Fortran-Based Photographic Emulsion Calibration Procedure for Use in Quantitative Spectrometry J. A. Holcombe,'
D. W.
Brinkman, and R. D. Sacks2
Department of Chemistry, University of Michigan, Ann Arbor, Mich. 48 104
A procedure is described using time-sharing computing facilities and FORTRAN language which allows accurate photographic emulsion Calibration for quantitative spectrometric work. Two new features are Incorporated in this two-step calibration procedure which extend its operational range from just above gross fog to very high density values approaching saturation and render it useful without empirically determined parameters for emulsions having greatly different properties. First, multiple sets of data points are generated from a preliminary curve fitted in four segments to quadratic equations. These generated sets are superimposed to give a larger number of points from which to obtain the final Calibration curve. Second, the accuracy of this superimposition is improved by using a modified Seidel function, which when plotted vs. log relative exposure produces a nearly linear curve. The final calibration curve is obtained as four overlapping segments each fitted to a fifth-degree equation. The procedure was tested for SA1, 103-0, and Tri-X emulsions along with a hypothetical emulsion having high contrast and high inertia. Standard deviations are presented for the preliminary curve fit, the linear fit to the modified Seldel function, and the final curve fit for the four emulsion types tested.
T h e use of photographic detection for quantitative spectrometric studies requires a knowledge of the relationship between the photographic image density and the exposure required to produce such an optical density. In general, this relationship in graphical form is referred to as a n emulsion calibration curve. A calibration curve with optical density plotted as a function of log relative exposure, commonly referred to as an H and D curve after Hurter and Driffield ( I ), assumes the general shape shown in Figure 1. As can be seen, a linear relationship between optical density and log exposure may exist only for a small region of the curve. In addition, the slope and dynamic range of this region vary widely with different emulsion types, different wavelengths of incident light, and different developing procedures. Attempts to linearize the calibration curve by mathematical transformations of the density values have been made by a number of workers with only moderate success (2-7). This is not surprising since the relationship between optical density and exposure is not analytical. Many of the more effective means of linearizing the curve require a fair degree of empiricism in determining parameters which are used in the transformation of density values, e.g., Arrak ( 6 ) and Kaiser ( 7 ) functions. A t best, these methods result in approximate linearization for densities below the shoulder region of the H and D curve and often are inadequate in defining densities very near the gross-fog level of the emulsion. Present address, Department of Chemistry, University of Texas, Austin, Texas. To whom rorrespondence should be directed.
With the availability of digital computers, spectrometric data reduction has become a less time-consuming task, and a few efforts have been directed toward computer proressing of emulsion calibration data. Margoshes and Rasberry (8) have compiled a computer program which draws on the principles involved in the Kaiser transformation for an attempted linearization of the calibration curve. The program is written in BASIC and can be used with time-shared computer facilities. However, since a linear relationship is a necessary assumption for the determination of two empirical parameters required in their method, a spectral range of about 3 nm per calibration curve is suggested. In addition, it is obvious this linearity cannot be attained if the toe and shoulder regions of the H anu D curve are included. T h e procedure described here does not require linearity and is readily applicable for wavelength ranges of 10 nm or more per calibration curve, making it more convenient if a large spectral range is to be covered. Also, since the entire density range from gross fog to very high density values can be used, the need for stepped exposures and their attendant complications is eliminated. Heemstra (9) and Decker and Eve ( 1 0 ) have devised programs for emulsion calibration and for density-to-intensity conversion. However, these programs are most suitable for use with a dedicated computer and, consequently, are of marginal utility to a majority of practicing spectroscopists who have access to time-sharing facilities. Additional efforts t o use digital computers for calibration or density-tointensity conversion programs are cited by Margoshes and Rasberry (81. The work conducted in this laboratory dictated the use of several different emulsion types over a wide wavelength range. Therefore, it was essential t h a t the emulsion calibration procedure require only a minimum of input data. In addition, accurate calibration was required over the entire range from the gross-fog level to optical densities greater than 2.5. T h e method described here employs the basic two-step calibration approach and uses the inherent computational *speed of the digital computer to permit additional data treatment which results in an increased precision of the calibration procedure. The coefficients of the equations describing each calibration curve then are stored in an external file for future use in a separate density-to-intensity conversion program.
