Advisory Jonathan W. Amy Richard A. Durst G. Phillip Hicks
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Donald R. Johnson Charles E. Klopfenstein Marvin Margoshes
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Harry L. Pardue Howard J . Sloane Ralph E. Thiers
Photon Counting for Spectrophotometry HOWARD V. MALMSTADT, MICHAEL L. FRANKLIN,1 and GARY HORLICK2 School of Chemical Sciences, University of Illinois, Urbana, IL 61801
Advantages over other light-measurement systems provided by the photon-counting method include direct digital processing of the inherently discrete spectral information, decrease of effective "dark current," improvement of signal-to-noise ratio, sensitivity to very low light levels, accurate long-term signal integration, improved precision of analytical results for a given measurement time, and less sensitivity to voltage and temperature changes QUALITY of tens of thousands of THEresearch and routine spectrophotom-
eters depends directly on the operating characteristics of photomultiplier (PM) tubes and their associated electronic readout and power supply circuits. The various types of instruments in which P M tubes are utilized indicate something about their importance. The PM tube is now found in essentially all of the commonly used molecular uvvisible absorption, fluorescence, phosphorescence, reflectance, laser-Raman, atomic absorption, atomic emission, and atomic fluorescence spectrometers and also in specialized rapid scan, submicrosecond time-resolved, T-jump, chromatogram scanning, multichannel sparksource direct readers, densitometers, and other types of instruments (1). Tn nearly all instruments it has been standard practice to measure the output, signal of the PM tube by using analog techniques. That is, the tube is operated under conditions and with measuring circuits so that an output current or voltage is obtained whose magnitude is directly proportional to the radiant power incident on the photocathode. This has proved to be a generally acceptable mode of operation. 1 Present address, Medical School. University of Colorado, Denver, CO 80210. - Present address, Department of Chemistry, Universitv of Alberta, Edmonton 7, ALT, Canada.
However, it has become increasingly apparent that in some spectrophotometers the output signal of the PM tube can be advantageously measured by using direct digital techniques. In the digital mode the P M tube and associated circuitry provide discrete electron pulses so that the number of counted pulses is directly proportional to the number of photons incident on the photocathode. This approach is commonly called "photon counting." Compared to other light-measurement systems, the apparent advantages (3) provided directly or indirectly by the photon-counting method are direct digital processing of the inherently discrete spectral information, decrease of effective "dark current," improvement of signal-to-noise ratio, sensitivity to very low light levels, accurate longterm signal integration, improved precision of analytical results for a given measurement time, and less sensitivity to voltage and temperature changes. The basic and practical characteristics are presented to illustrate that photon counting can be made widely applicable for many types of spectrophotometry including absorption, fluorescence, emission, and scattering methods. Also, some of the difficulties are considered. Even in those cases where the P M tube is used as an analog detector, the photon-counting concepts can be used for the analysis of its performance, and these can be very useful.
Several applications of photon counting will be illustrated, including considerations for high-precision spectrophotometry. PM TUBE AS DIGITAL OR ANALOG TRANSDUCER
The intensity of a light signal falling on the PM tube is directly dependent on the rate at which photons arrive at the photocathode (Pk). This rate fluctuates as a result of radiation noise (photon noise) inherent in the incoming light, and the fluctuation is, in general, random (3). When photons of a specific wavelength arrive at the photocathode, they eject photoelectrons with an efficiency that depends on the quantum efficiency, Q\, of the photocathode surface (4, 5). The photoelectrons from the cathode are attracted to the first dynode by electrostatic focusing. However, not all of the photoelectrons reach the first dynode, and this collection efficiency, /, is typically about 75%. There is a high probability that each photoelectron that reaches the first dynode will eject several secondary electrons (-5). The transfer efficiency, g, of electron bursts between dynodes is almost 100%, so that the number of anode pulses is nearly equal to the number of photoelectrons reaching the first dynode, assuming negligible dark pulses. The number of electrons in each anode pulse depends greatly on the P M voltage, but the number is typically 10s to 107 electrons per pulse. Even at constant P M voltage, the statistical nature of secondary emission from the dynodes introduces an amplitude fluctuation of the anode pulses. Tf it is assumed that there is negligible pileup of anode pulses, i.e., nearly all anode pulses are resolved, then the number of anode pulses per second, Na, can be written Na = gfQ*Pk (1) The counting of the anode pulses, which are directly related to the num-
ANALYTICAL CHEMISTRY, VOL. 44, NO. 8, JULY 1972 ·
63 A
Instrumentation
CHART RECORDER
DIGITAL-TO-ANALOG CONVERTER
PHOTOMULTIPLIERTUBE AND ENCLOSURE Shutter
Dynodes
hy Cathode
Figure 1. Block diagram of practical photon-counting system (2)
Collector Anode
To Dynode Pins
Resistor Chain
POWER SUPPLY
DIGITAL READOUT AND PRINTER c=
0-2000 V dc
ber of photons incident on the cathode, provides the measurement technique appropriately called ''photon counting." Although the output at the anode of the PM tube is inherently a series of pulses, the output signal can be expressed as an average rate of flow of electrons per second or current, as summarized in Equation 2.
