2201
Anal. Chem. 1981, 53, 2201-2206 (32) Aclkman, R. G. I n “Progress in the Chemistry of Fats and Other Lipids”; Holman, R. T., Ed., Pergamon Press, Oxford. Vol. 12, 1972, 16!5-284, (33) Jamieson, ti. R. i n ““Topics in Lipid Chemistry”; Gunstone, F. D.,Ed., Logos Press: London, 1970; Voi. 1, 107-159. (34) Bailey, A. \/.; Pittman, R. A,; Magne, F. C.; Skau, E. L, J. Am. Oil Chem. SOC.1965, 412,422-424.
Stray Light Ratio
(35) Hammonds, T. W.; Cornelius, J. A,; Tan, L. Analyst (London) 197’1, 96,659-664.
RECEIVED for review March 27,1981. Accepted July 30,1981. We thank the Fonds d’Aide et de Cooperation (FAC) of France for a grant for A.R.
easurements
Wilbur Kaye Beckman Instruments, Pnc., Irvine, California 927 13
Two new methods of elxpreslng and measuring the stray light ratio in spectrophotometers are described. The first of these methods involves a comvolutlon of the detected radlant power spectrum of the instrument wlth the slit function. The convolutlon Integral is performed over wavelength intervals dlctated by limits that distinguish stray from primary light. The second simpler method utilizes the optlcal properties of the blocking filter both io reduce and to measure the remote stray Ilght. l h e latter method has been automated In two new microprocessor controlled spectrophotometers. These methods are capable of measuring the stray llght ratio at any wavelength and in the presence or absence of any sample and, consequently, are far superior to conventional stray llgM tests when applied to Instruments using moderately narrow band blocking filters.
Stray light is a well-known source of error in spectrophotometer measurements. Its significance increases with sample absorbance. Unfortunately, the accurate measurement of stray light has been nearly impossible. The presence of any test material in the beam always affects the level of stray light. If the spectrophotometer is equipped with efficient blocking filters, even relatively narrow band or sharp cutoff materials conventionally used to test for stray light may absorb most of the stray light and lead to a gross error. This situation was encountered in developing the Beckman DU-5 spectrophotometer. When testing this instrument for stray light using a NaNOz solution following the ASTM (1) procedure, an unbelievably low level of stray light was measured. The reasons are now obvious, The “NOz test solution absorbed nearly all of the potential stray light and led to an underestimation of stray light by a factor of 500X. Different methods had to be developed and are described below. The new methods3 proved to be more accurate than the ASTM test (and moreovt?r measure the stray light in the presence of any sample. A major difficulty resides in the definition of stray light. The mogt widely accepted definition is that given by ASTM ( I ) which expresses stray light as “radiant energy of wavelengths remote from those of the nominal pass band transmitted through the monochromator ...”. T h e term “remote” is imprecise and, in practice, varies with the material used to measure the stray light. In this paper, stray light is defined as detected radiant power of wavelengths more than L units away from the center, X, of the monochromator pass band. Under this definition, stray light must always be qualified by the parameters L and X. The parameter I, is called the “limit”
distinguishing stray from primary radiation. This limit may have any specified value greater than the spectral slit width (SSW). The smaller the L , the more nearby stray light is incorporated in the measurement. This refinement in definition is practical only when using a test method that incorporates the “L”parameter. §uch a test method is described here. It involves the convolution of the detected radiant power (DRP) spectrum (sometimes called the single-beam energy spectrum or relative instrument spectral function) with the slit function of the monochromator. The L value determines the limits of the convolution integration. The stray light by either of the above definitions is seldom of interest. Rather one desires the ratio of the stray light to the total DRR. The quantity measured by the ASTM test is such a ratio and is called the stray radiant energy (SRE) or sometimes the stray radiant power ratio. The ratio measured by the new test described here is called the stray light ratio (SLR). The concept of qualifying a stray light measurement by a limit is not new. I t was first suggested by Poulson (Z),but no way of incorporating the limit in an experimental test was then known. Later a convolution method similar to that described here was attempted, but the measurement of the slit function was difficult and confined to wavelenghts provided by intense laser sources (3). With the introduction of improved instrumentation of very high signal-to-noise ratio, it is now possible to obtain slit functions with more convenient sources ( 4 ) . In addition to a rigorous convolution test for the SLR, a simplified test is also described. I t does not require a convolution or knowledge of the slit function. I t has been automated and incorporated in two new microprocessor-controlled spectrophotometers. While it measures only remote stray light, it can be applied in the presence or absence of any sample and hence avoids the larger error of conventional tests.
