Current methods of determining the refractive index of chemicals and materials, such as ellipsometry and reflectometry, are limited by their inability to analyze highly absorbing or highly transparent materials, as well as the required prior knowledge of the sample thickness and estimated refractive index. Here, we present a method of determining the refractive index of solutions using the photoacoustic effect. We show that a photoacoustic refractometer can analyze highly absorbing dye samples to within 0.006 refractive index units of a handheld optical refractometer. Further, we use myoglobin, an early non-invasive biomarker for malignant hyperthermia, as a proof of concept that this technique is applicable for use as a medical diagnostic. Comparison of the speed, cost, simplicity, and accuracy of the techniques shows that this photoacoustic method is well-suited for optically complex systems.
© 2013 Optical Society of America
The refractive index of a material describes the group velocity of light as it propogates through that medium. This property is highly correlated with both the density of the medium, and the absorptive properties of the medium. Using Kramers-Kroenig analysis (mathematical relationships that relate the complex and real parts of a physical system) it is possible to estimate many material properties, including refractive index. However, in recent years, the legitimacy of this analysis has been questioned for heterogenous biological materials, such as hemaglobin, due to the complex nature of the analysis . Measurement of the refractive index is based upon the fundamental Fresnel equations, which describe the refraction, reflection, and transmission of light at an interface between two media with non-matching refractive indices. In recent years, the gold standard of measurement of this property has been either reflectometry or ellipsometry, depending upon various sample properties, such as its transparency, and thickness, as well as overall cost, and the necessary data precision. However, for highly absorbing materials, partially transparent materials, or entirely unknown materials, both techniques demonstrate significant drawbacks that prevent the widespread adoption of refractive index measurements beyond typical materials characterization. Here, we explore a low cost, simple, alternative method based on the photoacoustic effect. We demonstrate that our photoacoustic method, Photoacoustic Spectroscopy/Total Internal Reflection Photoacoustic Spectroscopy (PAS/TIRPAS) refractometry, can be successfully used to determine the refractive index of both dyes, as well as a physiologically relevant concentration of myoglobin [2, 3] in phosphate buffered saline.
Reflectometry is a technique in which a polarized beam of light, operating in two linear polarizations, S and P, optically interrogates a sample. The reflected light from the sample is then measured by a photodetector. Both S and P polarizations, along with the incident angle, are recorded in order to obtain the real component of the refractive index. Equation 1 shows how the refractive index of a material is related to the reflection coefficients and angle of incidence.Equation 1 is used to determine the real part of the refractive index of a material using reflectometry methods .
1.2. Critical angle analysis
In a special case, the real component of the refractive index can be determined by measuring the critical angle, or the angle at which total internal reflection occurs. This angle can be determined using equation 7. This method simplifies the analysis of Fresnel’s equations and allows the refractive index of the sample to be found directly, if the refractive index of the substrate, n1, and the angle of incidence, θ1, are known.
Ellipsometry, a closely related technique to reflectometry, can be described with a slight alteration to Equation 1. The relative permittivity of a material, ε̃, can be found, and is directly related to the refractive index of a material by Equation 3 as explained in .
Each of these methods has limitations. Reflectometry’s main limitation lies in the fact that the technique does not take into account surface roughness or optical scattering effects. Therefore, the actual measurement of the refractive index is a combination of the optical contributions from both refractive index and surface or substrate roughness. Additionally, reflectometry typically has less success with materials that have many highly absorbing layers, due to the light being unable to be measured from being completely absorbed.
Ellipsometry has similar issues with measuring materials that are highly absorbing for the same reasons. Additionally, ellipsometry has the additional limitation of being unable to determine a single optical property independently of the thickness of a material. This can lead to erroneous results if the operator is not appropriately trained and makes incorrect assumptions or initial guesses in the curve fitting program to determine refractive index and layer thickness.
