Abridged Spectral Fluorescence Imaging An innovative Graduate Student Research Report

Transcription

1 Abridged Spectral Fluorescence Imaging An innovative Graduate Student Research Report Principle Innovator Mahnaz Mohammadi, Graduate student Chester F. Carlson Center for Imaging Science Rochester Institute of Technology Prof. Roy S. Berns, Advisor November

2 Abstract The true spectral reflectance factor of a series of fluorescent paints was reconstructed using different abridged method, calculation and filter fluorescence reduction methods, and adopted for imaging using a multi-channel digital camera. The reconstructions were simulated using a virtual camera and also an image-based reconstruction was performed. The performance of the system was highly dependent upon the sharp short wavelength cutoff filters. The purpose of these filters was reducing the amount of luminescence emerging from a fluorescent sample. The fluorescence imaging system was also highly dependent upon the calibration target. The project was divided into four stages: Stage I: Preparing a series of fluorescent paints and measuring with a commercial bi-spectrometer, Stage II: Simulated spectral fluorescence imaging based on two different abridged spectral methods, Stage III: Imaging system construction and testing, Stage IV: UV Fluorescence imaging. Introduction The measured spectral radiance of a fluorescent sample using a spectrophotometer with polychromatic illumination and monochromatic detection is a curve that consists of reflected and luminescent components, " T (#) = " S (#) + " L (#) (1) where β T (λ), β S (λ), and β L (λ) are the total, reflectance, and luminescence radiance factors, respectively. Since the luminescence radiance factor of a fluorescent sample is illuminant dependent, the total radiance factor is also dependent upon the illuminant. In order to accurately measure the reflected and luminescence components, a bispectrometer is used, having independently controlled monochromatic illumination and detection [1]. An abridged method to separate the two components is also a technique proposed in the literature [2, 3, 4]. 2

3 Allen [2] introduced an abridged method using just two sharp short-wavelength cutoff filters to calculate the true reflectance (reflected radiance factor). The idea behind his theory is reducing the luminescence in the overlap region, in which both excitation and emission occurs at the same or shorter wavelengths, the anti Stokes shift [5], and excluding all the excitation wavelengths to measure the true reflectance in wavelengths larger than the emission range. These two sharp short-wavelength cutoff filters are called fluorescence -weakening and fluorescence -killing filters. Allen s idea was known as calculation method. The idea proposed by Eitle and Ganz [3] was based on the measurement of the total radiance factor using a non-filtered source and a series of sharp short-wavelength cutoff filters. The wavelengths of the incident light that excite fluorescence would be excluded by using the short-wavelength cutoff filters. The problem regarding the overlap region is still inherent in this method. These filters reduce the amount of fluorescence at this region but the excitation is not completely eliminated. Hence, the estimated reflected radiance, β S, would be higher in this region. This theory was called filter fluorescence reduction method. The calculation and filter fluorescence reduction methods were employed in spectral imaging of a series of fluorescent paints. The samples were the Golden acrylics Fluorescent paints containing blue, green, magenta, orange, red, and yellow colorants. A set of sharp short-wavelength cutoff filter was used in a simulated and imaged-based abridged spectral fluorescence imaging system to estimate the true spectral reflectance factor. A SVD-based pseudo inverse technique was used to derive a transformation matrix to transform simulated and imaged-based digital counts to true spectral reflectance factor. The spectral accuracy of the method was analyzed by root mean square error (RMS%) between the estimated and the measured true reflectance factor by a Labsphere BFC-450 bispectrometer. Experimental a. Preparing a series of fluorescent paints and measuring with a commercial bispectrometer 3

4 In order to spectral fluorescence imaging, a series of Golden acrylic artist fluorescent paints was selected. All mastone paints were laid down on Leneta white papers. Table I shows the name of the six selected fluorescent paints. Table I List of Golden artist fluorescent paints used in spectral fluorescence imaging. No. Name 1 Golden Fluorescent Blue 2 Golden Fluorescent Green 3 Golden Fluorescent Magenta 4 Golden Fluorescent Orange 5 Golden Fluorescent Red 6 Golden Fluorescent Chartreuse (Yellow) An illuminant-independent bi-spectral matrix called Donaldson matrix 1 generated by measuring the radiance of each fluorescent paints with a commercial bispectrometer, Labsphere BFC-450. The total radiance, luminescence, and reflectance factors of the paints were calculated based on the corresponding Donaldson matrix. Figure 1 shows these quantities of each fluorescent paints. A target was made containing the six fluorescent paints and hereafter is called Fluor Target. was Figure 1. Spectral total, reflectance, and luminescence radiance factors of six Golden artist fluorescent paints measured by Labsphere BFC

