Correction of Right-Angle Fluorescence Measurements for the Absorption of Excitation Radiation John F. Holland, Richard E. Teets, Patrick M. Kelly, and Andrew Tlmnlck” Department of Biochemistry and Department of Chemistry, Michigan State University, fast LansingI Michigan 48824
The effect of excitation beam absorption on measured values of fluorescence has been studied wlth a computer-centered spectrofiuorimeter capable of measuring fluorescence and absorbance slmuitaneously. This effect appears to be independent of the nature of the absorbing species and the excitation and emisslon wavelengths. A model is proposed and tested which corrects fluorescence, observed at 90°, for the attenuation of the excitation beam caused by the absorbance of the fluorophore and any chromophores present in the cell. The resuitlng absorptlon-corrected fluorescence is linear with the concentration of the fiuorophore in solutions wlth total absorbances as high as 2.0.
A large number of fluorimetric methods of analysis have been developed; however, few are used routinely because of the many instrumental, photophysical, and chemical variables which affect the accuracy of fluorescence measurements. The instrumental variables restricting the widespread application of fluorescence techniques have been carefully delineated by several investigators (1-4). Numerous corrections have been made for these instrumental variables which have resulted in several unique instrument systems (5-9) as well as commercially available corrected-fluorescence systems (10-12). The non-instrumental or photophysical variables which are intrinsically part of the system being measured have been defined (13). Of these variables, the most significant are the absorption processes which occur within the sample cell. These include the primary processes which act on the excitation beam and the secondary processes which act on the fluoresced radiation. The primary absorption processes, which are independent of all of the other photophysical and instrumental variables, reduce the intensity of the excitation radiation and, as a result, reduce the amount of the observed fluorescence. This effect has been noted by several investigators (2, 14, 15). To minimize it, the general recommendation of working with extremely dilute solutions has been made. However, this is not a “universal” remedy. Consider the case where a fluorophore is initially present at a very low concentration level but the solution absorbance is high due to the presence of other absorbing species. Continued dilution of such a system would not increase the accuracy of a determination. In addition, dilution may cause changes in conformation, bonding, solvation, and the degree of association as well as other chemical events which may alter the absorptionfluorescence processes and thereby introduce large unknown errors into the measurements. On the other hand, failure to dilute such a solution will introduce serious error into a fluorimetric determination if the fluorescence measurements are not corrected for the primary absorption processes. Some attention has been given to this problem. Parker and Barnes (17) proposed the use of a correction factor and several other investigators have made attempts to evaluate this factor as well as effects of primary absorption on fluorescence measurements (16,18,19). In addition, two different approaches 706
ANALYTICAL CHEMISTRY, VOL. 49,
NO. 6, MAY 1977
have been applied to unique experimental conditions to arrive at approximated corrections for the absorption of the excitation radiation (20,21). As a matter of practice, however, a scientific paradox has existed in this area up to the present time. Many investigators using fluorescence methods are usually quite aware of this absorption problem but, in general, have consistently either deemed it negligible, assumed it to be constant from sample to sample, or neglected it entirely. Analytical fidelity has suffered as a result. Furthermore, a viable correction cannot be realized until the various factors contributing to the absorption and emission processes are clearly understood and this knowledge is applied to the development of an effective correction scheme. Unfortunately, to date, very little is known about the theoretical basis of the proposed correction strategies, the chemical and instrumental conditions necessary for their application, and the accuracy of the resultant corrections. The major objective of this investigation was to delineate the nature of the primary absorption processes, study their effect on observed fluorescence, and to develop a model, more detailed than the ones previously proposed, which will serve as the basis for the automatic correction by a computerized spectrofluorimeter for the absorption related variations in fluorescence measurements. The necessary inputs to the computer were defined and a program has been written that will calculate these corrections in real time and output absorption-corrected fluorescence directly. This report also serves as a clarification and extension of the preliminary work on absorption-corrected fluorescence published previously (13).
