Figure 2. Visible spectrum of radiated sodium chloride
the visible transmittance spectrum showed a visual efficiency of 33.6%, a dominant wavelength of 480 millimicrons and an excitation purity of 55.5%,using the selected ordinate method. This procedure offers a low cost efficient approach to investigators interested in studying irradiation effects on thin polymer films. The technique works particularly well for plasma-deposited polymer films b u t can also be used for studying thermosetting polymer systems. Where pathlength is a problem, the freshly catalyzed polymer systems can be diluted with a suitable solvent, applied to the desired wet film thickness and then the solvent can be evaporated. The only criterion is t h a t the solvent be completely inert to the sodium chloride window.
a1 color changes due to the formation of "F" centers. Figure 2 shows the visible spectrum obtained. Calculations from
RECEIVEDfor review October 14, 1974. Accepted January 10, 1975.
350
400
450 500 WAVELENGTH Imillimicron~l
600
760
Simple Noise-to-Signal Ratio Monitor for Measurement of Noise in Direct Current Signals J. D. Ingle, Jr. Department of Chemistry, Oregon State University, Corvallis, OR 9733 1
The importance of the signal-to-noise ratio (S/N) for characterization, comparison, and optimization of chemical measurements is stressed by numerous researchers (1-6). T h e usefulness of this quantity stems from the fact that the reciprocal of t h e S / N is the noise-to-signal ratio (N/S) which is also the relative standard deviation of the signal. Hence, maximization of the S/N maximizes measurement precision. Optimization of precision will be most critical in those situations where the accuracy is limited by precision rather than by other factors such as interferences, readout resolution, or sample preparation problems. Two common criteria used for optimization of instrumental variables are maximization of the signal (S)or of the signal-to-background ratio (S/B),although neither criterion ensures the best precision. Doubling the signal may quadruple the background signal and its noise to yield a net decrease in S/N or precision. Changing a variable to increase the S/B may increase the relative noise in the signal and background and, hence, reduce precision. The above criteria are used because they are adequate in certain situations and because they are simply measured and calculated. A third criterion, maximization of the S/N, is the most powerful, but its use may be limited because of the need for more complex and time-consuming measurements and calculations. Calculation of the S/N requires t h a t an estimate of the root-mean-square (rms) noise (N) be obtained in a d dition to the signal. Three common techniques for measurement or calculation of the rms noise are discussed below (7). T o obtain an estimate of the S/N in each case, an estimate of the mean analytical signal must be obtained with appropriate background signal measurement or suppression. T h e ratio of the mean analytical signal to the rms noise is then taken either manually or with a computer. 1) Repetitive measurements of the signal can be made and the mean and standard deviation of the signal calculated in the usual manner. Enough points must be taken to
ensure that a good estimate of the standard deviation is obtained. This rather tedious procedure becomes attractive if the instrument is on-line with a computer so that the data acquisition and calculations are automated. An added advantage of computer utilization is t h a t once the data are in memory, Fast Fourier Transform techniques may be used to provide a noise spectrum which characterizes the frequency content of the noise. 2 ) The signal can be recorded for a period of time on a recorder or oscilloscope or by discrete measurements with a digital or analog meter. One-fifth of the peak-to-peak noise (i.e., the difference between the maximum and minimum excursions) is taken as the rms voltage (8). The noise is assumed to be Gaussian and the period of recording must be long enough to ensure t h a t excursions of h2.5 u from the mean are highly probable. Sometimes it is difficult t o decide whether a large signal excursion from the mean is due to the inherent noise or to an extraneous transient. 3) Finally, an rms noise meter (9) can be used which provides a voltage directly proportional by a known factor to the rms noise content of the input signal. Options 1 and 2 are rather tedious unless an on-line computer is employed. Option 3 is more attractive since it provides a direct estimate of the noise without calculation. However, rms meters can be expensive and, until recently, were fairly complex to construct. Recently ( 9 ) , circuitry was described which provides direct readout of the relative variance of a signal. The mean square noise and divider circuitry was constructed from a number of operational amplifiers and multiplier circuits. Relatively inexpensive integrated and/or hybrid divider and rms-to-dc converter modules have become available commercially. This paper describes the construction and performance of an inexpensive and simple N/S monitor which is built with the newly available modules described above. The circuit is designed to be applied to S/N and time constant situations normally expected for analytical spectrometric techniques. I t provides a simple alternative for direct S/N ANALYTICAL CHEMISTRY, VOL. 47, NO. 7, JUNE 1975
1217
1
HIGH
1 I
NONINVERT
1
1
RMS-TOOC
I
i
1 1
__ , D I V I O E R
I E,
X
l---
I
------I I INVERT
Figure 1. Block diagram of N/S monitor
calculation if an on-line computer is not available. T h e application of the instrument to two practical situations is described.