5 By mixing each pairs of six paints, a series of mixed fluorescent paints was made. A target containing 15 mixed paints is called Mixed Target. Also a mixture of each fluorescent paints with non-fluorescent titanium white were prepared and the corresponding target named as Mixed_White Target. The radiance factors of both mixed targets were also measured by Labsphere BFC-450. These targets will be used as a verification target to evaluate the accuracy of the developed spectral fluorescence imaging system. b. Simulated Spectral Fluorescence Imaging b.1. Calculation Method The idea of the Allen method was employed in fluorescence imaging. Simulated abridged fluorescence imaging was based on a high performance Roper Scientific, Inc. Photometric Quantix 6303E that uses a Kodak blue enhanced KAF6303E CCD, a set of six glass colored filters optimized for the best colorimetric and spectral performance 6, and a set of fluorescence-weakening and -killing filters was simulated using the cubicspline function for each fluorescent paint. The optimized excitation filters for the Golden acrylic fluorescent orange along with the excitation and emission spectra of the sample are shown in Figure 2. Figure 2 Emission (green line) and excitation (cyan line) spectra of Golden Acrylic Orange along with the optimized excitation filters; the red line is transmittance of the fluorescence-weakening filter, and the blue line is transmittance of fluorescence-killing filter. 5

6 The calibration target was the GretagMacbeth ColorChecker Rendition Chart (cc) and the fluorescent samples were the Fluor Target. Reconstruction was performed individually for each patches of the Fluor Target. Illuminant CIE D65 was used in all computations. The digital counts for all pixels of the calibration target with known reflectance factor was computed as, 750 D i = % R(")#$(")#S(") i +& "=380 (1) $(") = E(")#' (") where λ is wavelength, D i is the digital count of the ith channel, R(λ) is spectral reflectance factor of a pixel, and φ is the spectral power distribution of the desired illuminant. Having an excitation filter with transmittance of τ(λ) in front of the illuminant, CIE D65, results in a new illuminant, φ(λ). The S λ, is the spectral sensitivity of the camera for the ith channel combined with the transmittance of the colored filters, an IR cut-off filter, and any desired excitation and emission filters. A noise coefficient, η, was generated consisting of 50 values with normal distribution and zero mean value and standard deviation of 2.5% of the digital count of each patch of the calibration target. Based on a singular value decomposition technique, a transformation matrix, T, converting digital counts to reflectance values was derived for each part of the spectrum shown as Figure 2. It means that for part I, with no emission, no short-wavelength cutoff filter should be in the excitation path and a sharp long- wavelength cutoff filter should be used as an emission filter in front of the camera for excluding all the emissions. Each of the excitation filters was used in the path between the illuminant, CIE D65, and the fluorescent sample. The total radiance in the pass band of each filter was simulated separately. The simulated digital counts would be related to the spectral reflectance in part I. In part III, the fluorescence-killing filter was used in this excitation path to remove all the excitation wavelengths reaching the sample. All the simulated signals by this configuration would correspond to the spectral reflectance in part III. Using the fluorescence-weakening filter in front of the illuminant would reduce the amount of emission but not exclude all. The spectral reflectance in the overlap region was calculated using this excitation filter. Therefore, three transformation matrices for the three parts of the spectrum were derived. 6

7 The same excitation and emission filters described above were used to simulate the digital counts for the fluorescent samples. Since employing the fluorescenceweakening and -killing filters in the excitation path means changing the illuminant, called illuminants nos. 2 and 3, the spectral luminescence would vary under these illuminants. Therefore, Eq. (1) is not valid for the fluorescent samples. In this case, the luminescence under illuminants nos. 2 and 3 should be calculated. The inner summation in Eq. (2) is the emerged total radiance from a fluorescent sample under a new illuminant. 750% 750% D i = + ' D µ," ' & & 300 T 380 ( ) #$( µ ) ( ( * )* ) + # S(") i +, (2) where, D T ( µ," ) is the Donaldson total radiance factor matrix, measured with the Labsphere BFC-450, µ and λ are the excitation and emission wavelengths. The other terms are the same as before. Digital counts for each part of the spectrum for the fluorescent samples were calculated using Eq. (2). By having the transformation matrix and digital counts of the fluorescent sample for each part of the spectrum, the reflectance factor of the sample according to Eq. (3) was estimated, ˆ R = T" D (3) where, ˆ R is the estimated reflectance matrix-vector, D is the digital count matrix, and T is the transformation matrix. An independent-wavelength constant, K, which reduces the true emission using illuminant no. 2 was calculated based on the estimated total radiance factor under non-filtered and filtered illuminants at λ k. Once K was known, the reflectance factor in the overlap region was calculated. The goodness of the theory to estimate the reflectance for the Golden acrylic orange paint is shown in Figure 3. Errors in the very long wavelengths might be attributed to a lack of accuracy of the transformation matrix at long wavelengths. The same trend has been seen in estimating the true reflectance of the other paints. 7

