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Signal and data processing for atomic absorption spectrophotometry
;
pexzm&Mca Acta, Vol. 35B. 99. 795 to 806 FWgamon Press Ltd. 1980. Printed in Great Britain
Signal and data processing for atomic absorption spectrophotometry P. J. WHITE~IDE,T. J. STOCKDALE and W. J:
PRICE
Pye Unicam Ltd, York Street, CambridgeCBl2PX, U.K. (Received 19 June 1980) Abslract-The state-of-the-art of signal and data processing techniques for atomic absorption spectrophotometry is described and discussed. Aspects of optical and atomizer design of greatest importance for providing the best signal to noise S/N ratio and minimum curvature are summarized. In background corrected systems, amplifier gain and time constants must be carefully matched, especially for transient signals. A method is given for calculating the sampling time of peak search systems. Methods of signal averaging are described and the importance of precision calculations is stressed. The correct sequence of readings for calibration is discussed. The causes of curvature are shown for simple and complex curves and methods of correction are compared. Other desirable functions are calculation of sensitivity and detection limit, error warnings and external data output facilities.
INTRODUCTION RESULTS FROM early commercial atomic absorption instruments were usually displayed on an analogue device such as a meter or on a chart recorder if a permanent record was required. This readout was usually in percentage absorption on the earliest instruments or, later, in absorbance units. Concentration results were obtained by constructing a calibration graph from the absorbance readings obtained for a range of standard solutions of the element being measured. Absorbance readings for samples could then be related to concentration by means of this graph. Digital readout was the next stage in development, usually accompanied by some, elementary, form of curve correction in order to allow direct concentration to be set using scale expansion or contraction. This paper is concerned with the following generation of equipment where the use of programmable calculators and microcomputer systems allowed far more advanced signal and data handling techniques to be used.
SIGNAL HANDLING Before any data processing is performed, a signal must first be detected and processed to make it suitable for acceptance by the microcomputer. The signal must be generated in such a way that it contains enough information about the absorbance signal or signals to enable results of the desired accuracy to be obtained. For example, there would be little point in designing a high accuracy curve correction programme for electrothermal atomization if the resolution of the peak reader were relatively poor. As with all processing systems, the quality of result produced by an atomic absorption instrument will be only as good as the weakest part of the signal/data processor chain. Thus the starting point should be the design of the spectrophotometer itself. The important aspects of design of this part of the system have been discussed in detail [l] but the relevant points of the greatest importance are covered here. The major aim is to reduce the noise level on the signal to improve the quality of the raw data. The major types of noise are listed below. (i) Shot noise (signal to noise ratio proportional to w). (ii) Flame noise (seen as absorption or emission). (iii) Concentration noise. (iv) Noise from other components, e.g. lamp, electronics. The optical system should transmit as much energy as possible to give minimum shot noise, etc. This suggests a relatively simple optical system with as few components [l] W. J. PRICE, Specnochemical Analysis by Atomic Absorption. Heyden, London (1979).
795
796
P. J. WHITESIDE,T. J. STOCKDALEand W. J.
PRICE
omocl7.
om.
iiit%zA enw
005,
OM, 003. 0112.
om. I
:
0
20
: : : : : : , w a0 loo lal 140 160 BeamawItching frqmn9 (I-@
40
Fig. 1. Maximum error of absorbance correction as a function of beam switching frequency.
(especially reflecting surfaces) as possible. The system should also ensure that the smallest possible amount of light from the incandescent walls of a graphite furnace reaches the detector so that the decoding electronics can more readily separate this contribution from the “wanted” modulated emission from the hollow cathode or electrodeless discharge lamp. The monochromator must provide sufficient resolution to minimise curvature, as even with advanced curve correction methods, excessive curvature will lead to poor reproducibility at high concentrations. WELZ [2] shows that 0.2 nm is the narrowest bandpass normally required for routine atomic absorption analysis. For many determinations, where the lamp has a fairly simple spectrum in the region of the chosen element line, a wider bandpass may give a beneficial increase in energy without increasing curvature beyond acceptable limits. The frequency with which the absorbance signal is sampled is of great importance in resolving transient signals from electrothermal atomizers. This is especially true with background corrected systems where two transient signals are being compared. The leading edge of the fastest peak measured from temperature controlled small tube furnace systems has a width at half height of about 150 ms 131. This information may be used to calculate the desired measuring speed of the instrument. For example, if we wish to have a peak measurement error of less than 0.5% (chosen because other errors in a typical furnace system are usually greater than this and so peak measurement will not be a limiting factor in analytical accuracy) we can calculate the period of measurement as follows [4]. Peak height is given by epkra where t is the measurement time and k is a constant for the peak. For a peak with a width at half height of 150 ms the constant k may be calculated and used to determine the required time of measurement, viz. measurement
= 2 x j/w=26ms.
For a background corrected system, Fig. 1 [5] shows the variation of the maximum error with beam switching frequency for a peak where the leading and trailing edges of the background absorption signal are assumed to be Gaussian functions having widths of 0.5 and 1.1-s respectively. [2] B. WELZ, Atomic Absorption Spectroscopy. Verlag Chemie, Weinheim (1976). [3] P. J. W-IDE (Ed.), Atomic Absorption with Electrothermal Atomization. Pye Unicam, Cambridge (1977). [4] T. J. STOCKDALE,21st Coil. Spectr. Int. and 8th ht. Conf. Atomic Spectr. Cambridge (1979). [S] R. A. NEWSTEAD,W. J. PRICE and P. J. W-IDE, Prog. Anal. Atom. Spectrosc. 1,267 (1978).
Signal and data processing for atomic absorption spectrophotometry
y
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---
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1OOmV
T + 7mVoffsei
V----100mV ZeFoI
T -3mVoffsel
-
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signal
‘“by!~-&!% Lrba
=.OWA
Fig. 2. Effect of voltage offsets on background correction accuracy.
