Principal Component Analysis Calibration Method for Dual

Aug 23, 2005 - A major problem in PSP measurements arises because the Stern-Volmer calibration of the PSL's emission varies with temperature. To corre...
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Langmuir 2005, 21, 9110-9120

Principal Component Analysis Calibration Method for Dual-Luminophore Oxygen and Temperature Sensor Films: Application to Luminescence Imaging Muhammet Erkan Ko¨se,† Ahmed Omar,‡ Christopher A. Virgin,‡ Bruce F. Carroll,‡ and Kirk S. Schanze*,† Department of Chemistry and Department of Mechanical and Engineering Science, University of Florida, P. O. Box 117200, Gainesville, Florida 32611 Received April 14, 2005 Oxygen sensor films are frequently used to image air-pressure distributions on surfaces in aerodynamic wind tunnels. In this application, the sensor film is referred to as a pressure-sensitive paint (PSP). A Stern-Volmer calibration is used to relate the emission intensity ratio of a long-lifetime luminescent dye (the pressure-sensitive luminophore, PSL) to surface air pressure. A major problem in PSP measurements arises because the Stern-Volmer calibration of the PSL’s emission varies with temperature. To correct for the temperature dependence, a second luminescent dye that has an emission that varies with temperature (the temperature-sensitive luminophore, TSL) is incorporated into the sensor film. With such a dualluminophore PSP (DL-PSP), it is possible to measure the surface-temperature distribution with the TSL emission, and this information is then used to correct the temperature dependence of the PSL’s pressure response. In the present article, we report the application of a DL-PSP to obtain high-resolution airpressure distributions on a surface that is subjected to a 20 °C temperature gradient. Two different calibration methods are used to generate surface-temperature and air-pressure distributions from the luminescence imaging data, and a quantitative comparison of the results obtained from the two methods is provided. The first method is based on an intensity-ratio calibration that uses luminescence images collected at two wavelengths, one corresponding to the TSL emission and the second corresponding to the PSL emission. The second method is based on principal component analysis (PCA) of luminescence images obtained at four wavelengths throughout the spectral region of the TSL and PSL emission (hyperspectral imaging, 550-750 nm). The results demonstrate that the PCA method allows the measurement of surface air pressure with higher accuracy and precision compared to those of the intensity-ratio method. The improvement is especially significant at pressures near 1 atm, where the temperature interference is most pronounced. Surface-pressure distributions are measured with comparable accuracy and precision with the two methods.

* To whom correspondence should be addressed. E-mail: [email protected]. Tel: 352-392-9133. Fax: 352-392-2395. web: http://www.chem.ufl.edu/∼kschanze. † Department of Chemistry. ‡ Department of Mechanical and Engineering Science.

ment is conducted in a wind tunnel, the temperature of the model surface may change during the experiment; consequently, the air-pressure distribution determined from the luminescence from the sensor film has errors associated with the nonuniform temperature on the model surface. To correct for the temperature interference, the model’s surface-temperature distribution must be measured concurrently with the pressure-surface distribution. One way to achieve this is to use a dual-luminophore pressure-sensitive paint (DL-PSP) that contains a temperature-sensitive luminophore (TSL) dispersed along with a pressure-sensitive luminophore (PSL) in the polymer matrix.5-7 The general concept is that the emission intensity of the TSL varies only with temperature, whereas that of the PSL varies with pressure (and temperature). Thus, CCD images obtained at the wavelength corresponding to the emission from the TSL can be related to the surface temperature distribution, and this information can be used to correct the pressure-intensity calibration used for CCD images obtained at the wavelength corresponding to the PSL emission. In the previous article in this journal, we describe a novel approach to the formulation of a novel DL-PSP as

(1) Bell, J. H.; Schairer, E. T.; Hand, L. A.; Mehta, R. D. Annu. Rev. Fluid Mech. 2001, 33, 155-206. (2) Morris, M. J.; Donovan, J. F.; Kegelman, J. T.; Schwab, S. D.; Levy, R. L.; Crites, R. C. AIAA J. 1993, 31, 419-425. (3) Gouterman, M. J. Chem. Educ. 1997, 74, 697-702. (4) Schanze, K. S.; Carroll, B. F.; Korotkevitch, S.; Morris, M. J. AIAA J. 1997, 35, 306-310.

(5) Zelelow, B.; Khalil, G. E.; Phelan, G.; Carlson, B.; Gouterman, M.; Callis, J. B.; Dalton, L. R. Sens. Actuators, B 2003, 96, 304-314. (6) Mitsuo, K.; Asai, K.; Hayasaka, M.; Kameda, M. J. Visualization 2003, 6, 213-223. (7) Gouterman, M.; Callis, J.; Dalton, L.; Khalil, G.; Mebarki, Y.; Cooper, K. R.; Grenier, M. Meas. Sci. Technol. 2004, 15, 1986-1994.

Introduction Luminescent oxygen sensor films have been widely used for the measurement of surface air-pressure distributions on aerodynamic models.1-3 In this application, the oxygen sensor film is often referred to as a pressure-sensitive paint (PSP). When combined with scientific-grade CCD cameras, a PSP sensor affords air-pressure distributions with high spatial resolution and a wide dynamic range. The PSP method has many advantages over conventional approaches for surface air-pressure measurement (e.g., pressure taps installed at discrete locations on an aerodynamic model) in terms of cost, labor involved with prototype model construction, and the amount of data collected.1 Although PSPs offer many advantages, a major drawback in current technology is the temperature dependence of luminescence intensity-pressure calibration of the oxygen sensor film.4 When an aerodynamic test experi-

10.1021/la050999+ CCC: $30.25 © 2005 American Chemical Society Published on Web 08/23/2005