(
Na G anode pulsesX / electrons \ sec / \anode pulse/ e /coulombs \ \ electron /
=
1(A) coulombs sec
For example, if the number of anode pulses/sec, Na, equals 106, and the average electrons/anode pulse, G, equals 106, then = NaGe = 1.6 Χ 1(Γ7 A
Iw
(3)
However, this is an average current, and it is apparent from Equation 2 that the output current fluctuates as N„ and G fluctuate. That is, the ran dom-time behavior of the anode pulses as a result of the incident radiation, and the amplitude distribution caused by secondary electron emission cause the so-called "shot noise" on the PM analog signal. By use of suitable elec tronic filters, the fluctuations are aver aged or integrated so that the average current can be observed. Because an average current can be related to the number of pulses in unit time, it is 64 A
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ACCURATE PRESET TIMER
frequently convenient to determine the noise component of an analog PM signal by utilizing count statistics. PHOTON-COUNTING SYSTEMS
The required equipment used to implement photon counting in spectrophotometry is illustrated in Figure 1. The photomultiplier tube is enclosed in a compartment that must be perfectly light tight, and it is powered by a regulated high-voltage (HV) power supply. The output signal current pulses are coupled through a résistivecapacitive load or pulse transformer into a pulse amplifier. All pulses within a preset discriminator voltage range are counted by the digital counter during an accurate preset time interval. The total count per integration period is read from the digital counter or printer. An analog readout is often made available to provide graphic monitoring. A digital-to-analog converter converts the photon counts to a dc voltage which is sent to a chart recorder. Each of the blocks of Figure 1 is briefly considered so as to summarize the important characteristics. Photomultiplier Tube and Power Supply. Incoming photons eject photoelectrons with an efficiency that depends on the quantum efficiency of the photocathode surface. This efficiency is strongly dependent on wavelength; thus, a response characteristic is chosen that results in high efficiency for the wavelength of interest. When the PM
ANALYTICAL CHEMISTRY, VOL. 44, NO. 8, JULY 1972
is part of a spectrophotometer, the spectral characteristics of the source and monochromator must also be taken into account. The overall response characteristics are determined by the convolution of the spectral response of the detector with the spectral output of the source and optical system. The gain, frequency response, and dark-count characteristics of the PM tube are very important and are discussed in the next major section. The required operating voltages between PM tube electrodes are provided by connecting a chain of resistors across a stable HV povrer supply. The voltage drops across the resistors provide the voltage increments between successive electrodes (6). The applied voltages influence the pulse-height distribution, but as the applied voltage is increased, a value is reached where changes in PM voltage cause relatively little change in pulse height. Pulse Amplifier. A low-noise amplifier is required for photon counting because any noise induced by the amplifier increases the background count rate when the discriminator is set at a low level. The input of the amplifier should offer a minimum of shunt capacitance to reduce pulse degradation, and great care must be used in connecting from the anode of the PM to the pulse-amplifier input (2). An ac-coupled amplifier is usually employed because it eliminates the dc drift from the PM. Also, reducing the
Instrumentation
Ιθλν-frequoney cutoff of the amplifier reduces a considerable amount of noise. Bandwidths from 10 KHz to 100 MHz are used in photon counting to reject the low-frequency noise but still pro vide adequate pulse fidelity. The gain from the pulse amplifier must be stable so that the pulse-height shift does not change the number of photon counts getting through the dis criminator. Sharing the gain require ment between the PM and the amplifier requires that the amplifier voltage gain be about 100-1000 for use with most PM tubes. At high-count rates the amplifier duty cycle becomes large, and a base line shift owing to ac coupling results. This changes the number of pulses getting through the pulse-height dis criminator. It is often necessary to use a dc level restorer to provide a zero reference line. A simple diode clamp circuit can be employed with good results in some cases at count rates not exceeding 100 KHz. Other methods can be used to reduce, the base-line shift with · increasing count rate, such as the Robinson clamp, bi polar pulses, base-line shift compensa tion at the discriminator, or a dc am plifier system. In many instances using a fast ac amplifier and keeping the duty cycle low result in acceptable base-line shift without dc restoration. Pulse-Height Discriminator. A pulse-height discriminator useful for photon counting must be stable and sensitive to small voltages so that small signal pulses can be effectively counted ; the frequency response must be high so that the upper count rate is not limited at this stage. Tunnel diode discrim inators are available which operate at 50-mV sensitivity and at greater than 100 