The measurement time can be longer (i.e. lower frequency) with a flame system where a “steady state” signal is produced. Two other points are worthy of particular attention in background corrected systems. The first of these concerns the ability of the electronic circuitry to measure the true absorbance level in the presence of a high background absorption. For example, with a background level of 2 absorbance units, the signal levels in both the sample and background channels are reduced to 1% of their normal values corresponding to unattenuated light from the atomic line source and the continuum lamp source. Thus, with a high background absorbance, the signal levels in most instruments are likely to be in the region of 100 mV (assuming a “normal” operating level for modern solid state electronics of about 10 V). The presence of atomic absorption in addition to the background absorption lowers the signal voltage in the sample electronic channel further still. The signal voltages in the two electronic channels must be measured accurately with respect to zero volts, converted to absorbance levels in a logarithmic amplifier and then subtracted to give the atomic absorption signal. Any non-zero offset voltages present in the decoding or absorbance conversion circuitry produce an error in the measurement of the atomic absorption signal. An example of this is illustrated in Fig. 2. A well designed electronic system must include the facility to eliminate offset voltages by adjustment of component values. Alternatively, the system may be designed so that the sample and background signals time-share a single electronic channel. Both signals are then measured with respect to the same nominal zero voltage level and the presence of a small offset voltage is relatively unimportant. The second design point concerns the treatment of transient voltage signals by the electronic measurement circuit. The rapidly changing voltage levels in the sample and background electronic channels, encountered when a sample is being atomized in an electrothermal device, are modified by damping or smoothing components in the decoder and absorbance conversion circuits. It is essential that the time constants of any smoothing networks should be matched between the two electronic channels. Failure to achieve this will result in the kind of background correction error shown in Fig. 3 [5]. The resolution of the analogue to digital conversion circuit (A.D.C.) is also important for obtaining accurate results. For example, in order to resolve the fourth decimal place
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P. J. WHITESIDE,T. J. STOCKDALE and W. J. F%UCE
Fig. 3. Effect of unequal time constants on background correction accuracy.
of absorbance (as would be necessary in scale expanded operation) and still to allow operation at high absorbance readings, a resolution as high as one part in 2” may be necessary for flame work. For electrothermal atomization work, where smaller dynamic ranges are used and other errors are more significant, a poorer resolution would be adequate. The resolution of the A.D.C. circuit and the sampling time should, therefore, be different for flame and electrothermal atomization work if optimum results are to be obtained. For example, one current system (Pye Unicam SP9 Atomic Absorption Computer) uses a sampling time of 20 ms and a resolution of one in 215 for electrothermal atomization work and a sampling time of 100ms and a resolution of one in 2” for flame work. DATA HANDLING
Having obtained a digit&d signal of sufficient speed and resolution for the atomizer in use, we now consider how this should be processed for best analytical results. The raw signal is used to obtain a measured value which may be used for concentration calculations. For flame work, the signal is usually integrated over a chosen period of time and the result is corrected for time to give absorbance units for the signal and this figure is used for calculation. For electrothermal atomization work, the height of the furnace peak or the total area under the peak is used for calculation purposes. Most systems give a choice of peak height or peak area and ideally should allow both measurements to be performed simultaneously on each peak. (A discussion of which parameter, height or area, is likely to give best results is outside the scope of this paper and the reader is referred to other publications on the subject [l, 6,7]). A single integrated reading or peak measurement is unlikely to provide sufficient information for obtaining accurate results, and so it is usual to obtain several integrations or peak values and to calculate the mean value and use this for subsequent computation. With dynamic systems such as the atomizers used in atomic absorption, a mean value will give more reliable results. This is especially true of electrothermal atomization where an individual peak may be affected by occasional events such as contamination from the atmosphere or incorrect deposition of a droplet of solution (i.e. a “flier”) and this potential source of error would not become apparent unless a number of results were obtained and compared. The mean value of a series of N individual readings (X) is easily calculated automatically. In order to judge the likely error from measurement of this mean value, the standard deviation may also be calculated for the series of results. The standard deviation may be converted to a relative standard deviation (R.S.D.). This is most useful for comparison purposes as it is independent of the actual absorbance level being measured. Such an estimate of the precision value will aid in judging the likely accuracy [fj] K. M. ALDOUS, D. G. MITCHELLand F. J.
RAY, Anal. Chem. 45, 1990 (1973). [7] R. E. STURGEON,C. L. OWKRABARTI and P. C. BERTEIS,Anal. Chem. 47, 1240, 1250 (197%.