THEORY The skeletal structure of the calibration procedure is based on the two-step method for emulsion calibration. Instrumentally, the two-step method requires neither the elaborate step filter or rotating disc associated with the multistep methods, nor the extremely reproducible light source associated with the inverse-square procedure and exposure-time variation methods. However, the spectral data obtained from many of the other calibration procedures easily can be adapted to the two-step procedure. Harvey ( I 1 ) has made note of several inherent advantages ANALYTICAL CHEMISTRY, VOL. 47, NO. 3 , MARCH 1975
441
,Y
'"1 3 4
2.01
..Ot
/
1
1.0
2.0 3.0 LOG RELATIVE EXPOSURE
4.0
Flgure 1. General H and D curve showing the relatively short straight-line region 0.0 0.0
1.0
2.0
3.0
0,
Figure 3. A preliminary curve of clear-step density D, vs. absorbedstep density D, Point A represents the arbitrarily chosen highest density value at D, = D, = 3.0. Point B represents the gross-fog level of the emulsion. The four preliminary curve regions and the unity-slope dotted line D, = D, also are indicated
GE.,I>:-:
I 1 2 p::,-;
t
Figure 2. Block diagram outlining the computer procedure used to obtain complete emulsion calibration data from measured optical density pairs using a two-step neutral density filter
in the two-step method with its preliminary curve, and several texts give added reference to other calibration methods and their underlying principles and inherent problems (12, 13). The procedures used to obtain data for this calibration program are similar to those for the conventional two-step method and will not be discussed here. All data obtained from the film or plate is reported here as optical densities D; however the program easily can be transformed to accept data as transmittance values. Preliminary Curve Generation. Pairs of densities from the clear step D and the absorbing step D , for selected lines are recorded. These values are extracted from microdensitometer traces in the wavelength region of interest and used as input data for computation of the final calibration curves. The block diagram in Figure 2 outlines the sequence of operations performed by the computer. The input data generally are entered as peak heights measured from microdensitometer traces and are converted to density values after being entered. These points are ordered in magnitude from low to high by a subroutine, and the ordered data set is divided into four overlapping regions using the D , values to determine the boundaries of each region. A least-squares curve-fitting subroutine then is used to generate a seconddegree equation for each of the four regions. 442
After the first curve fitting, all points which deviate from the curve by more than two standard deviations are eliminated and the remaining points in each region refitted to another quadratic equation expressing D as a function of D,. Thus, one of the primary advantages in the use of the preliminary curve, the elimination of bad data, has been fully exploited in this section of the procedure. Also, by overlapping the regions on the preliminary curve, discontinuities a t the junction points could be minimized. Figure 3 shows the four regions and the corresponding D , values which determine the upper and lower limits of each region on the preliminary curve. The regions of point overlap should be noted here. These regional divisions were chosen to give maximum resolution in the low to moderate density region since these regions represent areas on the final calibration curve where a maximum change of slope is occurring. Additionally, regions 1-3 characterize optical densities which can be readily extracted and reliably measured from microdensitometer traces. At successively higher density values, the instrumental errors introduced by the microdensitometer become more predominent (14). Since the high density values are not extracted readily from the spectra used in the calibration procedure, only a minimal number of pairs of D a and D values can be collected easily in this region. Figure 3 shows a typical plot of the points comprising this preliminary curve. The points which were eliminated in the final curve fitting are shown as open circles. Graphical representation of the four separate regions and their overlap is also shown in this figure. At sufficiently high exposure values, the density should become independent of changing exposure (saturation). The extreme densities where this normally occurs again are often difficult to measure because of instrumental limitations. Therefore, this program arbitrarily provides such a set of high-density points a t a density of 3.0, Le., a transmittance value of 0.001. This upper limit is shown as point A of Figure 3. Similarly, a t extremely low exposure values, the exposure fails to overcome the inertia of the emulsion, and consequently, both the clear and the absorbed step yield optical densities equal to the gross fog of the emulsion (see point B in Figure 3). Several values of the gross-fog level are read in as input pairs along with the other spectral line densities t o ensure proper location. of the gross-fog level. This results in a final calibration curve which is reliable to density values approaching that of the gross fog. An
ANALYTICAL CHEMISTRY, VOL. 47, NO. 3, MARCH 1975
