Quantitative, Comparable Coherent Anti-Stokes Raman Scattering (CARS) Spectroscopy: Correcting Errors in Phase Retrieval

Abstract: Coherent anti-Stokes Raman scattering (CARS) microspectroscopy has demonstrated significant potential for biological and materials imaging. To date, however, the primary mechanism of disseminating CARS spectroscopic information is through pseudocolor imagery, which explicitly neglects a vast majority of the hyperspectral data. Furthermore, current paradigms in CARS spectral processing do not lend themselves to quantitative sample-to-sample comparability. The primary limitation stems from the need to accurately measure the so-called nonresonant background (NRB) that is used to extract the chemically-sensitive Raman information from the raw spectra. Measurement of the NRB on a pixel-by-pixel basis is a nontrivial task; thus, reference NRB from glass or water are typically utilized, resulting in error between the actual and estimated amplitude and phase. In this manuscript, we present a new methodology for extracting the Raman spectral features that significantly suppresses these errors through phase detrending and scaling. Classic methods of error-correction, such as baseline detrending, are demonstrated to be inaccurate and to simply mask the underlying errors. The theoretical justification is presented by re-developing the theory of phase retrieval via the Kramers-Kronig relation, and we demonstrate that these results are also applicable to maximum entropy method-based phase retrieval. This new error-correction approach is experimentally applied to glycerol spectra and tissue images, demonstrating marked consistency between spectra obtained using different NRB estimates, and between spectra obtained on different instruments. Additionally, in order to facilitate implementation of these approaches, we have made many of the tools described herein available free for download.