Erik M. Vartiainen

Direct extraction of Raman line-shapes from congested CARS spectra.

We show that Raman line-shapes can be extracted directly from congested coherent anti-Stokes Raman scattering (CARS) spectra, by using a numerical method to retrieve the phase-information hidden in measured CARS spectra. The proposed method utilizes the maximum entropy (ME) model to fit the CARS spectra and to further extract the imaginary part of the Raman susceptibility providing the Raman line-shape similar to the spontaneous Raman scattering spectrum. It circumvents the challenges arising with experimentally determining the real and imaginary parts of the susceptibility independently. Another important advantage of this method is that no a priori information regarding the vibrational resonances is required in the analysis. This permits, for the first time, the quantitative analysis of CARS spectra and microscopy images without any knowledge of e.g. sample composition or Raman response.

Quantitative coherent anti-Stokes Raman scattering (CARS) microscopy.

The ability to observe samples qualitatively at the microscopic scale has greatly enhanced our understanding of the physical and biological world throughout the 400 year history of microscopic imaging, but there are relatively few techniques that can truly claim the ability to quantify the local concentration and composition of a sample. We review coherent anti-Stokes Raman scattering (CARS) as a quantitative, chemically specific, and label-free microscopy. We discuss the complicating influence of the nonresonant response on the CARS signal and the various experimental and mathematical approaches that can be adopted to extract quantitative information from CARS. We also review the uses to which CARS has been employed as a quantitative microscopy to solve challenges in material and biological science.

Observation of buried water molecules in phospholipid membranes by surface sum-frequency generation spectroscopy

We investigate the structure and orientation of water molecules at the water-lipid interface, using vibrational sum-frequency generation in conjunction with a maximum entropy phase retrieval method. We find that interfacial water molecules have an orientation opposite to that predicted by electrostatics and thus are likely localized between the lipid headgroup and its apolar alkyl chain. This type of water molecule is observed for phospholipids but not for structurally simpler surfactants.

Phase retrieval approach for coherent anti-Stokes Raman scattering spectrum analysis

A noniterative phase retrieval method for coherent anti-Stokes Raman scattering spectrum analysis is presented. This method facilitates the computation of the real and imaginary parts of the effective third-order susceptibility χ when only its modulus is known. One obtains this result by approximating the squared modulus |χ|2 by the maximum entropy model and using some a priori information on χ.

Numerical phase correction method for terahertz time-domain reflection spectroscopy

We propose a numerical method for the misplacement phase error correction in terahertz time-domain reflection spectroscopy (THz-TDRS). The developed algorithm is based on the maximum entropy principle and can be readily implemented into data processing, allowing one to reveal material parameters of the opaque materials from the THz reflection measurements. The method resolves the phase retrieval problem in the THz-TDRS and dramatically simplifies the experimental procedure.

Phase Retrieval in Optical Spectroscopy: Resolving Optical Constants from Power Spectra

The problem of phase retrieval appears in optical spectroscopy when a power spectrum P(ω) =|f(ω)|2 is measured while the entire complex function f(ω) = |f(ω)|exp iθ(ω) is needed for obtaining the desired material properties. Recently we proposed a new approach to solve this problem in optical spectroscopy by using the maximum entropy model. Here we give a short review of its theory and show how to improve the phase retrieval procedure to work well in practice. The usage and applicability of the procedure, especially in reflectance spectroscopy of solids, are demonstrated with practical examples. Its use in other applications is also discussed.

Spectroscopic analysis of the oxygenation state of hemoglobin using coherent anti-Stokes Raman scattering

A method for noninvasively determining blood oxygenation in individual vessels inside bulk tissue would provide a powerful tool for biomedical research. We explore the potential of coherent anti-Stokes Raman scattering (CARS) spectroscopy to provide this capability. Using the multiplex CARS approach, we measure the vibrational spectrum in hemoglobin solutions as a function of the oxygenation state and observe a clear dependence of the spectral shape on oxygenation. The direct extraction of the Raman line shape from the CARS data using a maximum entropy method phase retrieval algorithm enables quantitative analysis. The CARS spectra associated with intermediate oxygenation saturation levels can be accurately described by a weighted sum of the fully oxygenated and fully deoxygenated spectra. We find that the degree of oxygenation determined from the CARS data agrees well with that determined by optical absorption. As a nonlinear optical technique, CARS inherently provides the 3-D imaging capability and tolerance to scattering necessary for biomedical applications. We discuss the challenges in extending the proof of principle demonstrated to in vivo applications.

Phase retrieval in nonlinear optical spectroscopy by the maximum-entropy method: an application to the |χ (3) | spectra of polysilane

A method of phase retrieval from the experimental modulus |χ(3)| spectra of third-order nonlinear optical susceptibility is presented on the basis of the maximum-entropy model. This method enables one to derive the real and the imaginary parts of χ(3) without using the nonlinear Kramers–Kronig calculation, which is usually hazardous in nonlinear optical spectroscopy because of the limited range of measurements. Theoretical and experimental modulus spectra of polysilane are analyzed. The results from the experimental modulus are compared with the Kramers–Kronig calculations as well as with the measured phase values. It is also shown how the method can be optimized to reduce the distortions that result from noise in the calculated spectra.

Erratum: “Observation of buried water molecules in phospholipid membranes by surface sum-frequency generation spectroscopy” [J. Chem. Phys. 131, 161107 (2009)]

i.e., interfacial water molecules having an ori-entation opposite to that predicted by electrostatics. Sincethis type of water molecule was observed for phospholipidsbut not for structurally simpler surfactants, we concluded thatmost likely this water is localized between the lipid headgroupand its apolar alkyl chain-buried water. This conclusion wasdrawn from an analysis of Sum-Frequency Generation (SFG)spectra using the maximum entropy method (MEM),

II: Dispersion Relations and Phase Retrieval in Optical Spectroscopy

Publisher Summary This chapter discusses dispersion relations and phase retrieval in optical spectroscopy. Kramers–Kronig (KK) relations have their origin in the principle of causality and are therefore connected to fundamental physics. They have been used in data inversion of linear optical constants. The KK relations also hold in most cases of nonlinear optical spectra. The shortcoming of KK analysis is the need for data extrapolation. The maximum entropy model helps in phase retrieval problems arising in both linear and nonlinear optical spectroscopies. There is no need for data extrapolation. Sum rules provide information about the microscopic properties of systems. Sum rules of general validity can be found for linear and nonlinear optical constants. The chapter discusses the Kramers-Kronig relations appearing in linear and nonlinear optical spectroscopy. In addition, the phase retrieval in linear reflection spectroscopy and in nonlinear optics with the aid of the maximum entropy procedure is considered. The chapter also reviews mathematical methods for optical spectrum analysis.