Chemical Imaging of Self-Assembled Monolayers on Copper Using

Aug 10, 2017 - ... at different frequency regions through reconstruction of the hypercube using a 3-dimensional total variation regularization algorit...
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Chemical Imaging of Self-Assembled Monolayers on Copper Using Compressive Hyperspectral Sum Frequency Generation Microscopy Desheng Zheng,† Liyang Lu,‡ 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: Sum frequency generation microscopy is a label-free optical imaging technique with intrinsic molecular vibrational contrast for surface studies. Recent developments of compressive sensing broad-band hyperspectral SFG microscopy have demonstrated the potential application for imaging monolayer at metal surfaces with micrometer spatial resolution. Here is presented the capability of chemical imaging of spatially patterned monolayers of 1octadecanethiol (ODT) and 16-methoxy-1-hexadecanethiol (MeOHT) molecules assembled on a copper surface. The spatial distributions of the monolayer with vibrational-spectral contrast are well-demonstrated at different frequency regions through reconstruction of the hypercube using a 3-dimensional total variation regularization algorithm (3DTV). Spatial-chemical distributions of each component are also reconstructed directly from the compressive measurements by endmember unmixing (CEU) scheme. Compared to 3DTV algorithm, the reconstruction from CEU shows spatial distribution of each component on the surfaces, and demonstrates the ability to characterize the domains of mixed-molecules on surfaces.

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INTRODUCTION Optical sum frequency generation (SFG) is a coherent secondorder nonlinear process, which has unique advantages for characterizing surfaces or interfaces with surface selectivity and sub monolayer sensitivity.1−4 This capability, when extended to microscopy, becomes especially useful for investigating spatially inhomogeneous systems on surfaces or interfaces to map the chemical inhomogeneity, orientation, arrangement of molecules, and domain formation.4−9 Sum frequency generation microscopes are designed based on far-field detection.6,7,10−14 With decades of developments, sum frequency generation microscopes have been increasingly used to study the complex systems, such as nonlinear materials,15 monolayers on metal surfaces,4,7,9,16 and biomaterials systems.8 However, typical applications are hindered by the intrinsic low signal intensity and long data acquisition times. Combining the compressive sensing technique with the SFG imaging is a potential method to address the low speed of data acquisition issues in surface studies.14,17 The mathematical theory of compressive sensing (CS) asserts that signals that are sparse in real-space or sparse through a mathematical transform can be perfectly recovered from a much lower measurement rate than Shannon−Nyquist sampling, by finding solutions to underdetermined linear systems with the constraint of sparsity.17−19 In other words, when conditions of sparsity of the signal in some basis or representations are satisfied, with incoherent measurements based on restricted isometric property, the perfect recovery of signal is possible from far N fewer samples, ∼kμlog k , than required by the Shannon− Nyquist sampling theorem. Here, k is the sparsity; μ is the © XXXX American Chemical Society

coherence between the basis of measurement and basis of the sparsity domain; N is the Shannon−Nyquist sampling rate. The sparsest solutions of the underdetermined linear systems could be computed based on the Greedy algorithms,20,21 S 1 minimization,22−24 or total variation (TV) minimization.25−28 Recently, the compressive sensing sampling technique adapted from the single pixel camera design has been used to narrowband and broad-band SFG imaging microscopes.14,29 This integration brings several features which make CS a unique and beneficial technique for SFG imaging. First, CS can be used to recover signals and images from fewer samples or measurements than that required by Nyquist−Shannon’s theorem; this has the potential to decrease the image acquisition time.14,29 Second, each measurement is the linear combination of the half total numbers of the pixels, which improved signal-to-noise ratio (SNR) by √(N /2) compared to faster scanning strategies.14,29 Third, it is adaptable to broadband hyperspectral imaging, which records the entire spectrum without wavelength scanning.14,29 Besides the above advantages, the broad-band femtosecond input pulses are advantageous (compared to the narrow-band) because of their higher damage threshold in terms of energy and higher nonlinear signal due to the higher peak power.5 Further, taking the advantages of the compressibility of SFG spectrum, the image quality could be increased dramatically with 3DTV reconSpecial Issue: Miquel B. Salmeron Festschrift Received: April 8, 2017 Revised: June 17, 2017

