Calibration of fiber optic based surface plasmon resonance sensors in aqueous systems

Analytica Chimica Acta 515 (2004) 291–302

Calibration of fiber optic based surface plasmon resonancesensors in aqueous systems

Darcy J. Gentleman, Louis A. Obando, Jean-Francois Masson,John R. Holloway, Karl S. Booksh∗

Department of Chemistry and Biochemistry, Arizona State University, Tempe, AZ 85287-1604, USA

Received 8 October 2003; received in revised form 15 March 2004; accepted 23 March 2004

Available online 28 May 2004

Abstract

This manuscript addresses two issues with calibration of surface plasmon resonance sensors which can track refractive index changesto measure correlated bulk properties. First, employing non-air references do not return the traditional parabolic dip in the SPR spectra;instead the returned SPR spectra are more ‘derivative’ in shape. Investigated are five different ways to calibrate SPR spectra when non-airreferences are employed. The minimum hunt method (MHM) calculates the position of this minimum by fitting a parabola to the curve. MHMis shown to consistently achieve prediction errors of 3×10−4 RI units (RIU) using an air reference and a RI calibration set of aqueous sucrosesamples measured with an Abbé refractometer accurate to 1× 10−4 RIU. Use of principal component regression (PCR) with air or waterreferences generates prediction errors at best the same as MHM but worse as the concentration range of samples increases. Second, a methodfor calibrating SPR spectra across a wide temperature range is presented. It is shown that this method is capable of successfully mitigating theeffect of temperature drifts up to 20◦C. MHM was subsequently used to predict the concentration of 0.00–6.99 wt.% KCl(aq) samples between6 and 29◦C, a range found in surface ocean waters. Prediction error as small as 0.073 wt.% correlates to 2× 10−4 RIU shows MHM holdsover a wide dynamic range.© 2004 Elsevier B.V. All rights reserved.

Keywords: Temperature compensation; Salinity monitoring; Principal component regression; Minimum hunt calibration

1. Introduction

Surface plasmon resonance (SPR) is used to sense changesin refractive index (RI). Any system in which an analyteor intensive property such as density or film thickness canbe correlated to a change in RI can potentially be moni-tored using SPR. Fields that have exploited this techniqueinclude biosensing[1–5], thin film detection[3,6,7] and en-vironmental applications including measurements of salinity[8–12]. Salinity is measured to 1 ppm in chemical oceanog-raphy, but climatological models are generally satisfied witha 10–100 ppm sensitivity range[17,18]. This wide applica-bility is due to the demonstrated sensitivity of SPR sensorsto changes in RI as small as 10−6 RI units (RIU) [6]. Suchsensitivity can be correlated to thickness changes of less than

∗ Corresponding author. Tel.:+1-480-965-3058;fax: +1-480-965-2747.

E-mail address: [email protected] (K.S. Booksh).

1 nm, temperature fluctuations on the order of 0.01◦C, andbulk concentration changes in the 100 ppm range[6,12]. SPRis therefore a highly sensitive technique available for sys-tems undergoing such changes. Comparatively, the most ac-curate commercial refractometer is able to monitor changesin the order of 10−5 RIU.

The physics of SPR has been described elsewhere[5–7].Light is coupled into a glass substrate and allowed to inter-nally reflect off the underside of a thin metal layer, typicallyAu or Ag. The evanescent field from this internal reflectionwill couple to the surface plasmon (SP) wave present in themetal if the wave vectors of the light and the SP match. Asthe value of the SP wave vector is dependent on the RI of themedium in contact with the surface, the angle of incidenceor wavelength of incident light that couples will change withthis RI. Thus the internally reflected light will have a de-creased intensity at a given angle or wavelength. Trackingthis intensity drop against angle or wavelength permits mea-surement of RI.

0003-2670/$ – see front matter © 2004 Elsevier B.V. All rights reserved.doi:10.1016/j.aca.2004.03.061

292 D.J. Gentleman et al. / Analytica Chimica Acta 515 (2004) 291–302

Instrumentally, SPR sensors traditionally consist of aprism and goniometer geometry known as the “Kretschmann”configuration but an increasing number of studies haveemployed fiber optic based sensors (FO-SPR)[5]. Obandoand Booksh have shown FO-SPR dip-probes can be eas-ily manipulated to access a large range of RIs, includingthose encountered in aqueous systems[13,14]. Taking withthis ability the fact that optical fiber systems are small,inexpensive and require no moving parts makes FO-SPR ahighly useful technique, especially for in situ applications.The sensitivity these probes are capable of is dependenton the wavelength resolution of the spectrometer and thecalibration model used.