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of results and also in monitoring a method on a day-to-day basis, where the usual precision for the analysis is known and the actual precision obtained may be compared with the usual value. This allows performance of instrument and operator to be monitored. The presence of a “flier” in a particular group of results may also be detected by the poorer precision for that series. Many analysts regret the decreasing use of chart recorders with atomic absorption systems as they allow baseline noise and the presence of fliers to be easily monitored, but calculation of precision does give a method of monitoring the quality of the raw signal which could otherwise become obscured in the calculation processes. For these reasons, it is now more usual to obtain results for flame work using several shorter integrations and calculating mean and precision, rather than using one, long, reading. Another method of obtaining a result based on the mean value is known as “running mean”. As before, the mean value @x)/N is calculated, but the number N is not pre-determined. After each reading, the display of the instrument indicates the mean value of the readings taken so far. For example, after the fifth reading, the display would show the mean value of the five readings. After several readings have been taken the displayed figure will become increasingly stable and when the variation is decided by the analyst to be within acceptable limits, the readings are stopped and the latest mean value used for calculations. This method of obtaining results thus allows the number of readings for each sample to be judged individually according to the signal variation present at that time. It would be difficult to apply directly to automated systems as, although the acceptable limits of variation could be pre-programmed, in certain circumstances if this level were never reached an open ended situation would occur where the instrument would remain trying to analyse one solution. A better use of the “running mean” mode of operation is to use it to establish how many readings are needed for the desired accuracy and then to recall this value and use it to programme the data processing system for routine analysis. CALIJSRM’ION
The readings obtained, by whichever of the foregoing methods, are used for calibration of the instrument and calculation of results in concentration units. A number of different types of reading may be required: for example, with the flame we may have: blank; standard(s); sample(s). The blank solution may contain the reagents and also the sample matrix to correct for contamination and background effects. The baseline is established by spraying the blank solution and setting the instrument to read zero. Autozero circuits often have a specification (for example, + or -0.002 A) which could lead to significant errors if high accuracy results at low absorbance levels are required. In such cases, the same integration and signal averaging processes used for standards and sample solutions should be applied to the blank. For example, if the system is set for 5 2-s integrations, this would also be used to establish an average reading on the blank solution and any deviation from zero observed would be used to correct all subsequent readings. The readings for calibration solutions are obtained next and curve correction applied if necessary. Correction methods are discussed in detail later. Samples are then sprayed and the information obtained from calibration solutions is used to compute concentration from the absorbance readings. The absorbance readings for all solutions should be obtained using identical integration and averaging procedures. There would be little value, for
P. J. W-E,
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T. J. STOCKDALE and W. J. tim
example, in using the mean value of ten integrations for the sample solutions if each calibration point were established with just one integrated reading. For electrothermal atomization work, additional readings may be required, for example : baseline; blank-height and/or area; standard(s)-height and/or area; sample(s)-height and/or area. Because an electrothermal atomization system produces transient signals, it is not possible to “back-of?” the blank value using ‘conventional autozero circuitry which requires a relatively continuous or “steady state” signal such as is found in flame analysis. These autozero facilities, however, still have a role to play in electrothermal work as they can be used to eliminate baseline drift by setting baseline zero before each atomize peak. In this way, the simple single beam optical system may be used to advantage giving high energy and low baseline noise for better detection limits, and the autozero giving baseline correction and so “double beam stability” without the energy and noise penalties of a conventional split double beam system. A series of readings of height and/or area on the reagent/sample matrix blank solution are then made and the average value of these are used to correct subsequent standard and sample readings. This blank correction is essential for furnace work as contamination and reagent blanks are an ever present source of error. Readings for the standards are then taken, curve correction applied if necessary, and results calculated from the sample readings. The ability to display height and area on each peak is of value in selecting which parameter is t? be used for calibration purposes. This is especially true if precisions on sets of height and area readings can be calculated independently, allowing the choice of the mode which gives best precision to be easily made. Curvature correction Probably the most important task of the data processing system is in curvature correction. Calibration graphs in atomic absorption are almost invariably curved and the linearization of these to allow concentration readout presents particular problems if results of the highest accuracy are to be obtained. Figure 4 shows a curve of commonly encountered form. This type of curvature is caused predominantly by stray light effects where the width of the emission line from the source lamp is greater than the absorption
A
A
--
Fig. 4. Stray light curvature.
Signaland data processingfor atomic absorptionspectrophotometry
801
line or where other element or gas lines cause light to be present within the bandpass of the monochromator which cannot be absorbed by atoms of the analyte element. It has recently been shown [8] that the emission line may be slightly shifted from the wavelength of the absorption line and this would also be a contributory factor. This gives an unabsorbable light value or limiting absorbance which causes the calibration to be a curve which becomes asymptotic to the limiting absorbance value. Where ‘this is the only form of curvature, and also in many cases where it is the predominant form, accurate curve correction may be obtained using the stray light equation, derived as follows [l]. If s is the unabsorbable and 1 is the absorbable light, then (s+1)T=s+IxlO-“bc, where T is the observed transmittance, tion. Therefore:
a absorptivity,
10 +abc = which is equivalent
b pathlength
and C concentra-
I (s+Z)T-s’
to lOf”bC =
(s+I)--s
(s+l)T-s’
or
=l-B
10-h&c
T-B
’
1-B abC = log T-B
’
if we put S
-=B, s+l i.e. the proportion of stray light. Finally we have
Curve correction based on this system has been shown to give very accurate results for many flame applications [9]. Figure 5 shows a calibration plot exhibiting curvature away from the concentration axis, often known as “reverse curvature”. This type of curve has a number of causes including ionisation and diffusion effects in electrothermal atomizers [lo]. The stray light method described above will clearly not cope with this form of curve and a more general method has to be used. A fitting of a general polynomial relationship between concentration and absorbance of the type C = p + qA + rA2 + sA3 is suitable, regression techniques often being applied to give the best fit [lo]. Other curve fitting functions, for example, parabolic functions or a pair of parametric cubic gunctions have also been used [9]. In many analyses, the curve encountered may be a combination of the previous two types (see, for example, Fig. 9). Here, none of the previously described fitting methods will be adequate as they all assume just one function for the curve. The following method used in the Pye Unicam SP9 Atomic Absorption Computer, can be used for such complex curves, as well as giving good results for the simpler forms. [8] A. REED, Ph.D. Thesis, University of London (1980). [9] T. J. STOCKDALE, P. J. WHITESRXand R. A. NEWSTEAD, 29th Pittsburgh Conference, Ckudand, Ohio (1978). [lo] P. J. WHITESIDE, An Introduction to Atomic Absorption Speclrophotometry.Pye Unicam, Cambridge (1979).
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P. J. WHITESIDE, T. J. STOCKDALEand W. J. PRICE
Fig. 5. Curvature from ionization effects.
The results on which curve fitting is based are obtained from a blank solution and up to five calibration standards. It is important that calibration systems should allow the ratios of calibration standard concentrations to be varied, although recommended ratios for best results may be indicated. This gives the analyst greater flexibility in choice and dilution of standards, and also allows calibration points to be chosen to reflect, for example, the turning points of a complex curve in order to give the processing system as much information as possible on which to base its curve correction. The concentration of the lowest standard is chosen such that the calibration from the blank to lowest standard of (0 and 1 in Fig. 6) is linear to within the accuracy desired for the analysis. For simple curves, further standards would usually be equally spaced over the remaining calibration range (i.e. from lowest to highest standard). For a curve with both positive and negative changes in gradient, the standards should be set at these points of inflexion for best results. An imaginary line from point 1 to point 2 defines gradient bl, in Fig. 6. An extrapolation of the previous segment provides gradient a,. Gradient c1 is the mean of a, and b,. c1 is used to produce a forcing term to define a parabola between points 1 and 2 which is used as the calibration relationship for establishing sample results (Fig. 7).