INSTRUMENTATION In order to remove completely the substantial errors that can arise from the use of two different instrument systems for the absorption and the fluorescence measurements, the computer-centered instrument for simultaneous absorption and fluorescence measurements described by Holland, Teets, and Timnick (13)was used throughout this study. The overall capabilities of this system enable the operator to perform either excitation or emission scans as a function of either wavelength or wavenumber. With the aid of a quantum counter and a correction table, the computer records three intensity measurements which are proportional to the number of quanta in each of the three beams, reference, sample, and fluorescence, represented by R, S, and F, respectively. From these quantities, transmittance, absorbance, fluorescence, corrected fluorescence, partial quantum efficiency, and total quantum efficiency can be calculated and outputted. DERIVATION OF THE ABSORPTION CORRECTION FACTOR Since all of the transmitting and reflecting elements in the optical system are identical for both the reference and the sample beams, the factors involving the cells are the only ones that need be considered to delineate the intensity differences between the two beams. Figure 1 illustrates the effect of the absorption processes within the cell on the intensity of the excitation radiation. Figure 1A presents a schematic of a side view of the reference cell. The incident monochromatic
absorbed by the fluorophore to the total quanta absorbed, QT.
AF = -QF AT QT A derivation of an expression which leads to this assumption I
has been published (22). (5) A fixed fraction of the fluorescence radiation generated within the observation window is viewed by a detector with uniform sensitivity.
i
ll
n
Flgure 1. Excitation beam attenuation. (A) Reference cell. (B) Sample
cell
radiation, Io, will be attenuated slightly by the cell itself and attenuated further by any absorption of the solvent in the blank. The beam emerges from the cell as a measurable quantity I, which is converted by the quantum counter to R. Figure 1B illustrates a more extensive attenuation as the beam passes through the sample cell. The beam emerges with the intensity I, which is converted to S. The absorption by the cell walls and the solvent is very nearly equal to that in the reference cell since matched cells and the same solvent are used. Consequently their absorptions may be omitted from further theoretical consideration. The lines x1 and x 2 in Figure 1B define the width of the window through which the fluorescence is observed. Ideally, the observation window should cover the entire cell, but in practice several factors make this infeasible. Fluorescence of the cell itself, light scattering by the cell-solution interface and internal reflections through the cell walls parallel to the emission observation angle can produce large inaccuracies in the measured values of fluorescence. The intensity of the beam at x1 and x 2 must be known in order to correct the measured fluorescence for the primary absorption processes. However, these values are not readily measurable and thus must be calculated from the measured quantities, R and S. Basic Assumptions. (1)The measured quantities, R, S, and F , are expressed in terms directly proportional to the absolute number of quanta involved (N). As shown below, the proportionality constants for the reference and sample beams are equal but may be different for the fluorescence Beam.
R = kN, S = kN, F := k ’ N f (2) The absorption processes within the cell exponentially attenuate the excitation beam.
(6) Only the fluorescence of a single fluorophore is measured and any absorbance of this fluorescence is negligible. (7) The effects of scattered light, refractive indices, and anisotropic characteristics are assumed to be negligible. Beam Intensity as a Function of Measurable Quantities. If it is assumed that the excitation beam is attenuated exponentially, the intensity at any point on the beam axis in the cell may be represented as a function of the distance from point of entry. Thus
d l = -Iacxdx (1) in which x is the distance from the plane of entry and a and c have the usual Beer’s law meanings. Upon integration, this yields I , = -(ac)x In IO In absorption measurements, the beam has passed through the entire cell, and thus x is equal to path length b. Replacing I, with S and Io with R, and assuming no absorption by the solvent
(3)
In SIR = -abc by the combination of Equations 2 and 3 X
X
( S I R ) = - In T (4) b in which T is transmittance, SIR. After taking the anti-
In I,/R
= - In
b
logarithm of Equation 4 and rearranging, the following expression is obtained
I,
=
(;
)
R exy? - In T = RT“lb
(5)
For convenience x l b is replaced by w ,the fractional distance across the cell. Thus Equation 5 becomes