unexposed portion of the emulsion often is used as zero density, and all subsequent density measurements are made relative to this value. This would place the gross fog (point H ) a t the origin of the graph shown in Figure 3. However, all densities in this laboratory are measured relative to the film or plate backing without emulsion and, as a result, yield a non-zero value for the gross fog a t point B. Calibration C u r v e Generation. Procedurally, the next operation in the two-step method is the actual accumulation of density points to be used in the final calibration curve. This traditionally is done by arbitrarily choosing a starting density value D near the low end of the D ,scale. However, to ensure that the final calibration curve reflects an accurate density- intensity relationship a t density values near the gross-fog level, it is necessary to locate the starting density value very near the gross fog. A portion of the preliminary curve in the low-density range, and the quadratic equation defining this region of the preliminary curve are shown in Figure 4. The coefficients A, B, and C are finite, real numbers which were computed previously in the curve-fitting step. A line defined by D , = D , also is shown in this figure. The intersection of the preliminary curve with this unity-slope line denotes the location on the preliminary curve where the density becomes invarient with changing exposure value. Point P denotes such an intersection in the low-density region and represents the gross-fog level of the film being calibrated. The D ,value a t P can be found by the simultaneous solution of the equations shown in Figure 4. This gives
/ 0.6I
0,
-
0.0
I
/?Dan)
(4 1
Here f ( D a ) represents the quadratic equation derived earlier in relating D, to D , on the preliminary curve. Each D , value generated in this manner is assigned a log relative exposure value using the criterion that consecutively generated D , values are separated on the log relative exposure scale by A s units where A s is the absorbance of the absorbing step of the step filter with the clear step taken as zero absorbance. Using the preliminary curve, the generation of D ,values could go on indefinitely with the majority of the density points lying near the assigned saturation region of the emulsion a t 3.0 density units. This results from the asymptotic approach of the preliminary curve to the unity slope line D , = D , a t high density values. Therefore, a means of
I
0.4
I 0.6
terminating the point-generating loop is required. If the point-generating process is terminated once the slope on the calibration curve becomes less than 0.1, adequately high density values are represented without an excessive number of points being generated near the 3.0 density region. Thus, point generation is terminated once Equation 6 is satisfied.
(3 1
bcn=
I
0.2 00
9% = I
= Do
Figure 4. The low-density region of the preliminary curve showing the intersection of the D, = D, line with the quadratic equation fit to the data of region one
(21
1 1
/
0.0
Dc 1 = .f(Dal) I I
. '0,
0.2-
I t can be shown that as long as the quantity under the radical sign is greater than zero, the sign before the radical in Equation 1 must be positive (+) to define the location of point P. A value of 0.02 density unit then is added to the D , value a t point P to define the initial starting point D,, for the subsequent generation of density values for use in the final calibration curve. Points to be used in the final calibration curve are generated by computer in an analogous fashion to that done in a graphical method. Equations 2 through 5 show the mathematical analogue to the traditional graphical method.
P.1
/ /
0.4
,
I
/
/
Here D C n and D,, represent the densities of the n t h generated point on the preliminary curve, and A , again is the relative absorbance of the step filter. Multiple Curve Generation. These generated points plotted us. appropriate log relative exposure values comprise the data typically used either in defining the H and D curve by traditional graphical methods or in linearizing the calibration curve by subsequent transformation of the density values. However, with large values of A s or emulsions having a high gamma, i.e., steep slope of the linear portion of the H and D curve, the number of points generated per curve is inadequate to define clearly the density-log exposure relationship when least-squares curve-fitting procedures are used. For this reason, a computational procedure is incorporated here which increases the total number of data points used in defining the calibration curve. These additional points increase the resolution along the entire length of the calibration curve and result in a much better curve fit of a simple polynomia1 expression to the calibration-curve data because of the increased number of points defining the final curve. Increasing the number of points is accomplished by generating many curves which are identical in shape to the initial curve. The main distinction in the new point sets is the slight change in the density values. These curves are displaced arbitrarily along the log exposure axis and need only be translated along the log exposure axis until one set of superimposed points results. This translation is similar in approach to that used with a multistep calibration technique (25). Defining the initial starting point for the cyclic generation of a second set of points is accomplished by adding 0.005 density unit to the initial density value D,, used for the first curve. The point-generating process then is used again to accumulate another set of data points (see Equations 2-5). These points define another H and D curve dis-
ANALYTICAL CHEMISTRY, VOL. 47, NO. 3, MARCH 1975
443
...
