HADAMARD TRANSFORM AND PROGRAMMED SCAN
MULTIELEMENT ANALYSIS MULTIPLEX VERSUS
SINGLE CHANNEL ATOMIC FLUORESCENCE SPECTROMETRY
FRANCIS WILLIAM PLANKEY, JR.
A DISSERTATION PRESENTED TO THE GRADUATE COUNCIL OF
THE UNIVERSITY OF FLORIDA
IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY
UNIVERSITY OF FLORIDA
This work is dedicated to my wife, Bonnie, who encouraged and
supported me in many, many ways and who spent lonely, patient hours in
order to make this work and my graduate program a success.
The author wishes to acknowledge the outstanding assistance of
his teachers and associates, especially the help and guidance of Professor
Sidney Siggia during the early years and Professor James D. Winefordner
during Graduate School. The enthusiasm and encouragement of these
latter two persons was the driving force of his academic work. Further-
more, he would like to thank Dr. Dave Johnson, Lucas Hart and Gail
Pokrant for .their help in many instances.
TABLE OF CONTENTS
ACKNOWLEDGMENTS . . .. .
ABSTRACT ........... .. vi
I INTRODUCTION TO FLAME SPECTROMETRY AND MULTIELEMENT
ANALYSIS . . 1
Atomic Methods of Analysis .. 1
Single Element Analysis . ... 2
Multielement Analysis . .. 3
II MULTIPLEX SPECTROMETRY SYSTEMS .. . 5
Types of Multiplex Spectrometry. . .. 5
Previous Spectroscopic Studies with Multiplex Methods. 6
Signal-to-Noise Relationships for UV-Visible HTS 8
III ATOMIC FLUORESCENCE COMPONENTS COMMON TO THE SYSTEMS
STUDIED .. . . 15
The Atomic Fluorescence Excitation Source 15
The Atomization Cell . . 16
The Optical System . . 20
IV THE HADAMARD TRANSFORM SPECTROMETER (HTS) SYSTEM 24
Hadamard Transform Spectrometry ..... 24
Implementation of the HTS System 25
The Fast Hadamard Transform (FTS) .. 30
Analytical Procedure with the HTS System ... 34
Results and Discussion .. . 36
V SINGLE CHANNEL SCANNING SPECTROMETER (SCSS) SYSTEM 49
Preliminary Discussion . 49
Description of SCSS Experimental Setup .. 50
Operation of the SCSS System . .... 56
Analytical Procedure with the SCSS System 57
Results and Discussion .. 59
VI COMPARISON OF MULTIPLEX AND SCANNING TECHNIQUES 77
VII PROGRAMMED SLEW SPECTROMETER (PSS) SYSTEM 82
Preliminary Discussion ............. 82
Description of Software . .. 83
Analytical Procedure with the PSS System 84
Results and Discussion . 86
VIII COMPARISON OF THE THREE SYSTEMS . 90
I AVERAGE SIGNAL-TO-NOISE RATIOS FOR THE UV-VISIBLE
SPECTRAL REGION .. . 93
II THE COMPUTER SYSTEM .......... 95
LITERATURE CITED .. . 100
BIOGRAPHICAL SKETCH . .. .. 103
Abstract of Dissertation Presented to the Graduate Council
of the University of Florida in Partial Fulfillment of the Requirements
for the Degree of Doctor of Philosophy
HADAMARD TRANSFORM AND PROGRAMMED SCAN MULTIELEMENT
ANALYSIS MULTIPLEX VERSUS SINGLE CHANNEL
ATOMIC FLUORESCENCE SPECTROMETRY
Francis William Plankey, Jr.
Chairman: James D. Winefordner
Major Department: Chemistry
The practice of sequential analysis for many trace elements by
flame spectrometry is explained and techniques for rapid sequential and
simultaneous multielement analysis are reviewed. Consideration of the
three flame spectrometric techniques, atomic emission, atomic absorption
and atomic fluorescence, leads one to the conclusion that the latter is
most suitable for multielement work. A description of, and justification
for using, a xenon arc continuum source and an argon separated
air/acetylene flame for multielement analysisare discussed.