MHz. Pulse-Pileup (Coincidence) Effects. Two effects are possible owing to pulse pileup at a fixed discriminator level. Two pulses which should each be counted can pile up so that only one count, is recorded. A net loss of one count results. Two smaller pulses can pile up and sum to produce a pulse large enough to be counted when neither pulse should have been counted; thus, a net excess of one count is re corded. The discriminator level de termines the relative importance of these two effects on the recorded count. At low discriminator levels when a large fraction of the theoretical count is recorded, the major effect is the loss of pulses owing to pileup. Discriminator-Level Setting. Be cause of the counting statistics, the standard deviation of a measurement is determined by the square root of the number of counts. This means the more counts recorded for a given mea 66 A
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surement time, the better the precision will be. The pulse-height discriminator level should, therefore, be set to accept the largest fraction of the theoretical signal counts possible without picking up a large amount of background pulses. By setting the discriminator level to accept the largest number of signal counts in a given observation time, both utilization of the frequency response of the system and less sus ceptibility to drift are realized. If the discriminator level is set so that only a small fraction of the theoretical count rate is admitted, a small drift, in dis crimination level causes a large change in count rate because the signal count rate changes rapidly with discriminator voltage in this region. Digital Counter. Fortunately, many new types of counters operate at rates of greater than 100 MHz so that this part of the system should not limit overall frequency response. Since the standard deviation is equal to the re ciprocal of the square root of the num ber of events counted, the number of readout digits having significance can bo estimated. Therefore, it is not nec essary to provide readout of the total recorded events, but it is rather the scaled-down counts that are significant. Accurate Preset Timer. Crystal clocks provide precision and accuracy better than 1 part in 106 for a wide range of time bases from 1 ^sec to 10 sec or more. Integration times in pho ton-counting applications usually range from 0.1 to 10 sec or the duration of a specific event. Digital-to-Analog Converter. The same pulses from the output of the pulse-height discriminator which are counted can be fed simultaneously to a digital-to-analog converter. This cir cuit shapes each input pulse so that each output pulse becomes equally weighted. The equally weighted pulses are then smoothed to provide a dc voltage output. A conventional diode pump circuit can be used after simple RC differentiation (6) to produce the analog output for locating trends in the counting data, such as peak-signal location during scanning. Chart Recorder. After the pulses are converted to a dc voltage, the ac curacy of the analog readout is deter mined by the reading accuracy and by the observation time. This integration time is determined by the time constant of the filter in the digital-to-analog con verter. Chart recorders are usually accurate to 0.5% of full scale \vith a reading error of about 0.2%. The sig nal pulse-height fluctuation has been removed, but the random-time distribu tion is still present in the signal. In many analog photometric measure ments the major portion of the un
ANALYTICAL CHEMISTRY, VOL. 44, NO. 8, JULY 1972
wanted fluctuation results from the reading error and not from the funda mental "shot noise limit" of the signal. Note that with digital readout of all the pulses, the reading error is elim inated, and wide dynamic range is available. Commercial Systems. Several com panies offer instrumentation packages or modules which can be used for pho ton counting at rates in excess of 1 MHz. Three of these systems are men tioned along with their specifications and special features. Solid State Radiations, Inc. (SSRI) offers a pulse-amplifier-discriminator combination with gain of 2400 and bandwidth from 10 KHz to 100 MHz. The pulse-pair resolution specification is 10 nsec. A shielded PM housing is also available along with dc power sup plies for the PM and amplifier. There is a separate module for each unit listed: PM housing and dynode chain PM and amplifier power supplies Pulse amplifier Digital computing counter Approximate total cost, S4700 The digital counter has se\-eral modes of operation useful in photon counting. There are two separate registers so both the background and signal counts can be stored separately. Both back ground and signal counts can be inte grated for equal preset periods in the synchronous mode. The background register can be subtracted from the signal register in still another mode of operation (7). Elscint Instruments manufactures a system with PM and preamplifier power supplies, counter, and amplifier in one instrument package. This sys tem has upper and lower level discrim inators; thus, an energy window can be set to eliminate large as well as small pulses. In the synchronous mode the background pulses are subtracted from the signal plus background by an up-down counter. However, it is often desirable to know both the background and the signal rate for error analysis, not simply the difference. A novel feature is the utilization of the upper discriminator level to correct for first-order pileup effects. Pulses exceeding the lower discriminator level are counted normally, whereas pulses exceeding the upper discriminator level are counted twice. This corrects for the case where two pulses add together to give a single pulse of twice the am plitude. The total amplification of the preamp and the amplifier is 300 with a pulse-pair resolution of 12 nsec. The modules necessary for photon counting are the following (8) :
