Superresolution vibrational imaging by simultaneous
detection of Raman and hyper-Raman scattering
Korenobu Matsuzaki,1Rintaro Shimada,1and Hiro-o Hamaguchi1,2,*
1Department of Chemistry, School of Science, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan 2Institute of Molecular Science and Department of Applied Chemistry, National Chiao Tung University,
1001 Ta Hsueh Road, Hsinchu 300, Taiwan *Corresponding author: [email protected]‐tokyo.ac.jp
Received March 31, 2011; revised June 4, 2011; accepted June 6, 2011; posted June 7, 2011 (Doc. ID 145139); published July 1, 2011
We have developed a superresolution vibrational imaging method by simultaneous detection of Raman and hyper-Raman scattering. Raman and hyper-Raman images obtained with the same laser spot carry independent information on the sample spatial distribution, owing to different signal dependence (linear in Raman and quadratic in hyper-Raman) on the incident light intensity. This information can be quantitatively analyzed to recover the incident light intensity distribution at the focal plane. A superresolution vibrational image is then derived by the constrained deconvolution of the images by the obtained incident light intensity distribution. This method has been applied to a TiO2nanostructure and the obtained superresolution image was compared with a scanning
electron microscopy image. The spatial resolution achieved by the present method is evaluated to be 160 nm, which is more than twice better than the diffraction limited resolution. © 2011 Optical Society of America
OCIS codes: 100.1830, 100.6640, 180.5655, 300.6330.
Spatial resolution beyond the diffraction limit (superre-solution) has always been a challenge in microscopy and microspectroscopy. Superresolution enables us to study the fine structures that are not accessible by con-ventional microscopy. In the past decade, superresolu-tion techniques such as stimulated-emission-deplesuperresolu-tion
microscopy [1,2], stochastic optical reconstruction
mi-croscopy (STORM) [3], and deconvolution microscopy
[4] have been developed based on fluorescence
micro-scopy. There has also been an attempt to achieve
super-resolution in Raman microscopy [5]. In this Letter, we
report on a novel superresolution technique based on Ra-man and hyper-RaRa-man microspectroscopy. It can provide us with a superresolution image by a single measurement in which Raman and hyper-Raman images are acquired simultaneously. Separate measurements of the standard
samples, such as polystyrene beads [5], are not required.
Raman microspectroscopy is the combination of microscopy with Raman spectroscopy. It enables us to study the chemical composition and its distribution in a sample under a microscope, on the basis of vibrational spectroscopy. The spatial resolution of Raman micro-spectroscopy is diffraction limited; when the excitation wavelength is 755 nm and the NA of the objective lens is 1.30, as in the case of the current study, the
diffrac-tion limited spatial resoludiffrac-tion is 0:61λ=NA ¼ 350 nm [6].
Hyper-Raman microspectroscopy [7], on the other hand,
is the combination of microscopy with hyper-Raman
spectroscopy [8]. Hyper-Raman spectroscopy is a
two-photon excited analog of Raman spectroscopy that detects a new radiation generated near the second har-monic of the incident laser light. Since hyper-Raman scat-tering is a two-photon excited process, its intensity scales quadratically to the incident light intensity. Owing to this nonlinearity, hyper-Raman microspectroscopy achieves spatial resolution superior to Raman microspectroscopy
by a factor ofpffiffiffi2[9]. Nonetheless, it cannot be made
sig-nificantly better than the diffraction limit.
We here show that the diffraction limit can be over-come by combining Raman microspectroscopy with
hyper-Raman microspectroscopy. Since Raman and hyper-Raman scattering intensities have different depen-dence on the incident light intensity, resulting Raman and
hyper-Raman images show different extent of “blur”.
Through the combined analysis of these two differently blurred images, we can determine the incident light in-tensity and the true distribution of sample molecules. That is to say, we can achieve superresolution by quan-titatively comparing Raman and hyper-Raman images. This is the principle of the present method.