The SPR spectrum resulting from FO-SPR sensors mea-suring aqueous samples may take one of the two forms. Ineither case, the sample spectrum is ratioed against that of areference spectrum. Air or water are two obvious referencesamples, as they are readily available and are reproducibleas a spectral reference. However, a reference could be anyreadily available standard, such as seawater at a given tem-perature. Probes that are constantly immersed in a given sys-tem would be candidates for a reference of this type, as thesmall deviation from a baseline would be the measurementof interest.

With the traditional reference of air, a “minimum” is pro-duced, as shown inFig. 1. The angles/wavelengths employedin the fiber optic measurement do not couple with the SPwhen exposed to gaseous samples (RI< 1.1). Therefore,when the probe is in air, the light will not be absorbed andthe air spectrum is the lamp intensity profile. The vertex ofthe minimum in the normalized sample spectrum of futureaqueous samples is here referred to asλSPR, and its valueis correlated to the RI of the sample. Calibration of thesespectra has been performed using the univariate “minimahunt method” (MHM)[13,15,16]. Simply, a parabola is fit-ted to the minimum and its vertex is equal toλSPR. Thefact that the MHM is an univariate technique means it can

Fig. 1. SPR spectrum for KCl(aq) ratioed against air reference.

be performed quickly and lends itself well to use in linearmodels.

In some cases, collection of an air reference is experimen-tally difficult or may damage the SPR active area. Examplesinclude deep sea analyses in and around hydrothermal ventswhere the sensor may drift over time. The seawater within afew feet of the vent would serve as a readily accessible ‘stan-dard reference’. Also, with SPR sensors imbedded in mi-crofluidic analyzers, it is often inconvenient or impossible tocollect air references. Stripping and rebuilding analyte spe-cific layers on the sensor surface requires recollection of thebackground reference between analyses. SPR probes func-tionalized with analyte selective polymers (such as swellablemolecular imprinted polymers) need time to re-equilibrateonce dried for reference to air background. When employ-ing sensors with these technologies it is more convenient tosimply flow a standard reference solution across the sensingsurface.

If the reference is a medium with an RI closer to that ofthe sample, a “derivative” spectrum is produced, as shownin Fig. 2. In this case, the reference RI is in the range thatcan be monitored using FO-SPR. The spectra will be a su-perposition of the lamp profile and the sample SPR signal.Here, there are several features that may be used to trackthe change in RI. As with the air-referenced spectrum,λSPRcan be attributed to the vertex of the minimum on the right.The cross-over point may also track with RI. As ratioing asample to a reference of the same RI would create a flat line,the amplitude and/or area of the parabolic features may alsotrack with RI.

Multivariate analysis is used in systems that may havemore than one feature that can be correlated to a propertysuch as RI. Principle component regression (PCR) is onesuch method that has found considerable use in the bur-geoning field of chemometrics. PCR established trends byprojecting the points in the measurement (in this case, each

Fig. 2. SPR spectrum for KCl(aq) ratioed against water reference.

D.J. Gentleman et al. / Analytica Chimica Acta 515 (2004) 291–302 293

pixel of a given spectrum) onto a plane that maintains themost amount of variation between them. This pattern recog-nition method hones in on the direction of maximal varia-tion, and this is used to track the change desired. The methodthus considers the entire spectrum as opposed to one sec-tion, and therefore can be highly sensitive to small changes.Therefore the “derivative” spectra of FO-SPR sensors lendthemselves well to the use of PCR.

This study demonstrates MHM with an air reference is thebest way to calibrate FO-SPR sensors for aqueous systemswhen possible. The MHM was found to consistently pro-duce prediction error as good as or better than use of PCRwith both air reference spectra and water reference spectra.Values for MHM were on the order of 3× 10−4 RIU; equalto the precision of the Abbé refractometer employed as thestandard reference method. Use of MHM with an air ref-erence achieved the same prediction error regardless of therange of RI values used in the calibration set. PCR predic-tion errors became worse as the range increased. Water ref-erence spectra produced prediction errors on the same orderas the air reference for small RI ranges, but were an orderof magnitude higher than air for a wide range of RI values.However, in many application scenarios, only a small cali-bration range is needed.