I,
=
(6)
RTW
and represents the intensity of the beam at any fraction of the cell length, w ,from the plane of entry. Fluorescence in Terms of Measured Quantities and the Observation Window. Let w1 = x l / b and w 2 = x 2 / b , Af = absorbance by fluorophore, A, = absorbance by chromophore, and AT = total absorbance = A f + A,. From assumption 3, F = K(quanta absorbed within observation window), and since the fraction of the total quanta absorbed by the fluorophore from assumption 4 is AF/(AF Ac), the fluorescence will be
+
Af V W , Af+A,
(3) For the duration of any observation period, the quanta fluoresced by any absorbing fluorophore species are linearly related to the quanta absorbed by that species
F=K
F =: k”@(Io - I ) where = quantum efficiency and k” = geometric and in-
By combining with Equation 6 and making a substitution for (AF + Ac) in terms of T , Equation 7 yields
strumental constant. (4)The ratio of the fluorophore absorbance to the total absorbance in the cell is equal to the ratio of the quanta, QF,
- Iw,)
or ANALYTICAL CHEMISTRY, VOL. 49, NO. 8, MAY 1977
707
F = 2*3KAfR(TWZ- TW,) In T
From Equation 6, I, = RT” = R exp(w In T),and substituting for I,, yields
Dependence of Corrected Fluorescence on Absorption. Several investigators have obtained fluorescence measurements that have been normalized or corrected for the intensity of the excitation radiation. Parker (4) and others refer to this quantity as “true fluorescence” while Turner designated it as “absolute fluorescence” (IO). In general these measurements have been made by ratioing a response proportional to the fluorescence intensity to a response proportional to the excitation beam intensity, F/Io. Since this ratio only corrects the fluorescence for fluctuations in Io, we propose the usage of term “source-correctedfluorescence”when this ratio is used. With this term in mind, two theoretical approaches will be described that embody the general principles behind absorption-corrected fluorescence. The first approach will be to assume that the sourcecorrected fluorescence ratio F / I o actually represents the limiting condition as absorption by the sample approaches zero. Io is generally measured as part of the incident beam before it enters the sample cell (5,9, 11)or after it has passed through the sample cell (IO). Neither of these methods corrects for intensity losses due to absorption within the sample cell. Absorption-corrected fluorescence may be represented as the sum of segments Aw wide across the window from w1 to w2;thus
S Iwdw = S R exp w In T d w
- FW
~
00
Iwl
F(w, t A,)
I(w, t
t
Aw)
F ( w l t 2Aw)
* .
I ( w l t 2Aw)
.-
F
~
2
Iw2
W2
Wl
WI
w1
On substituting the newly expressed value for the integral back into Equation 16
w2
-
w1
Solving Equation 8 for K A f and substituting into the above,
F , = 2 . 3 K A f ( ~ 2- w , )
(18)
Note that both approaches lead to the same solution and indicate an important relationship. Since (w2 - wl)will be a constant for any system as long as the observation and detection geometry are not altered,
F,
Af
(19) This result indicates that fluorescence values corrected in this manner will be linear with the absorbance of the fluorophore even in the presence of one or more chromophores. The Absorption Correction Factor. The absorption correction factor, f a , may be defined as
(9) As the absorbance approaches zero, it is easily recognized that this definition approaches the corrected fluorescence ratio FlIo. At this point, Equation 7 may be expressed as
Defining Equation 1 in terms of w, substituting A ~ ( 2 . 3for ) ac using Equation 2, and assuming a 1-cm cell path length, it is apparent that
dI, = 2.31w(Af+ A,)dw
(11)
However,
A I , = -dIW AW dw and solving Equation 11 for dIwldw,and substituting into Equation 12, yields
( - A I w ) = 2.31w(Af+ A , ) A w
(13)
Substituting back in Equation 10 gives
Fw = 2.3KIWAfAw
(14)
This produces from Equation 9
F , = 2.3KAfZ:W,:Aw= 2.3KAf(w, - ~
2
)
(15)
An equally appealing alternate approach would be to define corrected fluorescence as the observed fluorescence divided by the average intensity of the excitation beam across the window from w1to w2 Then
708
ANALYTICAL CHEMISTRY, VOL. 49, NO. 6, MAY 1977
which reduces Equation 17 to
F F,=-X R
fa
It should be noted at this point that Equation 20 is identical except in form with an equation presented by Parker and Barnes (17)for the correction factor fa
2.303A(x1- x 2 ) - 10-Ax2
= lo-Axl