THEORY The dark current corrected signal from a detector monitoring the output of a monochromator set to wavelength dial setting X can be expressed as
where P(A) describes the spectrum displayed when scanning the source spectrum in the single-beam mode. F(X - A) is the slit function of the monochromator. Convolution integrals of this type have been widely employed to study the interaction between instrument resolution and sample bandwidth ( 5 ) . A modification of this integral is used here to provide
0003-2700/81/0353-2201$01.25/00 1981 American Chemical Society
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ANALYTICAL CHEMISTRY, VOL. 53, NO. 14, DECEMBER 1981
a superior measurement of stray light. It is important to discriminate between t h e true wavelength A and t h e monochromator dial reading X. It will soon become evident when X # A. T h e function P(A) is equal t o t h e product of t h e spectral emission, E(A), of the source, t h e sensitivity, D(h), of t h e detector, the transmittance, B(A), of t h e blocking filter, and t h e effective transmittance, M(A), of the monochromator.
P(A) = E(A)D(A)B(A)M(A)
(2)
A reasonable approximation of this function for a particular blocking filter can be obtained by recording the single-beam output of the spectrophotometer as a function of wavelength while holding detector dynode voltage and monochromator slit width constant. Such a spectrum will be called the DRP spectrum. The slit function, F(X - A), can be obtained by scanning the apparent spectrum of a “monochromatic” source. All of the radiation is presumed t o be of wavelength h and the function described the apparent transmittance of a monochromator for this wavelength as a function of the dial setting X. Experimentally, one determines only a function proportional to F(X - A). It is not practical nor necessary to measure the absolute transmittance. Stray light, S(X,L)can be defined as the detected radiation of all wavelengths L units away from t h e dial setting X.
S(X,L) = P(A)F(X - A) dX
+ lmP(A)F(X - A) dX) fL
(3)
T h e absolute value of S(X,L)is seldom of concern, rather one desires t o know t h e stray light as a fraction of the total detected signal. This quantity is here called the stray light ratio, SLR, or S(X,L).
S(X,L) = KS(X,L)/P(X) (4) Equation 4 contains t h e constant K which must be experimentally determined. This is accomplished by ratioing the calculated SLR to the experimentally measured value at a dial setting remote from the band pass of the blocking filter. This is practical for holographic gratings because S(X,L) is nearly independent of X and L at these remote dial settings. In general, i t is not possible to express P(A) and F(X - A) by exact mathematical functions, and i t is necessary t o approximate eq 3 by the summation
S(X,L) = K($P(A)F(X --m
-
A)SX f ?P(A)F(X
-
+L
A)SX)
(5)
Steps of A wavelength units are used and
X-h=nA
(6)
T h e smaller A, the more accurate the estimation of the stray light. Incorporating SX into K , eq 5 becomes
S(X,L) = -L/6
m
P(X - n A ) F ( n A )+ C P(X - n A ) V ( n A ) ) ( 7 )
K( n=-m
n=L/A
Later it will be shown that the summation need be performed only over values of n that correspond to wavelength intervals of significant P( h). These intervals are effectively dictated by t h e blocking filters.