MHM with an air reference was further found to predictsalinity of a set of KCl(aq) solutions over a wide temperaturerange to the same degree of error as calibration at a singletemperature. The best prediction error for the entire set was0.1 wt.%, corresponding to a prediction error of 2× 10−4

RIU. This further buoys the efficacy of the MHM method andshows FO-SPR is a widely applicable technique that neednot go through elaborate calibrations prior to deployment.

2. Materials and methods

2.1. Probes

The manufacture of the probes used in this study has beendescribed previously[13]. Straight (ST) probes were madefrom 3M FT400EMT silica fiber with a TECSTM claddingand TEFZELTM buffer. The distal end was epoxied intoan SMA connector for coupling to a bifurcated fiber opticjumper conducting light from the source to the probe andback to the detector.

2.2. Sucrose solutions

The first solution set consisted of a dilution series of aque-ous sucrose solutions, with their RI and SPR spectra mea-sured at room temperature. Sucrose (Mallinkrodt) straightfrom the bottle was weighed using a digital analytical bal-ance (Mettler-Toledo) and diluted to volume with deionizedwater (Millipore). RI of the sucrose solutions was measuredusing an Abbé refractometer (Bausch & Lomb), accurate to1×10−4 RIU. One hundred solutions between 1.33 RIU (wa-

ter) to 1.41 RIU were created in this manner. The data weredivided into three subsets: the large subset consists of all thedata spanning the range from 1.33 to 1.41 RI; the mediumsubset spans 1.35 to 1.39 RI; the small subset spans 1.37 to1.38 RI. For the SPR spectra, a white LED (generic) lightsource was used, and both a Kaiser Holospec with a spectralresolution of 0.33 nm/pixel and an Andor/Jobin-Yvon 270 Mspectrometer with a spectral resolution of 0.07 nm/pixel wereused to collect the spectra. MATLAB (Mathsoft) R12 wasused for all the calculations.

2.3. Potassium chloride solutions

The second solution set consisted of a dilution series ofaqueous KCl solutions, held in an isothermal bath for SPRmeasurement. KCl(aq) is the standard solution used to cali-brate instrumentation used for seawater analysis[17], and istherefore analogous in its RI to that medium. KCl (EM Sci-ence/Merck KGaA) straight from a new bottle was weighedwith the analytical balance described above, and mixed withdeionized water (Millipore) in a 500.0 mL volumetric flask tomake a standard of 6.994 wt.%. The error due to the KCl notbeing dried was not significant in this study. A 15-memberset of solutions including pure deionized water and a dilu-tion series of 14 solutions between 0.499 and 6.994 wt.%,incremented by 0.5 wt.%, was created. The samples wereplaced in 20 mL scintillation vials immersed up to the neckin an isothermal circulating bath (Fisher/Ness), accurate to0.02◦C. Temperature of the samples with a K-type thermo-couple, accurate to 0.5◦C, and recorded manually from thereadout of a D-42 thermocouple reader (Omega) precise to0.02◦C. The thermocouple and SPR probe were affixed toeach other using thermocouple wire and ParafilmTM abovethe liquid line of the solutions. The probe’s sensing areaand the thermocouple tip were 5 mm apart and immersed toconstant depth. The light source for the SPR spectra was aQTH lamp (Oriel), and an Ocean Optics spectrometer witha spectral resolution of 0.2 nm/pixel was the detector.

The isothermal bath was raised from 0 to 30◦C in 1◦Cincrements. Spectra were collected in random order from allsolutions at every temperature increment 30 min after chang-ing the temperature. Between measurements, the probe wasdipped in deionized water and dried using a compressedair-can intended for dust removal. Previous studies had in-dicated this protocol did not result in probe drift. Four repli-cates were taken in succession in each sample. Air referenceswere collected at eleven different temperatures for compar-ison of the probe from day to day.