Instrumentation
Low-level counter spectrometer PM housing Fast preamplifier Approximate total cost, $3300 Ortec offers a NIM bin system which can be used for photon counting. The amplifier has a gain of 200 with a 4-nsec rise time. The signal is fed to a 100-MHz discriminator and on to a dual counter timer. Both background and signal plus background counts can be stored. The NIM bin system of fers some flexibility since it uses stan dardized plug-in modules. Additional modules can be plugged in to provide a teletype data logging system. The basic modules necessary for photon counting are as follows (9) : NIM bin and power supply HV power supply PM base Amplifier Dual counter timer with crystal time base Approximate total cost, $3200 BASIC CONSIDERATIONS IN UTILIZING PHOTON COUNTING
The possibility of measuring low-in tensity light with improved signal-tonoise ratio was one of the original rea sons for interest in photon counting and remains a major basic considera tion for any discussion of the topic (10-16). Other basic considerations which influence the applicability of photon counting and which are con sidered in this section are dynamicrange or frequency-response considera tions, dark count, and pulse-height distribution. Signal-to-Noise Ratio. The signalto-noise ratio of a photon-counting measurement may be considered from the point of view of counting statistics. The fundamental noise in a photoncounting system is the fluctuation in the signal count as determined by the sta tistics of the photon arrival at the photocathode. In general, the arrival of photons at the photocathode is random; thus, the probability of fluc tuations about the rate of arrival is de termined by taking the square root of the number of counts (17). For the specific ease of a Gaussian distribution, the reciprocal of the square root of the number of counts is equal to the stand ard deviation. On this basis the "sig nal-to noise ratio" for a single measure ment can be estimated by dividing the count by the square root of the count. Many photon-counting measurements are made in situations such that un wanted background pulses are present. In these cases the background count must be subtracted from the measured 68 A
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background plus signal count. This makes the signal-to-noise ratio ex pression more complicated (10-13). The fluctuation in the signal count (noise) is calculated by using the stan dard equation for the counting sta tistics of a difference. This equation can take the form: Fs = (Rs + 2 RBy*TU*
(4)
where Fs is the fluctuation in the signal count, Rs is the signal count rate, RJI is the background count rate, and Τ is the counting time. In this case it is assumed that the counting time is the same for the measurement of the back ground count and the signal plus back ground count. The signal is RST; thus, the signal-to-noise ratio can be ex pressed as: S_ _ R^T1'1 Ν ~ (1 + 2 RB/R,yi*
S _
103
102 Dark Pulses
101
RST^
(®
For a signal count rate of 2 cps and a background count rate of 100 cps, a signal-to-noise ratio of 4.5 can be achieved in 1000 sec. The stability of most photon-counting systems allows such long counting times. The relative rates of the signal and background counts (and, hence, the signal-to-noise ratio) can, to some ex tent, be controlled by adjusting the pulse-height discriminator. Thus, it is important to consider briefly the pulse-height distributions of both back ground (dark) and signal pulses. Pulse-Height Distribution of Pulses. Current pulses which have been caused by incident photons and. hence, have undergone the full amplification of the PM tube have a pulse-height distribution closely approximated bv a Poisson distribution (4. 18-21). The integral pulse-height spectra for sig nal and dark pulses for a 1P28 photomultiplier tube are shown in Figure 2. In this case all counts above a certain discriminator level were counted. Note that the pulse-height spectrum for the dark-current pulses is not the same as that for the signal pulses. It contains a larger number of smaller pulses than would be predicted on the basis of a Poisson distribution. This can be ex-
ANALYTICAL CHEMISTRY, VOL. 44, NO. 8, JULY 1972
Signal Pulses 10"
(5)
Equation 5 has two limiting forms. If the background rate is small with re spect to the signal count rate, the equa tion reduces to Β, 1 / 2 !" 1 / 2 , the square root of total signal count. Thus, for a total count of 106 the signal-to-noise ratio is 1000. If the background count rate is large with respect to the signal count rate, Equation 5 becomes the fol lowing:
Ν ~ (2 RB)v*
10=
0.1 0.2 0.3 0.4 0.5 0.6 DISCRIMINATOR VOLTAGE (V)
Figure 2. Integral pulse-height spectra of signal and dark pulses (2)
