Reports: UR649348-UR6: Measurement of the Refractive Index of Highly Turbid Media

Samir Bali, Miami University

The total number of refereed articles published by my group since July 2010, that acknowledge financial support by this PRF grant, is SEVEN, three in 2010, and two apiece in 2011 and 2012.

It is important to emphasize that this grant enabled me to provide excellent one-on-one mentoring to undergraduate and Master's students at Miami University. This has resulted in twenty-four appearances by Miami undergraduates as co-authors with me on the refereed publications mentioned below. These undergraduates made eleven research presentations themselves at international and regional meetings. One of these was an invited talk given by my student Kashi Goyal at the premier annual international meeting of the American Physical Society for Atomic, Molecular and Optical Physics (DAMOP). She was one of only six undergraduate students nationwide to present at DAMOP's Undergraduate Research Symposium. All Kashi's expenses were paid by DAMOP. Besides this invited talk, there were two other talks given by my undergraduates at Frontiers in Optics (FiO), which is the premier annual international conference of the Optical Society of America. The remaining eight presentations by the undergraduates were posters.

Similarly, for Masters' students, there have been eight appearances as co-authors on refereed publications, and they have made two research poster presentations by themselves at DAMOP.

In 2012 the PI was honored to be selected for the research described above as one of four researchers of 184 grant awardees to be featured in "Researcher Stories" at the site of the Annual Report on Research 2011 from the American Chemical Society Petroleum Research Fund. A detailed interview with the PI, along with lab photos is posted on the ACS website at

Our interest is in optical sensing of turbid media, for applications in accurate, non-invasive, in-situ sensing of petroleum samples. Turbid media refer to disordered, or random, media such as a colloidal suspension that generate extensive multiple scattering of the incident light thereby acquiring a "milky" hue and becoming nontransparent.

As stated in the original proposal, we proposed to demonstrate a first real-time simultaneous measurement of the real and imaginary parts of the refractive index of a highly turbid medium – this had eluded researchers despite receiving considerable attention over the past several decades. The real part describes the "usual" bending of the light ray at the interface, while the imaginary part is directly related to the attenuation owing to scattering and/or absorption of the beam in the turbid sample.  

In our 1st paper, published in Optics Letters in 2010, we made important progress toward accomplishing this goal. We achieved this by observing the real-time reflectance profile of a divergent laser beam incident on the surface of the turbid medium. In this paper, not only did we measure the reflectance data in unprecedented detail around the critical angle region, we also proposed a novel empirical model for total internal reflection (TIR) in turbid media that enabled us to fit the TIR data better than any existing models.

This paper elicited a Comment from a prolific Finnish group that had been working on this problem for many years. They pointed to oscillations in our data, and raised doubts about the appropriateness of our model for describing such data. We published a Reply to this Comment in Optics Letters in 2011, in which we provided new insights into total internal reflection (TIR) from turbid media. We showed that there are not one but two oscillations in the data, depending on whether the particle size is less than or more than the laser wavelength. Because this Reply showed new experimental data, and required new analysis, and was selected by the editors of Optics Letters for the Virtual Journal of Biomedical Optics, we count this Reply as our 2nd paper.

Next, for our 3rd paper, we applied our newly proposed methodology toward an accurate measurement of the complex refractive index of milk and milk-cream mixtures. We published our results in Journal of Dairy Science in 2010.

For our 4th paper, published in 2012 in Reviews of Scientific Instruments, we decided to critique the most widely used method of refractive index measurement for turbid media, the so-called method of "differentiation". It had long been known that this method has errors, but the consensus amongst scientists was that these errors are a) small, and b) could be calculated in advance and eliminated if necessary. We proved that both of these suppositions are abjectly false.

According to the Journal of Citation Reports, Optics Letters is the 3rd most cited out of 79 refereed journals in the field of "Optics", and is the 7th highest in its 5-year impact factor (3.4). The Journal of Dairy Science is the top most journal out of 55 refereed journals in the field of "Agriculture, Dairy and Animal Science" in total number of citations, and is the 2nd highest in 5-year impact factor (2.9). Reviews of Scientific Instruments is the 2nd most cited out of 58 journals in the category Instruments and Instrumentation, and has a 5-year impact factor 1.75.

In addition, we published three more experiments: The first work is in Laser Physics Letters in 2010. According to Journal of Citation Reports Laser Physics Letters has the highest impact factor of all (9.97) out of 58 journals in the category Instruments and Instrumentation. In this work we measured light-induced atomic energy-level shifts in laser-cooled Rubidium atoms. The second and third works were published in American Journal of Physics, in 2011 and 2012.  American Journal of Physics is the topmost education journal in Physics, and the 3rd most cited out of 33 journals in education across all scientific disciplines. In these works we uncover subtle yet important fundamental aspects of laser-atom interaction via cutting-edge demonstrations suitable for the advanced undergraduate laboratory. I am indebted to the Petroleum Research Fund for enabling us to purchase equipment for the refractive index sensing lab that is freely shared with our other lab.

In summary, we made significant progress toward the goals outlined in the proposal while also engaging undergraduates in the science of discovery.