3rT
.*
/-
5
LOG
I
I
10 IS LOG RELATIVE EXPOSURE
20
Figure 5. The first three in a series of data sets generated from the preliminary curve.
4-
2
I
-41
RELATIVE
EXPOSURE
Figure 6. Seidel curve showing all of the points after superimposition
of the modified Seidel data from the individual curves and conversion to Seidel values. The four regions for the final curve fitting also are indicated
( a ) :Normal H and D data points; ( b ) : Modified Seidel fuction data points
s placed along the log exposure axis. This process then is repeated for the generation of additional point sets. T o determine when enough point sets have been generated, a counter is used to keep an internal record of the number of points generated in the density region between 0.9 and 1.6 density units. This region is chosen since it generally represents the steepest portion of the curve where the minimum number of log exposure points will be generated per unit density. Thus a point-generating loop proceeds until the total number of data points in this density region is greater than 16. Multiple C u r v e Linearization a n d Superimpositon. At this point, a series of distinct calibration curves has been generated. However, each curve has an insufficent number of points to obtain a good polynomial fit. Graphically, they take on the appearance of Figure 5a where the first three point sets have been drawn. As was noted, the conventional two-step procedure stops with the generation of the first curve shown in Figure 5a, and these points then are connected to obtain a curve having the general shape of the actual H and D curve. While increasing the number of points defining this first curve can be realized experimentally by decreasing the absorbance value A of the step filter, this approach often results in poor resolution near the toe and shoulder regions of the curve where D , becomes indistinguishable from D because of the finite resolution of the microdensitometer. Next, the curves in Figure 5a must be superimposed to form a single set of points. This is done by translating all points from the second and subsequent curves along the log relative exposure axis until superimposition about the location of the initial set of points is achieved. Initial attempts a t translation involved fitting a linear equation to all density values between 0.4 and 1.6 in the first curve. The distance along the log exposure axis between a given density on this line and points lying in the same density region on the second and subsequent curves was calculated, averaged, and all points comprising that point set were moved by that distance. However, emulsions with high gamma or step filters with a high absorbance value give too few points in this density region. Therefore, it is necessary to perform a transformation on the density values within the program such that a larger number of points is obtained in a linear region. Since it is desirable t h a t the transformation not require additional empirically determined parameters, application of the Arrak or Kaiser functions was not attempted. The use of either of these transformation functions defeats the main objectives of simple data collection and identical treatment of all emulsion types. Seidel values S given by Equation 7 ( 1 6 ) were tested early in the program development. 444
(7 1
= log ( 1 0 D - 2 )
These provide some improvement in extending the linear region for emulsions with low gross fog but are relatively ineffective for emulsions with high gross fog. Since the Seidel transformation provides an effective, nonempirical linearization for H and D density points near zero density values, all density values here are reduced by a value equivalent to Dal, This effectively obtains calibration curves with a gross-fog level of zero. However, by referring to Equation 7, it can be seen that this requires the computa. tion of the logarithm of zero a t the D,, value. Therefore, a value of 0.01 is added to all reduced density values to permit calculations. This gives the normalized Seidel values Sn.
S, = log (10 'D+
-
Dal
+
n ~ l !
- 1)
( 8)
Again, this obtains some improvement in linearity when compared with the traditional Seidel values of Equation 7. Since some curvature usually still exists in the low density region, the program performs an additional Seidel transformation of the normalized Seidel values. This obtains the final modified Seidel values M,.
Attempts a t further transformation of the M , values resulted in obvious degradation of the linear region. A comparison of the linearity achieved using the modified Seidel values with the conventional density values is shown in Figures 5a and 5b. Only the first point sets are shown in Figure 5 , and the total number of sets actually generated again is dependent on the values of A , and the emulsion gamma. With all densities transformed to modified Seidel values, it is then necessary to fit a linear equation to some region in the first point set in order to superimpose the displaced sets onto the first point set. As can be seen in Figure 5b, the range of the nearly linear region extends to modified Seidel values greater than 4.0. A more than adequate number of points occurred in the range of modified Seidel values from 0.0 to 3.5. In addition, a linear fit with a relative standard deviation of less than 10% is obtained in most cases using this range of values. The straight line fitted to this region is shown in Figure 5b. The average distance along the log exposure axis between this line and the points of the second and subsequent curves within the same range of M values is determined, and all points of the second and subsequent point sets are translated appropriate distances along the log exposure axis. This results in the superimposition of all points onto the initial curve. Polynomial curve-fitting procedures now can be used easily and accurately with this large set of points. However,
ANALYTICAL CHEMISTRY, VOL. 47, NO. 3, MARCH 1975
514-1
103-0
TRI-X
HIGH INERTIA
Table I. I n p u t Data Necessary for Calibration P r o g r a m
1. Number of different wavelength regions being calibrated. 2. Absorbance of the step filter relative to the clear segment, 3 . Microdensitometer conversion factor given as density units per unit height measured from the t r a c e . 4 . Wavelenqth reejon being calibrated to nearest 100 A . 5. Number of p a i r s of optical density data for the wavelength region being calibrated. 6 . Peak heights measured from the microdensitometer t r a c e s and introduced by p a i r s corresponding to D , and D,. Typically about forty p a i r s distributed throughout the density range and the 100-A wide wavelength region a r e introduced.