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χ(2)NR is the nonresonant contribution typically attributed to electronic excitations of the substrate. The χ(2)R is associated with resonant vibrations of the adsorbate molecular layer and is significantly enhanced when the frequency of an incident infrared beam (ωIR) is coincident with a specific molecular vibrational mode, q. In eq 2, Aq, ωIR, ωq, and Γq are the amplitude, frequency of the IR beam, resonant frequency, and the damping constant of the qth SFG active vibrational mode, respectively. Eq 2 serves as the basis equation for the interpretation of SFG spectra and images. Aq (2) χeff = χR (2) + χNR (2) = ∑ + ANR eiϕ i ω − ω − Γ q IR q q

struction, which exploit the joint sparsity across the spectral image slices.28,30 The results presented in this study show the capability of this CS-SFG microscope to achieve images of the surface where the contrast is from the inherent vibrational spectra of the monolayer. These images are acquired using broad-band SFG spectroscopy, where the spatial information is encoded in a spatially structured input beam and the spectral information is resolved using spectrograph/CCD detection. The fidelity of the chemical maps (SFG images) was evaluated using both 3DTV and compressive endmember unmixing schemes, where the later proved to give better image contrast. The use of image compression was applied to the CS-SFG and suggests image compression of near 10:1 which directly results in image acquisition speeds of ten times faster. This work presents the hyperspectral chemical imaging of the spatial inhomogeneous mixed monolayers of 1-octadecanethiol (ODT) and 16-methoxy-1-hexadecanethiol (MeOHT) molecules assembled on copper surface, which provide the spatial distributions of the different components. 3DTV algorithm not only consider the spatial compressible of SFG image, but also consider the spectral compressibility of SFG signal, which bring better denoising effect to the SFG imaging comparing to narrow-band SFG microscope. The hyperspectral imaging cube reconstructed with 3DTV algorithm with the spatial distribution of vibration contrast has been well demonstrated at different vibrational regions. The hyperspectral imaging cube contains two axes for spatial (x,y) and one dimension (z) for the SF frequency (wavenumber), so that each voxel is a SFG intensity at a surface location and a spectral position.29 Since overlap of the intrinsic vibrational spectrum between methyl group and methoxy-group exists, compressive endmember unmixing (CEU) scheme based on total variation minimization is also used to reconstruct the SFG contributions of each component. Both algorithms have shown the consistent imaging results. Compared to 3DTV algorithm, reconstruction from CEU provides more information about spatial distribution of each species on the surface. This scheme of chemical imaging of monolayers will enable new ability to recognize the different molecules distributions even with significant overlaps of molecular vibrational spectrum in studying surfaces in biological and material science.

(2)

SFG spectra are complicated by the convolution between χ(2)res and χ(2)NR shown in eq 3. The ε and φ denote the phase of χ(2)R and χ(2)NR, respectively, and the phase difference between χ(2)R and χ(2)NR is the relative nonresonant phase ϕ which typically results in a complex SFG line shape.33,34 (2) 2 (2) (2) ISF ∝ |χNR | + |χR(2) |2 + 2|χNR ||χR |cos[ε − ϕ]

(3)

This SFG microscope operates on the principle of structured illumination and compressive sensing techniques. In the typical SFG surface spectroscopy setup the surface is illuminated by two laser beams (infrared and visible) with Gaussian-like profiles to generate sum frequency signal. In this SFG microscope the surface is impinged with a smooth profile infrared beam and a spatially structured visible beam. A pseudorandom Walsh−Hadamard pattern is encoded into the visible beam via a digital micromirror device (DMD) and then imaged to the surface to generate the SF signal, Figure 1. The

