Speedy Surface Explorations with Principal Component Analysis

• Abstract
• Full Text HTML
• Hi-Res PDF[412 KB]
• PDF w/ Links[86 KB]

• Figures
• Citing Articles

Surface chemistry is involved in a wide range of important biological interactions, such as those on cellular membranes, as well as in industrial and pharmaceutical applications—yet probing the subtle structural qualities of surfaces has remained a challenge. But now, in a new AC paper (DOI 10.1021/ac901832u), Nathan Begue and Garth Simpson of Purdue University combine a technique called nonlinear optical Stokes ellipsometry (NOSE), which can acquire data rapidly, with an equally speedy analysis method that merges linear curve fitting with principal component analysis (PCA); this overall approach can quickly decipher subtle characteristics of surfaces with unprecedented precision.

Nonlinear optical ellipsometry offers a unique approach for polarization-dependent surface analysis that may add information beyond that from nonlinear optical imaging techniques that rely on signal intensity alone. Ellipsometry data can be converted into tensor elements that describe in detail the nonlinear optical properties of a sample and provide structural insight. Yet limitations such as the need to physically adjust samples and optical elements to maintain sign and phase information have limited the method’s applicability.

The development of NOSE, an extension of the nonlinear optical ellipsometry technique, allowed, for the first time, lightning-fast measurements without the need for physical movement. This shifted the bottleneck from data acquisition to analysis; it still required onerous nonlinear fitting approaches. The new method described in Begue and Simpson’s paper provides faster data analysis by turning a nonlinear problem into a linear one.

The researchers first validated the new method on a Z-cut quartz crystal, which has well-characterized nonlinear optical properties with respect to rotation angle. The experimental setup involved directing a time-varying polarization state of light at the sample from an ultrafast laser; 80 initial polarization states were generated. Then, the nonlinear elements from second harmonic generation—light with double the initial frequency—were collected on two orthogonal detectors.

“What we’ve done in this work is developed methods to do some of the most precise polarization analysis we can conceive of for second harmonic generation,” says Simpson. “When you increase the precision, you increase the information content.”

The crystal was examined with several different rotation angles, and then the data was analyzed using both nonlinear and linear methodologies to determine which method could better back-calculate the rotation angles. “From tracking the polarization changes, we can extract five parameters” using the linear analysis, says Simpson. “These parameters are related to the tensor elements, which are in turn related to the nonlinear optical properties of the surface.” The linear methodology in combination with PCA outperformed the nonlinear curve-fitting methodology, not only by speed of analysis, but also in terms of the precision of the crystal’s back-calculated rotation angle.

“I think this is really good because usually when you gather signal in nonlinear optical detection and you want to reduce to a structure, you have to apply nonlinear fitting. That type of fitting is not very easy and is time consuming,” says Zhan Chen of the University of Michigan Ann Arbor.

In a more challenging test of the method, Begue and Simpson collected data from four monolayer dye films and analyzed it with PCA. The four dyes are very similar in structure—all are achiral charge-transfer dyes. NOSE traces of incident polarization versus signal intensity appear similar among the dyes, but a comparison in principal component space reveals a clear separation.

“By using PCA and applying it to the new technique, they’ve made the method more accessible,” says John Conboy of the University of Utah. “Doing nonlinear regression on a dataset has inherent problems. The use of PCA has found fruit in analytical chemistry and allows you to reduce your data to the important things and pull those things out.”

Simpson intends to use the method to study crystal polymorphs, which occur if a molecule orients itself in multiple arrangements in a lattice and can be difficult to rapidly detect. “Polymorph screening is routinely done in pharmaceuticals to determine all the polymorphs that can exist under reasonable conditions,” notes Simpson. “These methods are fantastic for selectively identifying subtle differences in data sets. If that’s the question you want to ask, then this is the toolkit for doing it.”

“I think this is an excellent paper,” says Chen. “They are trying to develop a data analysis method to make this kind of tool as friendly as possible and also provide some unique information that other techniques cannot not provide to understand important problems.”

Citing Articles

View all 1 citing articles

Citation data is made available by participants in CrossRef's Cited-by Linking service. For a more comprehensive list of citations to this article, users are encouraged to perform a search in SciFinder.

SciFinder Links

• Get Reference Detail
• Get Citing