Fig. 6. Curve correction process-step
1.
Signal and data processing for atomic absorption spectrophotometry
Fig. 7. Curve correction process-step
803
2.
This process is repeated for the next segment as shown in Fig. 7. bz is the observed gradient from point 2 to point 3, a2 is an extrapolation of b, and c2. is the mean gradient. Again c1 is used to produce a forcing term to define the calibration in the form of a parabola from point 2 to point 3 (Fig. 8). The process is repeated to complete the curve (Figs. 8 and 9). Up to five calibration standards may be used. .In this way complex curves can be fitted satisfactorily, as the method does not assume that the curve can be fitted to a single function. This system has been found to give less than 1% error even for many complex curves, and for simple curves the fitting error is usually considerably less. It should be noted that a basic assumption of this form of curve correction is that the curve must pass through the calibration points. This is fundamental to accurate curve correction systems as these points represent the only absolute information known about the path of the curve. A system which computes a best fit through the points is clearly in error if any of the points are missed by the line. The foregoing information constitutes the basis of data processing systems. In practical systems certain additional requirements are desirable in order to obtain optimum results for routine analysis.
Fig. 8. Curve correction process--step
3.
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P. J. WHITESIDE, T. J. STOCKDALE and W. J. PRICE
Fig. 9. Curve correction process-step 4.
Fully automatic calibration and recalibration with autosamplers Both flame and electrothermal atomizer autosamplers should incorporate a means of identifying blanks, standards and samples to allow automatic calibration and sample analysis, and also automatic recalibration at intervals chosen by the analyst. The use of microprocessor controlled automatic systems usually enables all data reading and calibration facilities that are possible with manual systems to be carried out automatically. This means that the choice of integration time, number of standards and curve correction programme for example does not need to be limited. Calibration with certified reference material In a procedure where aqueous synthetic standards are used to establish a calibration, and linearisation is carried out with one of the functions described earlier, the ultimate slope of the calibration may be adjusted by use of a reference material of the same type as the sample. This will compensate for minor interference effects and help to achieve maximum analytical accuracy. The programme used should enable a solution of a reference material to be used for finally setting the slope of the linear calibration. This procedure can be used to eliminate matrix interferences and systematic errors from other equipment, e.g. balances, pipettes and flasks, if the same equipment is used for samples and reference materials. Standard additions calibration
The method of standard additions is most useful for samples whose matrix composition may not be known exactly, especially with electrothermal techniques, but has the disadvantage that, as in any extrapolation procedure, the errors in standard additions are magnified in the final results. A programme for establishing the line of best fit for calibration and for computing the concentration of the sample saves much time in drawing graphs for each determination which would be the normal procedure. It therefore eliminates errors due to observation, but has to assume that a straight line calibration is produced. The programme should therefore establish a straight line of best fit using the method of least squares and should also print out the linearity regression factor [9]. The latter will give an indication of the degree of confidence which can be placed in the final result. As in conventional calibration, the absorbance reading for the sample and each addition should be the mean of several results.
Signal and data processing for atomic absorption spectrophotometry
805
In order to establish a linear calibration, it would be perfectly permissible to use the stray light equation to linearise, provided that stray light is proved to be the predominant cause of curvature. It would not be recommended to perform standard additions when other forms of curvature are present, or to use other linearisation functions as a false relationship could easily be established. OTHER FUNCTIONS
Reciprocal sensitivity and detection limit A useful facility in analytical investigation is the calculation of reciprocal sensitivity and detection limit from a chosen number of replicate readings of sample standards, etc. The number normally chosen is 10, as from experience this is the least number from which a sensible standard deviation for this purpose can be calculated. Detection limit is calculated from a series of alternate readings of blank and a low standard. The blank readings on either side of each standard reading are averaged and subtracted from the standard reading. The standard deviation in concentration units of the 10 corrected standard readings is then calculated and multiplied by 2 to give the accepted definition of detection limit. A programme providing this facility may be used on a routine basis to check the performance of an instrument. This can be a useful facility in laboratories where regular checks on performance are essential. Error warnings A number of error warnings can be built into data processing systems in order to alert the operator to instrument faults or operator error. The more usual error signals are listed below: (i) self test, fault indication and diagnostic programme; (ii) instrument working outside permitted absorbance range; (iii) background corrector working outside permitted absorbance range; (iv) sample absorbance outside calibrated range; (v) excessive curvature (for example -10% to +40% curvature may be tolerated using the segmented system described previously). Data output Facilities should be available for transmission of the data and result to external facilities. These might be a teletype to format a report of results or an external computer which collects and formats data for several instruments in a laboratory. An external computer may also be used for additional processing of data, such as collecting and performing statistical analysis on large numbers of sample results, although the basic atomic absorption data processing (i.e. integration, peak measurement, curve correction, etc.) is probably best left to the dedicated system in the atomic absorption instrument. An example of the use of such an external computer system has been described recently for large numbers of vegetable samples produced in a major investigation of toxic element contamination over a large site [ll]. A choice of different outputs is desirable to allow easy matching to external systems. Current loop, RS232C and data bus interfaces are commonly employed. CONCLUSION The application of microprocessor-based signal and data processing systems to atomic absorption spectrophotometers extends the range of capability and enables results of a high confidence level to be obtained in a short time. The handling of the raw signal before this is processed into useable analytical information is a function of the equipment which is often not well understood or [ll]
MAFCY
R. HARRIS, TLM DAVIDSONand N. W. LEPP, 5th Pye Unicam Analytical Conference,London
March (1980).