EXPERIMENTAL SECTION Instrumentation, Transmittance spectra reported here were taken with a Beckman Model 5270 spectrophotometer. DRP and SLR measurements were obtained on a modified Beckman Model DU-8 spectrophotometer. This is an unmodulated, single-beam, microprocessor-controlled instrument of high S / N and good linearity. These properties are essential to cover the extreme
dynamic range required in this study. A Beckman low-pressure mercury-vapor lamp and tungsten-halogen source were used with an S-20 photomultiplier detector. The DU-8 monochromator consists of a 1200 lines/mm grating in a Littrow mount of 300 mm focal length. In some cases, it was necessary to remove dynode voltage from microprocessor control. The detector was then powered with an H P Model 5621A regulated power supply. DU-8 spectra were recorded by using an external Beckman 10 in. analog recorder. This recorder was coupled to the output of the detector preamplifier at the indicated test points on the signal processor board. Filters. Two types of filters, isolating and blocking, are required for these measurements and the optical properties of these filters need to be known accurately. The isolating filters are required to eliminate all but a narrow band of radiation for determination of the slit function. The bandwidth of the isolating filter must be significantly (>lox) narrower than that of the blocking filter. Moreover, the transmittances of both filters must rapidly approach zero at wavelengths more than one bandwidth away from the band center. The isolating filters are of the narrow-band ( 9) at wavelengths shorter than 290 nm and between 405 and 650 nm. Blocking filters designed for the other spectral regions are similar t o the UV filter but span slightly wider wavelength intervals. Slit Function. The slit functions of the DU-8 spectrophotometer and their dependence on source wavelength were determined by using the “singlet” lines a t 254, 334, 436, and 546 nm. The weakest of these lines and the most difficult one to use is the 334-nm line. The slit function recorded for this line, isolated with the filters described by Figure 1, is shown in Figure 3. The
t 320
330
340
350
nrn Figure 4. Emission spectrum of the mercury vapor lamp, unfiltered. 40X and 1600X scale expansions were obtained by varying attenuation on the preamplifier output and on the recorder span. The expansions to 23000 and 65700X were obtained by increasing dynode voltage. All four curves within the interval 300-370 nm utilzed two interference filters. The 313- and 365-nm emission lines from the lamp are over 1OX more intense than the 334-nm line and two filters are required to eliminate these lines. They are visible when using only one filter, but a single filter reduces the continuum adjacent to these lines to insignificance in comparison to the stray component. However, even two filters in series do not totally eliminate the continuum immediately adjacent to the 334-nm line. Fortunately, one can readily calculate the contribution of continuum radiation from a knowledge of the filter transmittance ratio and the unfiltered source intensity. The former is obtainable from Figure 1 and the latter from Figure 4. The continuum radiation will be attenuated in proportion to T i / T334while the stray light component will be attenuated by a wavelength invariant constant. The true slit function a t X is equal to
F(X - 334) = (Ix- IxT,i/ T334)/ I 3 3 4 Correction for the continuum component is necessary only for wavelengths within 15 nm of the primary wavelength.
ANALYTICAL CHEMISTRY, VOL. 53, NO. 14, DECEMBER 1981
2204
r----7--r
lo -
I
'
I
7
c
10 -
i
1 .
7
~
~
A-X
Flgure 5. Effect of monochromatic source wavelength on the slit function.