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SFG SPECTROSCOPY There are a number of reviews which introduce the theoretical background of SFG and its applications.3,31,32As shown in eq 1, SFG is a second-order nonlinear optical process which involves two laser beams spatially and temporally overlapped on the surface, to induce a second order polarization, P(2)SF. Here, Ivis and IIR are the intensity of the visible and infrared laser pulses, respectively, and χ(2)eff is the second order susceptibility.1 The second order nonlinear optical process is forbidden in a medium with inversion symmetry under the electric dipole approximation, but are active at the interface where the inversion symmetry is broken.2 Thus, SFG is a highly surface sensitive technique. (2) 2 (2) 2 ISF ∝ |PSF | ∝ |χeff | : I visIIR

Figure 1. Schematic diagram of the compressive sensing broad-band hyperspectral sum frequency generation microscope based on counter propagation oblique configuration. G1-G2, plane ruled reflectance gratings; M, protected silver mirrors; TL, tubelens; L1-L2, doublet lens; Obj, long working distance objective lens; RL1-RL2, the 1:1 relay lenses; FM1-FM2, flip mirrors; DMD, digital device mirror; LN-CCD, liquid nitrogen cooled CCD.

DMD modulates the beam to a binary on/off pattern that then only generates signal where the mirrors are “on”. Since the patterns are randomized with mirrors 50% “on” and 50% “off” each pattern samples the surface areas differently. Over the acquisition of signal from many such known pseudorandom patterns the image of the surface is reconstructed via reconstruction algorithms, as described herein. By spectrally resolving each SFG signal a chemical image of the surface is obtained.

(1)

The second-order susceptibility χ(2)eff shown in eq 2 contains both a nonresonant contribution χ(2)NR and a resonant contribution χ(2)R, which relates the induced second-order polarization response with the intensity of the incident beams. B

DOI: 10.1021/acs.jpcb.7b03339 J. Phys. Chem. B XXXX, XXX, XXX−XXX

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EXPERIMENTAL SECTION Structure Illuminated Compressive Sensing Broad Band Hyperspectral SFG Microscope. The homemade microscope was designed in the oblique configuration to adapt to the conventional SFG spectroscopy measurement.29 Figure 1 depicts the schematic layout of the setup. Briefly, the picosecond visible pulse beam from second harmonic bandwidth compressor (SHBC, light conversion) is expanded and collimated, then perpendicularly incident on the grating G1. The first order diffraction beam is reflected to the digital micromirror device (DMD, ViALUX Discovery 4100) with incident angle at 24° to DMD normal. After the patterned DMD reflection, the spatially modulated visible beam is reduced by a tube lens (TL) and a long working distance objective lens (Obj, Mitutoyo), then perpendicularly incidents on the grating G2. The first order diffraction beam after G2 illuminates on the sample with an incident angle (relative to the surface normal) of 60° after passing the 1:1 relay lens (RL1). The femtosecond IR beam from Lyra (light conversion) strikes on the sample from counter direction at an incident angle (relative to the surface normal) of 60°. The structured visible beam and IR beam overlap temporarily and spatially on the sample. The generated SF signal in the phase matching direction passes the 1:1 relay lens (RL2) and is reflected to the spectrograph by mirrors. RL2 with larger NA is used to adapt the variation of the SFG signal direction during the wavelength tuning of IR beam. Lens L1 and L2 are used to control the beam size and NA to match the requirement of spectrograph (SP2500, Acton). After the spectrograph, the SFG signal is recorded by liquid nitrogen cooled CCD (PyLoN 100B/LN, Princeton Instrument). In this setup, the plane ruled reflectance grating G1 is used to compensate the difference of optical distances, which are induced by the tilted incident on the DMD surface and the counter incident angle to the sample relative to the IR beam.29 This compensation is important for the view field of this microscope, by maximization of temporal and spatial overlap of the visible beam profile with that of the IR laser at the sample surface. The plane ruled reflectance grating G2 is used to correct the rectangle distortion from the oblique imaging and to make the image plane of DMD overlap with the sample surface.11,14,35 The choice of groove density and blaze angle of each grating are based on the experiment configuration and the diffraction efficiency. To synchronize the DMD pattern with the LN-CCD recording, the LN-CCD is externally triggered by the TTL sync-out from DMD. The current hyperspectral microscope has the spectral resolution about 8 cm−1, and lateral resolution about 2 μm with DMD finest binning.29 Auxiliary beam from a reference diode laser (RDL) is used to align the sample position, which is counter-directed passing the same beam path of visible beam between flip mirror 1 (FM1) and flip mirror 2 (FM2). The distance from sample to DMD is the same as that from sample to reference CCD. Once the sample is well-imaged on the reference CCD, the image of the modulated DMD pattern is in-focus at the sample surface. All SFG conducted under ppp polarization conditions (input beams are p-polarized and output detected as p-polarized). The infra band is centered at 2860 cm−1 with a bandwidth of 120 cm−1, to optimized the contrast with one central IR setting. The second harmonic of the Pharos laser is around 515 nm. SFG signal is approximately 2500 counts at the 2850 cm−1 peak in a 1 s acquisition. Power at the sample is approximately 30 mW