Multiplex spectrometry is explained and types of multiplex
methods for simultaneously coding many spectral intervals at a detector
are covered. Results of the application of multiplex methods with the
advantage derived from multiplexing are presented. Of the three
multiplexing techniques, Fourier transform, frequency correlation and
Hadamard transform, only the latter has been chosen for implementation
In this work. Signal-to-noise relationships are investigated for the
multiplex and the single channel cases, and example calculations
A description of the 255 spectral interval Hadamard transform
spectrometer (HTS) covering about 25 nm in about 25 s, and the software
for performing the transform is presented followed by a description of
the analytical procedure and the results obtained for Ni, Co, Fe, Mn, Mg,
Cu, Ag and Cr analysis. Spectra and estimates of the limits of detection
are given for these elements.
The construction and operation of a computer controlled single
channel scanning spectrometer (SCSS) is described, and the results for the
analysis of those elements done with the HTS plus Zn, Cd, Au, Pb, Sn and
Tl are presented. Next, a comparison of the results of analyses of the
two methods is made, and the cause of the serious disadvantage of the
multiplex method, based on proportional noise in the system, is proposed.
The results indicate that in the case of atomic fluorescence flame
spectrometry, the large background signal results in a factor of about
100 times poorer signal-to-noise ratio for the HTS system as compared
to the SCSS when the scanning times are equivalent.
Using the same equipment as in the SCSS, it is possible to slew
rapidly between intervals of interest and thereby spend more time
measuring analytically useful wavelengths. The S/N increase, proportional
to the measuring time, is demonstrated, and the improved limits of detection
for 13 elements are compared with the SCSS limits.
INTRODUCTION TO FLAME SPECTROMETRY AND MULTIELEMENT ANALYSIS
Atomic Methods of Analysis
Flame spectrometric techniques have become the most widely used
methods for the determination of trace quantities of metals in solution.
Atomic emission spectrometry (AES) has been reviewed by Pickett and
Koirtyohann (1), atomic absorption spectrometry (AAS) has been described
by Lewis (2) and atomic fluorescence spectrometry (AFS) has been
explained by Winefordner and Elser (3). The three techniques have been
critically compared by Winefordner, Svoboda and Cline (4).
Each of the flame techniques measures the interaction or emission
of electromagnetic radiation by ground state or excited state atoms.
In AES, the excitation of ground state atoms is by thermal means in a
flame. The excited atoms emit light of a characteristic (for each
element) frequency, and the intensity of the light is directly proportional
to the concentration of atoms in the flame. In AAS, the ground state
atoms in the flame absorb radiation (from a suitable source) of a certain
frequency, characteristic of the element. The amount of light absorbed
is proportional to the concentration of the specified element in the
flame cell. In AFS, a light source is also used but in this case, the
radiation is used to excite ground state atoms in a flame. These
radiationally excited atoms emit characteristic radiation and the
Intensity of fluorescence is proportional to the concentration of atoms
In the flame cell.
Conventionally, the three techniques differ substantially only
in the mechanism of excitation of the atomic species; otherwise, they
share much of the same instrumentation. Usually, a dispersive device
monochromatorr) is used to isolate the characteristic radiation of
Interest-and a photomultiplier/amplifier/readout detection system is
used to produce a signal proportional to the radiant flux striking the
photocathode and thus proportional to the intensity of the emission,
fluorescence or absorption. More detailed descriptions of flame
techniques are available in books by Mavrodineanu (5) and Hermann
and Alkemade (6).
Single Element Analysis
The usual procedure in the analysis of several metals in several
samples is as follows. The monochromator dispersing element, usually a
grating, is positioned so that a spectral line of the first element of
interest is Isolated at the detector. A blank solution, and a series
of standard solutions containing known concentrations of the first
element, are then aspirated into the flame, and the appropriate intensity
readings are recorded. The concentration range should include or bracket
the concentration of the unknowns. If such a concentration range cannot
be determined immediately then dilution of the sample and subsequent
analyses are generally necessary. Each,of the unknown samples is then
aspirated and the corresponding intensity readings are recorded. After
the analytical curve of intensity (corrected for blank) vs. concentration
is constructed, the concentration of the first element in each sample is
determined from its intensity value on this curve. The next element is
selected, the monochromator is scanned to the appropriate wavelength
and the next characteristic frequency spectral line is isolated. The
procedure is repeated for each element.
Recently, there has been much effort expended to develop
multielement techniques with which many elements can be determined
simultaneously or in rapid sequence. The longest established multielement
technique has involved the use of the photographic emulsion detector.