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well as the characterization of its temperature- and pressure-dependent luminescence spectroscopic properties. In this DL-PSP formulation, tris-(1,10-phenanthroline)ruthenium(II) dichloride (Ruphen) is used as the TSL, tetrakis-1,5,10,15-(pentafluorophenyl)porphine platinum(II) (PtTFPP) is used as the PSL, and poly-4-tertbutylstyrene-co-2,2,2-trifluoroethyl methacrylate (p-tBSco-TFEM) is the oxygen-permeable binder. To eliminate molecular-level interactions between the two luminescent dyes, Ruphen is encapsulated in polyacrylonitrile (PAN) nanoparticles, and the Ruphen/PAN particles are dispersed together with PtTFPP into the p-tBS-co-TFEM binder. Although the two dyes emit at different wavelengths (Ruphen λemmax ≈ 580 nm, PtTFPP λemmax ≈ 650 nm), the Ruphen emission band is broad; consequently, its low-energy side overlaps with the PtTFPP emission. This overlap results in decreased sensitivity of the PtTFPP emission intensity to pressure compared with its response when it is dispersed alone in p-tBS-co-TFEM. In the work described in this article, we demonstrate the imaging application of the DL-PSP to correct the surface air-pressure distribution obtained on a substrate that has a 20 °C temperature gradient imposed on its surface. Two different methods are used to calibrate pressure (P) and temperature (T) image maps constructed from the DL-PSP image data. The first is the conventional intensity-ratio method,1 which uses image data obtained at two wavelengths that correspond, respectively, to λmaxem of the TSL (Ruphen) and λmaxem of the PSL (PtTFPP). The second approach is novel and uses principal component analysis (PCA) of CCD images collected at four separate wavelengths spanning the spectral region of the emission from Ruphen and PtTFPP (550-700 nm). The PCA approach allows one to extract eigenvectors that are optimized with respect to P and T responses, thereby improving the accuracy and precision of the estimated surface-pressure and temperature distributions. In previous work, we described the application of PCA to emission spectral data from a PSP;8,9 however, the work described herein is the first time that PCA analysis has been applied to PSP image data. A detailed description of the methods used for data reduction using both the intensity-ratio and PCA methods is provided. In addition, a statistical analysis of the results is presented that clearly shows that the PCA method affords an improvement in the accuracy and precision of the estimated surface-pressure maps compared to those obtained from the intensity-ratio method. Principal component analysis is a generally applicable multivariate analytical method that is used for a variety of applications where one seeks to understand correlations within large data sets. The underlying theory of PCA and related multivariate methods with emphasis on applications to chemical systems is provided in a monograph by Malinowski.10 The primary literature also contains many examples of applications of PCA to problems in chemical spectroscopy11-20 as well as an analysis of hyperspectral (8) Carroll, B. F.; Hubner, J. P.; Schanze, K. S.; Bedlek-Anslow, J. M. J. Visualization 2001, 40, 4053-4062. (9) Carroll, B. F.; Omar, A.; Hubner, J. P.; Schanze, K. S. The 10th International Symposium on Flow Visualization, Kyoto, Japan, 2002. (10) Malinowski, E. R. Factor Analysis in Chemistry, 3rd ed.; John Wiley and Sons: New York, 2002. (11) He, H.; Xu, G.; Ye, X.; Wang, P. Meas. Sci. Technol. 2003, 14, 1040-1046. (12) Nelson, M. P.; Aust, J. F.; Dobrowolski, J. A.; Verly, P. G.; Myrick, M. L. Anal. Chem. 1998, 70, 73-82. (13) Sasic, S.; Clark, D. A.; Mitchell, J. C.; Snowden, M. J. Analyst 2004, 129, 1001-1007. (14) Gomez Martin, J. C.; Spietz, P.; Orphal, J.; Burrows, J. P. Spectrochim. Acta, Part A 2004, 60A, 2673-2693.

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imaging data (spatially correlated image data obtained at many wavelengths).21,22 Although the work documented here is the first to describe the application of PCA to correct for the temperature interference in PSP measurements, several other groups have been active in the development and application of DL-PSPs. In particular, Khalil and coworkers developed a DL-PSP in which tris-[3-(3-phenanthryl)-1-(9-phenanthryl)propane-1,3-dione][1,10-phenanthroline]-europium(III) and 1,5,10,15-tetrakis-(pentafluorophenyl)porpholactone (PtTFPL) were used as TSL and PSL, respectively. Although not clearly described, the binder for their DL-PSP is a silicone-polycarbonate copolymer.5 Another DL-PSP system was reported by Mitsou and co-workers that utilized rhodamine B as TSL, PtTFPP as PSL, and poly(isobutyl methacrylate-co-2,2,2trifluoroethyl methacrylate) as the binder. Despite the fact that the emission of rhodamine B was not strongly temperature-dependent and spectral overlap between the rhodamine B and PtTFPP emissions decreased the intensity-pressure response, they were able to obtain temperature-corrected surface-pressure distributions in a verification test carried out using a wing model in a wind tunnel. Although an error analysis of the image data was not presented, the estimated pressures obtained from the temperature-corrected CCD image data were in reasonable agreement with the pressure tap data.6 Khalil and co-workers described a DL-PSP that uses a (fluoro/ isopropyl/butyl)acrylate (FIB) copolymer as the binder and magnesium tetra(pentafluorophenyl)porphine and PtTFPL as the TSL and PSL, respectively. Fortuitously, the temperature dependence of the two dyes is almost the same over the entire pressure range investigated; therefore, using a ratio of the emission from the two dyes almost eliminates the temperature dependence in the pressure response.23 In addition to the intensity-based DL-PSPs, several reports describe the application of lifetime-based DL-PSP systems to correct for temperature in PSP image data. Hradil and co-workers describe a DL-PSP consisting of an inorganic phosphor and tris-(5,7-diphenyl-1,10-phenanthroline)ruthenium(II) dispersed in a sol-gel matrix. By using an intensified CCD, they were able to resolve the luminescence decay of two emitters because they have large differences in lifetime.24 Gouterman and Coyle also developed a lifetime-based DL-PSP by using an Eu(III) phosphor and PtTFPP dispersed in FIB.25 Neither of these studies reported an analysis of precision and accuracy in the recovery of the surface pressure and temperature values. Most previously published work regarding DL-PSPs has focused on the chemistry issues related to their formula(15) Hasegawa, T. Anal. Bioanal. Chem. 2003, 375, 18-19. (16) Malecha, M.; Bessant, C.; Saini, S. Analyst 2002, 127, 12611266. (17) Turek, A. M.; Krishnamoorthy, G.; Phipps, K.; Saltiel, J. J. Phys. Chem. A 2002, 106, 6044-6052. (18) Turek, A. M.; Krishnamoorthy, G.; Sears, D. F., Jr.; Garcia, I.; Dmitrenko, O.; Saltiel, J. J. Phys. Chem. A 2005, 109, 293-303. (19) Zhang, F.; Brueschweiler, R. ChemPhysChem 2004, 5, 794796. (20) Zhou, J.; Varazo, K.; Reddic, J. E.; Myrick, M. L.; Chen, D. A. Anal. Chim. Acta 2003, 496, 289-300. (21) Liu, Y. L.; Chen, Y. R.; Wang, C. Y.; Chan, D. E.; Kim, M. S. Appl. Spectrosc. 2005, 59, 78-85. (22) Budevska, B. O.; Sum, S. T.; Jones, T. J. Appl. Spectrosc. 2003, 57, 124-131. (23) Khalil, G. E.; Costin, C.; Crafton, J.; Jones, G.; Grenoble, S.; Gouterman, M.; Callis, J. B.; Dalton, L. R. Sens. Actuators, B 2004, 97, 13-21. (24) Hradil, J.; Davis, C.; Mongey, K.; McDonagh, C.; MacCraith, B. D. Meas. Sci. Technol. 2002, 13, 1552-1557. (25) Coyle, L. M.; Gouterman, M. Sens. Actuators, B 1999, 61, 9299.