Figure 5 shows semilog plots of F(X - A) vs. X - A at the four source wavelengths corrected for the above continuum radiation. Except for the 546-nm source line, the f values decrease with increasing wavelength and are slightly smaller at positive X - X settings than at equivalent negative X - X values. It is conceivable that this anomalous wavelength dependence at 546 nm is related to the scatter of unwanted radiation a t the inside walls of the monochromator. Alternatively, it may be a property of the grating. It is not surprising that the grating would scatter more short than long wavelength radiation. Possibly the anomalous scatter is related to the Wood grating anomaly (8)which for this grating is centered a t 555 nm. Clearly the intensity of light diffracted by the grating in this wavelength region is anomalous and the DRP spectra shows this. I t is not obvious that light of these wavelengths should be anomalously scattered. Futher studies are needed to clarify this point. Nevertheless, it seems reasonable to use the F(X,334) data throughout the interval fo the blocking filter described by Figure 2. For most spectrophotometers the stray light ratio is nearly independent of SSW. It may, therefore, appear surprising that the normalized slit functions, at X - X values exceeding the SSW, vary linearly with SSW. In a monochromator with a slit image magnification of unity and equal width entrance and exit slits, the peak DRP increases linearly with slit width for a monochromatic light source and quadratically for a white light source. This difference arises from the character of the spectrum falling on the inside of the exit slit. This "internal" spectrum with a monochromatic source consists of not only an intense and sharp image of the entrance slit but also a weak and diffuse band of monochromatic radiation on either side of the sharp slit image. When the grating is rotating to a position to place this diffuse band on the exit slit, the detected signal increases with the square of the slit width. Thus when normalizing the slit function on its peak value, the signal at wavelength settings different from the source wavelength will be f o y d to vary linearly with slit width. The slit function where X # X is already very small and its absolute value decreases quadratically with slit width; hence the certainty with which it can be determined rapidly deteriorates as slit width decreases. On the other hand, less can be known about the character of the near stray light as slit width is increased. The 2 nm SSW used here is a compromise between these factors. DRIP Spectra. The detected radiant power (DRP) spectrum is that obtained when plotting the dark current compensated detector output as a function of dial setting X when using a "white" source. It is determined primarily by the transmittance spectrum of the blocking filter. There is no need to know the absolute value of this spectrum. The solid curve in Figure 6 shows the normalized DRP spectrum when the blocking filter described by Figure 2 is in the beam. The transmittance of this blocking filter is known to be less than lo4 below 290 nm and above 405 nm; hence the observed DRP in these regions must arise from stray light. Under ordinary circumstances, one would expect to use this blocking filter only within the interval 325-385 nm. The DRP spectra are obtained most easily with an autoranging DVM coupled to the preamplifier output.
~
&
~
0
Flgure 6. Solid curve: normalized DRP spectrum of the DU-8 with the
UV blocking filter in the beam. Dashed curves: stray light spectra.
Similar blocking filters are used to abridge the spectra at other wavelength intervals. The Convolution. The convolution can be viewed as the summation of a set of slit functions similar to Figure 3, each normalized to the DRP spectrum a t the X value and truncated to eliminate the intervals X f L. In the examples shown here, steps of A = 5 nm were used. There is no necessity to use X values outside the 300-400-nm region because there is negligible radiation at wavelength outside this interval, However, it is desirable to calculate the stray light a t dial settings outside this interval in order to determine the K value of eq 7. It is usually adequate to compute the K value at a wavelength at least 30 nm away from the interval of significant DRP. For the blocking filter shown in Figure 2, the X values should then run from 270 to 430 nm. From eq 6, it can be seen that n should range from X-/A - X-/A = 27015 - 40015 = -26 to Xmax/A- Xmh/A/A = 43015 - 300/5m = +26. Equation 7 then becomes -L/5