Because this method is very slow and usually requires a subsequent
scanning of the plate, photographic detection has been bypassed as a
viable system by most flame spectroscopists. Recently, Busch and
Morrison (7) reviewed multielement systems. Types of detection systems
which have been investigated include scanning monochromators (8-12),
movable detector (13), non-dispersive rotating filter detector (14),
sequentially pulsed source AFS (15), direct reading spectrographs (16-19)
and imaging devices (20-26).
For detector-noise limited situations, as in the infrared (IR)
spectral region, multiplex methods have been used to increase the
signal-to-noise ratio and to decrease the analysis time. Speculation
about the use of a multiplex method (7,24,27), such as Fourier transform
or Hadamard transform spectrometry, in the ultraviolet (UV) region has
led to the present study of the comparison of multiplex and single
channel methods in multielement atomic fluorescence spectrometry.
Each of the three atomic techniques, AES, AAS and AFS,has been
used by various researchers for multielement analysis. Each technique
has certain advantages and certain disadvantages. The instrumental
system for AES requires no light source and is quite simple. A flame
atomizer supplies sufficient energy to excite most elements whose
resonant lines lie above about 350.0 nm (4). However, the spectrum of
many elements is very complex in this spectral region and a good high
resolution monochromator is necessary. Also, some elements do not have
resonance lines which can be excited by the thermal energy present in
analytical flames. Recent developments in induction coupled plasmas (28)
may improve this excitation energy problem but AES is presently limited
in multielement analytical flame spectrometry.
In AAS, almost every metallic element can be measured at trace
quantities. The source need not be extremely intense since the measured
quantity in AAS is the attenuation of the source intensity by the absorbing
atoms. However, the radiation must be directed from the source through
the flame and into the dispersive system. In order to avoid very complex
optical arrangements, one source must then be used for multiple elements.
This is a severe limitation because commercially available AAS sources
are limited to about six elements.
In AFS, an intense source of radiation is required for the
radiational excitation of the atoms in the flame. If such a source is
available, AFS becomes the technique of choice because fluorescence
spectraare relatively uncomplicated compared with those in AES and no
optical geometry problems are present because fluorescence is emitted in
all directions and a non-1800 source-flame-monochromator optical
alignment is suitable. Because AFS has these advantages, it alone was
studied in this project.
MULTIPLEX SPECTROMETRY SYSTEMS
Types of Multiplex Spectrometry
Normal single channel spectrometer systems measure the intensity
in one spectral interval at a time. Three multiplexedd methods" have
been devised to measure the intensities of more than one spectral
interval at the same time with one detector. Each of these multiplex
methods uses a coding device to enable the transformation of the total
Intensity into the intensities at the individual spectral intervals.
In Fourier transform multiplex spectroscopy, a Michelson
interferometer is used to encode the high frequency electromagnetic
radiation used in spectroscopy into an audio frequency interferogram (29).
In this system, all of the spectral intervals, over a wavelength region
determined only by optics and detector, are multiplexed on the detector.
A-computer is used to perform a Fourier transform of the coded interferogram
to decode the intensity versus mirror displacement signal to an intensity
versus wavelength spectrum. This technique has found wide application in
the infrared (IR) spectral region. Low (30-33) has written an excellent
review of Fourier transform spectrometry (FTS).
A second type of multiplex method can be based on the modulation
of line sources at different frequencies. If signals due to the sources
are allowed to fall on a single detector, each of the wavelengths in the
sources will be frequency coded and multiplexed (34). The individual
wavelength intensities can be recovered either by locking-in on their
modulation frequency or, alternatively, by performing a Fourier
transformation. This type of correlation spectrometry can only be used
in analyses where line excitation sources are used such as AAS or AFS.