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tion. However, a PSP imaging application that is related to that described in the present article was reported several years ago by Woodmansee and Dutton. This group quantitatively compared the temperature correction of PSP data acquired on a transverse jet-in cross flow by using several different data reduction methods. They evaluated isothermal, in-situ, k-fit, and temperaturecorrected pressure PSP calibration results against data acquired by using pressure taps.26 The intensity-ratio calibration used in this work resembles the a priori calibration described by Bell et al.;1 however, in the present work the DL-PSP data is analyzed by using two different mathematical algorithms. Experimental Section Preparation of Pressure-Sensitive Paint. The syntheses of p-tBS-co-TFEM and Ruphen/PAN nanospheres is described in the preceding article in this journal.27 To prepare the primer base coat, 140 mg of p-tBS-co-TFEM and 125 mg of titanium dioxide (Tronox CR-800) were dissolved in 4 mL of CH2Cl2, and the solution was stirred overnight. The solution was then sprayed at 20 psi with a commercially available airbrush gun onto precleaned aluminum coupon using air as the propellant. The base coat was allowed to dry in an oven at 100 °C for 30 min before applying the PSP coat. The PSP coating was prepared by mixing 80 mg of p-tBS-coTFEM, 0.45 mg of PtTFPP, and 0.8 mL of Ruphen/PAN acetone solution in 3 mL of CH2Cl2. (The amount described here is sufficient to cover an area of 8 in2.) The PSP solution was coated onto the substrate in same manner described for the primer layer, and the PSP was then dried at 80 °C for 1 h. A borosilicate microscope glass slide was also coated simultaneously to allow data to be collected with a fluorescence spectrometer. Fluorescence Spectrometer and CCD Imaging Measurements. Steady-state emission spectroscopy was carried out on a commercially available fluorescence spectrophotometer (SPEX industries, F-112A). Samples were excited at 465 nm. Temperature and pressure were controlled by placing the samples in a home-built chamber. The pressure was controlled with a vacuum pump and monitored with a vacuum gauge (model DPI 260, Druck). The temperature was controlled by a water recirculating bath (model RTE 140, Neslab) and was monitored by a thermocouple. The photoluminescence from the DL-PSP was monitored in a “front-face” geometry relative to the excitation beam through a borosilicate window in the sample chamber. Integrated areas under the emission spectra between 535 and 580 nm (Ruphen, TSL) and between 635 and 680 nm (PtTFPP, PSL) were used for the calibration plots. Full-field DL-PSP photoluminescence images were collected with a thermoelectrically cooled 14-bit CCD camera with 512 × 512 resolution (Photometrics, model CH250).. The coupon was illuminated by a blue LED array (λmax ≈ 465 nm). CCD images were collected through 550/40 nm (03 FIV 044, from Melles Griot), 600/10 nm (03 FIV 046, from Melles Griot), 650/10 nm (03 FIV 048, from Melles Griot) and 700/10 nm (03 FIV 058, from Melles Griot) band-pass filters. The filters were installed in a filter wheel positioned in front of the CCD camera. Care was taken not to move the CCD camera when the filter wheel was rotated. A set of four “reference” images was first obtained by using the band-pass filters with the coupon under an isothermal condition and a single pressure condition. The CCD shutter was opened for sufficent time (10-50 ms, depending on the filter used) to obtain an optimum signal-to-noise ratio. After acquisition of the reference images, a set of dark images (illumination LEDs off) was collected with the same exposure times. After collecting the reference and dark images, the coupon heating and cooling systems were activated to establish the temperature gradient on the coupon. When the thermal gradient was stable, the pressure in the chamber was varied, and a set of four images was collected

Figure 1. Experimental setup for CCD image data collection. Thermocouple locations are shown as X marks. using each of the band-pass filters at 13 different pressures (4 wavelengths × 13 pressures ) 52 “run” images). Prior to the pressure and temperature analysis, image ratios Iref/I were obtained by the following procedure. First, the dark background was subtracted from each of the raw reference and run images. Then, each run image was ratioed to the reference image obtained at the corresponding wavelength. In most cases, image registration was not needed because the object and camera were fixed securely during the experiments. However, in some cases slight (subpixel) registration improved the quality of the ratioed images. In these cases, the image registration toolbox (projective transformation) in Matlab was utilized to ensure the correct alignment of images. Finally, the ratioed images were subjected to spatial filtering (Matlab imfilter command, 10 × 10 pixels). Within each of the resulting ratioed images, there are five specific locations where the temperature is known (at the positions where the thermocouples are located, see “X”s in Figure 1). Because images were obtained at 13 different pressures using 4 different band-pass filters, this gives rise to 5 × 13 ) 65 known pressure/temperature conditions at which Iref/I can be calibrated for each of the 4 DL-PSP emission wavelengths, (This gives a data matrix consisting of 4 wavelengths and 65 unique pressure/ temperature combinations.) The Iref/I values for each of the unique conditions were taken as a single pixel in the image at the location in the CCD image matrix corresponding to the thermocouple position on the surface of the coupon.

Data Analysis Methods Intensity-Ratio Calibration. In this method, two empirical expressions are used to fit the pressure (P) and temperature (T) for the known conditions to the emission intensity ratios (Iref/I) collected at two emission wavelengths corresponding to the emission from the TSL and PSL,1

P ) a1 + b1X + c1Y + d1XY + e1X2 + f1Y2 + g1X2Y + h1XY2 + i1X2Y2 (1) T ) a2 + b2X + c2Y + d2XY + e2X2 + f2Y2 + g2X2Y + h2XY2 + i2X2Y2 (2) where X ) IrefTSL(P0, T0)/ITSL(P, T), Y ) IrefPSL(P0, T0)/ I (P, T), the TSL and PSL superscripts refer to images obtained with the 550/40 nm and 650/10 nm filters, respectively, and Iref(P0, T0) is the emission intensity collected with the coupon at the reference condition (P ) PSL

(26) Woodmansee, M. A.; Dutton, J. C. Exp. Fluids 1998, 24, 163174. (27) Kose, M. E.; Carroll, B. F.; Schanze, K. S. Langmuir 2005, 21, 9121-9129.