:li*,*, ,I ,
,
*,
Y
0 VI
b
,,
**
,
***
t**",
,
,
,
u
~
LOG
Table 11. Relative S t a n d a r d Deviations (h)for the Quadratic F i t to the Preliminary Curve I
2
3
4
SA 1 Tri-X 103-0 High inertia
0.0502 0.0210
......
0.0396 0.0500 0.0346
0.0186 0.0424 0.0290
0.0110 0.0115 0.0374
0.0344
0.0112
0.0153
0.0102
EXPOSURE
tion, and modified Seidel function for four emulsion types. Note the considerable improvement in linearity obtained from the modified Seidel function
Reglam
Emulsion
RELATIVE
Figure 7. Examples of plots of optical density, traditional Seidel func-
the constant D a l from Equation 8 is included and will vary as the gross fog of the emulsion. Consequently, this represents another number which would have to be stored in a permanent file for future use with a density-to-intensity conversion program. It is a simple matter to transform all M values back to densities if desired. However, better curve fitting of the final calibration points is realized if true Seidel values as defined by Equation 7 are used in place of densities. This is a consequence of attempting t o apply polynomial curve-fitting procedures t o density values which asymptotically approach the density value of t h e gross fog. T h e Seidel function, however, provides enough deviation from an asymptotic approach t o permit curve fitting t o simple polynomial expressions. A plot of the resulting Seidel values us. log relative exposure of the superimposed points is shown in Figure 6. Attempts t o fit the entire curve of Figure 6 to various degree polynomial functions were unsuccessful, and i t was necessary to divide the calibration points into four overlapping regions. T h e regions used are shown in Figure 6. Once again, the overlap prevents any discontinuity at the junctions between adjacent sections. A curve-fitting subroutine is used t o obtain a least-square fit t o each region using polynomial expressions. T h e coefficients from the polynomial equations then are stored in a permanent file and can be retrieved from t h e file a t any future time by a second program which performs quantitative density-to-intensity conversion.
EXPERIMENTAL The program is written in FORTRAN IV for use on an IBM 360/ 67 duplex system. No internal operations possibly unavailable on other systems have been included. The input data necessary for the operation of the calibration program is given in Table I. The output includes an ordered listing of the input data, the wavelength being calibrated, and information about each calibration curve including the number of points in the curve, the Seidel and log exposure values for each point, the degree of the polynomial equation and the coefficients of the polynomial. Although the
degree has been fixed as five for the results reported here, it is readily varied in the program and thus is included in the output. Relative standard deviation of the curve fit also is obtained for each region. The data for the four emulsion types tested were' obtained o n a 1.0-m Czerny-Turner, plane-grating spectrometer (Jarrell-Ash Model 78-460). The calibration spectra were obtained through a two-step, neutral-density filter using a three-ampere dc iron arc as a radiation source. Spectrum Analysis No. 1 (SAL) plates, 103-0 plates, and Tri-X panchromatic film, all from Eastman Kodak, were calibrated using the procedure described here after processing for five minutes with Kodak D-19 developer. These three emulsions were chosen because of their rather different calibration-curve profiles. The S A 1 has a very low gross fog and a high gamma; the Tri .X has a moderate gross fog and low gamma, and finally the 103-0 has a moderately high gamma with an extremely high gross fog of nearly 0.4 density unit. In addition, the H and D curve for the SA1 emulsion was modified graphically t o simulate an emulsion having high gamma and very high inertia. Corresponding input data pairs then were obtained from the modified curve. This results in a calibration curve with a long toe region and a relatively sharp break between the toe and the linear regions. Density values were obtained on a Joyce-Loebl Mark 111-B microdensitometer. Care was taken to obtain density values covering the entire density range. This required securing density pairs in the four density regions of Figure 1 as well as in the three overlap regions in order to avoid discontinuities in the preliminary curve.