No published results of this type of system are available at the present
In the third multiplex method, a normal grating system is used to
disperse a wavelength region onto a specially constructed mask which
allows some spectral interval intensities to pass onto the detector
while blocking some other intensities. In this way, an equation relating
the total intensity (or the flux reaching the detector) to a linear
combination of the separate spectral interval intensities (fluxes reaching
the detector) is formed. A series of linearly independent equations is
formed for example when the mask is constructed in a manner related to
mathematical Hadamard matrices, and so this method is called Hadamard
transform spectrometry (HTS). HTS thus codes a specific wavelength
region in a binary,-on (intensity passed) or off (intensity blocked),
fashion. A computer program is used to solve the set of simultaneous
equations formed in the HTS process. A review of HTS principles and
application in the IR spectral region can be found in articles by Ibbett,
Aspinall and Grainger (35), Decker and Harwit (36) and Nelson and
Previous Spectroscopic Studies with Multiplex Methods
Of these three multiplex methods discussed in the previous
section, only the first and third have been previously used in
spectroscopic studies. Commercial instruments are available for FTS and
tITS in the IR region. The utility of these multiplex methods in the IR
is a result of the signal-to-noise (S/N) advantage. Fellgett (38) has
shown that in a detector-noise limited case (such as IR spectrometry),
a signal-to-noise ratio increase can be expected. The so-called Fellgett,
or multiplex, advantage is the ratio of the S/N of the multiplex method
to the S/N of a single channel (slit) system and is given by
F m = N
*here N is the number of spectral intervals multiplexed on the detector.
N = 2 X1
I and X) are the extremes of the wavelength range reaching the detector
and S) is the bandpass of the spectral interval. In FTS, 6X depends on
the displacement increment of the mirror while in HTS, 6X depends on the
dimensions (size of a unit slit) of the Hadamard mask. In either case,
N usually ranges from a few hundred to a few thousand.
The Fellgett advantage is calculated using equal analysis time for
the single channel (slit) and the multiplex system. If, on the other hand,
it is desired to maintain the same signal-to-noise ratio in both systems,
the increase in analysis speed is directly proportional to N for the
multiplex methods. It is this factor which led to the investigation of
the use of a multiplex method for atomic analysis in the ultraviolet (UV)
spectral region, in a desire to be able to rapidly scan a fairly wide
wavelength region with good resolution.
FTS systems utilize an interferometer to transform radiation,
e.g., frequencies of 010 Hz, to an interferogram, e.g., frequencies
of '102 Hz. Interferometric methods are adaptable without tremendous
problems to the IR and near IR regions, where wavelengths are of the order
of fractions of a mm to a few pm. Because alignment procedures in
Interferometry require tolerances of a fraction of the wavelength of the
light being observed, it is quite difficult to achieve stable interfer-
ometry in the 200-700 nm region of the spectrum. For this reason, FTS has
not been evaluated for multielement atomic analysis.
Correlation spectroscopy has recently been discussed, but since
it is limited to use with line sources and requires individual modulation
for each element to be analyzed, it has not yet been studied.
The HTS method uses well-developed dispersion technology and
requires only machine shop tolerances. It is capable of retrofit into
existing monochromator systems, and only a Hadamard mask is needed to
implement the system. The HTS system was therefore chosen for investi-
gation of the use of a multiplexing technique to decrease analysis time
in multielement atomic analysis.
Signal-to-Noise Relationships for UV-Visible HTS
The Fellgett advantage is only applicable to multiplex systems
in which the major source of noise is in the detector. In other words,
the advantage is only realized in systems where the noise does not
increase with an increase in the signal reaching the detector. This Is
the case in the IR region where only noisy detectors (high noise
equivalent sources) are available. In the UV-visible region, photomultiplier
detectors of very low noise are used and the major source of noise is
the quantum noise or shot noise of the source. This type of noise bears
a square root dependence on the total signal; it is due to the random
arrival of photons at the detector. No gain in S/N can be expected from
the Fellgett advantage for multiplex methods in the UV-visible region if
the S/N is averaged over the entire wavelength region measured (39).
(See Appendix I for a proof of this statement.)
A single channel scanning spectrometer (SCSS) system which covers
N spectral intervals in T seconds will measure each interval for T/N
seconds. The signal in that time will be proportional to the number of
photons incident on the photomultiplier tube, I, and the time, T, and so
will be IT/N. Assuming that shot noise is the dominant noise, the noise
will be the square root of the signal. (The signal-noise relationship
follows a Poisson distribution, where the standard deviation of the
population is equal to the square root of the mean of the population.)
Now, the signal-to-noise for one spectral interval will be
(IT/N)/(IT/N) = (IT/N)2. Therefore, the S/N ratio depends only on
the signal which is involved with the particular spectral interval of
Interest and is independent of the signals in other spectral intervals.
There are three limiting cases which are useful for comparing
HTS in the UV-visible region with the SCSS:
First, the case of one line falling in one spectral interval
will be considered. This single line, of flux I, will be allowed to
pass to the detector for (N+1)/2 separate measurements and will be
summed each time. With the assumption of no background, the other
(N-1)/2 measurements will have no intensity reaching the detector.