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14.57 psi, isothermal coupon at T ) 24.3 °C). Coefficients a1-i1 and a2-i2 were determined from a least-squares fit of at least 9 of the 65 known pressure and temperature combinations by using a regression routine available in SigmaPlot (SigmaPlot version 8.0, SPSS Inc.). Although the Stern-Volmer relationship is mathematically simpler than expressions 1 and 2, the polynomials provided much better fits of the calibration points and therefore gave an improved prediction of unknown pressures and temperatures. Although these equations were arrived at empirically, there are several reasons to expect that nonlinear expressions are needed to represent the pressure and temperature intensity-ratio calibration surfaces adequately. First, the Stern-Volmer response of the PSL is nonlinear and typically requires either a two-site quenching model28 or a second-order polynomial to obtain an adequate representation of the Iref/I versus P data. In addition, there is some degree of “cross talk” between the PSL and TSL dyes because of spectral overlap, and this is represented by the cross terms in eqs 1 and 2. Principal Component Analysis Calibration. Principal component analysis is used for reducing data matrices to their lowest dimensionality by the use of orthogonal factors, which in turn results in predictions for recognizable factors.10 In order for a data matrix to be factor analyzable, it should be possible to model the data as a linear sum of product terms of the form n

dik )

rijcjk ∑ j)1

(3)

(4)

where D is the experimental data matrix and R and C are the scores and loading matrices, respectively. From a known matrix of D, the objective is to find R and C matrices that can reproduce the original data matrix as in eq 4. Initially, the data matrix is decomposed into eigenvectors and eigenvalues. The first mathematical step is to find the covariance matrix, which is inherently a square matrix:

Z ) DTD

(5)

Then this matrix is diagonalized by finding a matrix Q such that

Q-1ZQ ) [λjδjk]

(6)

This step can be easily calculated by using an eigenvector solver, from which one also obtains eigenvectors to the corresponding eigenvalues. Therefore, we can write the following equation

Zqj ) λjqj

(7)

where qj is the jth column of Q. Because these columns (also called eigenvectors) constitute a mutually orthonormal set, we can use the following relationship:

Q-1 ) QT

R ) DQ

(9)

C ) QT

(10)

and

Using these two equations, the data matrix can be reproduced from R and C, which is referred to as abstract reproduction. The procedure explained so far is a general scheme for abstract factor analysis.10 However, in principle component analysis, R and C are found in a different manner. In this method, the eigenvectors are consecutively calculated so as to minimize the residual error in each step. Therefore, each successive eigenvector accounts for the largest variation in the data. When all of the eigenvalues are calculated by using eq 6, the variation corresponding to the largest eigenvalue and eigenvector is subtracted from the covariance matrix as shown in the following equation:

R1 ) Z - λ1q1q1T

(11)

From this residual matrix, the second principal eigenvector and its associated eigenvalue are calculated.

R1q2 ) λ2q2

(12)

To obtain the third eigenvector, we define R2 as

R2 ) Z - λ1q1q1T - λ2q2q2T

In eq 3, rij is the jth factor associated with row i, and cjk is the jth factor associated with column k. We will refer to rij as scores and cjk as loadings. Equation 3 can also be written in matrix multiplication form

D ) RC

By exploiting eq 8, one can show that

(8)

(28) Demas, J. N.; DeGraff, B. A.; Xu, W. Anal. Chem. 1995, 67, 1377-1380.

(13)

When one continues in this fashion, the remaining eigenvectors and eigenvalues are extracted in succession.10 Target Transformation. As pointed out in the previous section, the R and C matrices constitute an abstract solution. Although they have mathematical meaning, they do not have any physical or chemical meanings in their present form. Target transformation allows one to obtain physically or chemically meaningful factors. This is achieved by applying a transformation matrix, which can be combined with eq 4 as below:

D = D ) (RT)(T-1C)

(14)

Here, T is the transformation matrix, which is a square matrix of dimension n, where n is the number of significant factors determined by PCA. The transformation matrix has the following form for a data matrix that can be described with two principal factors:

T)

[

a cos(θ) -b sin (θ) c sin (θ) d cos(θ)

]

(15)

If the transformation is orthogonal (i.e., it preserves the angles between the factor axes), then a, b, c, and d are unity. However, if the transformation is nonorthogonal, then these constants should be determined by taking into account prior information about the real factors.8,10 Factor Analyzability of Dual-Luminophore PSP Data. In order for a data set to be factor-analyzable, it should be possible to represent the data in matrix form as shown in eq 3; here we demonstrate that DL-PSP data fits this criterion. DL-PSP data consists of emission intensities from the TSL and PSL at various P-T conditions, which are obtained by using a fluorescence spectrometer or a CCD imager fitted with band-pass filters. The absolute intensity obtained in any luminescence

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measurement depends on many factors. The observed emission intensity can be described as

Iobs(λem) ) ANdyeφdyeF(λem)

(16)

In eq 16, A is a constant that is affected by many factors (e.g., light intensity impinging on the sample, photodetector and monochromator or band-pass filter efficiency, support electronics amplification factors, etc.), Ndye is the number of excited-state dye molecules, φdye is the quantum yield for emission, and F(λem) is the emission intensity distribution function (i.e., the spectral band shape of the fluorescence and/or phosphorescence emission). Ideally, in PSP experiments, everything but pressure and temperature are constant. Therefore, any change in P and/or T will change φdye. Hence, eq 16 can be recast as follows:

Iobs ) A′φdyeF(λem) where A′ ) ANdye

(17)

Consider a situation in which two dyes contribute to the total emission intensity at a given wavelength (e.g., a TSL and PSL). Then, the above equation becomes

Iobs(P, T, λ) ) ATSL′φTSL(P, T) FTSL(λem) + APSL′φPSL(P, T) FPSL(λem) (18) In general, a TSL displays little or no pressure sensitivity. Incorporating the constants with F(λem), one obtains

Iobs(P, T, λ) ) φTSL(T) FTSL(λem)′ + φPSL(P, T) FPSL(λem)′ (19) where FTSL(λem)′ ) ATSL′ FTSL(λem) and FPSL(λem)′ ) APSL′ FPSL(λem). Note that eq 19 is very similar in nature to eq 3 with n ) 2. With this theoretical background, we can now seek R and C matrices consistent with the physical phenomena described in eq 19.