RESULTS A N D DISCUSSION Table I1 summarizes data for the quadratic curve fit to the four overlapping regions of the preliminary curve. Since the gross-fog level of the 103-0 emulsion is 0.40 density unit, there are no data in the first region, and thus a quadratic curve is not generated for this region. In no case is the relative standard deviation greater than 5.0%. Figure 7 shows the first set of points generated from the preliminary curve for each of the film types tested with optical densities, Seidel values, and modified Seidel values plotted as functions of log relative exposure. All data correspond to a step filter having a relative absorbance A , of 0.60 absorbance unit for the absorbing step. As can be seen in the optical density plots in the top row, there is a n obvious lack of resolution for any type of curve fitting if the multiple-data-set generation procedure suggested here was not used. In addition, multiple curve generation would be unsatisfactory using only these points since there are too few points on the straight line portion to allow accurate superimpositioning.
ANALYTICAL CHEMISTRY, VOL. 47, NO. 3, MARCH 1975
445
for first- through seventh-degree polynomial least-squares curve fits to each of the four Seidel curve regions of Figure 6 for the four emulsion types tested. Polynomial expressions of first through seventh degree were evaluated to determine an optimum compromise for the four different Seidel curve profiles. It should be noted here that all relative standard deviations presented in Tables I11 and IV are expressed as errors relative to exposure values and not log exposure values. In general, relatively little improvement is obtained with
Table 111. D a t a for the Linear Fit to the Modified Seidel Values No. of points Emulsion
i n linear region
SA 1 Tri-X 103 -0 High inertia
3 5 4 4
Re1 stdard dev
-)
(7
0.0141 0.112 0.023 1 0.0947
Table IV. Relative S t a n d a r d Deviations (k)for the Final Curve Fit in the Four Regions for Various Degree Polynomials Polynomial d e g r e e Emulsion
SA 1
Region
1 2 3 4
Tri-X
1 2 3 4
103-0
2
3
4
5
6
7
0.0362 0.0142 0.0122 0.0429
0.00815 0.00692 0.0116 0.0160
0.00750 0.00627 0.00954 0.0158
0.00696 0.00622 0.00965 0.0158
0.00685 0.00574 0.00928 0.0154
0.00701 0.00483 0.00935 0.0155
0.00683 0.00494 0.00935 0.0156
0.0340 0.0952 0.0476 0.102
0.0300 0.0623 0.0473 0.063 1
0.0296 0.0476 0.0473 0.0586
0.0221 0.0459 0.0474 0.0610
0.0270 0.0489 0.0470 0.0509
0.247 0.0374 0.0469 0.0458
0.0435 0.0469 0.0458
1
...
...
...
...
...
.. .
...
0.135 0.0164 0.0141
0.0693 0.00812 0.00871
0.0352 0.00522 0.0168
0.0241 0.00522 0.00655
0.0233 0.00603 0.00535
0.595 0.00546 0.00515
0.0219 0.00631 0.00522
0.195 0.138 0.0365 0.0633
0.0550 0.0501 0.0232 0.0338
0.0302 0.0381 0.0222 0.0339
0.0277 0.0303 0.0220 0.0351
0.0278 0.0298 0.0224 0.0336
0.0282 0.0297 0.0219 0.0334
0.0261 0.0297 0.0218 0.0335
4
1 2 3 4
I t is of interest to note that while the Seidel plots do show a decreased curvature in the toe region relative to the optical-density plots, they are far from linear. This is most apparent with the high-inertia and the high-gross-fog (103-0) emulsions. This clearly illustrates the pitfalls in the common practice of performing optical density-to-intensity conversion based on the assumed linearity of the Seidel transformation. Only in the case of Tri-X emulsion which has a low gamma and a very short toe region are the Seidel data nearly linear from the gross-fog level to moderately high density values. The modified-Seidel plots a t the bottom of Figure 7 show a considerable improvement in linearity for all cases except the Tri-X. The improvement for the high-gross-fog (103-0) and the high-inertia emulsions is particularly significant. Since the Seidel plot for Tri-X is nearly linear a t low exposure values, the modified Seidel transformation over-corrects these data and somewhat increases the curvature of the plot. Table 111 lists the data for the superimposition of the modified Seidel data sets for each of the emulsion types tested. The number of points in the modified Seidel range from 0.0 to 3.5 used to define the linear function for superimpositioning the data sets is greatest for Tri-X because of its low gamma and smallest for SA1 because of its very high gamma. The relative standard deviation for the linear curve fit is excellent for SA1 and 103-0. The fit is somewhat poorer for the Tri-X and the high-inertia emulsion. While this does have an adverse effect on the superimposition of the data sets, the final composite Seidel data obtained are quite adequate as is shown by the final curve-fit data in Table IV. This table contains relative standard deviations 446
...