3. Results and discussion

3.1. Sucrose series

In order to assess which method to use for calibration ofFO-SPR, three ranges of RI samples were culled from the


Fig. 3. Small range calibration set for sucrose. Calibration set (�) andpredicted points (×). Inset shows spread distribution without inclusion ofwater’s RI. The (�) at the bottom lefts is that of deionized water.

data. The “small” range is shown inFig. 3, the “medium”in Fig. 4, and the “large” inFig. 5. The small range con-sists of points furthest from the 1.33 RIU of water, mediumstretches to the middle of the measurement set, and largeincludes the entire range. Each set had half its points usedto create a calibration curve, and the other half were treatedas unknowns for the purposes of prediction. The calibrationcurve was fitted to a third-order polynomial:

y = a + bx + cx2 + dx3 (1)

wherex is the RI andy theλSPRas shown inFigs. 3–5. Fouror five probes were used to collect data from the samples,as one probe was scratched during analysis and thus not in-cluded in the affected sets. Both the low spectral resolutionKaiser and high spectral resolution Andor spectrometer sys-tems were used.

Fig. 4. Medium range calibration set for sucrose. Calibration set (�) andpredicted points (×). The (�) at the bottom left is that of deionized water.

Fig. 5. Large range calibration set for sucrose. Calibration set (�) andpredicted points (×).

The MHM fits a parabola to the minimum of the spec-trum and uses this as theλSPR value. In the case of theair-referenced set, this is obviously the single minimumshown inFig. 1. For water-referenced sets, the minimumcorresponds to the bottom of the right side of the derivativecurve, and therefore MHM can be used for both air- andwater-referenced sets. As PCR is sensitive to small changesin the data, it was assumed that it would be better at han-dling the water-referenced sets, and perhaps produce a smalladvantage over the MHM for air-referenced sets. Other uni-variate calibration models were constructed for the three setsusing four different possible trends: (a) area under the pos-itive portion of the derivative curve; (b) square of the areaunder the positive portion of the curve; (c) absolute valueof the entire area under the curve; (d) area under the firsthalf of the positive portion of the curve. The trend givingthe best prediction in each case is reported here.

Figs. 6–8show MHM gives root-mean-square errors ofprediction (RMSEP) values below 5× 10−4 RIU for bothspectrometers with the air reference. It is clear from themeans shown inFig. 12athat MHM is consistently below5 × 10−4 RIU overall. The only exception to this is oneprobe on the Kaiser instrument in the large range, shown inFig. 8a. The Andor spectrometer is consistently better withMHM, due to its spectral resolution being 0.07 nm/pixel, asopposed to the Kaiser’s 0.33 nm/pixel. A higher resolutionmeans there are more pixels within the minimum, and it ispresumed this allows a better parabolic fit.

Two-way ANOVA performed on the air-referenced cali-bration sets inFigs. 6–8found neither the probes are northe spectrometers are significantly different. TheF-valuescomputed are shown inTable 1. Due to the reproducibilityof these probes demonstrated in previous study, the varianceof replicates was insignificant for the current study[19].

It is clear fromFigs. 6–8that as the range of RI valuesincreases, PCR becomes progressively worse at predicting


Fig. 6. RMSEP for each probe using the small calibration set and an air reference. Grey bars for calibration points; black bars for predicted points. (a)MHM with Kaiser data, (b) PCR with Kaiser data, (c) MHM with Andor data and (d) PCR with Andor data.

Fig. 7. RMSEP for each probe using the medium calibration set and an air reference. Grey bars for calibration points; black bars for predicted points.(a) MHM with Kaiser data, (b) PCR with Kaiser data, (c) MHM with Andor data and (d) PCR with Andor data.

Table 1Two-way ANOVA results comparing air-referenced probes and spectrometers

Calibration set Compared factors DOF F Fcrit (P = 0.05)

Small (Fig. 6a and c) Spectrometers 1 6.220207 7.70865Probes 4 2.419689 6.388234

Medium (Fig. 7a and c) Spectrometers 1 2.919137 10.12796Probes 3 0.913747 9.276619

Large (Fig. 8a and c) Spectrometers 1 2.086123 10.12796Probes 3 2.143287 9.276619


Fig. 8. RMSEP for each probe using the large calibration set and an air reference. Grey bars for calibration points; black bars for predicted points. (a)MHM with Kaiser data, (b) PCR with Kaiser data, (c) MHM with Andor data and (d) PCR with Andor data.

the RI using air references.Fig. 12aclearly demonstratesthe quick rate at which PCR fails, as the prediction erroreven for the Andor spectrometer is more than double that ofthe MHM set. The reason for this is not clear. One possibleexplanation in the case of using the absolute value of the areaunder the curve is that the data is linearized, but the standarddeviation of the scatter increases from 10−4 to 10−3 RIU.