GENERAL DESCRIPTION OF INSTRUMENT In this section, a description of the instrument and its operation is presented. The equations which describe the transfer function and frequency response are discussed. Figure 1 shows a block diagram of the total N/S monitor. The input signal ( S ) is connected both to a high pass (hp) filter and to a voltage inverter whose output ( - S ) is in turn connected to the denominator input ( x ) of a divider ciruit. T h e hp filter blocks the dc signal and very low frequency noise and drift. The non-inverting voltage amplifier amplifies the transmitted noise by a factor g which can be selected to be 1, 10, 100, or 1000. The amplified noise then passes into the rms-to-dc converter which has a transfer function of 1 V output per 1 V rms input and an adjustable output low pass filter. T h e output of the rms-to-dc converter ( g N )is connected directly to the numerator input ( 2 ) of the divider which has a transfer function of 10 z / x . The equations which express the relationship between the input, S / N , and the output voltage Eo, are:
- 10 g N / S N / S = - Eo/10 g . E, =
Power connections and trimming potentiometer connections are not included but are wired exactly as specified by the manufacturer, OA 1 (Analog Devices, A540J) trimmed for zero offset with g = 1000. RMS-to-DC module (Analog Devices 440J) trimmed with output offset potentiometer to 10.0 m V with 10.0 mV input and with scale factor potentiometer to 1.000 V with 1.000 V input. Power supplied by Heath EU 801-11 digital power supply. All resistances given are in ohms and resistors are selected to possess values within 1 YO of the values specified in the Figure. All capacitances given are in pF with f 1 0 % tolerance. The 2.7- and 10-pF capacitors are tantalum and the 150-pF capacitor is electrolytic. SIand S2 are rotary switches.
filter is formed with a parallel combination of a capacitor and resistor in the feedback loop of an operational amplifier, then there would be no interaction. The absolute values of the power transfer functions for a high and low pass filter are given (7) by Equations 4 and 5 , respectively lH(ja)lhp = (1
+
(wThp)-2)-"2
(4)
lH(ja) I l p = (1
+
(WT1p)2)-"2
(5)
(1) (2 )
Hence the SIN is directly calculated from Equation 3 with the measured output voltage (Eo)and the selected gain factor (g). The noise N in Equation 3 represents the rms noise in whatever signal (background or background plus analytical) is connected to the input of the monitor. I t does not represent the total noise in the measurement which takes into account both the noise in the blank measurement and the noise in the total signal (background plus analytical). Ideally, the N/S monitor should neither reduce nor increase the relative noise a t the input. The noise is increased if the N/S monitor circuitry adds significant noise on top of the input noise. This is negligible as will be discussed later. T h e noise is reduced if the bandwidth of the N/S monitor is comparable to the bandwidth of the spectrometer electronics. The upper cutoff frequency of the N/S circuitry was chosen to be higher than the high frequency cutoff of typical spectrometer electronics and, hence, it is not limiting. T h e noise from a spdctrometer is usually from dc to some limiting frequency. The high pass filter of the N/S monitor unfortunately filters out some low frequency noise in addition to the dc signal. T o understand the effect of this h p filter, consider a typical spectrometer whose equivalent noise bandpass is controlled by a simple low pass filter of time constant qP.This low paes filter and the high pass filter of the N/S monitor are assumed not to interact. If the spectrometer low pass 1218
Figure 2. Schematic of RMS noise circuit
ANALYTICAL CHEMISTRY, VOL. 47, NO. 7, JUNE 1975
The noise equivalent bandpass for a simple low pass filter, Afl, and for an independent low pass-high pass filter combination, Afl-h, is calculated from Equation 6
*f
=
l*
/ H ( j O ) 12da
(6)
to be
l H ( j a ) I l p 2 d u = 1 / ( 4 ~ ~ ~ ) (7)
(Th~/4T1p)/(T1p
+
Thp)
(8)
Note that, for a given 7lP, LfJAf1-h is 1/2, 10/11, 100/101, and 1 as (7hp/+lP) is respectively 1, 10, 100, and a. This means t h a t Thp should be chosen to be about ten times greater than 71p to ensure t h a t the high-pass filter does not significantly reduce the input noise. Selection of the hp time constant does involve a compromise since one must wait about 4-5 7hp for the output of the hp filter and, hence, also the N/S circuitry to respond to a change a t the input of the hp filter.