where A is the absorbance per cm path length and x1 and x 2 are the distances in cm from the front of the cell to the mask edges. The foregoing derivation of Equation 17 was presented to fill a serious gap since, to date, only two minor attempts have been made to elucidate its origins and to delineate the chemical and instrumental conditions necessary for its application (18, 19). RESULTS AND DISCUSSION Chemical and Instrumental Considerations. At this point, it is apparent that Equation 17 will be valid only if the assumptions used in its derivation are reflected in the chemical and experimental measurement conditions. Assumptions 2, 3, 4 , 6 , and 7 can be satisfied by the correct choice of fluorophores and chromophores. The validity of assumption 1 is obvious, based upon the instrumental discussion. However, the requirements of assumption 5 are quite stringent and further consideration is needed. It can be seen from Figure 1B that the fluorescence information contained along the horizontal axis from x1 to x 2 is of utmost importance. Ideally, as a first requirement of assumption 5, all this lateral information should reach the detector but this goal cannot be achieved without some minor geometric modifications because of the orientation of the
PRIMARY MASK
,906
30
SECONDARY MASK
w*08crn
- 750 - 60' 145"
- 30' IMAGE ROTATOR
FIELD LENS
Figure 2. Geometric and optical configuration for the collection of fluorescence
0
PRIMCRY MCSK
SECONDARY MASK
1
I
> EXCITATION BEAM
0
PRIMARY yASK
SECONDARY M,CSK
EXCITATION BEAM
Figure 3. Limiting conditions for the fluorescence observation angles for point sources across the sample cell. (A) Maximum. (6)Minimum emission monochromator slits. Two courses of action can be followed if the slit height of the monochromator is larger than the horizontal dimension of the fluorescence window. The f i t would be the 90° rotation of the emission monochromator so that the slit is in a horizontal orientation and the second would be the 90° rotation of the fluorescence cell image through the use of a dove prism or a set of front surface mirrors. Front surface mirrors were used in this study. The optical configuration chosen for this study and shown in Figure 2, utilized a focusing lens positioned to give a 1:l image ratio at the entrance slit and a field lens which was compatible with the optical speed of the emission monochromator. The edges of the mask at x1 and x 2 confine the observation window to ti fixed fraction of the total fluorescence viewing area. Thus, the first requirement of assumption 5 is met. The second requirement assumes that the fluorescencemust be observed at a fixed observational angle at any point across the fluorescence window. Unfortunately, this goal can never be fully realized, only closely approached. The solution to the problem involved the placement of a second mask, with thk same window dimensions, w,as the window in the primary mask, at a distance, d , from the source of fluorescence as shown in Figure 3. Geometric consideration indicated that for a constant distance, the observation angle, 8, for a point source at the center of the observation window was the maximum while the observation angle, +, for point sources a t either edge of the window was a minimum. Consequently 8 and represent the limiting values for the observation angles across the fluorescence window. These observation angles were calculated as a function of d. The differences between % and 4 for various d values expressed as relative percent error, are plotted in Figure 4 (curve A). Curve B, shows the variation of % with d. Points for these two curves were calculated for
+
=
9
15"
5
i
'0
I
2
3
4
5
6 ' "
LDCotlon of the secondary mask Id). crn
Flgure 4. The variation of optical parameters as a function of seoondaly mask distance from the source of fluorescence. (A) Relative percent error in the observation angles. (B) Observation angle at cell center a window width, w ,of 0.8 cm. Note that as the error between 8 and 9 approaches zero, the observation angles also go to zero. In other words, the ideal situation would be to collect only radiation which is parallel to the optical axis. Unfortunately, this would require a large secondary mask distance and would drastically reduce the radiation collection efficiency. Consequently, a maximum error of 170or a secondary mask distance of 4.0 cm was chosen as a compromise. At this distance, the error in observation angles across the cell is small while the angle is large enough to permit the passage of a reasonable amount of fluorescence to the detector. The third requirement of assumption 5 is concerned with the uniformity of the detector sensitivity. A simple test for uniform cathode sensitivity was made by measuring the emission from a series of quinine sulfate solutions with and without a diffuser in front of the phototube. Because of the scatter from and absorption by the frosted glass diffuser, the fluorescenceintensities in these two sets of measurements were not the same but the shapes of the resulting fluorescenceconcentration plots were identical. From this, it was concluded that the cathode sensitivity was uniform for beam dimensions normally falling on the cathode. At this point, it