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P. J. WHITESIDE,T. J. STOCKDALEand W. J. PRICE
appreciated. It is important that the best observation times and sequences as well as the most suitable measurement time constants are selectable both in flame and electrothermal atomisation. Errors caused through non-optimization of instrument parameters can be identified and quantified. In a truly versatile atomic absorption system, calibration procedures and subsequent data production can be chosen according to the needs of the analyst and the nature of the basic information given by the particular atomizer and technique employed.
pexzm&Mca Acta, Vol. 35B. 99. 795 to 806 FWgamon Press Ltd. 1980. Printed in Great Britain
Signal and data processing for atomic absorption spectrophotometry P. J. WHITE~IDE,T. J. STOCKDALE and W. J:
PRICE
Pye Unicam Ltd, York Street, CambridgeCBl2PX, U.K. (Received 19 June 1980) Abslract-The state-of-the-art of signal and data processing techniques for atomic absorption spectrophotometry is described and discussed. Aspects of optical and atomizer design of greatest importance for providing the best signal to noise S/N ratio and minimum curvature are summarized. In background corrected systems, amplifier gain and time constants must be carefully matched, especially for transient signals. A method is given for calculating the sampling time of peak search systems. Methods of signal averaging are described and the importance of precision calculations is stressed. The correct sequence of readings for calibration is discussed. The causes of curvature are shown for simple and complex curves and methods of correction are compared. Other desirable functions are calculation of sensitivity and detection limit, error warnings and external data output facilities.
INTRODUCTION RESULTS FROM early commercial atomic absorption instruments were usually displayed on an analogue device such as a meter or on a chart recorder if a permanent record was required. This readout was usually in percentage absorption on the earliest instruments or, later, in absorbance units. Concentration results were obtained by constructing a calibration graph from the absorbance readings obtained for a range of standard solutions of the element being measured. Absorbance readings for samples could then be related to concentration by means of this graph. Digital readout was the next stage in development, usually accompanied by some, elementary, form of curve correction in order to allow direct concentration to be set using scale expansion or contraction. This paper is concerned with the following generation of equipment where the use of programmable calculators and microcomputer systems allowed far more advanced signal and data handling techniques to be used.
SIGNAL HANDLING Before any data processing is performed, a signal must first be detected and processed to make it suitable for acceptance by the microcomputer. The signal must be generated in such a way that it contains enough information about the absorbance signal or signals to enable results of the desired accuracy to be obtained. For example, there would be little point in designing a high accuracy curve correction programme for electrothermal atomization if the resolution of the peak reader were relatively poor. As with all processing systems, the quality of result produced by an atomic absorption instrument will be only as good as the weakest part of the signal/data processor chain. Thus the starting point should be the design of the spectrophotometer itself. The important aspects of design of this part of the system have been discussed in detail [l] but the relevant points of the greatest importance are covered here. The major aim is to reduce the noise level on the signal to improve the quality of the raw data. The major types of noise are listed below. (i) Shot noise (signal to noise ratio proportional to w). (ii) Flame noise (seen as absorption or emission). (iii) Concentration noise. (iv) Noise from other components, e.g. lamp, electronics. The optical system should transmit as much energy as possible to give minimum shot noise, etc. This suggests a relatively simple optical system with as few components [l] W. J. PRICE, Specnochemical Analysis by Atomic Absorption. Heyden, London (1979).
795
796
P. J. WHITESIDE,T. J. STOCKDALEand W. J.
PRICE
omocl7.
om.
iiit%zA enw
005,
OM, 003. 0112.
om. I
:
0
20
: : : : : : , w a0 loo lal 140 160 BeamawItching frqmn9 (I-@
40
Fig. 1. Maximum error of absorbance correction as a function of beam switching frequency.
(especially reflecting surfaces) as possible. The system should also ensure that the smallest possible amount of light from the incandescent walls of a graphite furnace reaches the detector so that the decoding electronics can more readily separate this contribution from the “wanted” modulated emission from the hollow cathode or electrodeless discharge lamp. The monochromator must provide sufficient resolution to minimise curvature, as even with advanced curve correction methods, excessive curvature will lead to poor reproducibility at high concentrations. WELZ [2] shows that 0.2 nm is the narrowest bandpass normally required for routine atomic absorption analysis. For many determinations, where the lamp has a fairly simple spectrum in the region of the chosen element line, a wider bandpass may give a beneficial increase in energy without increasing curvature beyond acceptable limits. The frequency with which the absorbance signal is sampled is of great importance in resolving transient signals from electrothermal atomizers. This is especially true with background corrected systems where two transient signals are being compared. The leading edge of the fastest peak measured from temperature controlled small tube furnace systems has a width at half height of about 150 ms 131. This information may be used to calculate the desired measuring speed of the instrument. For example, if we wish to have a peak measurement error of less than 0.5% (chosen because other errors in a typical furnace system are usually greater than this and so peak measurement will not be a limiting factor in analytical accuracy) we can calculate the period of measurement as follows [4]. Peak height is given by epkra where t is the measurement time and k is a constant for the peak. For a peak with a width at half height of 150 ms the constant k may be calculated and used to determine the required time of measurement, viz. measurement
= 2 x j/w=26ms.
For a background corrected system, Fig. 1 [5] shows the variation of the maximum error with beam switching frequency for a peak where the leading and trailing edges of the background absorption signal are assumed to be Gaussian functions having widths of 0.5 and 1.1-s respectively. [2] B. WELZ, Atomic Absorption Spectroscopy. Verlag Chemie, Weinheim (1976). [3] P. J. W-IDE (Ed.), Atomic Absorption with Electrothermal Atomization. Pye Unicam, Cambridge (1977). [4] T. J. STOCKDALE,21st Coil. Spectr. Int. and 8th ht. Conf. Atomic Spectr. Cambridge (1979). [S] R. A. NEWSTEAD,W. J. PRICE and P. J. W-IDE, Prog. Anal. Atom. Spectrosc. 1,267 (1978).
Signal and data processing for atomic absorption spectrophotometry
y
a-o-
---
197
1OOmV
T + 7mVoffsei
V----100mV ZeFoI
T -3mVoffsel
-
c. T2ctmcW’
signal
‘“by!~-&!% Lrba
=.OWA
Fig. 2. Effect of voltage offsets on background correction accuracy.