n=-26
+26
+ n=L/5 C P(X -- 5n)F(5n))
S(X,L) = K( C P(X - 5n)F(5n)
This summation was conveniently programmed on an H P 41CV calculator. The bulk of this program was devoted to addressing the stored P and F data. The K was then selected_so that the calcuated S(270,L ) equaled the observed P(270). At X = 270 nm, S(270,L) is almost independent of L. The dashed lines in Figure 6 trace the stray light S(X,L) for three values of L. The dip seen in each of these curves is a consequence of the spectral distribution of primary light. The calculated S(X,L) is bound to decrease when the interval of most intense DRP is considered to be primary rather than stray light. The shape of the dip also varies with L. The absolute value of S(X,L)is of little concern and actually is unknown even after the above evaluation of K. The important quantity is the ratio of the stray relative to the primary radiation. This quantity has been defined as the stray light ratio (SLR). Obviously, it can be evaluated only a t wavelengths where there is appreciable primary light and this is the interval within which a blocking filter would be used for any absorption measurement. Thus the SLR spectra in Figure 7 are the ratios of dashed to solid curves of Figure 6. Influence of the Sample. All samples will absorb some of the stray as well as primary radiation; however, one does not usually know how much of the stray light is absorbed. It will be shown that the SLR can be profoundly influenced by the sample. Solutions of NaNOz will be used to illustrate this point. A solution of 50 g/L of NaNOz is recommended by ASTM for testing the SRE in the 300-385-nm region ( 1 ) . Figure 8 shows the absorbance spectrum of 1 cm of a 5 g/L NaNOz solution as recorded by the 5270 spectrophotometer. The absorbances at other concentrations are readily calculated from Beer's law. Thus a 50 g/L solution should have an absorbance of 16.8 a t 353 nm. The DRP spectra obtained on the DU-8, with different concentration solutions in the beam along with the UV blocking filter, are shown in Figure 9. The DRP readings a t wavelengths outside the 290-405 nm interval clearly show that the sample strongly influences SLR.
ANALYTICAL CHEMISTRY, VOL. 53, NO. 14, DECEMBER 1981 lo-'
I
I
10-1
2205
I
10-5
10-8
10-4
lo-!
10-1
10-
Flgure 7. SLR spectra of the DU-8 with the UV blocking filter.
z'!(t --I------
1.OP
Figure 10. DRP and SLR spectra of the DU-8 with 1 cm of 18 g/L NaNO, in the beam.
i 5 glL NaN0. PATH = 1 cm REF = AIR SSW = 0 5 n m
100 Y
t
0 i!oo
1
1
1 300
-
41
I 500
700
600
BOO
nm
Flgure 8. Absorbance spectrum of 1 cm of 8. 5 glL NaNO, solution.
,
10- 7
400
300
-
350
A, nm
Flgure 11. SLR spectra with varying concentrations of NaN02 in the 10-7
Fr:-> 3UO
beam.
50 glL
I 350
400
X (nm)
Figure 9. DRP spectra of the DU-8 with varying concentrations of NaNO, in the beam.
Convolutions of the 18 g/L solution DRP spectrum with the 334-nm slit function are graphed as dashed lines in Figure 10. The solid line is the DRP spectrum. Note the offset abscissa scale. All data axe normalized t,o the maximum DRP of the solvent at
365 nm. The stray light is a large fraction of the DRP and would introduce serious errors into the measured absorbance if stray light were ignored. S (T;,L)is nearly independent of L near the wavelength, 350 nm, of maximum sample absorption because there is little detectable radiation here. Figure 11 summarizes the variation of the SLR, s(X,15), as functions of X for the several NaNOz solutions. The data for the most concentrated solution (50 g/L) are subject to significant error because the P(A) data did not include values near 700 nm where
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ANALYTICAL CHEMISTRY, VOL. 53, NO. 14, DECEMBER 1981
10’L
I
300
I 350 h(nm)
I
400
Flgure 12. SLR spectra of the DU-8 measured by the modified test.