has been shown that all the requirements of assumption 5 have been met. In addition, since all of the assumptions can be considered to be valid if the proper fluorophores are used in conjunction with the instrumental configuration outlined above, then the application of Equation 20 to the raw fluorescence data should give a linear relationship between fluorescence and the fluorophore absorbance. Absorption-Corrected Fluorescence. The emission optical system was constructed so that the dimensions of the fluorescence window, w 1 and w2, were 0.10 and 0.90, respectively. Experimental fluorescence curves were obtained for two series of solutions. The first series was composed of a number of pure quinine sulfate solutions which were one normal in H2S04. The absorbances of these solutions ranged from 0.007 to over 2.0. The second was a series of solutions which had a constant quinine sulfate concentration in 0.1 N H2S04and an increasing concentration of a chromophore, 2,5-dihydroxybenzoic acid. The first solution in this series was pure fluorophore. Figures 5A and 6A show the experimental results for the pure fluorophore and the mixture, respectively. The absorption-corrected fluorescence values a t each experimental point for the pure fluorophore were calculated by the following process. Since the correction factors for the fluorophore solutions which have an absorbance value below 0.06 are close to unity and are almost independent of the window parameters, w1 and w2, the absorption-corrected fluorescence values for all solutions under this absorbance limit ANALYTICAL CHEMISTRY, VOL. 49, NO. 6, MAY 1977
709
rameters whereas wl and w2 are not. The calculated di‘ I mensions of the fluorescence window were found to be 0.11
lot---
./ 01
c,------
I 01
10
20
ABSORBANCE
Flgure 5. Fluorescence as a functlon of absorbance for quinine sulfate in 1.0 N H2S04in the range from 1 X to 3 X M. (A) Source-corrected fluorescence. (E) Absorptioncorrected fluorescence
01
02
05
10
2.0
ABSORBANCE
Figure 6.
Fluorescence as a function of increasing amounts of chromophore, 2,5dihydroxybenzoic acid, in the presence of 1 X M quinine sulfate in 0.1 N H2S04. (A) Source-corrected fluorescence. (E) Absorption-corrected fluorescence
were calculated by the use of Equation 17 and the measured window dimensions, 0.10 and 0.90. The equation of the best straight line through these theoretical points was calculated by the use of a linear least squares fit. This equation was then used to calculate the absorption-corrected fluorescence values for the remaining points. The theoretical fluorescence values at each experimental point for the mixture were calculated from the first experimental point by the use of Equation 17 and the measured window parameters. Qbviously, the absorption-corrected fluorescence value for each point on the curve in Figure 6A should be equal since the concentration of the fluorophore in each solution is the same. Finally, all the experimental data were input to a Fortran program named RTFACT in the form of transmittance, source-corrected fluorescence, and the corresponding calculated absorption-corrected fluorescence. The program is based on a modified Simplex optimization method similar to the ones outlined by Deming and Morgan (23). The program, which utilizes a modified form of Equation 17, fits the measured fluorescence to the calculated absorption-corrected fluorescence by varying w1and w. The fluorescence window width, w was used because w1 and w are independent pa-
710
*
and 0.91 and me in excellent agreement with the measured values of 0.10 and 0.90. The calculated dimensions were then submitted into a subroutine which is contained in a modified version of the spectrofluorimeter program outlined previously (13). This subroutine uses a close approximation of Equation 20 to calculate the needed correction factors. This approximation consisted of the substitution of the first seven terms of the Taylor expansion of exp (w In 2“) for the denominator (Yz- Y1).The calculation of the correction factors for each data point is performed automatically during the data reduction procedures, and application of these factors to the measured source-corrected fluorescence yields the absorption-corrected fluorescence curves shown in Figures 5B and 6B. Note that these figwes show that the absorption-corrected fluorescence is linear with fluorophore absorbance, up to a solution absorbance of 2. The error from linearity at this absorbance is about 3% for both curves. The practical upper limit of 2 absorbance units was chosen since beyond this point the accuracy of the measured transmittances used in the correction factors is uncertain. Based on these results, it is apparent that the correction method as outlined properly compensates for the primary absorption processes even in the presence of chromophores.