Figs. 9–11show MHM is capable of producing simi-lar prediction error with water-referenced spectra as withair-referenced, so long as the small or medium ranges of data

Fig. 9. RMSEP for each probe using the small calibration set and a water reference. Grey bars for calibration points; black bars for predicted points. (a)MHM with Kaiser data, (b) PCR with Kaiser data, (c) MHM with Andor data and (d) PCR with Andor data.

are used. PCR is more consistent with the small and mediumranges. However, both techniques have large prediction er-ror when confronted with the full range of the RI samples.Again, this is best illustrated from the RMSEP means inFig. 12b.

A second two-way ANOVA analysis comparing the vari-ance of the spectrometers and that of the prediction methodsshows that PCR does not provide an advantage to predic-tion in this study. The results for this second ANOVA areshown inTable 2. The significant difference in the short cal-


Fig. 10. RMSEP for each probe using the medium calibration set and a water reference. Grey bars for calibration points; black bars for predicted points.(a) MHM with Kaiser data, (b) PCR with Kaiser data, (c) MHM with Andor data and (d) PCR with Andor data.

Fig. 11. RMSEP for each probe using the large calibration set and a water reference. Grey bars for calibration points; black bars for predicted points.(a) MHM with Kaiser data, (b) PCR with Kaiser data, (c) MHM with Andor data and (d) PCR with Andor data.

Table 2Two-way ANOVA results comparing means from prediction models and spectrometers

Calibration set Compared factors DOF F Fcrit (P = 0.05)

Small (Fig. 12, first two bars) Spectrometers 1 35.13659 10.12796Prediction models 3 4.22439 9.276619

Medium (Fig. 12, middle two bars) Spectrometers 1 7.426987 10.12796Prediction models 3 33.23605 9.276619

Large (Fig. 12, last two bars) Spectrometers 1 1.210881 10.127696Prediction models 3 1.321446 9.276619


Fig. 12. Mean of the RMSEPs for all the data sets. For each labeled pair, the left bar is the mean Kaiser data and the right bar is the mean Andor data.(a) Air reference RMSEPs and (b) water reference RMSEPs.

ibration set between the spectrometers can be attributed toPCRs high error on the Kaiser. The significant difference inthe medium calibration set between the prediction modelsshows that PCR is not as reliable as MHM. The general lackof difference between MHM and PCR means the former issufficient for SPR data analysis.

Water-referenced spectrum produces a derivative shape,with the amplitude of the peaks being greatest when the dif-ference in RI between the sample and the water is greatest.This large range set includes samples closest in RI to wa-ter. If the sample is close in RI to that of water, the deriva-tive curve is very close to being a flat line. The failure ofMHM to produce good prediction values here is probablydue to the parabolic fit becoming progressively poor. Thefact the Kaiser results, with a lower spectral resolution, havea markedly worse prediction supports this conclusion, giv-ing the fewest points for a parabola to fit.

PCRs inability to perform much better than MHM witha set containing small changes in RI was not predicted, butis clearly demonstrated inFig. 12b. Perhaps the method istoo sensitive to noise fluctuations in the spectra and wandersfrom the true trends. Physically, these results suggest the useof a reference too close in RI to that of the sample simplycannot produce a good calibration model.

This calibration set is ultimately limited by the accuracy ofthe refractometer used, which was 1× 10−4 RIU. As MHMis capable of prediction error on the order of 3× 10−4 RIUusing an air reference, it is concluded that this techniqueallows the best sensitivity for FO-SPR.