The total signal from the line, of.intensity I, will be IT(N+1)/2N and
the signal-to-noise is thus (IT(N+1)/2N)2 (still assuming only shot noise).
The gain in signal-to-noise at the spectral interval of interest, due to
the longer observation time, is then given by
G = HTS [IT(N+1)/2N] N+
(S/N) 1 [.1 2
SCSS [ IT/N]
This advantage is essentially the same as the Fellgett advantage for HTS
in the IR (37). It should be pointed out that the noise of all the N
spectral intervals is exactly the same as the noise associated with the
spectral Interval which contains the single spectral line and, again
assuming no background, this noise would now cause the baseline to
fluctuate around a level of zero in the other N-1 spectral intervals.
Therefore, .the average (S/N) is exactly equal to the average (S/N)scsS
and there is no average advantage. However, in the SCSS case almost all
of the noise is associated with the line peak, and the baseline thus has
little noise. In the HTS, the noise is distributed evenly over the
entire spectrum, and therefore the peak signal has less noise in the
HTS than in the SCSS, and the baseline signals have less noise in the
SCSS. This is true in any case where the HTS has an advantage and
the advantage is only associated with the peak signals.
The second case of interest involves the S/N relationship of a
weak line in the presence of a strong line. In this case, the noise in
each spectral interval will essentially be due to the noise from the
strong line. Thus, the S/N of the weak line will be equal to the S/N
of the strong line divided by the ratio of intensity of strong line to
intensity of weak line. In the case of two lines of intensity ratio
(N+1)/2 to 1 or greater, the S/N of the weak line would be the same or
better in the SCSS system as in the HTS system. This degradation of the
S/N is called the multiplex disadvantage and results when two or more
dissimilar signals are measured simultaneously with one detector. If
the noise is related to the total signal at the detector, the multiplex
disadvantage will degrade the S/N of very small signals in the presence
of very large signals.
The third case is somewhat more realistic since a background, I ,
is now considered at all of the spectral intervals observed by HTS. At
all N mask positions approximately N/2 slots allow the background to
pass and at (N+1)/2 positions the line of interest with intensity Is Is
also passed. The total signal, ITHT,which will be summed will be
I = N+I I + N I
The shot noise figure associated with this signal will be
N .= N I + N I
HTS 2 j i
Since the signal of interest is still N+1 Is the S/N ratio in the HTS
system is given by
In the SCSS, the signal of interest is given by
= I + I
The noise is then (I.
+ 1.8 ) and the S/N ratio is
(I. + I. )
The gain in S/N at the line peak is then
G = HTS
is the average background intensity,
N+1 I +
- B A
Evaluating the limiting cases shows that if the average background is
small compared to the intensity of the line of interest (I B s)
then G reduces to [(N+1)/2] as in the first case considered.
Otherwise, if Is << B then G becomes 1//2. In this circumstance the
HTS system is worse by a factor of 0.7 compared with the SCSS.
In the previous exercise, only shot noise (or quantum noise) was
considered and noise which is proportional to the background (flicker
noise from a flame for example) or to the source (i.e., ripple noise in
an AFS source) was neglected. Instrumentation has been developed to
minimize the effects of these types of noises but even the best
instrumental system may allow some small part of this so-called
"proportional" noise. This noise is characterized by being directly
proportional to the total signal which is associated with the noise.
For low level signals the few percent proportional noise is usually
negligible compared to the square root relationship shot noise. However,
in the HTS system, with a significant background at each spectral
interval the total influence of an average background of 11 at each
2 B -B
interval is N2 + N 7B compared with II contribution in the SCSS.
This factor of (N2 + N)/2 would almost certainly cause the majority of
noise in the Hadamard system to be due to proportional noise if the
background is significant.
To illustrate the concepts of this chapter it is instructive to
examine a possible example in multielement AFS by the two methods.
Consider the use of photon counting. Also, consider that the background
consists of 1000 counts accumulated in each spectral interval for the
counting period and that two lines of 100 counts and 5000 counts per
measurement interval are to be determined in the same analysis time,
by the HTS and SCSS system (255 spectral intervals are to be measured in
The SCSS will measure each spectral interval for 0.1 s and will
accumulate 1000 counts for each spectral interval while measuring the back-
ground alone and 1100 and 6000 counts while measuring the line peak spectral
intervals. The shot noise on 1000 counts is about 32 and the shot noises at
the lines plus background are about 33 and 77 respectively. If proportional
noise is all due to the background and is 1.0% then proportional noise is
10 counts at each channel. Shot noise is thus dominant, and the (S/N)scsS
of the weak and strong lines are 3.0 and 64.5 respectively.