8 Figure 3 Reflectance factor of Golden acrylic orange; the blue line is measured with the Labsphere BFC-450 and the red line is reconstructed using simulation fluorescence imaging based on the Allen s method. The Allen method described above is an accurate method when the reflectance of an individual fluorescent paints was subject to be reconstructed. Meanwhile, this method could be a proper approach when a spectroradiometer was a device detector. There is some limitation, which makes the Allen s method not be a proper one for fluorescence imaging. Here, some of these limitations are listed. 1. The system was very sensitive to wavelength selection for calculating the independent-wavelength constant to reconstruct the reflectance factor in the overlap region, 2. Since different fluorescent paints have different fluorescence characteristics, there is no guarantee that the independent-wavelength constant can be calculated at the same wavelengths for all fluorescent paints, 3. The noise of the imaging system might be increased using three transformation matrices to convert the digital count to the reflectance factor, 4. Selection of fluorescence -weakening and -killing filters is depend upon the excitation and emission characteristic of each fluorescent paints. Therefore, each fluorescent paints requires a set of short-wavelength cutoff filter. b.2. Filter Fluorescence Reduction Method 8

9 The limitations explained in the previous section make the Allen s method to be a proper one just for individual fluorescent paint. Hence, it cannot be a general solution for fluorescence imaging when a target containing more than one fluorescent paints was a subject to be reconstructed. Another approach based on filter fluorescence reduction method proposed by Eitle and Ganz [3] was studied for fluorescence imaging. This method was based on measuring the total radiance factor using a non-filtered source and a series of sharp short-wavelength cutoff filters. This idea was adopted for fluorescence imaging. A set of real sharp short-wavelength cutoff filters was ordered. The transmittance factor of these filters was measured by GretagMacbeth Color Eye 7000 and is shown in Figure 4. The filters were selected based on simulation process to reconstruct the reflectance factor using the Allen s method and the fluorescence characteristic of each fluorescent pigments, separately. Figure 4 Transmittance factor of Rosco sharp short-wavelength cutoff filters. The goal in the new approach, filter fluorescence reduction method, was developing a fluorescence imaging system which could be applied for a target containing both fluorescent and non-fluorescent paints. Also, there should be no limitation for the number 9

10 of fluorescent paint. In order to achieve these goals, some modification has been done on the process explained earlier. They are: 1. Different calibration target was employed to calibrate the fluorescence spectral imaging system. 2. Color Checker and Fluor Target were the targets for testing the system, 3. Mixed Target and Mixed_White Target were employed as independent fluorescent verification targets. 4. The modified Sinarback 54 camera, with 6 channels, was simulated instead of Photometric Quantix 6303E, the specification of this camera will explain in the next section, 5. Each sharp short-wavelength cutoff filter assumed as a channel in the fluorescence imaging. In order to verify the accuracy of the measured radiance of the fluorescent paints under a desired illuminant with a commercial spectroradiometer, Photoresearch PR650, the radiance of each paints under a desired illuminant was calculated using the corresponding bispectral matrix of each paints. Figure 5 shows the measured and calculated radiance of the Fluor Target under a corrected Tungsten light with a blue filter to simulate the daylight. The spectral power distribution of the light source is shown in Figure 6. The performance shown in Figure 5 approves a high accuracy of spectroradiometer to measure the radiance of fluorescent paints. 10

11 Figure 5 The measured (red line) and calculated, using bispectral matrix (green line), radiance of Fluor Target. Figure 6 Spectral power distribution of Tungsten light corrected with a blue filter to simulate the daylight. 11