Critical angle analysis is highly accurate and inexpensive, however, it requires a prism setup which can be optically complicated and physically large. Additionally, the material of the prism must be of a larger refractive index than the sample in order for the condition for total internal reflection to be fulfilled, which poses problems for unknown samples and increases cost.
1.5. The photoacoustic effect
An alternative to all of these methods relies on the photoacoustic effect. The photoacoustic effect is generated by the absorption of light into a sample, which induces pressure in the form of an acoustic wave. The simplest equation to describe photoacoustic excitation is equation 4 from Viator et al.  that describes the pressure distribution of a generated photoacoustic plane wave. The magnitude of the resulting acoustic wave relies directly upon the optical absorption coefficient of the material.equation 5 is the optical penetration depth or measure of the distance the light travels until it decays to of its initial optical intensity. Equation 4 with various experimental techniques are used to analyze the thickness, absorption, and imaging of many materials from blood vessels to thin films. [7–12]
1.6. Total Internal Reflection Photoacoustic Spectroscopy (TIRPAS)
When the refractive index of one medium is larger than that of a second medium, Snell’s law, equation 6, shows that beyond the critical angle, θc, light is totally internally reflected back into the first medium.
When θ ≥ θc, and sinθ2 → 1
This configuration produces total internal reflection, and generates a special type of nearfield optical effect called the evanescent field. The evanescent field can be perturbed to reduce the reflected coefficient of light if a sample material of appropriate optical absorption or scattering is sufficiently near the field. This type of frustrated total internal reflection is the basis of many characterization systems including attenuated total reflectance .
Recently, a method of generating a photoacoustic response from optical absorption through a pulsed evanescent field was rediscovered by Goldschmidt et al. [14, 15], who used the technique in conjunction with modern lasers to improve the method’s sensitivity. This technique is graphically demonstrated in Fig. 1. The method has been used successfully to detect β -hematin to demonstrate the technique’s potential as a new type of biosensor .
In the 1980’s, this technique [16–26] was explored as an alternative method to photoacoustic spectroscopy, due to total internal reflection photoacoustic spectroscopy’s (TIRPAS) ability to determine information about materials at an interface. This type of information was never achievable with normal incidence photoacoustic spectroscopy (PAS), due to the generally large optical penetration depth obtained with low absorption materials using the PAS method as can be seen in Fig. 2. TIRPAS was used to determine dye adsorption properties at a glass/solution interface for interfacial phenomena studies as part of a cyclic voltammetry project.
The excitation of the photoacoustic effect using TIRPAS is fundamentally different than that by typical PAS experiments due to the fact that the evanescent field is interacting with absorbers close to the interface as opposed to the photoacoustic effect being excited by propagating photons through normal incidence. This type of excitation limits the optical penetration depth to the penetration of the evanescent field which is nearly always much less than the optical penetration depth of propagating photons through a typical material. The evanescent field component in polarization parallel to the optic is given by Equation 8 which comes from Equation 9 and Equation 10, as presented by Muessig et al. .14]. The penetration depth shown in Equation 11 describes the point at which the non-propagating evanescent field decays to of its original intensity. This distance can be roughly used as the depth that can be analyzed with the photoacoustic effect in TIRPAS.
1.7. Surface Plasmon Resonance Photoacoustic Spectroscopy (SPRPAS)
Another method, related to TIRPAS, was explored in the early 1980s that used the resonant effect of surface plasmons to induce a photoacoustic effect for the detection of materials at an interface as well. Several groups [27–43] used this approach to understand the technique and to detect various materials, such as nicotine, and various gases of interest. The optical setups varied significantly, however, these methods generally used a laser pulse not meeting the excitation requirement for thermal confinement in the samples of interest. The entire systems were enclosed in photoacoustic cells for the detection and characterization of materials with properties related to and including refractive index. This technique, however, differs from TIRPAS in that TIRPAS uses pulsed laser light which interacts with a sample directly by the evanescent field. The related surface plasmon technique uses the generated evanescent field with an intervening metal layer to generate surface plasmons for detection of materials adsorbed on the surface of the metal layer.