Raman and hyper-Raman images obtained by raster scanning can be expressed in the incoherence limit [10] as
R ¼ χ I; H ¼ χ I2; ð1Þ
where Rðx; yÞ and Hðx; yÞ are Raman and
hyper-Raman images, respectively, χðx; yÞ and Iðx; yÞ are the
sample distribution and the incident light intensity on
the focal plane, respectively, and asterisks () denote
two-dimensional convolution. Coordinates ðx; yÞ have
been omitted from the equations for simplicity. In the
second equation, I2ðx; yÞ is used instead of Iðx; yÞ
be-cause hyper-Raman scattering intensity is proportional to the square of the incident light intensity. Our goal is
to determineχðx; yÞ as accurately as possible. In this
for-mulation, we took only the two-dimensional structure of the sample into account. This simplification is valid if the sample is thinner than the focal depth of the objective lens, as in the case of the current experiment.
First, we determine the incident light intensity Iðx; yÞ
by eliminatingχðx; yÞ from Eqs. (1). This can be done by
convolvingI2ðx; yÞ to the first equation and Iðx; yÞ to the
second equation:
R I2¼ H I ¼ χ I I2: ð2Þ
In principle, Iðx; yÞ can be obtained by solving this
equation. However, this equation is ill-posed and cannot
July 1, 2011 / Vol. 36, No. 13 / OPTICS LETTERS 2545
be solved as it is. If we try to do so, the solution will be contaminated by artifacts arising from the noise present
in Rðx; yÞ and Hðx; yÞ, and the solution will eventually
converge toIðx; yÞ ¼ 0. In order to avoid this, we
intro-duce Tikhonov regularization [11]; we obtain Iðx; yÞ by
solving the following least squares problem:
ε ¼ jR I2− H Ij2þ γjI − I
0j2: ð3Þ
Here, γ is the regularization parameter, which is
deter-mined by the L-curve method [12], and I0ðx; yÞ is an
approximated solution to Eq. (2) obtained under the
as-sumption that Iðx; yÞ can be expressed by a Gaussian
function. A Gaussian function was chosen because
Eq. (2) readily yields an analytical solution ifIðx; yÞ is
a Gaussian. By solving the least squares problem under
the nonnegative constraint (Iðx; yÞ ≥ 0) using the
gradi-ent projection method [13],Iðx; yÞ can be obtained.
Next, we determine the sample distributionχðx; yÞ by
the deconvolution ofRðx; yÞ and Hðx; yÞ. Theoretically, it
is sufficient to use only one of the equations in Eqs. (1) to
obtainχðx; yÞ. However, we found that, by using both of
the equations simultaneously for deconvolution, better spatial resolution can be achieved because the noise
pre-sent inRðx; yÞ and Hðx; yÞ can be efficiently suppressed.
This simultaneous deconvolution can be implemented by the following least squares problem:
ε ¼ jR − χ Ij2þ jH − χ I2j2þ γjχj2: ð4Þ
Here, first two terms are for the deconvolution ofRðx; yÞ
andHðx; yÞ, and the last term is for Tikhonov
regulariza-tion. As in Eq. (3),γ is the regularization parameter and is
determined by the L-curve method [12]. Furthermore,
nonnegative constraint (χðx; yÞ ≥ 0) is imposed on
χðx; yÞ. Solving this least squares problem by the gradient
projection method [13], sample distributionχðx; yÞ can
be determined, with spatial resolution beyond the diffrac-tion limit.
In order to use the procedure given above, Raman and hyper-Raman images must be obtained simultaneously
using the common Iðx; yÞ. This was done by a
labora-tory-made simultaneous Raman and hyper-Raman
micro-spectroscopic imaging system (Fig. 1). The excitation
light source is a picosecond mode-locked Ti:sapphire os-cillator (755 nm, 3 ps, 82 MHz) pumped by a cw 532 nm
Nd:YVO4 laser. Average power at the sample position
is adjusted to 20 mW by a variable neutral density filter. The excitation light is introduced into an inverted micro-scope, and is focused onto the sample by an objective
lens (40×, NA 1.30). Raman and hyper-Raman scattering generated at the focal position is collected by the same objective lens in the backscattering configuration. Ra-man scattering is separated from the excitation light by a laser line filter and two edge filters, introduced into a polychromator via optical fiber, dispersed in the polychromator, and detected by a CCD camera. Hyper-Raman scattering is separated from the incident light by a dichroic mirror and a color glass filter, dispersed in a polychromator, and detected by a CCD camera. The sample stage is equipped with a piezo stage, and the sample can be raster scanned to give Raman and hy-per-Raman images simultaneously. Laser output and the intensity of the second harmonic generated by a beta-barium borate crystal are monitored inside the
autocor-relator in Fig. 1throughout the imaging experiment, in
order to make corrections to the intensities of Raman and hyper-Raman scattering, respectively. This allows us to eliminate the effect of laser intensity and pulse duration fluctuation.