12 A virtual digital camera was simulated using the spectral sensitivity of Sinarback 54, the measured radiance of each targets with Photoresearch PR650, and Eq. (4). 750 D = $ R(") # S(") + % i "=380 i (4) where λ is wavelength, D i is the digital count of the ith channel, R(λ) is spectral radiance of a pixel. The S λ, is the spectral sensitivity of the camera for the ith channel combined with an IR cut-off filter. The other terms are explained earlier. Based on a singular value decomposition technique, a transformation matrix, T, converting the simulated digital counts to radiance values was derived using the calibration target. The radiance of each target was estimated using Eq. (4), ˆ R = T" D (5) Where D, [(6 " n) " m] matrix, is the digital count matrix, T, [38 " (6 " n)] matrix, is the transformation matrix, and ˆ R is the estimated radiance. Here, n represents the number of short-wavelength cutoff filter and m stands for the number of patches in the target. For example, having two sharp short-wavelength cutoff filters makes a (12 " m) matrix of digital count. As it was said earlier, the reflectance factor of the Fluor Target was employed in the calibration target. This was because of changing the total radiance factor under different illuminant. For each short-wavelength cutoff filter, a corresponding transformation matrix was needed if the total radiance factor was used in the calibration target. We needed to obtain a set of data as reflectance factor that not being varied under different illuminant. Because of these reasons the reflectance factor of the Fluor Target was used in the calibration target. Figure 7 shows an example, of reconstructing the reflectance factor of Color Checker and Fluor Target using the filter fluorescence reduction method with three shortwavelength cutoff filters. The performance of the simulated fluorescence imaging based on filter fluorescence reduction method using different verification targets is summarized in Table II. The range of cutoff wavelengths of the selected Rosco filters was in between nm. Since the goal was reconstructing the reflectance factor of a group of paints, the selection of short-wavelength cutoff filter and the number of filters would be critical 12

13 issues in the accuracy of the fluorescence imaging. If the cutoff wavelength of the filters occurs at very long wavelengths, most of the excitation wavelengths would be removed and less energy reaching the sample that might excite luminescence. On the other hand, a very short wavelength cutoff filter would not be a proper one for the paints that fluoresce at long wavelength such as red fluorescent paint. Therefore, selection of the filters is very important. Figure 7 Spectral reflectance factor of Fluor Target. Green line represents the measured with Labsphere BFC-450 and red line represents the reconstructed using the simulated filter fluorescence reduction method. Calibration target was Color Checker, Fluor Target, and Mixed_White Target. Table II. Statistical results of the spectral RMS% error between the measured reflectance factor with Labsphere BFC-450 and the reconstructed based on the simulated filter fluorescence reduction method using three sharp short-wavelength cutoff filters. Calibration target was Color Checker, Fluor Target, and Mixed_White Target. Target Average Minimum Maximum Std Dev. Fluor Target Mixed Target Color Checker

14 c. Imaging system construction and testing Images of the targets and a uniform grey background were captured using a modified Sinarback 54 digital camera in its eight-shot mode. The Sinarback 54 is a three channel digital camera that incorporates a Kodak KAF-22000CE CCD with a resolution of pixels. This camera has been modified by replacing its IR cut-off filter with clear glass and fabricating two filters used sequentially, resulting in a pair of RGB images 7. For this experiment, a pair of tungsten lights, Broncolor Plus G, positioned at 45 0 angles to the center of the painting was used. Since the fluorescent paints fluoresce highly in the daylight, a pair of converting blue filter was inserted in front of the tungsten light to simulate CIED65 illuminant. Figure 8 shows the total radiance factor of the Fluor Target and a perfect diffuse white called Halon measured by Photometric PR650. As it was expected the total radiance factors under tungsten + blue filter are larger than the radiance factor under the tungsten light. Therefore, the modified tungsten light was used during all imaging as a light source for having the maximum possible fluorescence. Figure 8 Total radiance factor of the Halon and the Fluor Target measured by Photoresearch PR650. The green line represent the radiance factor under the tungsten and the red line represents the radiance factor under the tungsten + blue filter. 14