and 5 mW for the IR and visible, respectively, with a repetition rate of 5 kHz. Sample Preparation. The copper coated silicon wafer is prepared by vacuum evaporation of ∼2 nm Ti on to a Si(100) wafer then deposition of 100± 5 nm of Cu metal at a rate 1.5 ±0.5 Å/s. The Cu substrate contains a thin oxide. ODT monolayer pattern on the substrate is created by microcontact printing lithography.36−38 The master polydimethylsiloxane (PDMS) stamp to form patterns is wetted with a drop of 1octadecanethiol (ODT) solution (∼5 mM in ethanol) for several seconds and then blown with dry nitrogen. The stamp is then contacted to copper surface for up to 15 min. After detaching the PDMS stamp, the stamped substrate is immersed in 16-methoxy-1-hexadecanethiol (MeOHT) solution (∼5 mM in ethanol) up to 20 min. Finally, the sample with monolayers is washed by ethanol and puffed dry with nitrogen gas. The regions where the PDMS stamp contacted will be deposited with monolayer of ODT; the bare regions in the first step will be deposited with self-assembled monolayer of 16-methoxy-1hexadecanethiol. Data Processing/Analysis. Exposure time of LN-CCD is set at 1 s per frame and the illumination time of DMD is set at 1.07 s. The 70 μs longer illumination time of the DMD is set to ensure the LN-CCD is in the waiting state before the trigger signal from the DMD TTL sync-out for next pattern. 128 × 128 pseudorandomly permuted Walsh−Hadamard matrix with 3 × 3 micromirrors binning is loaded to the DMD memory via java code, which makes the SFG microscope resolution at 8 μm in this study. Cosmic ray spikes in the spectra are removed through the medium filter in Matlab. Each spectrum is further purified with wavelet denoising before reconstruction. Considering the inherent similarity of the image slices between neighboring wavenumber, the hyperspectral imaging cube is reconstructed by the 3DTV algorithm.30,39 To demonstrate the molecular distribution of the monolayers, compressive endmember unmixing (CEU) scheme based on total variation minimization is used to reconstruct the SFG imaging of each component.40

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RESULTS AND DISCUSSION Hyperspectral SFG Imaging of ODT-MeOHT Monolayers (Spectrum and Structure). Spontaneously adsorbed alkanethiols from the solution form densely packed and highly oriented self-assembled monolayer films on many metal surfaces.41,42 The SFG spectra of ODT monolayer and MeOHT monolayer on copper substrate in the C−H stretching region (Near 2860 cm−1) are shown in Figure 2. There are 3 dominant peaks shown in the spectrum of ODT monolayer, at 2850, 2870, and 2920 cm−1, respectively. According the previous assignment, the peak at 2850 cm−1 is from the CH2 symmetric stretch, while the peaks at 2870 and 2920 cm−1 are due to the CH3 symmetric stretch and Fermi-resonance, respectively.43 The methylene mode at 2850 cm−1 illustrates the significant population of gauche conformations, since the methylene modes in a finite all-trans polymethylene chain are rigorously centrosymmetric, and thus SFG silent.44 In this study, the copper substrate is oxidized due to ambient exposure conditions for several hours and is consistent with previous results, that the surface oxidation of the copper could induce the number of gauche defects to increase.16,45−48 The sum frequency spectra of MeOHT on copper surface show 6 peaks in the C−H stretching region, Figure 2. Based on literature assignments,49,50 the doublet at 2810/2830 cm−1 is C