Now, for the HTS, the background is measured at 128 spectral intervals
(on the average) and is summed for each channel 255 times. The lines are
summed 128 times. The shot noise associated with each spectral interval
( (255) (128)(1000) + (128)(100) + (128)(5000) )
or 5770. The signal for the first line is measured 128 times and so is 12800;
the second line signal is 640000. From shot noise considerations, the (S/N)
of the first line is then 2.2 and the second line is 111. However, if
proportional noise is 1% of the background level then for 128 spectral
intervals the proportional noise is 1280 counts. This noise is independently
measured 255 times, and therefore the porportional noise is
( (255)(1280)2)1 = 20440.
Noise values add quadratically and so the total noise in the HTS system is
( (5770)2 + (20440)2)i = 21239
Now the (S/N)HTS for the two lines is reduced to 0.6 and 30, a factor of 5,
and 2.2 times worse for the two lines by HTS as compared with the SCSS.
It can be seen that in a real system, the scanning technique might
be shot noise limited while the multiplex technique may suffer tremendous
losses in S/N because of proportional noise.
ATOMIC FLUORESCENCE COMPONENTS
COMMON TO THE SYSTEMS STUDIED
The Atomic Fluorescence Excitation Source
In recent years, most AFS workers have been using intense line
sources of excitation. Metal vapor discharge lamps (MVL's)(40,41),
hollow cathode lamps (HCL's)(42,43), electrodeless discharge lamps
(EDL's)(44,45) and, more recently, tunable dye lasers (TDL's)(46) have
been shown to be excellent single element AFS sources. In most cases,
these sources have to be tuned, adjusted or thermostated for optimum
performance for one specific element. The results obtained thereby are
quite good for most elements limits of detection range from a few
hundred ng/mi down to fractions of a ng/ml for more than 30 elements (3).
Some attempts have been made to use multielement HCL's (47) and
-especially multielement EDL's (48) as AFS sources. Combination problems
and optimization trade-offs have severely limited use of multielement
sources in multielement AFS (49). If single element sources are used in
multielement AFS each must be individually powered and adjusted for
optimum conditions. Furthermore, the spatial arrangement of such a
situation becomes difficult if more than 4 to 6 sources are to be used.
Continuum sources have been used in the past (50-53) with some
-success. Workers note two difficulties with continuum sources: the spectral
radiance of xenon arcs falls off rapidly below about 250 nm (where many
useful resonance lines occur), and scattering by the incompletely
vaporized particles in the flame leads to high backgrounds and thus to
poorer detection limits when compared to intense line sources. Despite
these shortcomings, the xenon arc lamp appears to be the source of choice
in multielement AFS at the present time for three reasons: first,
although the lamp's output drops off below 250 nm, some fraction of the
output is still available down to about 200 nm (see Figure 1) allowing
excitation of just about every element of interest; secondly, only one
source is necessary, which simplifies the front-end geometrical
arrangement, e.g., even if six-element combination sources (as EDL's)
could be made, still five source/power supplies, lens/chopper systems
would be needed to allow excitation of 30 elements, compared with one
continuum source with one power supply; finally, the continuum source
is convenient to operate, requires only minimal adjustment and Is
stable after a few minutes warm up time, as shown in Figure 2. The
particular continuum lamp used in this study is a high pressure, short
arc xenon lamp with aTr internal aluminum parabolic reflector. The
manufacturer claims that this lamp collimates 85% of the total arc
output and uses a sapphire window for output down to at least 200 nm.
The Atomization Cell
Flames are the most common atomizers for present-day atomic
spectroscopy. A sample is aspirated into a flame, usually with a
premixed, laminar flow burner, where the solvent is evaporated, and the
solute vaporized and atomized by the thermal action of the flame. Much
of the previous work in AFS has made use of the low quenching combustible
gases such as oxyhydrogen or hydrogen-air diffusion flames; molecular
*- AISN31NI 3AIlY738
--- AIISN31NI 3AI V738
species such as CO and CO2 enhance the non-radiational deactivation
(quenching) of excited atoms in the flame. The hydrogen flames are also
much cooler than hydrocarbon flames and have higher burning velocities
and therefore the desolvation, vaporization and atomization processes,
which are very necessary to avoid scattering of the continuum source
radiation,.are not as efficient. The use of the cooler hydrogen flame
and real samples necessitates a scatter correction even when used with
line sources (54).