1.8. PAS/TIRPAS refractometry
PAS/TIRPAS refractometry is a new technique that combines the advantages of both the photoacoustic effect and the evanescent field to determine the refractive index of materials. It should be noted that a similar, but more computationally and physically complicated non-thermally confined photoacoustic refractometry technique was accomplished in the early 1990s. In that case, researchers relied upon the analysis of resonant optical modes in Langmuir-Blodgett films [44–47] and were able to produce refractive index estimates on the order of 0.01. In traditional reflectometry, light is measured after its interaction with a sample in two linear polarization states to determine refractive index. In PAS/TIRPAS refractometry, a laser beam is scanned across a sample at changing angles of incidence to collect acoustic waves from both the PAS and TIRPAS regimes, as well as any location inbetween. This experiment allows for the direct observation of the light-induced acoustic wave, which changes drastically in peak to peak voltage between the PAS and TIRPAS regimes. This was shown experimentally in previous data from Goldschmidt et al. , and can be physically shown to be different by Fig. 2. The drastic change in peak to peak voltage can be easily explained by comparing equations 5 and 4 with equation 11 which for typical values gives an order of magnitude or more difference in photoacoustic pressure.
Here we demonstrate a simple, robust technique based upon the large changes in optical penetration depth for the determination of the real component of the refractive index of dyed liquids and the biologically relevant material, myoglobin, for potential disease detection.
2. Materials and methods
2.1.1. Direct Red dye 81 solutions
The dye solutions were made with a 50% polyethylene glycol (PEG, m.w. 200) 50% H2O solution along with the dye at 125, 250, 500, and 750 μg/ml respectively. The PEG was added in order to shift the refractive index closer to the middle range of the ATAGO R-5000 refractometer to provide easier measurement and comparison with the PAS/TIRPAS refractometer. Each solution was mixed for at least 5 minutes before testing using a hot plate/stirrer (Corning PC 220). The mixing directly preceeded each test to reduce the effects from dye settling on the prism surface.
2.1.2. Myoglobin solution
The myoglobin solution was made by mixing 460 μg of dry horse skeletal myoglobin (Sigma Aldrich #M0630-250MG) per 1 ml of phosphate buffered saline (Fisher #BP2438-4). As with the dye solutions, the myoglobin was mixed for at least 5 minutes before testing using a hot plate/stirrer. The myoglobin solution did not have added PEG to it since the refractive index was within the readable scale on the handheld refractometer.
2.2. PAS/TIRPAS refractometer
The device, shown in Fig. 3, works on the principle of exciting a photoacoustic effect in the sample at different angles of incidence. The samples were interrogated with vertically polarized 532 nm laser light generated by a Q-switched Nd:YAG laser (Surelite I-20 Continuum). The acoustic signal was detected using a 15 MHz transducer with a 1” focal length (Olympus #U8472001).
2.2.1. Laser leveling
The PAS/TIRPAS holder was leveled relative to the optical table by a Micromark digital level (Micromark #: 84519). The interrogating laser beam was leveled relative to the table as well by a setup similar to a Michaelson interferometer except that the output of the setup was placed on a flourescent card where the two beams could be made coincident to level the beam. Thorlab’s mirrors, a beam splitter, and cage system connectors were used to create this setup (Thorlabs #: CM1-BS013 and #: PF10-03-G01). The PAS/TIRPAS refractometer was aligned by viewing the incident and reflected spots on a sheet of fluorescent paper and adjusting the incident reflected laser to overlay it on that of the reflected beam.
2.2.2. Labview automation
A Sherline stepper motor XY base (Sherline 5200-CNC) was used, along with a 4” rotary table (P/N 8700), right angle attachment (P/N 3701), and 3-jaw chuck (P/N 1041) to hold and position the rotational mount made of a prism and custom machined PTFE rodstock. The rotary table was controlled by Labview. The angular spectrum settings were set to scan a range of angles where the critical angle was initially assumed to be. The Labview program stepped the motor at 0.01 degree increments across the entire range of angles. At each increment, the Labview program measured as stated the photoacoustic wave’s peak to peak voltage.