plained if the pulse components of the dark current are examined. Figure 2 should be considered specific to this tube. The specific shape can differ for different photomultiplier tubes and even for the same tube under different experimental conditions (different dynode voltages, magnetic defocusing). Dark Current. There are a number of sources of dark currents in a photomultiplier. Some of the more common sources are discussed by Lallemand (22). Among these are thermionic emission, cold-field emission, radioac tivity, arid ohmic leakage. The first three are pulsed in nature. The pulses from thermionic emission and cold-field emission often originate down the dynode chain and, hence, do not undergo full amplification in the tube. These pulses give rise to the larger number of smaller pulses in the pulseheight spectrum of the dark current. In addition, a dramatic increase in the count, rate at low discriminator levels is evident in the dark-current pulseheight spectrum (Figure 2). These pulses arise from stray electrical noise and amplifier-induced noise. Pulses originating from cosmic rays and radio active potassium (β particle emission) in the glass envelope of the tube should result in a slightly elevated level of higher pulses in the dark current than would be expected on the basis of a Poisson distribution, but these are gen erally negligible for practical spectro photometry. Therefore, an upper dis-
Instrumentation
criminator level is not required. Pulses induced from the 60-Hz power line also contribute to the pulsed dark-current component. The different, characteristics in the pulse-height spectra of signal and dark current mean that pulse-height dis crimination can be used to reject rela tively low pulses and thus selectively discriminate against most dark-current pulses with respect to signal pulses (13). For a 1P28 PM tube used by the authors (at 900 V), a dc dark cur rent of 4 X 10~10 A was reduced to an equivalent dark current of 3.9 X 10~12 A (41 counts/sec), as calculated by us ing Equation 2 with a G value of 6 X 103 electrons/count. Another source of dark current is ohmic leakage. The photon-counting method is insensitive to the ohmic com ponent of the dark current because of its dc nature. The rapid increase in dark count with applied voltage is shown in Figure 3. Cooling a photomultiplier tube will reduce the dark current. Typically, the dark current will approach a mini mum value by about - 3 0 ° C {23). However, note that the spectral sensi tivity of a photomultiplier tube is also markedly affected by temperature, of ten in a complex manner. Several cases are summarized by Budde and Kelly (2/f). In addition, cooling of the photomultiplier tube does not necessar ily improve the signal-to-noise ratio for photon-counting experiments (25), and in one case for signal count rates in excess of 8000 photons/sec, the sig nal-to-noise ratio was decreased by cooling (25). Frequency-Response Considera tions. The major problem in photon counting at the light levels often desir able for practical spectrophotometry is that the measurement system must be fast enough to preserve the high-fre quency response of the photomultiplier detector. At present there is a cross
over point where it is necessary to shift from photon counting to conventional dc current measurement which depends on the frequency response of the mea surement system and incident light lev els. In Figure 4 the outputs from two different photon-counting systems are shown. The frequency responses for the two systems are measured by trig gering the oscilloscope on individual dark pulses. For the first measurement system the RC decay time is 4 ^sec, as shown by the envelope of current pulses in Figure 4A. The output signal shown in Figure 4B, which corresponds to a dc current of 5 X 10~8 A, indicates that individual pulses are not, resolved. The second measurement system has a fre quency response twenty times faster, as shown by Figure 4C. The output shown in Figure 4D, which also corre sponds to a photocurrent of 5 X 10~8 A, indicates that nearly every signal pulse is resolved. These photographs illustrate the importance of frequency response of the entire system when us ing photon counting at light levels typically important in spectrometric methods.
DARK PULSES 1 χ 1(Η°Α
Β
SIGNAL PULSES
5χ1(ΗΑ
C
DARK PULSES
1 X 1(H°A
0
Relationship Between Photocurrent and Count Rate. A plot of log pulse count rate vs. log photomultiplier cur rent is shown in Figure 5 for a photoncounting system that we have used ex perimentally. The theoretical countrate line shown on the figure was cal culated from the typical gain value of the 1P28 PM at an applied voltage of 900 V (RCA Phototubes and Photo cells Technical Manual, pp 7-60). This curve was verified by extrapolat ing the signal pulses curve of Figure 2 to zero discriminator level at the value of dc photocurrent used to take the curve. The theoretical count-rate line represented the total number of signal pulses available for counting at a spe cific photomultiplier dc current level. This dotted line will be translated horizontally depending on the amplifi-
6 5
Figure 3. Photo multiplier dc dark current vs. applied anode-to-cathode supply voltage
A
4 3 2 1
200 400 600 800 ANODE-TO-CATHODE SUPPLY VOLTAGE (V)
1000
0
D
SIGNAL PULSES 5 χ 1 ( Η Α HORIZONTAL TIME BASE 2 ^EC/DIVISION