Iobs(P, T, λ) ) R1(λ)C1 + R2(λ)C2

(20)

In eq 20, R1(λ) ) FPSL(λem)′, R2(λ) ) FTSL(λem)′, C1 ) ΦPSL(P, T), and C2 ) ΦTSL(T). By using this information, we seek a transformation matrix that will afford the spectral shape of each luminescent dye once the abstract factors are calculated. However, it has been argued that finding such a matrix is not easily accomplished in most systems.9 Indeed, in the course of this work we had difficulty in determining such a transformation matrix for the spectroscopic data matrix, D. In addition, a transformation that seeks to separate the spectra of the individual dyes does not necessarily lead to an optimal solution to separate the pressure and temperature response of a DL-PSP. Because the emission quantum yields of the TSL and PSL are dependent on temperature, we can alternatively seek a transformation matrix that will afford matrices that separate the temperature and pressure responses of the coating (e.g., R1(P), C1(P), R2(T), and C2(T)). Note that this condition is met only when the temperature responses of both the TSL and PSL are similar and the temperature dependence of the PSL’s emission intensity is independent of pressure (i.e., an “ideal PSP”).29 Fortunately, the temperature response of PtTFPP in poly-t-BS-co-TFEM is independent of pressure. However, (29) Puklin, E.; Carlson, B.; Gouin, S.; Costin, C.; Green, E.; Ponomarev, S.; Tanji, H.; Gouterman, M. J. Appl. Polym. Sci. 2000, 77, 2795-2804.

the temperature response of the emission from the Ruphen/PAN nanospheres (∼ -1.42% °C-1) is very different than that of PtTFPP (-0.53% °C-1) in this binder.27 Thus, as shown below, PCA analysis of the spectral data for the DL-PSP used in the present work does not allow us to resolve two important eigenvectors, where one is purely dependent on temperature and the other one is purely dependent on pressure. However, it is possible to optimize the target transformation so that one eigenvector expresses mainly the pressure dependence of the dualluminophore data with a small temperature dependence, C1(P, σT), whereas the second expresses most of the temperature dependence with a small pressure dependence, C2(T, σP). Experimental data obtained on the PtTFPP-Ruphen/ PAN/poly-tBS-co-TFEM DL-PSP using a fluorescence spectrometer (spectroscopic data set) and a CCD camera equipped with band-pass filters was subjected to the PCA analysis outlined above by using two different macros written using Matlab (version 6.1.0, release 12.1, MathWorks, Inc.). One macro applies PCA analysis to spectroscopic data comprising a 261 × 40 matrix (D261×40, 261 wavelengths and 40 P/T conditions), whereas the second executes the same algorithm for CCD image data comprising a 4 × 65 matrix (D4×65, 4 wavelengths and 65 P/T conditions). More detailed information is given below concerning the methods used, and the Matlab macros are available as Supporting Information. The coefficients resolved from the PCA analysis (C1(P, σT) and C2(T, σP)) were used to fit pressure and temperature according to eqs 1 and 2 by using least-squares regression analysis in SigmaPlot. Results and Discussion PCA Calibration Results for the Spectroscopic Data Set. To develop an understanding of the method, PCA was initially carried out on a spectroscopic data set. Thus, emission spectra were collected with a fluorescence spectrometer using PtTFPP-Ruphen/PAN/poly-tBS-coTFEM DL-PSP at the 40 different P-T combinations listed in Table 1. These data were collected by equilibrating the DL-PSP-coated coupon at a given temperature, and then emission spectra were obtained at seven different pressures. (In this series of experiments, the seven pressure values used at the different temperatures are not identical; there are slight mismatches because the pressure was established by manual control of a pressure valve.) The set of 40 emission spectra for the pressure/temperature conditions are displayed in Figure 2A. The emission maximum (λmax) for PtTFPP is ∼650 nm, whereas Ruphen exhibits a broad emission with λmax ≈ 580 nm. However, the red side of the emission band overlaps the PtTFPP emission. The PCA algorithm was applied to the spectroscopic data matrix, D261×40 (i.e., the experimental data in Figure 2A). The analysis produced two significant eigenvalues (out of a total of 40), which account for 99.91% of the variation in the raw data, D. As pointed out above, the initial PCA produces abstract factors that do not have physical significance. For example, one of the abstract eigenvectors features negative amplitude. (The abstract factors are shown in Supporting Information). After the PCA, a nonorthogonal transformation matrix was applied (eq 21) to the rotation of abstract eigenvectors C1 and C2. The coefficients and rotation angle in the transformation matrix (a - d and θ, eq 15) were determined semiempirically on the basis of the following guidelines: (1) one of the eigenvectors is mostly pressure-dependent, whereas

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Table 1. Conditions and Their Corresponding C Matrix Elements environmental conditions temperature (K)

pressure (psi)

322.6 322.6 322.6 322.6 322.6 322.6 322.6 322.6 312.1 312.1 312.1 312.1 312.1 312.1 312.1 312.1 302.7 302.7 302.7 302.7

1.19 2.10 4.24 6.20 8.18 10.25 12.09 14.69 0.97 2.22 4.22 6.17 8.39 10.56 12.07 14.69 1.22 2.08 4.05 6.33

environmental conditions CT matrix elements C1,1 C1,2 C1,3 C1,4 C1,5 C1,6 C1,7 C1,8 C1,9 C1,10 C1,11 C1,12 C1,13 C1,14 C1,15 C1,16 C1,17 C1,18 C1,19 C1,20

C2,1 C2,2 C2,3 C2,4 C2,5 C2,6 C2,7 C2,8 C2,9 C2,10 C2,11 C2,12 C2,13 C2,14 C2,15 C2,16 C2,17 C2,18 C2,19 C2,20

the other is mostly temperature-dependent; (2) negative emission intensity is not permitted; and (3) one of the eigenvector elements should group into five different sets, and elements within each set should have similar values. The final constraint arises because of the manner in which the spectral data were obtained (i.e., five temperatures and seven pressures (Table 1)). Thus, if one of the eigenvectors represents temperature variation, the corresponding elements of this temperature eigenvector should be similar in value for the same temperature (i.e., C2,1 = C2,2 = C2,3 = C2,4 = C2,5 = C2,6 = C2,7 = C2,8 and C2,9 = C2,10 = C2,11 = C2,12 = C2,13 = C2,14 = C2,15 = C2,16, etc.). With these guidelines, the transformation matrix shown in eq 21 was generated.