3.2. KCl(aq) results

One of the great challenges with SPR spectroscopy is mit-igating the effect of temperature fluctuations on the efficacyof calibration and analysis. At room temperature a 0.1◦Cchange in water temperature results in a 10−5 RI drift [6].One school of thought for minimizing the effect of temper-ature drift is to employ two SPR sensitive regions. One re-gion will change withT, while the sensing will respond totemperature and analyte concentration changes. The alter-native school of thought is to calibrate the sensor across adistribution of temperatures. For many in situ applicationswhere the temperature gradient is extreme or dynamic, it isimpossible to place two sensors close enough together to re-liably monitor the same environment. In this case a singlecalibration model must be built that spans all temperaturesencountered.

A novel linear model constructed at a given temperaturefor a set of KCl(aq) solutions was found to produce the sameprediction values at other temperatures within the set. There-fore FO-SPR need not be calibrated over the entire tempera-ture range in order to produce accurate readings. RMSEPs assmall as 0.161 wt.% are attainable from constructing a cal-ibration model over a range of KCl(aq) concentrations from0.000 to 6.994 wt.% and temperatures from 6 to 29◦C. Thesevalues correspond to an approximate RI range of 1.33–1.35RIU, based on the RI change in seawater over the sametemperature range[20]. A RMSEP as small as 0.073 wt.%is attainable for isothermal conditions. As the RI of seawa-


Fig. 13. PositionλSPR for all concentrations of KCl(aq) between 6 and 29◦C. Data are one of the four replicate sets.

ter in this temperature range changes approximately 2.0 ×10−3 RIU/wt.% [20], these results are consistent with theRMSEPs acquired in the sucrose data set for air references.

Fig. 13 shows theλSPR over all concentrations for eachtemperature between and including 6 and 29◦C. Comparingthe trends and the RMSEPs for the different air references,the results were statistically similar. As the difference inRI between air and an aqueous solution is relatively high,minor changes to the probe will not manifest themselves ina significantly differentλSPR. Thus the air reference taken

Fig. 14. Regression lines an data points of KCl(aq) for 6◦C (�) and 29◦C (�) with predicted line of best fit for 19◦C and its actual points (+). Dottedlines indicate 95% confidence limit.

at 25◦C has been arbitrarily chosen as the reference for allthe discussions to follow.

A four-step calibration model was constructed to predictthe concentrations at given temperatures. First, the slopesand intercepts for the regression lines of the temperature ex-tremes (6 and 29◦C in Fig. 14) are calculated using the firstreplicate set. It is assumed that the lines of best fit for theλSPR values of the samples at a given temperature will belinearly interpolated between these extremes. A proportion-ality constant may be calculated based on the position of an


Fig. 15. Error in prediction of all concentrations of KCl(aq) between 6 and 29◦C using the linear model described in the text. Data shown are three ofthe four replicate sets.

unknown temperature between 6 and 29◦C:

p = Tunk − T1

T2 − T1(2)

The intercept for the unknown temperature’s line of best fitis then calculated using this proportionality constant:

bunk = b1 + p(b2 − b1) (3)

The slope of the line fitting the samples at a given temper-ature also proportionally changes between the extremes:

munk = m1 + p(m2 − m1) (4)

Fig. 14 shows the calibration line for 19◦C calculated us-ing this model. The crosses indicate the actual SPR pointsof the three replicate sets at 19◦C, showing the calibrationmodel produces a line that is a good approximation of a

Table 3Errors of prediction for various temperature ranges

Bounding temperatures(◦C)

Temperature(s) predicted(◦C)

Standard deviation ofRMSEP-T’s (wt.%)

Overall RMSEP (wt.%) Overall arithmetic mean(wt.%)

6.29 6→ 29 0.054 0.161 0.0387.29 7→ 29 0.057 0.164 0.0186.16 6→ 16 0.058 0.167 0.011

17.29 17→ 29 0.021 0.107 −0.01519 19 N/A 0.073 0.00418.20 19 N/A 0.075 −0.01617.29 19 N/A 0.091 −0.0556.29 19 N/A 0.135 0.1129 9 N/A 0.113 −0.0118.10 9 N/A 0.121 −0.0446.16 9 N/A 0.131 0.0606.29 9 N/A 0.122 0.042

line of best fit. To determine the success of the model, thepredicted concentrations for the latter three replicate sets ofeach temperature in question were subtracted by the trueconcentration of the sample. This absolute concentration er-ror result for the model with 6 and 29◦C as the boundingtemperatures is shown inFig. 15.