The measurement time can be longer (i.e. lower frequency) with a flame system where a “steady state” signal is produced. Two other points are worthy of particular attention in background corrected systems. The first of these concerns the ability of the electronic circuitry to measure the true absorbance level in the presence of a high background absorption. For example, with a background level of 2 absorbance units, the signal levels in both the sample and background channels are reduced to 1% of their normal values corresponding to unattenuated light from the atomic line source and the continuum lamp source. Thus, with a high background absorbance, the signal levels in most instruments are likely to be in the region of 100 mV (assuming a “normal” operating level for modern solid state electronics of about 10 V). The presence of atomic absorption in addition to the background absorption lowers the signal voltage in the sample electronic channel further still. The signal voltages in the two electronic channels must be measured accurately with respect to zero volts, converted to absorbance levels in a logarithmic amplifier and then subtracted to give the atomic absorption signal. Any non-zero offset voltages present in the decoding or absorbance conversion circuitry produce an error in the measurement of the atomic absorption signal. An example of this is illustrated in Fig. 2. A well designed electronic system must include the facility to eliminate offset voltages by adjustment of component values. Alternatively, the system may be designed so that the sample and background signals time-share a single electronic channel. Both signals are then measured with respect to the same nominal zero voltage level and the presence of a small offset voltage is relatively unimportant. The second design point concerns the treatment of transient voltage signals by the electronic measurement circuit. The rapidly changing voltage levels in the sample and background electronic channels, encountered when a sample is being atomized in an electrothermal device, are modified by damping or smoothing components in the decoder and absorbance conversion circuits. It is essential that the time constants of any smoothing networks should be matched between the two electronic channels. Failure to achieve this will result in the kind of background correction error shown in Fig. 3 [5]. The resolution of the analogue to digital conversion circuit (A.D.C.) is also important for obtaining accurate results. For example, in order to resolve the fourth decimal place
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Fig. 3. Effect of unequal time constants on background correction accuracy.
of absorbance (as would be necessary in scale expanded operation) and still to allow operation at high absorbance readings, a resolution as high as one part in 2” may be necessary for flame work. For electrothermal atomization work, where smaller dynamic ranges are used and other errors are more significant, a poorer resolution would be adequate. The resolution of the A.D.C. circuit and the sampling time should, therefore, be different for flame and electrothermal atomization work if optimum results are to be obtained. For example, one current system (Pye Unicam SP9 Atomic Absorption Computer) uses a sampling time of 20 ms and a resolution of one in 215 for electrothermal atomization work and a sampling time of 100ms and a resolution of one in 2” for flame work. DATA HANDLING
Having obtained a digit&d signal of sufficient speed and resolution for the atomizer in use, we now consider how this should be processed for best analytical results. The raw signal is used to obtain a measured value which may be used for concentration calculations. For flame work, the signal is usually integrated over a chosen period of time and the result is corrected for time to give absorbance units for the signal and this figure is used for calculation. For electrothermal atomization work, the height of the furnace peak or the total area under the peak is used for calculation purposes. Most systems give a choice of peak height or peak area and ideally should allow both measurements to be performed simultaneously on each peak. (A discussion of which parameter, height or area, is likely to give best results is outside the scope of this paper and the reader is referred to other publications on the subject [l, 6,7]). A single integrated reading or peak measurement is unlikely to provide sufficient information for obtaining accurate results, and so it is usual to obtain several integrations or peak values and to calculate the mean value and use this for subsequent computation. With dynamic systems such as the atomizers used in atomic absorption, a mean value will give more reliable results. This is especially true of electrothermal atomization where an individual peak may be affected by occasional events such as contamination from the atmosphere or incorrect deposition of a droplet of solution (i.e. a “flier”) and this potential source of error would not become apparent unless a number of results were obtained and compared. The mean value of a series of N individual readings (X) is easily calculated automatically. In order to judge the likely error from measurement of this mean value, the standard deviation may also be calculated for the series of results. The standard deviation may be converted to a relative standard deviation (R.S.D.). This is most useful for comparison purposes as it is independent of the actual absorbance level being measured. Such an estimate of the precision value will aid in judging the likely accuracy [fj] K. M. ALDOUS, D. G. MITCHELLand F. J.
RAY, Anal. Chem. 45, 1990 (1973). [7] R. E. STURGEON,C. L. OWKRABARTI and P. C. BERTEIS,Anal. Chem. 47, 1240, 1250 (197%.
