Resolved Sum-frequency Generation with Broadbandwidth Infrared Pulses. Opt. Lett. 1998, 23, 1594−1596. (14) Florsheimer, M.; Brillert, C.; Fuchs, H. Chemical Imaging of Interfaces by Sum Frequency Microscopy. Langmuir 1999, 15, 5437− 5439. (15) Hunt, J. H.; Guyot-Sionnest, P.; Shen, Y. R. Observation of C-H Stretch Vibrations of Monolayers of Molecules Optical SumFrequency Generation. Chem. Phys. Lett. 1987, 133, 189−192. (16) Zhu, X. D.; Suhr, H.; Shen, Y. R. Surface Vibrational Spectroscopy by Infrared-Visible Sum Frequency Generation. Phys. Rev. B: Condens. Matter Mater. Phys. 1987, 35, 3047−3050. (17) Huang, J. Y.; Shen, Y. R. Sum Frequency Generation as a Surface Probe. In Laser Spectroscopy and Photochemistry on Metal Surfaces; Dai, H. L., Ho, W., Eds.; World Scientific: Singapore, 1995; pp 5−53. (18) Allgeyer, E. S.; Sterling, S. M.; Gunewardene, M. S.; Hess, S. T.; Neivandt, D. J.; Mason, M. D. Combining Total Internal Reflection Sum Frequency Spectroscopy Spectral Imaging and Confocal Fluorescence Microscopy. Langmuir 2015, 31, 987−994. (19) Lee, C. M.; Kafle, K.; Huang, S.; Kim, S. H. Multimodal Broadband Vibrational Sum Frequency Generation(MM-BB-V-SFG) Spectrometer and Microscope. J. Phys. Chem. B 2016, 120, 102−116. (20) Kuhnke, K.; Hoffmann, D. M.; Wu, X. C.; Bittner, A. M.; Kern, K. Chemical Imaging of Interfaces by Sum-frequency Generation Microscopy: Application to Patterned Self-assembled Monolayers. Appl. Phys. Lett. 2003, 83, 3830−3832. (21) Smith, K. A.; Conboy, J. C. A Simplified Sum-Frequency Vibrational Imaging Setup Used for Imaging Lipid Bilayer Arrays. Anal. Chem. 2012, 84, 8122−8126. (22) Raghunathan, V.; Han, Y.; Korth, O.; Ge, N. H.; Potma, E. O. Rapid Vibrational Imaging with Sum Frequency Generation Microscopy. Opt. Lett. 2011, 36, 3891−3893. (23) Miyauchi, Y.; Sano, H.; Okada, J.; Yamashita, H.; Mizutani, G. Simultaneous Optical Second Harmonic and Sum Frequency Intensity Image Observation of Hydrogen Deficiency on a H-Si(1 1 1) 1 × 1 Surface after IR Light Pulse Irradiation. Surf. Sci. 2009, 603, 2972− 2977. (24) Romberg, J. Imaging via Compressive Sampling. IEEE Signal Process. Mag. 2008, 25, 14−20. (25) Metzler, C. A.; Maleki, A.; Baraniuk, R. G. From denoising to compressed sensing. IEEE Trans. Inf. Theory 2014, 1406, 4175. (26) Larsen, N. B.; Biebuyck, H.; Delamarche, E.; Michel, B. Order in Microcontact Printed Self-Assembled Monolayers. J. Am. Chem. Soc. 1997, 119, 3017−3026.

quickly as a function of compression ratio. The D-AMP algorithm includes a nonlocal image denoising step inside of the conventional approximate message passing (AMP) reconstruction algorithm25 and provides a highly smoothed recovery that distorts edges as the amount of compression is increased and still operates on each wavelength image as if it is independent. However, the 3DTV algorithm previously used for sparsity in two spatial dimensions and also sparsity in temporal dimensions35,36 can, in this case, be exploited for joint sparsity in both spatial as well as spectral dimensions across slices to recover the entire 3D hyperspectral data cube. With the additional spectral interband constraints, it initially shows more accurate reconstructions than the other two methods and proves more robust than the other two in terms of image quality as fewer measurements are acquired. A new chemical imaging microscope for surface studies based on broad-band vibrational SFG spectroscopy coupled with compressive imaging has been developed. The spatial resolution is accomplished by a structured illumination beam using a combination of a visible wavelength laser, a spatial light modulator, and a three-dimensional reconstruction algorithm. When combined with an infrared laser on the sample for SFG, compression better than 5:1 is achieved, which translates to image acquisition that is 5 times faster than that of traditional systems. This study demonstrates that efficient chemical imaging is possible with contrast based only on the label-free inherent vibrational spectrum of molecules at any given chemical interface. Given the second-order nonlinear mixing required for SFG, the work presented here represents significant proof that this can be adapted to a variety of laserbased linear and nonlinear microscopies.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpclett.6b00507. Details of instrumentation; normalized mean square error; comparison between raster scanning and the compressive sampling; and comparison of imaging speed between the broad-band SFG microscope and narrowband SFG microscope (PDF)

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AUTHOR INFORMATION

Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The Authors thank the W.M. Keck Foundation for support of this project.

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REFERENCES

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