2
3
High inertia
1
ANALYTICAL CHEMISTRY, VOL. 47, NO. 3, MARCH 1975
polynomials beyond third degree. However, there is sufficient improvement between third- and fifth-degree polynomials for the 103-0 and high-inertia emulsions to justify using the higher polynomial. Thus, the program described here fits each region of the final composite Seidel data to a fifth-degree equation and stores the resulting coefficients in a permanent file for later use with a density-to-intensity conversion program. Thus, this method offers a highly reliable and accurate emulsion calibration procedure which permits quantitative work over a dynamic range extending from the gross fog to optical densities greater than 2.7 density units. In addition, the procedure can be applied directly to emulsions of widely differing properties without resort to empirically determined parameters. Coupling the emulsion calibration program with a density-to-intensity conversion program also developed in this laboratory permits highly quantitative spectrometric work in a minimum amount of time using ,photographic emulsions. Copies of both programs are available upon request. These include a list of the key variables and their functions in the program and a sample output from each program. LITERATURE CITED (1) F. Hurter and V. Driffield, J;,Soc.Chem. lnd., 9, 455 (1890). (2) T. Torok and K. Zimmer, Quantitative Evaluation of Spectrograms by Means of I-transformation,'' Heydon, London, 1972. (3) R. A. Sampson, Mon. Nof. Roy. Asfron. Soc., 85, 212 (1925). (4) E. A. Baker, Roc. Roy. Soc. Edinburgh, 45, 166 (1925). (5) J. W. Anderson and A. J. Lincoln, Appl. Spectrosc., 22, 753 (1968). (6) A. Arrak, Appl. Spectrosc., 11, 38 (1957). (7) H. Kaiser, Spectrochim. Acta, 3 , 159 (1948). (8) M. Margoshes and S. D. Rasberry, Spectrochim. Acta, Part B, 24, 497 (1969). (9) R. J. Heemstra, U . S . Bur. Mines Rep., R17447 (1970).
(15) C. E. Harvey, Spectrochim. Acta, Part B, 25, 73 (1970). (16) H. Kaiser, Spectrochim. Acta, 2, 1 (1941).
(10) R. J. Decker and D. J. Eve, Spectrochim. Acta, Part 6, 25, 479 (1970). (11) C. E. Harvey, "Spectrochernical Procedures." Applied Research Laboratories, Glendale, Calif., 1950. (12) J. R. Churchill. lnd. Eng. Chem., Anal. Ed., 16, 653 (1944). (13) "Methods For Emission Spectrochemical Analysis," 3rd ed., American Society for Testing Materials, Philadelphia, Pa., 1960. (14) R . Gerbatsch and H. Scholze, Spectrochim. Acta, Part E, 25, 101 (1970).
RECEIVEDfor review August 2, 1974. Accepted November 11, 1974* This work was supported in part by Science Foundation Grant, GP-37026X.
Quantitative Determination of Blood Glucose Using Enzyme induced Chemiluminescence of Luminsl Debra T. Bostick and David M. Hercules Department of Chemistry, University of Georgia, Athens, Ga. 30602
Blood glucose is measured using enzymatic conversion of P-D-glucose to D-gluconic acid and hydrogen peroxide in an immobilized glucose oxidase (EC 1.1.3.4) column. The peroxide subsequently reacts with a mixed luminol-ferricyanide reagent to produce chemiluminescene, proportional to P-D-glucose concentration. The method is linear between lo-' and 10-4M glucose, and correlates well with standard methods for glucose determination. With prior adsorption of uric acid, the chemiluminescent technique may be used for urine glucose analysis. The system may also be applied to the analysis of hydrogen peroxide in the lo-* to lO+M range.