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of results and also in monitoring a method on a day-to-day basis, where the usual precision for the analysis is known and the actual precision obtained may be compared with the usual value. This allows performance of instrument and operator to be monitored. The presence of a “flier” in a particular group of results may also be detected by the poorer precision for that series. Many analysts regret the decreasing use of chart recorders with atomic absorption systems as they allow baseline noise and the presence of fliers to be easily monitored, but calculation of precision does give a method of monitoring the quality of the raw signal which could otherwise become obscured in the calculation processes. For these reasons, it is now more usual to obtain results for flame work using several shorter integrations and calculating mean and precision, rather than using one, long, reading. Another method of obtaining a result based on the mean value is known as “running mean”. As before, the mean value @x)/N is calculated, but the number N is not pre-determined. After each reading, the display of the instrument indicates the mean value of the readings taken so far. For example, after the fifth reading, the display would show the mean value of the five readings. After several readings have been taken the displayed figure will become increasingly stable and when the variation is decided by the analyst to be within acceptable limits, the readings are stopped and the latest mean value used for calculations. This method of obtaining results thus allows the number of readings for each sample to be judged individually according to the signal variation present at that time. It would be difficult to apply directly to automated systems as, although the acceptable limits of variation could be pre-programmed, in certain circumstances if this level were never reached an open ended situation would occur where the instrument would remain trying to analyse one solution. A better use of the “running mean” mode of operation is to use it to establish how many readings are needed for the desired accuracy and then to recall this value and use it to programme the data processing system for routine analysis. CALIJSRM’ION
The readings obtained, by whichever of the foregoing methods, are used for calibration of the instrument and calculation of results in concentration units. A number of different types of reading may be required: for example, with the flame we may have: blank; standard(s); sample(s). The blank solution may contain the reagents and also the sample matrix to correct for contamination and background effects. The baseline is established by spraying the blank solution and setting the instrument to read zero. Autozero circuits often have a specification (for example, + or -0.002 A) which could lead to significant errors if high accuracy results at low absorbance levels are required. In such cases, the same integration and signal averaging processes used for standards and sample solutions should be applied to the blank. For example, if the system is set for 5 2-s integrations, this would also be used to establish an average reading on the blank solution and any deviation from zero observed would be used to correct all subsequent readings. The readings for calibration solutions are obtained next and curve correction applied if necessary. Correction methods are discussed in detail later. Samples are then sprayed and the information obtained from calibration solutions is used to compute concentration from the absorbance readings. The absorbance readings for all solutions should be obtained using identical integration and averaging procedures. There would be little value, for
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example, in using the mean value of ten integrations for the sample solutions if each calibration point were established with just one integrated reading. For electrothermal atomization work, additional readings may be required, for example : baseline; blank-height and/or area; standard(s)-height and/or area; sample(s)-height and/or area. Because an electrothermal atomization system produces transient signals, it is not possible to “back-of?” the blank value using ‘conventional autozero circuitry which requires a relatively continuous or “steady state” signal such as is found in flame analysis. These autozero facilities, however, still have a role to play in electrothermal work as they can be used to eliminate baseline drift by setting baseline zero before each atomize peak. In this way, the simple single beam optical system may be used to advantage giving high energy and low baseline noise for better detection limits, and the autozero giving baseline correction and so “double beam stability” without the energy and noise penalties of a conventional split double beam system. A series of readings of height and/or area on the reagent/sample matrix blank solution are then made and the average value of these are used to correct subsequent standard and sample readings. This blank correction is essential for furnace work as contamination and reagent blanks are an ever present source of error. Readings for the standards are then taken, curve correction applied if necessary, and results calculated from the sample readings. The ability to display height and area on each peak is of value in selecting which parameter is t? be used for calibration purposes. This is especially true if precisions on sets of height and area readings can be calculated independently, allowing the choice of the mode which gives best precision to be easily made. Curvature correction Probably the most important task of the data processing system is in curvature correction. Calibration graphs in atomic absorption are almost invariably curved and the linearization of these to allow concentration readout presents particular problems if results of the highest accuracy are to be obtained. Figure 4 shows a curve of commonly encountered form. This type of curvature is caused predominantly by stray light effects where the width of the emission line from the source lamp is greater than the absorption
A
A
--
Fig. 4. Stray light curvature.
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line or where other element or gas lines cause light to be present within the bandpass of the monochromator which cannot be absorbed by atoms of the analyte element. It has recently been shown [8] that the emission line may be slightly shifted from the wavelength of the absorption line and this would also be a contributory factor. This gives an unabsorbable light value or limiting absorbance which causes the calibration to be a curve which becomes asymptotic to the limiting absorbance value. Where ‘this is the only form of curvature, and also in many cases where it is the predominant form, accurate curve correction may be obtained using the stray light equation, derived as follows [l]. If s is the unabsorbable and 1 is the absorbable light, then (s+1)T=s+IxlO-“bc, where T is the observed transmittance, tion. Therefore:
a absorptivity,
10 +abc = which is equivalent
b pathlength
and C concentra-
I (s+Z)T-s’
to lOf”bC =
(s+I)--s
(s+l)T-s’
or
=l-B
10-h&c
T-B
’
1-B abC = log T-B
’
if we put S
-=B, s+l i.e. the proportion of stray light. Finally we have
Curve correction based on this system has been shown to give very accurate results for many flame applications [9]. Figure 5 shows a calibration plot exhibiting curvature away from the concentration axis, often known as “reverse curvature”. This type of curve has a number of causes including ionisation and diffusion effects in electrothermal atomizers [lo]. The stray light method described above will clearly not cope with this form of curve and a more general method has to be used. A fitting of a general polynomial relationship between concentration and absorbance of the type C = p + qA + rA2 + sA3 is suitable, regression techniques often being applied to give the best fit [lo]. Other curve fitting functions, for example, parabolic functions or a pair of parametric cubic gunctions have also been used [9]. In many analyses, the curve encountered may be a combination of the previous two types (see, for example, Fig. 9). Here, none of the previously described fitting methods will be adequate as they all assume just one function for the curve. The following method used in the Pye Unicam SP9 Atomic Absorption Computer, can be used for such complex curves, as well as giving good results for the simpler forms. [8] A. REED, Ph.D. Thesis, University of London (1980). [9] T. J. STOCKDALE, P. J. WHITESRXand R. A. NEWSTEAD, 29th Pittsburgh Conference, Ckudand, Ohio (1978). [lo] P. J. WHITESIDE, An Introduction to Atomic Absorption Speclrophotometry.Pye Unicam, Cambridge (1979).
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Fig. 5. Curvature from ionization effects.
The results on which curve fitting is based are obtained from a blank solution and up to five calibration standards. It is important that calibration systems should allow the ratios of calibration standard concentrations to be varied, although recommended ratios for best results may be indicated. This gives the analyst greater flexibility in choice and dilution of standards, and also allows calibration points to be chosen to reflect, for example, the turning points of a complex curve in order to give the processing system as much information as possible on which to base its curve correction. The concentration of the lowest standard is chosen such that the calibration from the blank to lowest standard of (0 and 1 in Fig. 6) is linear to within the accuracy desired for the analysis. For simple curves, further standards would usually be equally spaced over the remaining calibration range (i.e. from lowest to highest standard). For a curve with both positive and negative changes in gradient, the standards should be set at these points of inflexion for best results. An imaginary line from point 1 to point 2 defines gradient bl, in Fig. 6. An extrapolation of the previous segment provides gradient a,. Gradient c1 is the mean of a, and b,. c1 is used to produce a forcing term to define a parabola between points 1 and 2 which is used as the calibration relationship for establishing sample results (Fig. 7).