Figure 4. Comparison of pulse-resolu tion capabilities of two measurement systems which have different frequency responses. A, B: RC time constant is 4 ittsec; C, D: RC time constant is 0.2 ,usec
cation of the photomultiplier as the average charge content of the pulses changes with the voltage applied to the photomultiplier tube. However, the total number of signal pulses at a given light level remains constant. In practice a pulse-height discrimi nator must be used to reject unwanted noise pulses in the measurement, system (see Figure 2). This will also elimi nate a certain fraction of the signal pulses. Two experimental curves taken at 70 and 27% of the theoretical count rate are also shown in Figure 5. They both have slopes of 45°, indicat ing that the photocurrent and the count rate are directly proportional. At higher count, rates they both tail off at
ANALYTICAL CHEMISTRY, VOL. 44, NO. 8, JULY 1972
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Instrumentation
absorption measurement not readily apparent from analog measurements. The error in an absorbance value as a result of counting statistics can be cal culated in two steps. First the error in one-over-transmittance (IlT) is cal culated by using the standard error equation for a ratio. The final equa tion is as follows :
10'· Amplifier 3 (JB Point
10f
Figure 5. Count rate vs. photocurrent for theoretical and two experimental curves at different percent discriminator levels. Anode-to-cathode supply voltage is 900 V
10=
Erh
10"
10
102
101
ion
lo-io
io-9
io-8
IQ-7 IO-«
PHOTOMULTIPLIER CURRENT (A)
a point corresponding to the upper 3 dB response of the pulse amplifier. Note that the upper 3 dB response of a pulse amplifier may be misleading with respect to the maximum average count ing frequency that can be measured without rolloff. The time distribution between photons from the light source is random; thus, at a certain instan taneous time the frequency of the pulse sequence may be greater or less than the average rate. Experimentally, the measurement system frequency response should be at least 25 times greater than the maxi mum average pulse rate that is mea sured to keep the pileup error less than 1% at this maximum rate. The crossover point between using photon counting or conventional dc current measurement for the experi mental system used to obtain Figure 5 is about 10~8 A, which corre sponds to a count rate of 100 KHz for the 1P28 PM operated at 900 V. Since the crossover point depends on the fre quency response of the measurement system, it should be feasible to extend the system to equivalent dc currents approaching 10~fi A. This would cor respond to a counting rate of about 10 MHz. Precision on the basis of count ing statistics of about 0.03% would thus be obtained for a 1-sec observa tion time. APPLICATIONS OF PHOTON COUNTING
Precision Absorption Spectropho tometry. The absorbance of a sample can be measured by using a photoncounting measurement system. The transmittance is calculated by dividing the total count obtained for the sample 72 A
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channel (Ns) by the total count ob tained for the reference channel (Nr), provided the counting times for both measurements are identical. The ab sorbance is log (Nr/Ns). The analyti cal curve for acidic dichromate shown in Figure 6 was obtained by use of a photon-counting measurement system in conjunction with an absorption spec trophotometer. Consideration of the measurement er ror from the viewpoint of photon counting results in an important clari fication of the possible precision of an
%EA = log (1/Γ + Erl.) - lo 8 (l/D logd/D
XWu/o (8) Calculated theoretical errors in ab sorbance for assumed values of refer ence and sample counts are shown in Table I (26). The theoretical percent error has a broad minimum, changing only slightly between 0.3 and 2.3 ab sorbance units. This broad minimum is greatly different from the error curve determined by the classical reading er ror of an analog scale (27). This is il lustrated in Figure 7. The photoncounting plot values were taken from
Table I. Calculated Error in Absorbance for Assumed Values of Reference and Sample Counts Reference counts = 2.000 χ 10 6 Sample counts
1.990 χ 1.950 X 1.800 X 1.500 X 1.000 X 5.000 χ 2.500 X 2.000 χ 1.000 X 2.000 X 1.000 χ 5.000 χ 2.000 χ
ANALYTICAL CHEMISTRY, VOL. 44, NO. 8, JULY 1972
10e 10 6 10e 10° 10« 10s 105 10 5 10 5 104 10* 10 3 10 3
(7)
where Erls is the error in Nr/Ns (ί/Τ). If background counts are neg ligible, the errors in the reference count (Er) and in the sample count (Es) are equal to the square roots of the respec tive counts ; if not, Equation 4 is used to calculate these errors. The final relative percent error in absorbance, % EA, is calculated from the error in \/T as:
3
10-12
~ Ws [-NT +-N7]
Absorbance, A
0.0022 0.0110 0.0457 0.1249 0.3010 0.602 0.903 1.000 1.301 2.000 2.301 2.602 3.000
Theoretical % error
19.962 3.973 0.975 0.375 0.176 0.114 0.102 0.102 0.108 0.154 0.138 0.235 0.322
Instrumentation 1.8 1.6 1.4 1.2 1.0 0.8 0.6 0.4 0.2 20
60 100 140 PPM DICHROMATE
180
Figure 6. Analytical curve for acidic dichromate taken at 360 nm (2) by using photon counting where absorbance = log[(photon counts) r e t /(photon C O U n t S ) , ample]
a ι m Analog Readout b —>··»—• Photon Counting
10.0!