In order that the multielement systems investigated would have
maximum versatility, the higher temperature air/acetylene flame was used
for all of the AFS work in this study. Although the quenching species in
this flame, together with a higher background, could mean a factor of
5 to 100 lower (poorer) fluorescence quantum yields, the flame proved
to be an excellent atomization source and no noticeable scatter was
observed even when aspirating solutions with more than 500 jg/ml of solids.
The flame was produced by a premixed nebulizer/burner assembly
together with a capillary type burner head (55). The flame was separated
by an argon sheath. The fuel/air flow rates were established so that the
flame was slightly fuel-rich; the cones above the capillaries were
somewhat "fuzzy" and had some noticeableyellow color. This fuel/air
ratio led to the lowest background and allowed good atomization of all of
the-elements studied. Some improvement might be possible if the flame
were changed to maximize the S/N for each individual element, but this
would have been too complicated for the present study and so was not
attempted. The flow rate for acetylene was 1.5 1 min for air 9.7 1 min"
and for argon 15.5 1 min" as measured with a wet test meter.
The Optical System
The front-end optics and source/atomizer were the same in all
of the work described later in this study. The source was focused
through a chopper operated at about 50 Hz. The chopped radiation was
collected by a lens and focused into the flame. On the other side of
the flame a 140 mm diameter, UV enhanced mirror with a 62 mm focal
length focused the source radiation back into the flame. At right
angles to the source light path, a lens collected the fluorescence and
formed a 1:1 image of the flame at the entrance slit of the monochromator.
All of the lenses used were of fused quartz. Figure 3 shows a block
diagram of the front-end arrangement used throughout this study, and
Table 1 lists the components used and their sources.
Few problems were encountered with the present set-up. However,
It should be stressed that the mirror behind the flame and in line with
the source should not focus the exciting beam directly back into the
continuum lamp because of the danger of overheating the source and
destroying the lamp. A procedure involving slight defocusing of the
mirror-source optics was adopted after the explosive destruction of a
lamp. This procedure reduced the fluorescence signal by only 10-20%.
The major emphasis in this study was to develop and evaluate
systems for multielement analysis. While doing this, it was also
possible to compare multiplex and single channel methods in the UV-visible
spectral region. Much of the equipment used throughout this study was
exactly the same for both the Hadamard and programmed scan systems;
however, in the multiplex system an analog detection system was used
and in the single channel set-up a digital detection (photon counting)
system was employed. This led to problems in a direct comparison of the
Hadamard and scanning methods. The primary advantage of the digital
O Monochro -
/ Doubling Mirror
Figure 3.-- Atomic Fluorescence Source and Flame Cell Arrangement used
throughout this study.
COMPONENTS OF THE ATOMIC FLUORESCENCE
SOURCE AND FLAME CELL.
Xenon Arc Continuum
and Power Supply
2*' focal length
140 mm diameter,
62 mm focal length
46 Hz, 50% duty cycle
San Carlos, CA 94070
Norwalk, CT 06852
Oak Ridge, NJ 07438
Optical Industries, Inc.,
Costa Mesa, CA 92626
detection system was one of dynamic range. The analog system, coupled
to a computer, allowed a dynamic range of only 1024 discrete levels.
The photon counter has a dynamic range of about 10 However, in this
study a range of only 105 was normally used. The second advantage of
the digital system is one of convenience, i.e., the photon counter
needs no adjustment between ranges while the analog system had to be
switched through different ranges.
So, although a comparison was sought, it was felt that the best
system available should be developed with the equipment on hand. When
the results are discussed (see Chapters IV and V) possible advantages
due to the analog/digital detection systems will be noted.