SPECIFIC DESIGN CONSIDERATIONS The h p filter, non-inverting amplifier, and rms-to-dc converter were mounted on vector board in a metal box with appropriate switches and connectors as shown in Figure 2. This circuit is particularly useful by itself since it is basically an rms noise monitor if a readout device is attached to the output (point D). Point C can also be moni-
0.0 L from
D
I C 6 0 SEC+I
Figure 3. Schematic of divider circuit Power connections and trimming potentiometer connections are not included but are wired exactly as specified by the manufacturer. OA2 (Analog Devices, A540J) trimmed to zero offset with gain of -10. Divider circuit (Analog Devices, AD532J) with X = 2.00 V trimmed to 0.000, 1.000, and 10.00 V with Z = 0.000 V (Vas potentiometer), with Z = 0.200 V (SF potentiometer), and with Z = 2.000 V ( X , potentiometer), respectively. Power supplied by Health EU 801-1 1 digital power supply. All resistances are in ohms with 1YO tolerance, Capacitances are in FF with &IO% tolerance. Ss is a single pole double throw switch
tored to make peak-to-peak (p-p) noise measurements without the problems of drift, yet with calibrated amplification which is needed under high S/N conditions where the input p-p noise is small and its measurement somewhat limited by readout resolution. The high pass filter is required because the rms-to-dc converter responds to dc voltages. Without the h p filter, the converter output would correspond to the signal plus noise. Circuitry could be used to suppress out the dc signal before it enters the rms circuitry; however, error is likely since it is difficult to exactly suppress out the signal because of noise. Also the suppression would have t o be changed every time the signal was altered. The non-inverting amplifier gain (g) is usually adjusted to bring the rms content of the signal a t point C up to between 0.1 and l V. The resistors for the non-inverting amplifier were selected so that g is within 1%of the specified value. Because the maximum input to the rms-to-dc converter is 10 V, the input rms noise should be no greater than about 3 V to ensure t h a t a peak noise excursion does not carry over the input maximum. After trimming, the accuracy of the rms-to-dc converter transfer function was measured to be better than 1% for dc inputs from 0.01 to 10 V. For the best accuracy, the input (point C) should be adjusted to be greater than 0.1 V rms. The averaging time constant of the converter (basically a low pass filter time constant) is adjusted with an external capacitor and is equal to 10 msec (50 msec/pF)C,, where C,, is the capacitance of the external capacitor. A capacitance of 150 pF was chosen to yield an averaging time constant of about 4.5 sec. In general, it takes about 20 seconds for the rms-to-dc converter to respond to an input change if the h p filter time constant is not limiting. T h e manufacturer of the rms-to-dc converter states t h a t the averaging time constant should be about ten times the period of the smallest frequency to be measured. This is somewhat impractical for noise from spectrometers which is often in the 1- to 0.01-Hz range. Hence the output of the rms-to-dc converter is connected to a recorder and is followed for 30 to 60 seconds to obtain a good average. In general, the instantaneous rms voltage fluctuates about f 5 0 % around the mean rms value. With the input shorted and a gain of 1000, the rms noise contribution from the circuitry is less than 2 mV. Figure 3 shows a schematic of the inverter and divider circuitry which is mounted on vector board in a metal box with appropriate connectors and switches. This circuit is also useful by itself and can be applied in various situations
+
Figure 4. Tracing of typical output f r o m N/S monitor Conditions similar to those specified in Table II