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positions A−F of Figure 2. Image D has demonstrated the best image contrast since the difference of the spectrum reach the maximum at CH3(sym) stretching at 2870 cm−1. The bright bands in image D have most of their SF intensity contributed from the ODT monolayer than that from MeOHT monolayer as seen in the spectra of Figure 2. Image B and F have shown a similar pattern as image D with bright wide bands alternated with dark narrow bands, also from the ODT monolayer. The contrast in these two images (B and F) is however poor due to the common spectral overlap with methoxy-terminated SAM. Meanwhile images A and E also have shown the striped patterns but with inverted contrast, bright narrow bands alternated with dark bright bands as compared to images B, D, and F. Image C has shown image contrast that is different from pure ODT or pure MeOHT, it is difficult to judge which monolayer’s contribution is dominating, since the SF intensity near this point is almost equal between the two SAMs. Gauche defects in the methylene chain are common to many SAMs on Cu.45,46 This is likely due to the defects in the PDMS sample or the Cu substrate, where micro-contact printing on Cu substrates is much more difficult than on Au. A more detailed analysis and interpretation of this local feature is given in the SI. The majority of the image contrast presented is due to the direct spectral differences between ODT and MeOHT, thus CS-SFG provides essentially chemical contrast, however, it is still challenging to judge the exact distributions of different species on the surface, since their contributions also are changing as the wavenumber. The complex line shape in these SFG spectra with contributions from Cu, ODT, and MeOHT render quantitative analysis difficult thus far. For example, the intensity near 2830 cm−1 is resonant with the methoxy-group; however due to interference of the strong CH2 methylene signal (ODT) and Cu (NR background) an apparent coincidental peak is present (Figure 2). This effect reduces the contrast in the image; see Figure 3A. Local spectra retrieved from the image cube are given in Figure 4. The green curves in Figure 4A and B show the corresponding local spectrum retrieved from the region 1 and region 2 shown in Figure 3E. The spectrum of region 1 has shown the most similarity to that of MeOHT monolayers on copper, while the spectrum of region 2 has shown the most similarity to that of ODT monolayers on copper. These further confirm the bright bands are dominated by MeOHT monolayers in Figure 3A and E, and the bright bands are dominated by ODT monolayers in Figure 3B, D, and F. With linear least-squares decomposition, the spectrum of region 1 and region 2 could be decomposed into 3 terms; ODT monolayers, MeOHT monolayers, and the residual, which mostly arises from the nonlinear interferences between copper, MeOHT, and ODT. Contributions of interference terms are more complex than that from pure components, which depends on the relative phase of the pure terms, see eq 3. Each component might show positive or negative contribution to the total SF intensity, as illustrated in the residual curves in Figure 4. For example, at 2850 cm−1 the contribution of interference terms show dominant positive contributions to the SF intensity, this positive contribution gives Figure 3C good image contrast, but is ambiguous as to which molecules dominates, as described in SI. At 2920 cm−1 the contribution of interference terms show negative contributions to the SF intensity, this negative contribution results in Figure 3E and F demonstrating poor image contrast, thus showing a limitation if only considering the pure components as linear contributions.

Figure 2. Spectra of ODT- monolayer and MeOHT monolayer on copper surface. Letter assignments in the spectra refer to regions on the patterned surface according to Figure 3.

assigned as the symmetric stretch of the out-of-plane CH2 in terminal methoxy-group (OCH3), which is different from the methylene (chain) group. The dominant peaks at 2850 and 2920 cm−1 are most likely from the CH2 symmetric stretching and CH3 Fermi-resonance, respectively (OCH3). Other features in the spectra are left unassigned or might be due to interference with the nonresonant Cu background signal.51 In both the ODT monolayer and the MeOHT monolayer there is a significant population of gauche conformations as shown by the high intensity of CH2 symmetric stretching, 2850 cm−1. The spectral difference between the MeOHT monolayer and the ODT monolayer conveys the good molecular image contrast, especially at 2830 and 2870 cm−1, respectively. The intensity of the respective peaks includes the contributions from the cross-sectional differences of the vibrational modes, molecular orientations, and molecular density. Contrast mechanisms in CS-SFG imaging are discussed below. Here the 3DTV algorithm is used to reconstruct the SFG signal and deduce the heterogeneity of monolayer since the 3DTV has shown better normalized mean square errors at high percentage of pattern.29 3DTV allows for a reconstruction of the image at each band (wavenumber) in the spectra. Figure 3A−F displays the corresponding images at the spectrum