T)

[

0.1139 cos(343.8) -0.1255 sin (343.8) 0.5448 sin (343.8) 0.2404 cos(343.8)

]

(21)

Multiplication of the abstract R matrix by eq 21 (nonorthogonal transformation matrix) affords the row matrices R1 (blue line) and R2 (green line) displayed in Figure 2B. R1 represents the fundamental spectrum (score matrix for the first eigenvector) for eigenvector C1(P, σT) (the pressure eigenvector), whereas R2 represents the fundamental spectrum (score matrix for the second eigenvector) for eigenvector C2(T, σP) (the temperature eigenvector). (Plots of the eigenvectors before and after target transformation are shown in Supporting Information.) Note that R1 is similar in band shape to the phosphorescence spectrum of PtTFPP in the poly-tBSco-TFEM binder.27 This is consistent with the fact that the PtTFPP component dominates the pressure dependence of the DL-PSP emission. Note that there is some intensity at ca. 590 nm in R1 that arises from the (weak) pressure dependence of the Ruphen emission. Row matrix R2 features two peaks, one at ∼580 nm and a second at ∼650 nm. The shape of R2 is consistent with the fact that the emission from both luminophores is temperaturedependent. The plots shown in Figure 3A and B show the fractional contributions of the first and second eigenvectors to the reconstructed data matrix, D′′(Figure 3C) for the conditions given in Table 1. As noted above, the pressure conditions for each of the temperatures differed slightly; consequently, it is difficult to discern from Figure 3A that C1 varies with pressure but is rela-

temperature (K)

pressure (psi)

302.7 302.7 302.7 302.7 292.9 292.9 292.9 292.9 292.9 292.9 292.9 292.9 282.1 282.1 282.1 282.1 282.1 282.1 282.1 282.1

8.81 10.13 12.40 14.68 1.08 2.15 4.14 6.03 8.30 10.08 12.15 14.68 1.18 2.02 4.10 6.08 8.59 9.99 12.15 14.68

CT matrix elements C1,21 C1,22 C1,23 C1,24 C1,25 C1,26 C1,27 C1,28 C1,29 C1,30 C1,31 C1,32 C1,33 C1,34 C1,35 C1,36 C1,37 C1,38 C1,39 C1,40

C2,21 C2,22 C2,23 C2,24 C2,25 C2,26 C2,27 C2,28 C2,29 C2,30 C2,31 C2,32 C2,33 C2,34 C2,35 C2,36 C2,37 C2,38 C2,39 C2,40

tively temperature-independent. However, it is easy to see from Figure 3B that C2 varies with temperature but is only slightly pressure-dependent. This is evident because the spectra are grouped into five sets, with each set corresponding to a given temperature condition. Hence, the results indicate that the target transformation successfully resolves most of the pressure and temperature variation of the total emission from the DL-PSP by using two factors. Even though the separation is not perfect (C1 is still slightly temperature-dependent whereas C2 is slightly pressure-dependent), the PCA method leads to improved accuracy for both temperature and pressure estimation. This conclusion is supported by comparing the pressure response (at constant temperature) of the raw emission intensity ratio from the PtTFPP PSL (I14.7 psi/I, obtained at 650 nm, Figure 4A) with the pressure response of 1/C1 (Figure 4B). This comparison clearly shows that the pressure eigenvector (C1) is much more strongly pressuredependent than the raw emission intensity ratio. Specifically, over the 1-14.7 psi range, the raw intensity ratio varies by a factor of 2.2, whereas 1/C1 varies by a factor of 5.2. Moreover, the PCA method also eliminates the small pressure response of the Ruphen/PAN emission. Specifically, as can be seen in Figure 4A (filled circles), the raw emission intensity for the Ruphen component of the DL-PSP (monitored at 580 nm) varies approximately 10% over the 1-14.7 psi range, whereas the temperature eigenvector (C2, Figure 4B) is virtually pressure-independent. In summary, the PCA of the spectroscopic data set illustrates that it is possible to separate the pressure and temperature dependences of the DL-PSP. In the next section, the application of PCA to CCD image data will be presented because it is one of the main objectives of this study. Principal Component Analysis of CCD Image Data. CCD image data was obtained on a DL-PSP-coated coupon installed in a pressure chamber as described in the Experimental Section. The coupon was subjected to a temperature gradient, and there were five thermocouples installed to provide five specific points on the surface where the temperature is calibrated. CCD images were obtained at 13 different pressures, affording 5 × 13 ) 65 known P-T conditions. At each pressure, CCD images were obtained with four different band-pass filters covering

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Figure 2. (A) Experimental emission spectra of DL-PSP at various pressure-temperature combinations listed in Table 1. Excitation wavelength: 465 nm. (B) Fundamental spectra (row matrices, R) for the two largest eigenvalues.

the spectral range from 550 to 700 nm. Thus, the PCA algorithm was applied to a matrix of size 4 (wavelengths) × 65 (pressure-temperature combinations), D4×65. The transformation matrix used for the CCD image data was the same as the one optimized for the spectroscopic data (eq 21); however, the rotation angle (θ) was empirically chosen to be 10° in order to maximize the pressure and temperature decoupling in C1(P, σT) and C2(T, σP) for the CCD calibration data set. To allow the prediction of the pressure and temperature values at unknown points on the model, the C1 and C2 values determined from PCA for the calibration data are fitted to pressure and temperature using eqs 23 and 24, where the coefficients were determined by a nonlinear least-squares regression in SigmaPlot. These expressions provide “calibration surfaces” that are then used to predict P and T for any combination of C1 and C2 values that are recovered from points on the coupon surface where P and T are not known. The correlation coefficients for the empirical fits were 0.999 or better. The confidence interval of fits at 95% for P and T are also given with the equations below.

Figure 3. (A) Contribution of the first fundamental spectrum (R1) to total emission at various pressure-temperature combinations. (B) Contribution of the second fundamental spectrum (R2) to total emission at various pressure-temperature combinations. (C) Reconstructed spectra D′′ ) R1C1 + R2C2 obtained by combining the total contributions from the two largest eigenvalues.