where ratioing is required. T o use the divider circuit with the best accuracy, the input and output voltages must lie in certain ranges. First, the denominator input x must be negative so a voltage inverter with gains of -1 and -10 is necessary for cases in which the signal is positive. The gain -10 is used if the signal is too small. Both gains are accurate to 1%.The divider chosen had differential inputs so t h a t it could be wired to accept positive or negative voltages without an inverter. The x input voltage must be between -0.5 and -10 V. Originally a S/N meter was constructed so t h a t the output of the rms-to-dc converter was connected to the x input. This configuration was not acceptable because of small dynamic range and inadequate accuracy. Problems occurred because the instantaneous noise and, hence, the x input varied f50% so that, in order to prevent limiting, the average voltage a t point F had t o be adjusted t o be between about -1 and -6 V. Also the accuracy of the divider function is much more dependent on the magnitude of the denominator than the magnitude of the numerator and, for large S/N, the gains of 1000 and -10 were not always sufficient to bring the amplified noise (point F) up to 1 V. Because of the above problems, the signal is connected after inversion to the divider denominator input ( x ) which yields a larger dynamic range and better accuracy. T o use the N/S monitor in real situations, the two modules and the spectrometer are connected as shown in Figures 2 and 3. The spectrometer signal (point A ) is adjusted to be between 1 and 3 V since the highest accuracy is achieved if the denominator is near the value to which it was trimmed. The gain is adjusted so that the amplified rms noise (point D) is between 0.1 and 3 V although it can be as low as 0.01 V. The N/S monitor output is followed on a recorder and varies about f5O% around the mean value because of the variation in the instantaneous rms noise or numerator input as shown in Figure 4. Hence, the denominator (point F) should be a t least 50% greater than the numerator (point D) to prevent the divider output from limiting. In general, the output is recorded for 30 to 60 seconds (after an initial delay of about 20 seconds after a change a t the input) to achieve a good average on the recorder. T h e accuracy of the transfer functions of the circuits involved is usually not limiting since the N/S can be estimated t o within only a few percent because of fluctuations in the output. In other words, the output is inherently noisy, although differences of 25% in the N/Scan easily be seen. Usually for optimization of experimental variables, one is only concerned with significant changes in the relative S/N.
MODIFICATIONS TO THE CIRCUIT The N/S monitor has been designed for use with instrumentation which has S/N's which vary from about 1 to 1 X ANALYTICAL CHEMISTRY, VOL. 47, NO. 7, JUNE 1975
1219
Table I. Measured a n d Calculated RMS Noise a n d S / N Relative incident
*
radiant power
Condition'
1
1 2 2a 2b 2C
10 102 103 104 105 106 106 0
a
Calculatedd
noise, ( m V )
rms noise ( m V )
14 3.0 4.0 12 12 1.1 0.32 0.12 0.13 0.09 0.18 9.0
10 10 10
3 4 5 6 7 7a
Measured rms
16 3 .O
... ...
...
1.2 0.32 0.10 0.12 0.08 .I.
...
Measurede SIX
0.083 0.37
... ... ...
1.2 3.3 7.7 9.9 10
...
...
C alculared
SIN
10-3
0.071 0.35
... ... ...
0.92 3.1 8.1 7.7 11
... ...
a Indicates relative incident radiant power as specified in column 2 and high and low pass time constants; No letter, T , = ~ Thp = 1 sec; a, TI^ = 1 sec, T h p = 10 sec; b, qI)= 0.1 sec, Thp = 1 sec; c, 71p = 0.1 sec, T h p = 10 sec. Relative to condition 1 at which PMT voltage = 1000 V and R, = 109 I! with 1P28 PMT (RCA). C Average dc voltage at point C divided by g. Peak-to-peak voltage at point B divided by 5g. e Reciprocal of average dc voltage at point G times -lOg. f Ratio of measured average signal at point A to measured RMS noise.
IO'
1
I
I
IO' RELATIVE
I
,
I
Io 4 I N C I D E N T R A D I A N T POWER IO2
I0
3
I
I os
Flgure 5. Dependence of N / S on incident radiant power
lo4 and for lp time constants between 0.1 and 10 seconds. Clearly, component values can be changed or additional amplification added to accomodate values outside these ranges. If a divider is not available, a log ratio circuit could be used t o provide an output proportional to the logarithm of the N/S or the S/N. This would be advantageous since a wide dynamic range of S/N could be displayed without changing the readout range. Also log ratio circuits often possess much greater input dynamic range and linearity than divider circuits. Of course, if desired, a n antilog amplifier could be added to provide linear readout in S/N.