Figure 3. Hyperspectral images reconstructed based on 3DTV algorithm. Images A−F are the slices from the corresponding spectrum positions A−F in Figure 2. B, D, and F have shown the pattern as ODT dominant, while A and E have shown the pattern as MeOHT dominant. Region C appears to contain mixed contributions, see SI. D

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Figure 4. Local spectrum retrieved based on 3DTV algorithm. (A) The local spectrum of region 1, which is marked in Figure 3E. (B) The local spectrum of region 2, which is from the local area marked in Figure 3E. The spectrum curves in green are the overall results from the selected regions; the spectrum curves in blue are the contributions from MeOHT; the spectrum curves in red are the contributions from ODT; the residuals are shown in black circles.

Figure 5. (A) Estimated abundance distribution of ODT monolayer on copper; (B) estimated abundance distribution of MeOHT monolayer on copper; (C) color coded molecule distributions the monolayer. The image reconstruction is based on CEU.

region suggesting that defects in the PDMS stamp are possible, as has been proposed previously.7,53 As noted, SFG is second-order coherent nonlinear phenomena, the intensity is not linearly dependent on the molecular density, and is influenced by the orientation of the molecules, however the molecular density distributions are well approximated by the linear unmixing method performed here. This might be due to the SFG signal is dominated by the crossterm in the squared amplitude, see eq 3 and SI; the contributions of each component are linear contributions to the total SFG signal. The Cu background term is squared and each cross term contains a contribution from the Cu NR signal, and thus displays the complex line shape. However, since each individual SFG spectrum, ODT/Cu and MeOHT/Cu, is used as the input to the unmixing algorithm this provides a more accurate analysis and better chemical contrast. That is, it accounts for the interference and line shape effects and since each random pattern is incoherent with each other the imaging process is well approximated as a linear spectroscopy. Although not a perfect solution, effect of Cu nonresonant contribution boosting the monolayer resonant signal (through an heterodyne effect)54,55 allows for the use of this linear unmixing scheme. All this has shown the ability of the spectral unmixing to characterize the spatial distribution of monolayers on surfaces using broadband SFG spectroscopy. Compressive Imaging. The images have also been reconstructed with compressive endmember unmixing scheme at different compressive ratios to realize faster image

Thus, the linear approach to analysis of the nonlinear spectra is limited. In addition, the single wavelength analysis of each individual molecule does not fully exploit the unique vibrational spectrum of the SAMs. Therefore, spectral unmixing approach is adopted below for improved chemical image contrast. Spectral Unmixing Reconstruction. Compressive endmember unmixing (CEU) scheme based on total variation minimization is used to reconstruct the SFG image of each component.40,52 This hyperspectral unmixing algorithm decomposes mixed pixels into a combination of pure spectra from each component, weighted by their correspondent fractions or abundances that indicate the proportion of each component in every pixel. Figure 5A has shown the contributions of ODT monolayer, which is consistent with the Figure 3D, since at 2870 cm−1, the intensity of ODT is much stronger than that of MeOHT monolayer. There is also signal between the bright bands that might come from contamination by the ODT deposited in the bare area during the microcontact process. Similarly, Figure 5B displays the same pattern as Figure 3C, suggesting the MeOHT monolayer is the dominant contribution to the SFG intensity, as shown in Figure 4A, see SI. Here, the MeOHT shows a more clear distribution between the bright bands. The MeOHT molecules may fill the gaps or defects in the patterns of microcontact printing.7,53 Figure 5C has shown color coded molecule distributions of the monolayer based on unmixing algorithm. The spatial distribution also shows that MeOHT appears in the stamped E