2.2.3. Data analysis
The angular spectra were analyzed by taking the derivative of the angular spectrum data to find the local minima corresponding to the reduction in photoacoustic signal amplitude. The process of taking the derivative of the angular spectrum data produced fairly noisy graphs that needed further data smoothing to correctly determine the critical angle. Kaleidagraph 4.1.0 was used with the smooth curve fit function to smooth the data so that the critical angle could be extracted from the data. This smooth curve fit function is based upon a combination of Stineman interpolation  combined with a weighting structure to smooth the data. The exact formula is described further in the appendix.
2.2.4. PAS/TIRPAS measurement
First, the laser beam was leveled using the technique described in section 2.2.1. Next, the sample holder was filled with sample liquid and the sample holder was leveled using the Micromark digital level by balancing the level on the unconnected acoustic sensor which was previously inserted into the sample holder. Finally, the Labview software described in section 2.2.2 was used along with the Sherline stepper motors to obtain the angular spectrum scan of the sample material. The angular scan was then used to determine the critical angle as explained in section 2.2.3.
2.3. Optical refractometer measurement
We used an ATAGO R-5000 refractometer along with a 532 nm line filter (Thorlabs #: FL532-10) and a polarizing beam splitter cube (Thorlabs #: CM1-PBS251) to limit the polarization and wavelengths measured to find the refractive index of the samples for comparison with our PAS/TIRPAS refractometry technique as shown in Fig. 4.
A typical result from the dye is shown in Fig. 5(a) and demonstrates a clear transition in photoacoustic peak to peak voltage at approximately 66 degrees. The derivative of the angular spectrum data was taken along with smoothing to obtain a more precise measurement of the transition as demonstrated by the arrow in Fig. 5(b). Figure 5(c) shows a second smoothing applied to the data in order to obtain the minima corresponding to the critical angle without shifts due to noise. Finally, it is straightforward to determine the critical angle from finding the minima in Fig. 5(d).
In order to demonstrate the utility of PAS/TIRPAS refractometry, we compared the results obtained with optical reference measurements with the ATAGO R-5000 refractometer setup. We show agreement between the two techniques to 0.006 refractive index units between the samples’ refractive index values using PAS/TIRPAS refractometry and the ATAGO R-5000 refractometer as shown in table 1.
As was shown in our results section, PAS/TIRPAS refractometry is an accurate and precise alternative to ellipsometry and reflectometry. Every dye solution’s refractive index measurement fell within the measurement range of the handheld refractometer. In the case of the Direct Red, 750 μg/ml, the sample-to-sample variability seemed to be more significant (0.005) than the other dyes. We believe this was due to dye settling over time. The myoglobin concentration seemed to have some divergence from the measured value with our handheld refractometer, however, this variability can be explained by the lower signal-to-noise ratio as shown in Fig. 6. However, variability of 0.006 is still fairly reasonable compared to the differences between reflectometry and ellipsometry for many materials and therefore this is not significant for our current demonstration of the technique’s capabilities. Therefore, PAS/TIRPAS refractometry has the capability to analyze both dyes and a biologically relevant analyte, myoglobin, for potential biosensing and biomedical monitoring. Our technique opens up significant potential for biomedical monitoring and adsorption state monitoring through the refractive index at a sample/prism interface.