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Figure 4. (A) Pressure response of PtTFPP emission centered at 650 nm (blank circles) and of Ruphen/PAN emission centered at 580 nm (filled circles). Data are collected by using the fluorescence spectrometer for the conditions that correspond to 292.9 K listed in Table 1. (B) Variation of C1 and C2 with pressure at 292.9 K.

P ) -3.098 + 8.792C1 - 3.040C2 - 5.782C1C2 2

2

2

2

2.023C1 + 15.36C2 + 2.639C1 C2 - 20.01C2 C1 + 7.498C12C22 ( 0.10 psi (95%) (22) T ) 237.3 + 107.8C1 + 14.16C2 - 13.52C1C2 36.59C12 - 0.2342C22 + 5.046C12C2 + 2.182C22C1 - 1.075C12C22 ( 0.40 K (95%) (23) To calculate the C1 and C2 values for an unknown pixel in the CCD images (unknown P and T), the data for one of the calibration conditions (the last column in the calibration data matrix, D4×65) is replaced with the data for the unknown pixel (a column of four Iref/I values corresponding to the four wavelengths at the unknown point). Then the PCA algorithm is applied to this new D′4×65 matrix. The newly found C1u and C2u for the unknown point are then put into eqs 22 and 23 to estimate P and T for the pixel. Initial results showed that this approach leads to an approximate 1% error in the predicted

P and T for the unknown pixel. This is because introducing an unknown column of data into the D matrix slightly changes the values of the C elements (for which eqs 22 and 23 are fitted) obtained from the original calibration data matrix, D4×65. In essence, the introduction of the unknown pixel data into the PCA analysis slightly changes the calibration surfaces defined by eqs 22 and 23. This problem was alleviated by computing corrected coefficients, C1uc and C2uc, for the unknown pixel that are evaluated such that they map back onto the original calibration surfaces defined by eqs 22 and 23.30,31 The procedure outlined above was applied to every pixel in the CCD image (231 × 426 ) 98 406 pixels). For each pressure image (this corresponds to the four ratio images obtained using the four different color filters), the PCA algorithm required ca. 2 h to calculate the P and T surface distributions on a WinTel-based PC (P4 CPU, 2.40 GHz, 1 GB ram). Table 2 collects the predicted average P values for the coupons at the 13 different pressures. (The average and standard deviations in P were determined by averag-

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Table 2. Accuracy of Average Pressure Estimates Obtained with PCA and Intensity-Ratio Methods PCA calibrationa

intensity-ratio calibrationb

P(exp) ( 0.01 psic

P(est)

σ(psi)

% error in P

P(est)

σ(psi)

% error in P

1.04 1.99 3.01 4.01 5.04 6.00 6.97 8.00 9.00 9.96 12.02 12.99 14.00

1.09 1.98 3.00 3.97 5.01 6.04 7.01 8.04 9.07 10.01 12.06 13.04 14.00

0.01 0.02 0.02 0.02 0.02 0.03 0.03 0.03 0.03 0.03 0.05 0.05 0.05

+4.8 -0.5 -0.3 -1.0 -0.6 +0.7 +0.6 +0.5 +0.8 +0.5 +0.3 +0.4 0

1.08 1.99 3.00 3.98 5.01 6.02 7.01 8.05 9.06 10.07 12.10 13.08 14.10

0.03 0.02 0.02 0.03 0.05 0.06 0.06 0.06 0.06 0.06 0.07 0.10 0.12

+3.8 0 -0.3 -0.8 -0.6 +0.3 +0.6 +0.6 +0.7 +1.1 +0.7 +0.7 +0.7

a Based on CCD data acquired at four wavelengths (550, 600, 650, and 700 nm). b Based on CCD data acquired at two wavelengths (550 and 650 nm). c Pressure determined by using a pressure gauge.

ing the estimated P values at all points in each image.) Note that the predicted pressures are very close to the experimental measurements and that the highest standard deviation is only 0.05 psi, indicating that the DL-PSP combined with PCA analysis provides good precision and accuracy when predicting pressure, even though the coupon is subjected to a ca. 20 °C temperature gradient. Figure 5 provides examples of CCD images obtained on the coupon surface as well as example P and T surface maps. The top two images in Figure 5 show uncorrected image ratios (Iref/I) for four pressures obtained at the wavelengths corresponding to the emission maximum for the Ruphen and PtTFPP dyes. Note that in each image there is a well-defined gradient in the uncorrected intensity ratio; because the pressure on the surface is constant, the gradient arises from the temperature gradient on the coupon. The bottom two images in Figure 5 show the PCA-calibrated P and T surface distributions. As expected, the pressure maps are spatially uniform, whereas the temperature maps quantify the temperature gradient created by the experimental arrangement. Quantitative information concerning the precision and accuracy by which temperature is predicted is provided (30) A set of corrected coefficients, C1uc and C2uc, for the unknown pixel are evaluated such that they map back onto the original eigenvector calibration surfaces defined by eqs 22 and 23. To accomplish the correction, the parameters ∆C1(P) and ∆C2(T) are defined as (a) ∆C1(P) ) C1(P) - C1(P)u and (b) ∆C2(T) ) C2(T) - C2(T)u, where C1(P) and C2(T) are the eigenvectors obtained from the calibration data set and C1(P)u and C2(T)u are the eigenvectors obtained when PCA is applied with one column of D4 × 65 replaced with a set of data from an unknown pixel. These equations afford ∆C1(P) and ∆C2(T) as smoothly varying functions of P and T, thus allowing one to determine ∆C1 and ∆C2 at the pressure and temperature condition corresponding approximately to the that of the unknown pixel. (The approximate P and T for the unknown pixel are determined by substituting C1u and C2u into eqs 22 and 23.) The C1uc and C2uc values for the unknown pixel are then computed by the equation Ciuc ) Ciu + ∆Ci, and the values are substituted into eqs 22 and 23 to determine the estimated P and T values at the unknown pixel. (31) To explore the effects of varying the parameters for the PCA analysis on the results, the size of the D matrix was varied (D4×15, D4×30, and D4×70) by decreasing the number of conditions used to explore the dependence of ∆C1 and ∆C2 on the size of the D matrix. It was found that as the dimension of D decreases ∆C1 and ∆C2 increase; consequently, the correction to C1u and C2u becomes more important. The effect of the number of different image wavelengths (band-pass filters) used on the results was also examined. It was found that the removal of the 700/10 nm filter data, thereby reducing D to a 3 × 65 matrix, had very little effect on the PCA results. However, decreasing D to a 2 × 65 matrix (using 550/40 and 650/10 filter images only) produced relatively poor results.