APPLICATIONS T o evaluate the N/S monitor and to demonstrate its potential, it was connected to the output of both a conventional molecular absorption spectrometer (sample cell removed) and an atomic emission spectrometer which were constructed from commercial modules (IO). In both cases, the anode of the photomultiplier was connected to the summing point of a n operational amplifier wired in the current-to-voltage configuration and the lp time constant was controlled by the values of the parallel capacitor and resistor combination in the feedback loop. T h e output of the OA (S)was connected to a digital voltmeter and to the N/S monitor. T h e photomultiplier voltage, feedback resistance, and other instrumental variables were adjusted so that the signal a t point A was between 1 and 3 V. 1220
ANALYTICAL CHEMISTRY, VOL. 47, NO. 7 , JUNE 1975
In the first experiment, the dependence of the S/N on the radiant power (P) from a tungsten lamp incident on a photomultiplier was studied. Initially the slit width and wavelength were adjusted so that the radiant power incident on the photomultiplier and the photocathodic current were small and the photomultiplier gain and feedback resistance were high. T h e photocurrent signal was about twice the dark current signal. Instrumental variables were then adjusted to vary the photocathodic current (Le., the radiant power incident on the photomultiplier) by the factor 10" where n was changed from 1 to 6. The rms noise (point D), the p-p noise (point C), and the N/S (point H) were measured with a recorder. Where necessary, the magnitude and the sign of voltages were adjusted with conventional operational amplifier circuits before display on the recorder. Table I shows the experimental and calculated values for the S/N and rms noise. Figure 5 is a plot of the experimental S/N vs. the relative radiant power incident on the photomultiplier. Comparison of experimental and calculated rms noise voltage shows agreement within f20%. This agreement is good when one considers the error of the p-p method and indicates that the rms-to-dc converter is working correctly. Comparison of the experimental and calculated S/N also shows good agreement and proper functioning of the divider. T h e data clearly indicate that experimental parameters such as slit width must be adjusted so as to maximize the incident light level t o obtain the best S/N. T h e curve in Figure 5 compares well with theoretical plots presented in another article ( 5 ) .For small relative P, the S/N increases faster than UT.This is because for condition 1, the dark current noise is about half the total noise and a n increase in the incident radiant power increases the signal by 10 and the noise by about 1/6. At higher radiant powers (conditions 2-4), the noise is predominantly photocurrent shot noise and the S/N is directly proportional t o v'F. At higher P (conditions 6,7), source flicker noise becomes dominant and the S/N levels off. The measurements discussed above were made with high- and low-pass time constants of one second. For conditions 2 and 7, the time constants were varied and the rms noise was measured. Comparison of the data for conditions 7 and 7a indicates that the rms noise is doubled when -If as calculated from Equation 8 has increased by 11/6. If the
noise were white, the rms noise would only have increased = 1.35 and so the l/f character of source flicker by noise is obvious. T h e equivalent experiment was run under condition 2. T h e increase in the rms noise observed between conditions 2 and 2a is that expected if white noise such as shot noise is limiting. Comparison of 2 to 2b data shows t h a t the noise increases by a factor of 4 for a relative increase in A f of 11 which reasonably follows the 4 3 dependence for white noise. Comparison of 2b and 2a data shows no measureable difference, which is expected because Af is little affected by the h p filter since T h p L 10 qp. In the second experiment, the N/S of the analyte emission signal from a 0.5 ppm Ca solution was monitored and the N/S recorded. The effect of three variables, HP pressure, flame height, and slit width, were studied. One variable was varied while the other two were held constant. In each case, the background emission signal was bucked out with a suppression voltage and the analyte emission signal adjusted between 1 and 3 V. The results shown in Table I1 were obtained in about 15 minutes and illustrate the utility of the N/S monitor for optimization of experimental variables. The N/S data take little more time to acquire than is normally needed to measure the signal and background voltages and no calculations were required. The simple experimental design used here does not illustrate the interrelationship between variables. The N/S monitor could be used with a sophisticated experimental design such as Latin Square (3, l l ) ,factorial (3, I I ) , or Simplex (12).
