R. B. Cook' and R. Jonkowe Cory Instruments Monrovia, California 91016
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I
Effects of Stray Light in Spectroscopy
Stray light can seriously affect absorption measurements. All too often, the effects of stray light are subtle, easily overlooked, and often ignored when considering the accuracy of photometric measurements. Parameters, such as resolution and wavelength accuracy, usually receive more attention. Yet stray light can cause significant errors in absorbance and concentration measurements as well as seriously degrade absorbance sensitivity, particularly at high absorbance. The following remarks are especially pertinent to measurements in the ultraviolet and visible reeions where most applications are quantitative determinations, rather than sample identifications and band position assignments. Techniques for estimating stray light have been discussed extensively elsewhere (1-4). In this paper, the effects of stray light on quantitative measurements, band shapes, and Beer's Law linearity are described. Factors giving rise to stray light are briefly stated, and t h e inability to make satisfactory corrections for the total stray light factors is described. ~
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As a consequence, absorbance values in the Iiterature are not corrected for SRE. Use of double monochromators (6) or suitable filters ($) reduces the SRE level, thereby increasing absorbance accuracy and reducing the need for such correction. Absorbance is defined as Abs = -log T
where T is the transmittance and determined by the ratio of sample and reference signals from the photometer
where I is the sample beam intensity and I. the reference intensity. If an absolute value for SRE were known for a particular sample, under a specific set of measuring conditions, the effect of stray light would be additive to both the sample and reference intensities. Then the measured absorbance could be estimated by the following formula M
Definition
Stray light, or stray radiant energy (SRE) is detected, unwanted radiation and is expressed as the percent radiation reaching the detector whose wavelengths are outside the spectral region isolated (SRI) range of wavelengths (1, 5). SRE is a function of instrument design, the particular instrument used, the light source, and the sample syst,em. Some factors which determine the SRE level are A. B. C. D.
monochromator design spectral distribution of source detector semitivity deterioration of optics E. wavelength F. sample-absorption, emission, and scattering charrtcteristics G . cells
Since SRE is a function of so many factors, some of them sample-rrlat,ed, it usually is not possible to correct an absorbance measurement for the effects (errors) attributable to SRE. SRE due to instrumental factors (A-E) can be experimentally measured using the method recommended by the ASTM (I) and very approximate corrections could be made. However, such correction becomes impractical when sample effects (F and G) are taken into account. Changes in SRE due to these factors cannot adequately be determined using the ASTM technique.
' Address correspondence to this suthor. ' Present address: Orbispbere Corporation, Geneva, Switzer-
land.
=
--log ( I + SRE') I, SRE'
+
where M is the measured absorbance value; Abs, the true value; and SRE', the stray light for these particular measurement conditions and sample characteristics expressed in units comparable to To. Defining SRE as SRE1/Io, the estimate for measured absorbance becomes 10-*ha + SRE M = -log 1 SRE
( +
The following discussion assumes that the sample does not absorb in the regions from which SRE originates and does not exhibit any scattering or luminescence. Although these conditions are rarely, if ever, completely met, this discussion illustrates one limiting case often approached by experience. Examples which follow show the types of problems and difficulties SRE can cause and the importance of minimizing its effect. A spectrophotometer cannot measure absorbances higher than its stray light level at a particular wavelength, since the detector will see nearly the same signal level (from stray light) regardless of higher absorbance levels. An apparent absorbance higher than -log (SRE) cannot be attained. For example, if an instrument has stray light of lYo at a particular wavelength, the instrument can never read more than 2 absorbance (1% transmission) at that wavelength. Volume 49, Number 6, June 1972
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easily with this graph for a given SRE and absolute absorbance. For example, an SRE of 0.01% at a true absorbance of 2.0 will give an error of about 0.004 Abs or a measured absorption of 1.996. The assumptions that the sample does not luminesce, scatter or absorb SRE must still hold for these corrections to be accurate. To accurately determine the errors for real samples, four sample parameters need to be known: luminescence spectrum, scattering losses, complete absorption spectrum, and SRE as a function of wavelength for the particular measuring conditions. To provide total corrections of absorption data, an equation can then be written as
Figure 1. The effect, of various SRE level* on a hypothetieol absorption bond with Goursion distribution ore shown. The true maximum absorbance is 3.000. The peaks ore noticeably RaWened b y the effects of SRE. (-.-. '1% 0.1 % SRE, - - - is 0.1 7' SRE, and is 0.01 SRE).
.. .