15 The Color Checker, Fluor Target, and Mixed Target were subject to be imaged. The Rosco filters were inserted in front of light source once at a time. The exposure time and the aperture size of the camera were adjusted. The radiance emerged from the targets for each patch of the targets was also measured by Photoresearch PR650. All Images were digitally flat fielded using the grey background followed by image registration. Totally, with an image captured under non-filtered light source, seven images were captured. The transformation matrix was derived using the measured spectral reflectance factors and the captured digital counts for the calibration target. A SVD-based pseudo inverse technique was used to derive the transformation matrix using Eq (5). Spectral reflectance factor of all targets, Color Checker, Fluor Target, Mixed Target, and Mixed_White Target, was estimated from linear photometric camera signals by a matrix transformation and Eq (5). All 2, 3, 4, 5, 6, and 7 possible combinations of the seven images were employed to derive the transformation matrix and finally reconstructing the spectral reflectance factor. The average spectral RMS% error between the measured and the reconstructed reflectance factor of the targets were calculated. Figures 9 and 10 show the trend of spectral performance using different combination of filters. These figures are based on the best result of each combination. As it can be seen from the figures, increasing the number of filters improved the spectral performance of both targets. The reason is that increasing the number of filters means increasing the number of channels in spectral imaging or in the other words collecting more data. The average spectral error gets to zero for the cases of having more than four filters. It means that the system is over determined. Based on this result, one can assume that three imaging would be enough for spectral fluorescence imaging. Since the best results of each combination of filters obtained when one imaging was under non-filtered light source, it is recommended to have two imaging using the proper short-wavelength cutoff filter and one imaging under non-filtered illuminant. 15

16 Figure 9 Average RMS% between the measured and the image-based reconstructed reflectance factor of the Fluor Target based on the filter reduction method. Figure 10 Average RMS% between the measured and the image-based reconstructed reflectance factor of the Color Checker target based on the filter reduction method. In order to investigate the effect of the calibration target in the performance of fluorescence imaging, different calibration targets was employed to reconstruct the spectral reflectance factor. The statistical results of the spectral RMS% error between the reconstructed and the measured reflectance factor using different calibration and 16

17 verification targets are tabulated in Table III. Pure fluorescent paints as calibration target, Fluor Target, performed reasonably to reconstruct the spectral reflectance factor of itself and Mixed Target. But such a target was not a proper calibration target to train the imaging system to be performed for non-fluorescent sample such as Color Checker or mix of fluorescent and non-fluorescent white paints. Therefore, a calibration target employed for an imaging system to be applicable for both fluorescent and nonfluorescent paints should also be contained a set of non-fluorescent paint. As it can be seen, the performance of Color Checker was significantly improved, average RMS% error to 2.04 using non-fluorescent sample in the calibration target. The performance of Mixed_White Target and Mixed Target were not acceptable as a point of spectral imaging view. The reason might be because of unbalanced number of fluorescent and non-fluorescent patches in the calibration target. In this case the nonfluorescent samples are dominant to train the system. To investigate this issue, the Mixed_White Target was added to the last calibration target. The performance of the new calibration target to reconstruct both fluorescent and non-fluorescent sample was reasonable. Selecting the calibration target is a critical issue in the performance spectral fluorescence imaging. More independent fluorescent and non-fluorescent targets should be evaluated using different calibration targets. Table III. Statistical results of the spectral RMS% error between the measured reflectance factor with Labsphere BFC-450 and the imaged-based reconstructed filter reduction method using three short-wavelength cutoff filters using different calibration target. Calibration target Verification target Average Minimum Maximum Std Dev. Fluor Target Fluor Target Fluor Target Mixed Target Fluor Target Mixed_White Target Fluor Target Color Checker Fluor Target+cc Fluor Target Fluor Target+cc Mixed Target Fluor Target+cc Mixed_White Target Fluor Target+cc Color Checker Fluor Target+Mixed _White+cc Fluor Target Fluor Target+Mixed _White+cc Mixed Target Fluor Target+Mixed _White+cc Mixed_White Target Fluor Target+Mixed _White+cc Color Checker

18 Since the performance of the calibration target including Fluor Target, Color Checker, and Mixed_White Target was higher than the other calibration targets, this target was selected as calibration target in the fluorescence spectral imaging for the specific verification targets. The spectral performance in reconstructing the reflectance of the four verification targets imaging under two filtered- and non- filtered illuminants are shown in Figures Figure 11 Spectral reflectance factor of Fluor Target. Blue line is the measured with Labsphere BFC-450 and red line represents the image-based reconstructed reflectance factor using the filter fluorescence reduction imaging with calibration target containing the Color Checker, reflectance factor of the Fluor Target, and the reflectance factor of the Mixed-White Target. 18