Table 3shows a prediction error as low as 0.073 wt.%is attainable using this linear model. As the number oftemperatures interpolated between increases, this errorrises to 0.17 wt.%. Using the regression model, the RM-SEPs over all concentrations at a given temperature werecalculated (RMSEP-T). Several temperature ranges areshown inTable 3. Comparing the standard deviations of theRMSEP-T’s between 6 and 16◦C to that between 17 and29◦C, the latter is almost a factor of 3 better, correspondingto the smaller error shown inFig. 15. The RMSEP over


all temperatures and concentrations in a given bound werecalculated, as was the arithmetic mean of the correspondingset. As Table 3 shows, the absolute value of the overallarithmetic mean is lower than the RMSEP in every case.This indicates there is no systematic bias in the data so theRMSEP is largely due to statistical spread.

Table 3shows the RMSEP for the second half of the dataset is better than for the first half. Focusing on the ability ofthe model to predict the concentrations at one temperature,it is clear the RMSEP increases mildly as the temperaturebounds get further apart. Both 19 and 9◦C have RMSEPson the order of 0.1 wt.%, which corresponds to 2.0 × 10−4

RIU [20] for seawater—3.5 wt.%—in the same temperaturerange. This prediction agrees well with the isothermal su-crose results, and suggests the MHM with air reference isapplicable to a wide variety of physical systems.

It is noted that the error inFig. 15 tends towards thenegative over time, and a sudden change occurs between16 and 17◦C. If the probe intrinsically redshifts over time,the measured concentration would be higher than the ac-tual concentration. The linear model assumes only blueshiftwill occur with increasing temperature. Thus the coinci-dence of redshift due to an intrinsic probe drift will resultin a predicted concentration smaller than the actual concen-tration. This would manifest itself in the errors tending tothe negative as time proceeds. This is exactly what is ob-served. The reason for the sudden jump between 16 and17◦C cannot be so easily explained. A sudden change inthe probe would not make sense initially as these temper-atures were measured in the middle of the third day of theexperiment. Perhaps there is a physical process at work onthe probe surface, causing both the redshifting of signal,and occasional abrupt changes in performance. Data col-lected from 0 to 5◦C was not included, as it had a high de-gree of noise. The reason for this is unknown, though theremay be a period of conditioning the probe experiences in itsfirst few hours of use. Further work must be done to char-acterize the probe in order to determine the cause of thisobservation.

4. Conclusions

Prediction of 3× 10−4 RIU is attainable for an aqueoussolution’s RI using multimode SPR calibrated using the uni-variate minima hunt method and a set of prepared aqueoussucrose RI standards. There is no advantage attained throughthe use of a multivariate method such as PCR in this instance.Use of the MHM results in prediction error of 0.1 wt.% forKCl(aq), which corresponds to a 2×10−4 RIU for seawater.Thus this univariate method is useful over relatively wideconcentration and temperature ranges. The linearity of themodel increases as the range of concentration and tempera-ture decreases. In order to determine the highest attainablesensitivity, calibration in a system with finer increments andsuperior temperature control is recommended.

The cause of the redshifting drift must be determined ifthe probe is to be used for prolonged monitoring. Character-ization of the probe’s surface using SEM imaging or othersurface-sensitive methods is encouraged. Also, as Au is notthe only metal capable of supporting an SP wave, perhapsuse of another metal such as Ag or Pt will alleviate thisproblem. The extent of the evanescent field is approximately100 nm from the surface of the fiber, so if anything is used tocoat the surface for protection, it must not exceed this limit.The attachment of thiolbonded species may protect the Ausurface while allowing sensing of the sample medium. If theshifting cannot be eliminated, it could perhaps be correctedstatistically. Further calibration studies must be conductedin order to determine is this is a more viable option.

Once optimized, fiber optic based SPR dip-probes couldcontribute to various systems needing in situ sensors. Theirsize scale lends well to applications in biosensing whereminimally invasive in vivo monitoring would be a boon toearly medical diagnostics. Their low cost of manufacturemeans large arrays could monitor large systems such as theprofile of salinity gradients, or haloclines, in a marine en-vironment. Such monitoring would result in more accurateclimate models.

Acknowledgements

National Science Foundation Oceans (NSF 0119999) forfinancial support.

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Calibration of fiber optic based surface plasmon resonance sensors in aqueous systems

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