a
CONCLUSIONS A N/S monitor which is relatively easy to build and to use has been described. I t should be useful in any of the applications described below. Optimization. For a given analyte concentration, spectrometric instrumental variables such as slit width, noise equivalent bandpass or time constant, lamp current, flame height, gas pressures can be varied to ascertain quickly their optimum values. Note that the precision of an analysis will be improved by S/N optimization only if the noise in the signals significantly contributes to imprecision. Calibration Curves. When preparing a calibration curve, one can simultaneously obtain a plot of S/Nvs. analyte concentration. This plot will point out the types of precision expected a t one concentration and a t what concentrations the precision is acceptable for a given situation. Error Detection. T h e output from the N/S monitor or the rms-to-dc converter can be monitored to detect instances of abnormally high noise such as due to transients. Such instances are more difficult to detect on the signal
Table 11. S / N for Optimization of Ca Flame Emissiona H2 pressurc, lbs/m,2
Flame S l i t w i d t h , i~
height,
CTP
N / S x 102
2.0 100 1.o 1.2 100 1.o 1.o 100 1.o 1.3 50 1.o 200 1.o 1.o 1.o 300 1.o 1.1 100 0.5 2.0 100 2.0 0 2 pressure = 15 lb/in.2, PMT voltage = 660-855 V. Signal a t point A adjusted to 1-3 V, g = 10, T , [ , = T~~ = 1sec. Ri = 108 ( 1 ,
readout device where a small amount of noise is on top of a relatively large signal. Additional circuitry could be used to block signal data acquisition a t times of abnormally high noise. Nature of Noise. The nature of the noise can be determined from the fluctuations in the rms noise or N/S voltages. In general, flicker or 1/f noise exhibits a greater number of larger excursions than white noise. The input high pass filter time constant can be varied to change If and thus to differentiate between white and 1/f noise. If the then white noise is dominoise is proportional to (If)1k2, nant.
LITERATURE CITED (1) J. D. Winefordner, W. J. McCarthy. and P. A. St. John, J. Chem. Educ., 44, 80 (1967). (2) W. J. McCarthy, "The SignaVNoise Ratio in Spectrochemical Analysis: Its Use in Optimization of Experimental Conditions in Spectrochemical Methods", in "Advances in Analytical Chemistry and Instrumentation", C. N. Reilley and F. N. McLafferty, Ed., Wiley-lnterscience, New York, NY, 1971, pp 493-518. (3) M. L. Parsons and J. D. Winefordner, Appl. Spectrosc., 21, 368 (1967). (4) T. Coor, J. Chem. Educ., 45, A533 (1968). (5) J. D. Ingle. Jr., and S. R. Crouch, Anal. Chem., 44, 785 (1972). (6) G. M. Hieftje, Anal. Chem., 44, (6), 81A; (7), 69A (1972). (7) H. V. Malmstadt, C. G. Enke, S. R. Crouch, and G. Horlick, "Optimization of Electronic Measurements", W. A. Benjamin, Inc., Menlo Park, CA, 1974. (8) V. D. Landon, Proc. hst. Radio Eng., 29, 50 (1941). (9) R. Steinitz, J. Grinberg, V. Bar, and A. Seidman, Rev. Sci. Instrum., 43, 656 (1974). (10) "MP-System 1000, Operation and Applications", McKee-Pedersen Instruments, Danville. CA. 1971, (11) H. A. Laitinen, "Chemical Analysis", McGraw-Hill, Book Co., Inc.. New York. NY, 1960, pp 570-574. (12) S.N. Demingand S. L. Morgan, Anal. Chem., 46, 1170(1974),
RECEIVEDfor review December 9, 1974. Accepted February 10, 1975. Acknowledgment is made to the donors of the Petroleum Research Fund, administered by the American Chemical Society for partial support of this research.
Device for Sampling Headspace from Canned Food R. E. Hurst Fisheries and Marine Service, Vancouver Laboratory, Department of the Environment, 6640 N. W. Marine Drive, Vancouver, B.C., Canada
The can sampling apparatus described here was developed as part of a program to study the volatile compounds in canned salmon using gas chromatography. During the initial stages of this work, a ZAHM air tester was used
(Zahm and Nagel Co. Inc.); however, inclusion of liquid in the gas sample presented a continuous problem. In the operation of this commercial device, the can is punctured and sealed in the center of the can lid which forces the lid down ANALYTICAL CHEMISTRY, VOL. 47, NO. 7, JUNE 1975
1221