Yo
Effects on Band Shapes
Stray light has the effect of flattening absorption band peaks since the effectis not linear with absorbance. Figurc 1 depicts effects of various SRE levels on a hypothetical absorption band with Gaussian distribution. The true maximum absorbance is 3.000. However, a 1% SRE flattens the band considerably, producing a measured absorbance of 1.958. Computer simulations are used to illustrate these effects since they cannot be readily demonstrated experimentally; stray light on a single instrument cannot be easily varied and controlled.
where M is the measured absorbance value, Abs(A,) is the absorbance at wavelength A,, SRE(X3 the stray light at A,, F ( h ) is the measure of the total luminescence emission excited at wavelength A 1 reaching the photodetector, and S is the measure of scattering losses (i.e., not reaching the detector). The last three parameters are quite dependent on the sample system and are not readily measurable. Indeed, this calculation becomes tedious and inexact since the parameters are approximate. However, the approximation given in (I) and plotted in Figure 2 is easy to determine and provides a rough idea of the magnitude of errors caused by stray light. (As stated earlier, this SRE correction is not suitable for correction of actual data.) Figure 3 indicates the level at which stray light begins to significantly affect a measurement. Percent error
Effects on Accuracy
SRE specifications are defined with respect to the total signal-producing energy passed by the monochromator under given conditions. Stray light of 0.1% means that 99.9% of the sample signal reaching the detector results from radiation inside the spectral region isolated (SRI) by the monochromator a t the 100% T level. When a sample absorbs radiation within the SRI, only the 99.9% is attenuated by the sample. The 0.1% from SRE is unaffected, assuming that the sample is not absorbing SRE. As a result, the relative error due to SRE is greater at the 0.1% transmission level (3.00 Abs) than at 10% (1.00 Abs). For the band shown in Figure 1, even 0.1% SRE gives a considerable peak error. The measured value is low by 0.3 Abs, a relative error of 10%. For a true absorbance of 1.0000 (10% T), the measured reading is (10% T 0.1% SRE)/(100% T 0.1% SRE) = 10.09% transmission, which corresponds to 0.9961 Abs or an error of 0.0039 Abs (relative error of 0.39%). Stray light becomes morc important at higher absorbance~. Figure 2 summarizes stray light errors as a function of true absorbance for five stray light levels. An cstimatc of the absorbance error can be determined
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Journal o f Chemical Education
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True Absorbance Figure 2. Absorbance erron due to SRE ore plowed os .function of true absorbance for five %troy light levels. .An estimate of the absorbance error can b e mode for o given SRE and obsolute absorbonce.
small range. Any continuous curve appears linear if sufficiently magnified. Beer's Law is the linear relationship between absorbance and concentration. For example, Figure 4, Curve I, depicts this linear function for an aqueous solution of Cr(NOa)$. If a stray light level of 0.9% were assumed, and the same measurements were made, Curve I1 would result. This curve is not a straight line and there is significant deviation from Beer's Law predictions at absorbances greater than 1.0. (A curve of similar shape as that obtained from SRE effects can result from Beer's Law deviations due to pbysiochemical effects, such as molecular associations.) If a narrow concentration range is examined on both curves in Figure 4, the absorbances in both cases appear linear with concentration even though they differ widely in absolute value (see Fig. 5). This apparent linearity can lead to incorrect results and a great loss in the measurement sensitivity.
Stray Light (percent) Figure 3. Percent error in absorbance ploned versus SRE indicetes where SRE begins to $igniRcantly offect absorption mearurements This graph shows tho? mearurementr can b e made to 4.0 Abr with lets than 0.1% error if the SRE level is 0.0001
%.
in absorbancc versus stray light levels is plotted for various measured absorbances. If the absorbance read on thc spcctrophotomcter is 2.0 and the SRE is 0.001%, then the relativc error is 0.02%. Even a measured 0.50 absorbance has a relative error of 1.86% for an SRE lcvel of 1.0%. On the other hand, this graph shows that measurements up to 4.0 Abs can be made with less than 1% error if the stray light is less than 0.001%. If the SRE is less than 0.0001% (which is attained with modern spectrophotometers), the errors to 4.0 Abs are less than 0.1%. High absorbance measurements can be made with insignificant error due to stray light if the SRE level is small. 0.976):
Effects on Beer's L a w Plots a n d Linearity
X Concentration (ARB1
Although stray light causes inaccuracies in absorption mcasuremcnts, inaccurate absorbance values obtained from a dilution series can still appear linear over a
Figure 5. If a narrow c?ncentrmtion range is examined on both curves in Figure 4, the mbrorbonce in both cases appear linear with concentrotion even though they differ widely in absolute value.