the blocking filter has a small transmittance and the sample a high transmittance. Nevertheless, the large influence of the sample on the SLR is quite evident. A Modified Test. A modified test for the SLR requiring no convolution or slit function measurement can be made by assuming stray light to be independent of wavelength and equal to the DRP at the absorption edge of the blocking filter. For the case of the UV blocking filter in the DU-8, the wavelength for the measurement would be 290 nm. Examination of Figure 3 shows that such a test would provide a stray light fairly close to S(1,25) for this specific case. In other cases, e.g., Figure 10, the modified test deviates more from any particular S(X,L). For convenience, the symbol S( X,R) denotes stray light measured by this modified test. R then stands for the nonspecific parameter “remote”. The SLR measured by this modified test is denoted S(X,R) and equals S(X,R)/P(X)where P(X) is measured with a reference or solvent in the beam. Figure 12 shows plots of S(X,R)vs. X for the various NaNOz solutions. Comparison of this figure with Figure 11shows that the modified test is not as accurate as the more rigorous convolution test, but it is far superior t o the ASTM test when the spectrophotometer incorporates relatively narrow band blocking filters. Furthermore, the modified test can be automated in a microprocessor controlled spectrophotometer. The new Beckman Model 42 and DU-5 spectrophotomeFrs have been so programmed and permit the determination of S(X,R)at any wavelength within the range of the instrument by simply identifying the stray light test and the desired wavelength. DISCUSSION Significance of the SLR. There are two major uses for the SLR. It provides a measure of instrument performance and under some circumstances can be used to correct for stray light error, hence permit more accurate absorbance measurements, particularly a t high absorbance. Spectrophotometers are usually specified for a SRE a t one or more wave-
lengths. The inference is sometimes given that these are “worst-case” values. This may or may not be true. Actually, the measurement of the SRE has not been worked out for all wavelengths. When used, the existing tests provide information about instrument performance only in the presence of the test reagents and can neither indicate stray light in the absence of the test materials (Le., evaluate instrument performance alone) nor indicate stray light in the presence of a n arbitrary sample. The conventional tests then meet neither of the major uses for stray light information. Comparison of Test Methods. The ASTM test equates SRE with the apparent transittance of a sharp cutoff sample a t a wavelength where the sample is essentially opaque. The data for such a test is provided in Figure 9. The apparent transmittance of the 50 g/L solution a t 355 nm is about 2 X lo-’. What is the significance of such a small number? I t does indeed indicate the SRE of this particular instrument in the presence of this sample, but differs by a factor of 500 from found in Figure 12 when only the the S(355,R) = 4 X solvent is in the beam. The measured SRE a t 355 nm would provide a very poor guide to the error likely to be encountered in measuring some other sample. Futhermore, the SRE data cannot be used in a comparative sense. For example, two instruments might exhibit the same SRE; yet the spectral distribution of the stray light could be entirely different. In general, far stray light has more influence than near stray light on the error introduced into an absorbance measurement. It should be noted that the SRE test was developed for instruments using either no blocking filters or less efficient ones such that much of the potential stray light would not be absorbed by the recommended test materials. T h e S R E measured with NaNOz is very sensitive to the cutoff of the blocking filter. Were it to be moved from 400 nm (Figure 2) to, say, 450 nm the ratio S(355,15)/SRE would be much less than 500. Coversely, were the edge moved 15 nm shorter, this ratio would be much larger than 500. What test and conditions should then be used by instrument manufacturers to specify stray light performance? All instruments are not equipped with blocking filters having properties suitable for the convolution or modified tests. Use of an adequate blocking filter solely for purposes of measuring stray light will yield information valid only when using this filter and hence will not characterize the basic instrument. For the present, it appears any specification of stray light should clearly reference the details of the test. LITERATURE CITED (1) (2) (3) (4) (5)
“Standard Method of Estimating SRE”, ASTM Designatlon, E-387-72. Poulson, R. E., Appl. Opt. 1964, 3 , 99. Kaye, W. Appl. Opt. 1975, 14, 1977. Kaye, W.; Barber, D.; Marasco, R. Anal. Chern. 1980, 52, 437 A . Stewart, J. E. Infrared Spectroscopy, Experimental Methods and Techniques”; Marcel Dekker: New York, 1970. (6) Brown, S.; Tarrant, A. W. S. Opt. Acta 1978, 25, 1175. (7) Hawes, R. C. Appl. Opt. 1969, 8 , 1063. (8) Stewart, J. E.; Gallaway, W. S. Appl. Opt. 1962, 1 , 421.
RECEIVED for review May 28,1981. Accepted August 31,1981.