19 Figure 12 Spectral reflectance factor of Mixed Target. Blue line is the measured with Labsphere BFC-450 and red line represents the image-based reconstructed reflectance factor using the filter fluorescence reduction imaging with calibration target containing the Color Checker, reflectance factor of the Fluor Target, and the reflectance factor of the Mixed-White Target. 19

20 Figure 13 Spectral reflectance factor of Mixed_White Target. Blue line is the measured with Labsphere BFC-450 and red line represents the image-based reconstructed reflectance factor using the filter fluorescence reduction imaging with calibration target containing the Color Checker, reflectance factor of the Fluor Target, and the reflectance factor of the Mixed-White Target. 20

21 Figure 14 Spectral reflectance factor of Color Checker. Blue line is the measured with Labsphere BFC-450 and red line represents the image-based reconstructed reflectance factor using the filter fluorescence reduction imaging with calibration target containing the Color Checker, reflectance factor of the Fluor Target, and the reflectance factor of the Mixed-White Target. d. UV Fluorescence Imaging Spectral filter fluorescence reduction imaging method was an approach to reconstruct the spectral reflectance component of fluorescence radiance. The goal of this method was eliminating a part of excitation wavelengths, which stimulate the fluorescent molecules to be emitted at the longer wavelengths. To reconstructing and rendering a painting containing fluorescent paints, the luminescence component of the fluorescence radiance should also to be reconstructed. Since the emission curve of a fluorescent paint is the characteristic of the paint and the curve shape is illuminant- independent, it was proposed to UV fluorescence imaging to determine the peak and bandwidth of emission spectrum of a fluorescent paint. The idea of UV fluorescence imaging is illuminating a 21

22 painting under UV light and imaging under visible range of spectrum. The digital camera should be calibrated under this illuminating condition. In order to UV fluorescence imaging, two long-wave UV lamps recommended by National Gallery of Art, Washington, DC, was ordered. The next step would be UV imaging under the new light and reconstructing the emission spectrum. Conclusions The abridged theory proposed by Allen [2] based on calculation method and Eitle and Ganz s theory [3] based on filter fluorescence reduction method to separate the reflectance and luminescence component of the total radiance emerging from a fluorescent sample was studied and implemented, via simulation and image-based, for abridged spectral fluorescence imaging. The Allen s theory was a proper method to image a painting containing an individual fluorescent paint. Since the fluorescence characteristic of fluorescent paints is varied, the accuracy of this method was not acceptable when just a set of fluorescence-weakening and killing filters was used for different fluorescent paints. Also the theory was very effective for the fluorescent samples with a large amount of luminescence. The spectral fluorescence imaging based on filter reduction method was a proper approach to aim this goal. The performance of this method was very dependent upon the selection of the sharp short-wavelength cutoff filters and the calibration target to train the spectral fluorescence imaging system. Optimizing a set of filters to employ for most common fluorescent paints is suggested as a future research. The study of the noise effect in fluorescence imaging is also recommended. Since the luminescence factor is highly illuminant- dependent, having knowledge of excitation characteristic of a fluorescent paint is required to predict the luminescence factor under different illuminant. Therefore developing a system to derive the excitation spectrum is recommended. Finally, these methods require rendering a real painting containing both fluorescent and non-fluorescent paints experimentally. 22

23 References: [1] R. Donaldson, Spectrophotometry of fluorescent pigments, Brit. J. Appl. Phys. 5, (1954). [2] E. Allen, Separation of the spectral radiance factor curve of fluorescent substances into reflected and fluoresced components, Applied Optics 12, (1973). [3] D. Eitle and E. Ganz, Eine Methode zur Bestimmung von Normfarbwertrn für fluorezierende proben, Textilveredlung 3, (1968). [4] F. T. Simon, The two-mode method for measurement and formulation with fluorescent colorants, J. Color Appearance 1(4), 5-11 (1972). [5] F. W. Billmeyer, Jr., Colorimetry of fluorescent specimens: A state-of-art report, NBS-GCR , [6] S. Quan, Evaluation and Optimal design of Spectral Sensitivities for Digital Color Imaging, PhD thesis, Rochester Institute of Technology, [7] See for the related papers. Acknowledgments This research was supported by CIS-Kodak innovative research grant. The author would like to thank Mrs. Azine Mohammadi as an undergraduate student to help making the samples and cooperating in performing part of measuring process. 23