As an illustration, assume that in the absence of stray light, an 8 ml aqueous solution of Cr(N03)~has an absorbance of 3. This solution is diluted with five 40 ~1 aliquots of water, and the absorbance values are then measured after each aliquot. Beer1s.Lawstates where Abs is absorbance, a absorptivity (extinction coefficient), b path-length, and c concentration. If a, b, and the weight of Cr(NO& remain constant, which are the conditions of the hypothetical experiment, then the absorbance can only be a function of the water volume Abs = 24/(8
-o 8
o.Sx
k
Concentrotion (ARB) Figure 4. Beer's Low relationship between absorbonce m d concentrotion is shown ICvrve I). If a stray light level of 0.9% were aswned, significant deviation would occur, resulting in Curve 11. A concentration of X giver an ablorbance of 3.
+ 0.0402)
where x is the number of added aliquots. Calculated Beer's Law values are plotted in Figure 6. The slope of the plot (change in absorbance per 40 increment) isO.015. If the same solutions were measured on a spectrophotometer with stray light of 0.9%, the results given in Figure 7 would be obtained. These values were calVolume 49, Number 6, June 1972
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Figure 7. The abrorbonse values from m e dilution series, plowed in Figure 6, ore colruloted with an SRE of 0.970 and replowed. The results ore lineor ond give a rlope of 0 . 0 0 1 6 AAbr/40 p l increment. This flgure demonshates the decrease in sensitivity of concentration me~suremenhif SRE is signiflcont.
Conclusion
A
20
do
I
do
zbo
Aliquots (PI H201 Figure 6. Calculated Beer's Low absorbance voluss of o CrlNOsla dilvtion series ore plotted or a function of aliquot. of H 2 0 added. The rlope lchonge in obrorbanse per 4 0 PI insrementl is 0.01 5.
culated from eqn. (I), where M is the value given in Figure 7, Abs is the value from Figure 6, and SRE is 0.9%. The slope of the curve in Figure 7 is 0.0016 AAbs/40 pl increment. The absorbance values, measured with 0.9% SRE, are linear in concentration; however, the slope or rate of change in ahsorbance differs by a factor of 10 from the slope obtained from Beer's Law predictions (Fig. 6). The sensitivity of concentration changes with rcspect to absorbance changes is decreased with significant stray light since the slope of the measured Beer's Law plots can be smaller than the true slope. I n other words, in the example, the 40 p1 increment of water is easier to detect with no stray light (AAhs/40 pl = 0.015) than with 0.9% SRE (AAbs/40 J = 0.0016). More importantly, large errors due to nonlinearity over large concentration ranges can occur when attempts are made to calculate the absorptivity of a standard solution from some lower (or higher) concentration and to extrapolate to higher (or lower) concentration levels when stray light significantly interferes with the absorbance measurement.
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Stray light introduces error into all absorbance measurements. Absolute magnitude of the error depends on the stray light magnitude and the ahsorbance level being measured. SRE is a systematic error and is repeatable under identical conditions. Stray light depends on many instrumental and sample factors which are usually independent. Correcting of measurements for the effects of stray light is usually impractical, hazardous, or impossible. Thus, where accurate data are required, only spectrophotometers with low stray light characteristics should be employed. Even with significant stray light levels, apparent ahsorbance linearity can he obtained over narrow concentration ranges. However, the data will disagree with Beer's Law predictions and limit the useful range and sensitivity of concentration measurements. Correct absorbance values are not only dependent on stray light, but also are a function of photometric repeatability and accuracy and wavelength accuracy. All of these parameters must be accurate in order to obtain accurate ahsorbance data. Literature Cited on Recommended Pmotioea in Spectrosoopy," American Society for Testing and Materials. Philadelphia. 1969, p. 94. SGAYIN, W., Anal. Chen., 35,561 (19631. (3) P o u ~ s oR. ~ ,E., Appl. Opt., 3, 99 (1964). (4) TONNICUET-. D. D.. J . O ~ t . S o ~ . A m e 1 . . 4 5 , 9 8(19551. 3 (5) "Optimum Speotrophotometer Parameters," Applications Report AR 14-2, hvsiisble from Car). Instruments, Monrovia, Calif. 91016. (81 Bnnam. R. P., "Ab~orption Spectroscopy," John Wilev & Sons, New York. 1962, p. 431.
(11 "Manual (2)