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Figure 6. (A)−(E) images reconstructed through CEU scheme at compressive ratio 2:1, 4:1, 8:1, 16:1, 32:1. The red color coded regions demonstrate MeOHT distribution; the green color coded regions demonstrate the ODT distribution. (F) Normalized mean square errors (NMSE) Plots for the reconstructed images at different compression ratio as (A)−(E) (see SI).

spatial and spectral components to some extent. Alternatively, nonlinear effects could be incorporated into the reconstruction algorithms. Future work will help account for these effects to allow for a clear and more quantitative image analysis.

acquisition. The image quality decreases as the compressive ratios increase from 2:1 to 32:1 as shown in Figure 6A to E. The red color coded area denotes MeOHT molecules and the green color coded area denotes ODT molecules, while the yellow area denotes mixing regions of the two components. As compression ratios increase from 2:1 to 8:1, the molecular stripe patterns are still apparent. However, as the compression ratio increases to 16:1, the stripe patterns become less welldefined. Thus, compressive sensing implies the fast imaging potential of the SFG microscope. Figure 6F has shown the normalized mean square error of the reconstruction results at different compression ratio. Both the ODT distribution image and MeOHT distribution image have shown the same trends as the compression ratio changes. It is well seen that before the compression ratio of 1:16, the NMSE is almost linear increasing as the log of the compression ratio, Figure 6. After this point the NMSE increases faster than before. NMSE quantitatively reflects the reconstructed image quality (see SI).56,57 Under current conditions the compression of up to a factor of 10:1 is reasonable and thus proportionally faster imaging speeds are achieved relative to the 100% patterns (1:1 compression). There are two major reasons the current setup cannot reach the compressive ratio as high as other reports in linear imaging of up to 32:1.18 The first is the signal/noise ratio in the SFG measurement. SFG signal is from the second-order nonlinear process, the signal is much lower than that from fluorescence or linear reflectivity. Even though compressive sensing itself has the partial denoising ability;40 the SNR is still a major factor influencing the image quality, at the low signal level. Another possible reason is that partial spatial coherence of the SFG signal from different pixels is present. This partial coherence of the SFG signal from the nearby pixels will decrease the reliability of the reconstruction results, since the reconstruction algorithm is taking the signal from each DMD pattern as linear summation of all the pixels as “on” status.40 The SFG signal still needs to be decoherent to satisfy the linear combination from different DMD blocks. Each SFG wavelength displays the partial interference at the CCD detector and thus mixes the

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CONCLUSION Spatial inhomogeneity of multicomponent monolayers is complicated both in terms of chemical composition and spatial distributions. The hyperspectral imaging of the spatial heterogeneity of the bimolecular monolayers using compressive sensing sum frequency generation vibrational spectroscopy is demonstrated here, through spatial inhomogeneous monolayers of 1-octadecanethiol (ODT) and 16-methoxy-1-hexadecanethiol (MeOHT) molecules assembled on copper surface. The SFG hyperspectral imaging cube of the monolayers has been reconstructed through 3DTV algorithm. The imaging contrasts of different vibrational modes have been well-demonstrated. With the broad-band SFG spectroscopy of each component known a priori, compressive endmember unmixing scheme is used based on total variation minimization to reconstruct the SFG contributions of each component. The spatial distribution of the MeOHT and ODT monolayer on copper surface has been well demonstrated. Both algorithms have shown the consistent imaging results. Compared to 3DTV algorithm, reconstruction from CEU has shown more information about spatial distribution of component on the surface. Though the SFG intensity is not linear to the molecular density, the SFG intensity mapping could include the molecular density and orientation information, if it has combined with linear imaging methods, the molecular orientation information could be deduced from the intensity imaging contrast. This chemical imaging of monolayers will enable new applications in studying biological systems and material systems.

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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.jpcb.7b03339. F

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Mode assignments, normalized mean square error, linear image reconstruction, SFG spectral effects on image contrast, and image reconstruction (PDF)

AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected]. *E-mail: [email protected]. ORCID

Steven Baldelli: 0000-0002-5747-259X Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors thank the W.M. Keck Foundation and NSF (CHE1610453) for support of this project.

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REFERENCES

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