ANALYTICAL CHEMISTRY, VOL. 49, NO. 6, MAY 1977
ACKNOWLEDGMENT We thank Thomas H. Edwards of the Physics Department, Michigan State University, for his invaluable aid in the design of part of the emission optical system presented in this paper. In addition we also acknowledge three undergraduates, Gregory Sindmack, Malcolm Warren, and Thomas Iler for their contributions to this work. LITERATURE CITED (1) E. J. Bowen and F. Waker, “Fluorescence ob Solutions", Longmane, Green, London, 1953. (2) D. M. Hercules, “Fluorescence and Phosphorescence Analysis”, Interscience, New York, 1966. (3) S. Udenfriend, “Fluorescence Assay in Biology and Medicine”, Academic Press, New York, 1969. (4) C. A. Parker, “Photoluminescence of Solution”, Elsevier, London, 1968. (5) C. A. Parker, Nature (London), 182, 1002 (1958). (6) H. C. Borresen, Act. Chem. Scand., 19, 2089 (1965). (7) F. R. Lipsett, J. Opt. SOC. Am., 40, 673 (1959). (6) P. Rosen and G. M. Edeiman, Rev. Scl. Instrum., 36, 809 (1965). (9) B. Wlthoit and L. Brand, Rev. Sci. Instrum., 39 (9), 1271 (1968). (IO) G. K. Turner, Sclence, 146, 364, 183 (1964). (11) Amerlcan Inst. Co., Sliver Springs, Md., Euli., 2392 D (1967). (12) Perkin-Elmer Corp., Norwalk, Conn., Instrum. News, 21 (2), 12 (1970). (13) J. F. Holland, R. E. Teets, and A. Timnick, Anal. Chem., 45, 145 (1973). (14) R. A. Passwater and J. W. Hewitt, Fluorescence News, 4, 9 (1969). (15) J. W. Longworth, Photochem. Photoblol., g, 589 (1968). (16) H. Braunsberg and S. B. Osborn, Anal. Chim. Acta., 6 , 92 (1952). (17) C. A. Parker and W. J. Barnes, Analyst (London), 82. 606 (19571. (18)W. E. Ohnesorge, Anal. Chlm. Acta, 31, 484 (1964). (19) J. E. 0111, Appl-Spectrosc., 24, 588 (1970). (20) M. Ehrensberg, E. Cronvall, and R. Rigler, FEBS Left., 18, 199 (1971). (21) J. S. Franzen, I.Kuo, and A. E. Chung, Anal. Biochem., 47, 426 (1972). (22) R. C. Michaeison and L. F. Loucks, J. Chem. Educ., 52, 652 (1975). (23) S. N. Deming and S. L. Morgan, Anal. Chem., 45, 278A (1973).
RECEIVED for review April 19, 1976. Accepted February 14, 1977. Financial support for part of this research was furnished
by NSF Grant GB 25116. A preliminary report of this work was presented as Paper 39 at the 19th Annual Detroit Anachem Conference in 1971. This paper has been approved by the Director of the Michigan State University Agricultural Experiment Station as journal article 6262.