Plane waves are acoustic waves that deliver most of their energy in a forward and backward direction. The initial pressure rise due to these waves can be described by equation 4. In order to obtain plane waves in photoacoustics the following equation must be satisfied: where d is the laser beam diameter and z is the acoustic near field/far field boundary as discussed by Viator . In the PAS regime this is generally followed since the pigment of the dyes combined with the low penetration depth along with the geometry of the incoming beam create these conditions. However, with myoglobin, the solution is much more transparent and therefore, plane waves are not necessarily always obtained at every angle of incidence. In the TIRPAS regime, plane waves are always obtained due to the penetration depth of the optical radiation being so small compared to the relative size of the beam, 500 nm vs. 1 mm beam size or more. This can create issues when peak to peak voltage is compared in the PAS and TIRPAS regimes since it is possible for the TIRPAS regime to have similarly sized peak to peak voltage as the PAS regime, despite the PAS regime having more optical penetration depth due to the differences between comparing plane waves in the TIRPAS regime to non-plane waves in the PAS regime. Our data with myoglobin shown in Fig. 6 suggest that this had an effect on our refractive index resolution since the acoustic waves from the PAS region with myoglobin do not show the typical plane wave configuration due to the low concentration of myoglobin used. An alternative method based upon integrated pressure may be more appropriate in the future.
Beyond the peak to peak differences, the two signals’ relative shapes are worth mentioning. The myoglobin wave’s complex shape comes from the fact that a cylindrical segment of sample is being excited that is giving rise to the acoustic wave. First, since angles of incident light smaller than the critical angle are used for the PAS regime, there is an effectively planar wave generated for both Direct Red and myoglobin when the refracted light transfers into the sample region at an angle close to 90 degrees from normal to the interface. This effect is due to the fact that the optical penetration depth is limited since the light is traveling nearly perpendicular to the sample/prism interface. However, at angles of incidence further away from the critical angle in the PAS regime, as shown in Fig. 6, the myoglobin’s signal starts to resemble a wave with more acoustic diffraction due to larger boundary waves being generated from the laser pulse incident at a lower angle of incidence from normal to the interface.
As can be seen from table 2, PAS/TIRPAS refractometry should have several uses for materials that are heavily opaque with unknown optical properties. This suggests the use of PAS/TIRPAS refractometry with metals as well as less homogenous materials for quick and simple critical angle analysis. PAS/TIRPAS refractometry has two major advantages over current methods that include the ability to analyze deeply opaque materials along with a true single wavelength determination of the refractive index without the need for complex model fitting needed for other techniques.
PAS/TIRPAS refractometry has shown promise in its ability to determine refractive index values for myoglobin at a diagnostically relevant concentration. This opens the technique to biological monitoring of myoglobin levels before and after surgery to aid doctors in the diagnosis of potential renal problems occurring from the accumulation of myoglobin after acute hyper-thermia or myocardial infarction. In addition, PAS/TIRPAS refractometry, if combined with an automated syringe pump, could be used for the monitoring of levels of important biological analytes in blood, urine, and for the determination of binding kinetics similar to surface plasmon resonance.
We have demonstrated a new photoacoustic technique that can be used in place of ellipsometry and optical reflectometry for the determination of the real part of the refractive index of liquid solutions. Additionally, we have demonstrated the refractometer’s capability to determine the refractive index of myoglobin at a diagnostically relevant concentration. This new technology has been shown to complement standard technologies such as ellipsometry and reflectometry for future biomedical testing.
6. Appendix 6.1. Stineman smoothing algorithm from Kaleidagraph 4.1.0
The smoothing function in Kaleidagraph’s software is based upon a combination of the Stineman interpolation method  with a weighting function. The step by step method is given below:
- Fit the Stineman interpolation function to the data.
- Apply a weighting function to the data to smooth the curve.
An array is then created using the following code:
The authors would like to acknowledge Bobbi J. Hauptmann and Ronald G. Phillips of the Boone County Lumber Building Technology Laboratory within the Department of Architectural Studies at the University of Missouri-Columbia for technical assistance. The authors would like to acknowledge Gordon Ellison for machining the components and for his design expertise. The authors would like to acknowledge Professor Teruo Hinoue for his email correspondence about the history of TIRPAS development. This research was funded in part by a National Science Foundation BRIGE Award ( 1221019). We thank Christine Brethorst for her assistance in performing experiments and analysis of this work
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