Figure 5. First and second rows: uncorrected CCD ratio images (Iref/I) obtained by using 550/40 and 650/10 nm filters at 6, 9, 12, and 14 psi, respectively. Third and fourth rows: false color predicted temperature (third row) and pressure surfaces (fourth row) obtained by using the PCA calibration method. Each surface image is 1 in. × 3.86 in. in size. The images were cropped from the same segment of a 2 in. × 4 in. coupon shown in Figure 1.

in Figure 6, where the estimated values are plotted as lines from the top to the bottom of the coupon for six different pressures. (The values comprising the lines were taken from a vertical column of pixels at the center of the coupon.) The calibration points (thermocouple locations) are shown in the plots as circles. Overall, it is evident that the PCA method accurately predicts the surface temperature. The highest error in estimated temperature was 0.4 K, and the average error was 0.2 K. Interestingly, it is evident that the average temperature of the coupon increases with decreasing pressure. This effect arises because the rate of convective cooling of the plate increases with the pressure in the chamber. Finally, it is also evident that the standard deviation in the predicted temperature increases with decreasing pressure. (This is evident as noise in the line plots at low pressures in Figure 6.) It is believed that the origin of this effect arises because at

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Figure 6. Predicted temperature gradient from the top to the bottom of the coupon as indicated by lines for six different pressures ((top) 1.99, 4.01, 6.00, 8.00, 9.96, and 14.00 psi (bottom)). The thermocouple data are depicted as circles. Only six estimated temperature lines are shown; the others are omitted for clarity.

lower pressures the D matrix is dominated by the PtTFPP emission and small variations in the intensity of the signal give rise to the error in T. Intensity-Ratio Method: Comparison with Principal Component Analysis. To provide a benchmark by which to assess the improvement in recovery of P and T values afforded by using DL-PSP data, the CCD image data was also subjected to intensity-ratio analysis. This method has been used by others to construct pressure and temperature surfaces from DL-PSP image data.1 Intensity ratios for 65 known P-T conditions for image data acquired using the 550/40 and 650/10 nm band-pass filters (2 × 65 ) 130 points) were fitted by nonlinear regression in SigmaPlot to eqs 1 and 2 affording the calibration coefficients shown in eqs 24 and 25. By analogy to the PCA calibration functions, the correlation coefficients for the nonlinear regressions were g0.999. The P and T calibration surfaces plotted by using eqs 24 and 25 are shown in Figure 7A and B, respectively. In these 3-D plots, the points represent the 65 known P-T calibration points, whereas the surfaces represent the functions in eqs 24 and 25.

P ) -3.842 + 5.895X - 0.9546Y - 1.332XY 2.323X2 + 41.12Y2 + 1.553X2Y - 35.50Y2X + 9.034X2Y2 ( 0.18 psi (95%) (24) T ) 261.3 + 48.88X - 54.55Y + 75.30XY 7.381X2 + 18.56Y2 - 28.62X2Y - 30.21Y2X + 11.64X2Y2 ( 0.42 K (95%) (25) It is important to note that the precision of the fit of the intensity-ratio pressure calibration data at the 95% confidence interval (eq 24) is 2 times that which is recovered for the PCA coefficient calibration (eq 22). By contrast, the 95% confidence intervals for fitting the calibration values for T by the intensity-ratio and PCA methods are similar (eqs 23 and 25). By using eqs 24 and 25, the P and T values at every pixel on the coupon surface were computed. Then the average and standard deviations in the pressure were determined, and the results are listed in the right set of columns in Table 2. It is evident that the average pressures

Figure 7. (A) Pressure calibration surface for obtained from the intensity-ratio method according to eq 24. (B) Temperature calibration surface obtained from the intensity-ratio method according to eq 25. In both plots, the P-T calibration points are represented as black dots.

predicted from the intensity-ratio method at high pressure are not as accurate as those recovered from the PCA method. The larger error likely results from the fact that the temperature interference is larger at higher pressures. In addition, the intensity-ratio method also gives rise to larger standard deviations for the pressure images, which likely results from the fact that the sensitivity of the image ratios to pressure is lower (cf. parts A and B of Figure 4). Summary and Conclusions A principal component analysis method has been developed and applied to the analysis of spectroscopic and CCD image data acquired at multiple wavelengths from a dual-luminophore pressure-sensitive paint. The results

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obtained by the PCA calibration are subjected to a statistical analysis, and they are compared with results obtained from a conventional emission intensity ratio calibration method. The analysis reveals that PCA calibration affords improved accuracy and precision in the prediction of surface pressures from CCD image data. The improvement in the pressure prediction is most evident at pressures near atmospheric, and this is significant because many wind tunnel tests are carried out with surface pressures near 14.7 psi. However, the ability to predict the surface-temperature distribution was not significantly improved by the PCA method. An analysis of spectroscopic data from the DL-PSP demonstrates that PCA eliminates the problem caused by spectral overlap of the emission from the temperatureand pressure-sensitive luminescent dyes by “decoupling” their response. This effect leads to improved accuracy and sensitivity in the pressure prediction. In addition, although it has not been demonstrated in the present work, the PCA method can be extended to PSPs that contain three or more luminescent dyes. For example, the formulation of a multiluminophore PSP that, in addition to the TSL and PSL, contains a temperature- and pressure-independent luminescent dye will allow the use of PCA to eliminate the need to acquire reference images. Eliminating the need for “wind-off” reference images would

Ko¨ se et al.

represent a significant breakthrough in the application of PSP to wind tunnel testing because movement and deformation of the model in the wind-on images relative to the wind-off images represents a significant interference in recovering accurate surface-pressure maps. Despite its advantages, the PCA method is computationally demanding; consequently, an analysis of large image data sets takes considerable time. To address this problem, we are in the process of developing a more efficient PCA algorithm that will decrease the amount of time needed to compute pressure and temperature surfaces. In addition, the relentless increase in computational performance that can be expected in the future will also decrease the computational time needed to implement PCA analysis to CCD image data. Acknowledgment. This work was supported by the NASA Constellation University Institutes Project at the University of Florida (grant no. NCC3-994). Supporting Information Available: Matlab macros for PCA analysis of spectroscopic and CCD image data. Plots of principal component spectra and eigenvectors before and after target transformation. This material is available free of charge via the Internet at http://pubs.acs.org. LA050999+