Fig. 6. Curve correction process-step
1.
Signal and data processing for atomic absorption spectrophotometry
Fig. 7. Curve correction process-step
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2.
This process is repeated for the next segment as shown in Fig. 7. bz is the observed gradient from point 2 to point 3, a2 is an extrapolation of b, and c2. is the mean gradient. Again c1 is used to produce a forcing term to define the calibration in the form of a parabola from point 2 to point 3 (Fig. 8). The process is repeated to complete the curve (Figs. 8 and 9). Up to five calibration standards may be used. .In this way complex curves can be fitted satisfactorily, as the method does not assume that the curve can be fitted to a single function. This system has been found to give less than 1% error even for many complex curves, and for simple curves the fitting error is usually considerably less. It should be noted that a basic assumption of this form of curve correction is that the curve must pass through the calibration points. This is fundamental to accurate curve correction systems as these points represent the only absolute information known about the path of the curve. A system which computes a best fit through the points is clearly in error if any of the points are missed by the line. The foregoing information constitutes the basis of data processing systems. In practical systems certain additional requirements are desirable in order to obtain optimum results for routine analysis.
Fig. 8. Curve correction process--step
3.
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P. J. WHITESIDE, T. J. STOCKDALE and W. J. PRICE
Fig. 9. Curve correction process-step 4.
Fully automatic calibration and recalibration with autosamplers Both flame and electrothermal atomizer autosamplers should incorporate a means of identifying blanks, standards and samples to allow automatic calibration and sample analysis, and also automatic recalibration at intervals chosen by the analyst. The use of microprocessor controlled automatic systems usually enables all data reading and calibration facilities that are possible with manual systems to be carried out automatically. This means that the choice of integration time, number of standards and curve correction programme for example does not need to be limited. Calibration with certified reference material In a procedure where aqueous synthetic standards are used to establish a calibration, and linearisation is carried out with one of the functions described earlier, the ultimate slope of the calibration may be adjusted by use of a reference material of the same type as the sample. This will compensate for minor interference effects and help to achieve maximum analytical accuracy. The programme used should enable a solution of a reference material to be used for finally setting the slope of the linear calibration. This procedure can be used to eliminate matrix interferences and systematic errors from other equipment, e.g. balances, pipettes and flasks, if the same equipment is used for samples and reference materials. Standard additions calibration
The method of standard additions is most useful for samples whose matrix composition may not be known exactly, especially with electrothermal techniques, but has the disadvantage that, as in any extrapolation procedure, the errors in standard additions are magnified in the final results. A programme for establishing the line of best fit for calibration and for computing the concentration of the sample saves much time in drawing graphs for each determination which would be the normal procedure. It therefore eliminates errors due to observation, but has to assume that a straight line calibration is produced. The programme should therefore establish a straight line of best fit using the method of least squares and should also print out the linearity regression factor [9]. The latter will give an indication of the degree of confidence which can be placed in the final result. As in conventional calibration, the absorbance reading for the sample and each addition should be the mean of several results.
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In order to establish a linear calibration, it would be perfectly permissible to use the stray light equation to linearise, provided that stray light is proved to be the predominant cause of curvature. It would not be recommended to perform standard additions when other forms of curvature are present, or to use other linearisation functions as a false relationship could easily be established. OTHER FUNCTIONS
Reciprocal sensitivity and detection limit A useful facility in analytical investigation is the calculation of reciprocal sensitivity and detection limit from a chosen number of replicate readings of sample standards, etc. The number normally chosen is 10, as from experience this is the least number from which a sensible standard deviation for this purpose can be calculated. Detection limit is calculated from a series of alternate readings of blank and a low standard. The blank readings on either side of each standard reading are averaged and subtracted from the standard reading. The standard deviation in concentration units of the 10 corrected standard readings is then calculated and multiplied by 2 to give the accepted definition of detection limit. A programme providing this facility may be used on a routine basis to check the performance of an instrument. This can be a useful facility in laboratories where regular checks on performance are essential. Error warnings A number of error warnings can be built into data processing systems in order to alert the operator to instrument faults or operator error. The more usual error signals are listed below: (i) self test, fault indication and diagnostic programme; (ii) instrument working outside permitted absorbance range; (iii) background corrector working outside permitted absorbance range; (iv) sample absorbance outside calibrated range; (v) excessive curvature (for example -10% to +40% curvature may be tolerated using the segmented system described previously). Data output Facilities should be available for transmission of the data and result to external facilities. These might be a teletype to format a report of results or an external computer which collects and formats data for several instruments in a laboratory. An external computer may also be used for additional processing of data, such as collecting and performing statistical analysis on large numbers of sample results, although the basic atomic absorption data processing (i.e. integration, peak measurement, curve correction, etc.) is probably best left to the dedicated system in the atomic absorption instrument. An example of the use of such an external computer system has been described recently for large numbers of vegetable samples produced in a major investigation of toxic element contamination over a large site [ll]. A choice of different outputs is desirable to allow easy matching to external systems. Current loop, RS232C and data bus interfaces are commonly employed. CONCLUSION The application of microprocessor-based signal and data processing systems to atomic absorption spectrophotometers extends the range of capability and enables results of a high confidence level to be obtained in a short time. The handling of the raw signal before this is processed into useable analytical information is a function of the equipment which is often not well understood or [ll]
MAFCY
R. HARRIS, TLM DAVIDSONand N. W. LEPP, 5th Pye Unicam Analytical Conference,London
March (1980).
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appreciated. It is important that the best observation times and sequences as well as the most suitable measurement time constants are selectable both in flame and electrothermal atomisation. Errors caused through non-optimization of instrument parameters can be identified and quantified. In a truly versatile atomic absorption system, calibration procedures and subsequent data production can be chosen according to the needs of the analyst and the nature of the basic information given by the particular atomizer and technique employed.