0.1
Ο
0.5
1.0 1.5 2.0 ABSORBANCE
2.5
Several cases have been considered by Hughes (28). At any specific absorbance value, the error may be decreased by simply in creasing the total number of counts. If the numbers of sample and reference counts used to calculate the absorbance value of 0.0457 in Table I are both in creased by a factor of 10, the percent error drops from 0.975 to 0.308. This emphasizes the importance of a highfrequency-response measuring system to minimize the counting time neces sary to achieve a desired precision. To achieve the precisions indicated in Ta-, ble I, counting times of 10 sec each for the sample and reference would be needed if the photon-counting system responds linearly to 200 KHz, and 100 sec would be needed if the maximum linear response was 20 KHz. So far it has been assumed that back ground counts are negligible. If sig nificant background counts are present and are not subtracted out, they cause a negative deviation from Beer's law directly analogous to that caused by stray light, as shown in Figure 8. With a reference count of 2.000 X 10G and an ignored background of 2.000 X 10s, there is a 2% negative deviation from Beer's law at an absorbance value of 2.0, and the analytical curve will be asymptotic to an absorbance value of 3.0. Of course, the background can be subtracted out to remove this devia tion. The error terms in Equation 7 must be calculated by using Equation 4. For a reference count of 2.000 X 10° and a background count of .1.000 X
0.01 0.1 1 10 100 1000 CONCENTRATION OF Cd (PPM)
Figure 9. Atomic fluorescence analyti cal curve for cadmium obtained with photon counting (32)
103, the % error at an absorbance of 2.0 increases from 0.154 to 0.161%. Application of Small Computer. The comparator output of a photoncounting system in an absorption spec trophotometer can be sent directly to a low-cost (less than $5000) laboratory minicomputer. The computer can be programmed to subtract dark counts from both reference + dark and sam ple 4- dark counts and then provide an
3.0
Figure 7. Precision of photon count ing and analog systems as function of absorbance (26)
3.50 f = 0.000 3.00
Table I, and the analog readout values are based on a photometric reading er ror of 0.1% in transmittance along a linear scale. The photon-counting measurement, with a reference count of 2.000 Χ 106, has an error of less than 0.2% from 0.3 to 2.4 absorbance units, whereas the error with the analog read out varies from 0.3 to 4.6%. The min imum error in the analog plot is 0.27% and occurs at an absorbance of 0.434, whereas the minimum error in the pho ton counting plot is 0.11% and occurs at an absorbance of 0.968. This posi tion of the minimum in the photoncounting plot is specific to the case where equal times are spent measuring the reference and sample counts. The position of the optimum absorbance may vary considerably, depending on the specific measurement conditions. 74A
·
f =-. 0.001 UJ
2.50
ο ζ
S 2.00 ο m
f = 0.01
< 1.50 1.00
f = 0.1
0.50
0.00 / ^ 0.00
8.00
16.00 24.00 CONCENTRATION
32.00
40.00
Figure 8. Effect of uncorrected background counts on analytical curve. Ratio of background counts to reference counts is f. Concentration axis is arbitrary
ANALYTICAL CHEMISTRY, VOL. 44, NO. 8, JULY 1972
Instrumentation
Continuous Automatic Measurement of
Nitric Oxide Emissions ... even in Hydrocarbons!
This n e w e s t LECO i n s t r u m e n t monitors and r e c o r d s t h e emission of nitric oxide from gasoline en gines, diesel engines, turbines, industrial a n d chemical p r o c e s s e s and combustion of fossil fuels, solid w a s t e s and organics such as tobac co. It is manufactured u n d e r license from Ford Motor Company, using the chemiluminescent reaction of nitric oxide with ozone to provide m e a s u r e m e n t s in a range from 0.1 p p m full scale to 10,000 p p m full scale, with accuracy 2 % of full scale. The d r y system utilized b y this LECO monitor eliminates interfer ence from h y d r o c a r b o n s . Infinite zero stability makes constant ad j u s t m e n t s unnecessary. Solid state circuitry provides increased d e pendability and simplified service.
LECO CORPORATION 3000 LAKEVIEW AVE. ST.JOSEPH. MICHIGAN 49085 · U.S.A.