Estimation of true blood glucose has been hampered by the relative nonspecificity of most analytical techniques. Glucose analysis based on the inherent specifity of an enzymatic reaction has provided the most accurate means for obtaining blood glucose concentration. The glucose oxidase method, originally described by Keston ( I ) , is the most commoniy employed enzymatic t,echnique for routine blood glucose analysis. T h e method i s based on the following reaction sequence: [3-o-glucose H,02
+-
+
O2
glucose oxidase - _ _ f
o-gluconic acid
chromogenic oxygen acceptor
+
H,O,
peroxidase
chromogen
in which the chromogen most frequently is 0-dianisidine or 0-toluidine. The first reaction is highly specific for glucose (2); however, the second reaction is subject to several interferences. These include reducing substances, such as bilirubin, ascorbic acid, uric acid, and drug metabolites, which may depress results by either competing with the chromogen for peroxide or by reducing the chromogen ( 3 ) .Negative error may also be observed if the pH is too acidic for the enzymatic reactions. Under these conditions, peroxidase is inhibited by fluoride and chloride ions which may be present in the reaction media as serum preservatives ( 4 1. Glucose estimation may he p H dependent if the pH of the final solution remains above four, since the absorption maximum of the oxidized chromogen is pH dependent above this value ( 5 ) . To circumvent many of the interferences associated with the peroxidase-coupled glucose oxidase method, the present technique monitors hydrogen peroxide concentration using the chemiluminescence of luminol (5-amino-2,3-dihy-
drophthalazine-1,4-dione).In the presence of certain metals, peroxide reacts with luminol in basic media to form an excited aminophthalate anion, which returns to ground state by the emission of a photon (6, 7). In the glucose oxidase-luminol coupled reaction sequence, the amount of light emitted is proportional to @-D-glucoseconcentration. Generally, metal ions possessing oxidation states requiring a one-electron transfer are capable of promoting the chemiluminescent reaction between peroxide and luminol in water (8). These have included Fe(I1)-containing compounds, such as hemin (9, 1 0 ) and hematogen ( I 1 ). Copper(I1) (12-16), as well as mixed Cu(I1)-persulfate( 1 7 )and Cu(T1)-hemin (18) solutions, have also been employed in the luminol reaction. Cobalt(I1) (19). Fe(II1) ( 2 0 ) , Fe(CN)e3- (21, 2 2 ) and SbC16- ( 2 3 ) have been cited as reagents capable of producing chemiluminescence in the presence of luminol and hydrogen peroxide. T h e present paper summarizes the chemiluminescent response promoted by several of the above metals, observed during attempts to establish a procedure for peroxide analysis based on the luminol reaction. I t further describes the adaptation and development of this analysis for the determination of blood glucose. A preliminary communication of this work has appeared ( 2 4 ) .Other workers have independently reported a similar method (25 ).
EXPERIMENTAL Apparatus. The chemiluminescence produced by the oxidation of luminol is followed in a continuous flow system using the apparatus shown in Figure 1. The system uses three 50-ml plastic syringes, containing luminol dissolved. in 0.1M H3B03-KOH buffer. KaFeiCN)e, or another metal, and an aqueous background of 0.004M acetate buffer. The syringes are driven by a Harvard Model 600-2-200 infusion pump, .capable of maintaining uniform flow against back pressures greater than 250 psi produced by the enzyme column. Solutions from the ferricyanide and luminol syringes are joined by a glass Y-tube containing a platinum coil t o enhance mixing. A platinum gauze plug is located father down the flow line for the same purpose. Samples are introduced into the acetate flow line by a Chromatronix SV-8031 sample injection valve. Either the acetate background or the same slug flows into the glucose oxidase column. The column itself is a 16-cm Pyrex tube with an i.d. of 4 mm; 2 cm from each end of the column, the i.d. is decreased to 3 mm to accommodate Chromatronix column fittings. As the glucose sample enters the column, hydrogen peroxide generated and carried in the column effluent to the cell where it reacts with the luminol-ferricyanide reagent. Nitrogen gas is bubbled through the cell to ensure uniform mixing. The chemiluminescence produced by the luminol-peroxide-ferricyanide reaction is detected by an RCA 1P21 photomultiplier ANALYTICAL CHEMISTRY, VOL. 47, NO. 3, MARCH 1 9 7 5
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