The sample used in the present study was a TiO2
na-nostructure prepared by etching a TiO2 (anatase) thin
film on a glass plate by photolithography. Its thickness was 170 nm. The film showed an isotropic polarized mi-croscope image in crossed-Nichol configuration, indicat-ing that it comprises randomly oriented nanocrystals. Raster scan imaging was done within the area of 4 μm × 4 μm by 70 nm pitch point-by-point measurements (57 points × 57 points). Exposure time was 3 s for each sample point, and the total acquisition time for Raman and hyper-Raman images was 3 h.
Figure 2 shows Raman and hyper-Raman spectra of
anatase-type TiO2. All of the observed bands are assigned
to the lattice vibrations of anatase-type TiO2 [14,15]. By
using the Raman band at 144 cm−1 and the broad
hyper-Raman band centered at 850 cm−1, Raman and
hyper-Raman images were obtained as in Figs.3(a)and 3(b).
The direction of they axis was chosen so that it coincides
with the polarization direction of the incident light elec-tric field. Through the procedure described above, the incident light intensity distribution was first determined
[Fig. 3(c)], followed by the superresolution image
[Fig. 3(d)]. From the comparison with the observed
Raman and hyper-Raman images, we can easily see the
improvement of the spatial resolution in Fig. 3(d).
Figure 3(e) shows the scanning electron microscopy
(SEM) image of the sample.
To evaluate the improvement of spatial resolution quantitatively, intensity cross sections along the dotted
Fig. 1. (Color online) Simultaneous Raman and hyper-Raman microspectroscopic imaging system.
Fig. 2. (Color online) (a) Raman and (b) hyper-Raman spectra of anatase-type TiO2.
lines indicated in Figs. 3(a),3(b),3(d), and3(e)are
ex-amined (Fig.4). Assuming that the SEM image shows the
true shape of the sample and the degradation of the spa-tial resolution can be expressed by a Gaussian function,
each of the cross sections in Fig.4are fitted by the
con-volution of a Gaussian and the SEM cross section, and the spatial resolution is obtained as the FWHM of the Gaussian. The spatial resolution determined in this man-ner was 620 nm for the Raman image, 390 nm for the hy-per-Raman image, and 160 nm for the superresolution image. As is stated above, the diffraction limited spatial resolution of the current system is 350 nm, and we have succeeded in achieving a spatial resolution more than twice better than the diffraction limited resolution.
Although we were able to achieve superresolution, we failed to reproduce the uniformity of the sample
thick-ness, as can be seen in the SEM image [Fig. 3(e)]. This
failure probably comes from the fact that we have naively
assumed in Eqs. (1) that Raman and hyper-Raman
scat-tering intensity is always proportional to the quantity of the sample, which is not true when, for example,
the crystal axis is not in the same direction everywhere inside the sample. From the viewpoint of examining sam-ple morphology, this fact limits the present method but it contains extra information, for example, on crystal orien-tation that SEM can never provide. Thus, the current method is complementary with SEM and other scanning microscopy methods.
In conclusion, we have developed a superresolution vi-brational imaging method based on simultaneous detec-tion of Raman and hyper-Raman scattering. This is a unique superresolution technique that provides us with both detailed molecular information characteristic of vibrational spectroscopy and sub-diffraction-limited spa-tial resolution of 160 nm at the same time, through in situ and noninvasive measurement without any pretreat-ments. This method will open up new possibilities for studying detailed molecular properties of microstruc-tures that have not, so far, been accessible by existing fluorescence superresolution techniques.
The authors acknowledge Prof. Tetsuya Hasegawa and Prof. Yasuo Wada for their help in sample preparation. Part of this study was conducted with support from the Toyo University Nanotechnology Network, which is part of the Nanotechnology Network Japan by the Ministry of Education, Culture, Sports, Science and Technology.
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Fig. 3. (Color online) (a) Raman and (b) hyper-Raman images of the TiO2standard sample, (c) incident light intensity distri-bution, (d) superresolution, and (e) SEM images of the TiO2 standard sample.
Fig. 4. (Color online) Intensity cross sections of Raman, hyper-Raman, superresolution, and SEM images along the dotted lines in Fig.3.