CIRCLE
76 A ·
129
ON
READER SERVICE
o u t p u t of % t r a n s m i t t a n c e (sample counts/reference counts) X 100, or absorbanee [log(reference c o u n t s / s a m ple c o u n t s ) ] , or log absorptivity, etc. T h e setup in our laboratory uses a programmed cell c o m p a r t m e n t (Model EU-721-11. H e a t h Co., Benton H a r b o r , M I ) to alternately place reference and sample cells into a single light p a t h . T h e desired time intervals for obtaining sample and reference counts a r e se lected on the teletypewriter. F o r recording spectra, t h e computer advances t h e wavelength b y a selected increment as requested b y teletype. At each wavelength t h e reference, sample, and background information are sent to t h e computer. T o obtain high-pre cision photometric d a t a at all wave lengths, t h e total reference count is maintained approximately a t a preset level. This is accomplished b y feed back to t h e monochromator, source, or the count integration timer so as t o compensate for changes of overall rela tive sensitivity of t h e spectrophotom eter. Raman and Fluorescence Spectro photometry. I n b o t h R a m a n and flu orescence spectrophotometry t h e inten sities of R a m a n or fluorescence bands radiated from samples a r e generally very low. Therefore, the photon-count ing technique has frequently been de scribed a n d applied for such applica tions (29—31). A n analytical curve ob tained for the atomic fluorescence of cadmium (32) over a wide dynamic range of 10 5 is shown in Figure 9. F o r this example t h e photon counts were integrated over a 10-sec period for each sample. I n R a m a n , atomic emission, absorption, a n d fluorescence techniques, the. sought-for signal is often superim posed on a large background interfer ence, so the use of synchronous photon counting is desirable for these applica tions (7, 12). This system is similar in principle to t h e computer system de scribed in t h e previous section. I t pro vides for two simultaneous channels of count information to be accumulated and then manipulated. Luminescence Decay-Time Mea surements. M a n y molecules, such as aroma tics, which are excited return to t h e ground state b y photon emission. T h e exponential luminescence decay curves of the emitted radiation provide useful chemical information. T h e de cay times might be in t h e nanosecond, microsecond, or millisecond time range. Although there are several techniques for making the longer decay-time mea surements, most techniques do n o t work well for t h e very short decay times. However, a rather new technique r e ferred to as t h e "single-photon tech n i q u e " can be used even for decay times
CARD
ANALYTICAL CHEMISTRY, VOL. 44, NO. 8, JULY 1972
of a few nanoseconds. This unique pro cedure makes use of t h e probability of measuring a single p h o t o n pulse p e r excitation pulse. Details of the method have been presented (9), showing a specific experimental system t h a t can be used for measuring decay times from 2 usee to 250 ,u.see.
REFERENCES (1) H. V. Malmstadt, M . L. Franklin, and G. Horlick, Progress in Nuclear Energy, Analytical Chemistry, Series IX, Pergamon, Elmsford, NY, 1972. (2) M. L. Franklin, G. Horlick, and H . V. Malmstadt, Anal. Chem., 41, 2 (1969). (3) R. C. Jones, in "Advances in Elec tronics," Vol V, ρ 18, L. Morton, Ed., Academic Press, New York, NY, 1953. (4) G. A. Morton, RCA Rev., 10, 525 (1949). (5) RCA Photomultiplier Manual, RCA Corp., Princeton, Ν J, 1970. (6) H. V. Malmstadt and C. G. Enke, "Digital Electronics for Scientists," Benjamin, New York, NY, 1969. (7) SSR Instruments, Bulletin on Model 1110 Photon Counter, Santa Monica, CA, 1972. (8) Elscint Scientific Instrumentation Catalog GMD-10, pp 71-73, Princeton, NJ. 1972. (9) O R T E C , Application Note AN35, Oak Ridge. T N , 1971. (10) R. R. Alfano and N . Ockman, J. Opt. Soc. Amer., 58, 90 (1968). (11) J. J. Barrett and N . J. Adams, I I I , ibid., 311 (1968). (12) F . T. Areccki, E . Gatti, and A. Sona, Rev. Sci. Instrum., 37, 942 (1966). (13) G. A. Morton, Appl. Opt.. 7, 1 (1968). (14) R. Jones, C. J. Oliver, and E . R. Pike, ibid., 10, 1673 (1971). (15) M. Jonas and Y. Alan, ibid., ρ 2437. (16) F . Roblen, ibid., ρ 777. (17) S. Goldman, "Frequency Analysis Modulation and Noise," ρ 306, Mc Graw-Hill, New York, NY, 1948. (18) M . Gadsden, Appl. Opt., 4, 1446 (1965). (19) F . J. Lombard and F . Martin, Rev. Sci. lustrum., 32, 200 (1961). (20) Z. Bav and G. Papp, IEEE Trans. Nucl.Sci.. 11, 160 (1964). (21) R. F . Tusting. Q. A. Kerns, and H . K. Knudsen, ibid., 9, 118 (1962). (22) A. Lallemand in "Astronomical Techniques," Vol I I , ρ 126, W. A. Hiltner, Ed., Univ. Chicago Press. Chi cago, IL, 1962. (23) R. Foord, R. Jones, C. J. Oliver, and E . R. Pike, Appl. Opt., 8, 1975 (1969). (24) W. Budde and P . Kellv, ibid., 10, 2612 (1971). (25) Y. D. Harker. J. D . Masso, and D . F . Edwards, ibid.. 8, 2563 (1969). (26) E . D . Jackson, P h D thesis, Univer sity of Illinois. Urbana, IL, 1970. (27) W. A. Blaedel and V. W. Meloche, "Elementary Quantitative Analysis," Harper and'Row, New York, NY, 1963. (28) H. K. Hughes. Appl. Opt., 2, 937 (1963). (29) M. R. Zatzick. Res.I Develop., 21, 16 (1970). (30) S. A. Miller, Rev. Sci. Instrum., 39, 1923 (1968). (31) Ε . Η . Eberhardt, Technical Applica tion Notes of I T T . Fort Wavne, I N , 1968. (32) K. P. Li, P h D thesis, University of Illinois, Urbana, IL, 1970.