THE HADAMARD TRANSFORM SPECTROMETER (HTS) SYSTEM
Hadamard Transform Spectrometry
The multiplex method of Hadamard transform spectrometry (HTS)
makes use of conventional grating spectrometer technology. In place of
a single exit slit, which is used to isolate a narrow bandpass (spectral
interval) region of the electromagnetic spectrum, a multi-slit mask is
used to allow portions of a much wider spectral region to reach the
detector. The mask is specially constructed to block some spectral
Intervals and allow others to pass. Therefore, the signal reaching the
detector for a given mask position, i, is given by
where the a .'s (j=1 to N) are either 0 (if the light is blocked at
spectral interval X.) or 1 (if the light is allowed to pass at spectral
Interval X.). When a set of N orthogonal equations is formulated with
various combinations of a..'s, then the individual X.'s can be determined
by solving the set of simultaneous equations given by N intensity
readings with N different mask configurations. Hadamard matrices give
the relationships necessary to form independent equations with a set of
N different masks or, alternatively, a cyclic mask, constructed so
that an orthogonal set of coefficients (aij's) can be created by moving
the mask one slot width N times at N positions to form the set of
Implementation of the HTS System
A cyclic mask can be designed for any N (N = 2n -1; n any integer)
according to the method of primative polynomials given by Nelson and
For this work, N = 2 -1 = 255 spectral intervals are covered at
the exit focal plane. A cyclic mask would then have 2N 1 = 509
transparent (open) and opaque (closed) slots. The order of l's (open
slots) and0's(closed slots) is determined once the first n (8 in this
case) coefficients are given. The first 8 coefficients used for this
mask were 10001110. The ninth coefficient can be found from the first
eight coefficients by modulo 2 addition. (In mod 2 addition 0 + 0 = 0,
1 + 0 1, 0 + 1 = 1 and 1 + 1 = 0 with carry = 1.) Now, if the first,
third, fourth and fifth coefficients are added, mod 2, the result is
the ninth coefficient. Thus the ninth coefficient is 1 + 0 + 0 + 1 = 0.
Each subsequent coefficient can be determined from the previous eight
coefficients in this same manner. The 509 coefficients, implemented into
the mask, are shown in Table 2. The coefficients at the first mask
position are determined from the portion of the mask consisting of the
first 255 coefficients 10001...to 00000 (see underlined section of
Table 2). The coefficients of the second mask position are formed by
shifting, one place to the right, and so are 00011...to 00001, and so
forth until the last (255th) mask position has coefficients 01000...to
255 SLOT CYCLIC MASK CODE: "1" DENOTES TRANSPARENT SLOT
AND "0" DENOTES OPAQUE SLOT. NOTE THAT THE 255 SLOT CYCLIC
MASK IMPLIES 509 TOTAL MASK SLOTS. THE UNDERLINED PORTION
REPRESENTS THE SLOTS ILLUMINATED AT THE FIRST MASK POSITION
10001 11000 10010 11100 00001 10010 01001 10111 00100 00010
10110 11010 11001 01100 00111 11011 01111 01011 10100 01000
01101 10001 11100 11100 11000 10110 10010 00101 00101 01001
11011 10110 01111 01111 11010 01100 11010 10001 10000 01110
10101 01111 10010 10000 10011 11111 10000 10111 10001 10100
00000 10001 11000 10010 11100 00001 10010 01001 10111 00100
00010 10110 11010 11001 01100 00111 11011 01111 01011 10100
01000 01101 10001 11100 11100 11000 10110 10010 00101 00101
01001 11011 10110 01111 01111 11010 01100 11010 10001 10000
01110 10101 01111 10010 10000 10011 11111 10000 10111 10001
The Hadamard spectrometer was constructed from a Czerny-Turner
scanning monochromator, a single pass, 0.35 m focal length, f/6.8 mount
with a 48 mm x 48 mm, 1180 lines per mm grating blazed for 250 nm.
The reciprocal linear dispersion with this configuration was approximately
2.0 nm/mm. The slits are straight-edged and bilaterally adjustable in
width from 5 to 2000 pm and in height with values of 12, 5, 3, 1 or
0.5 mm. The folding mirror at the exit slit was removed, and a
laboratory-fabricated translation stage was mounted at the front panel
with the front edge of the slide assembly (as shown in Figure 4)
mounted at the exit focal plane. A field stop, 0.510 in x 0.5 in,was
aligned to allow approximately 12.5 nm on either side of the exit focal
point to fall on the mask which was connected to the slide assembly.
The mask consisted of a copper-nickel bimetallic strip 1" x 3" x 0.010".
The 255 slot cyclic mask (509 total slots) was inscribed on the
blmetallic strip with each slot having a width of 0.002 in (50 pm) and
a height of 0.387 in; the total mask code length was 1.018 in. The
slide assembly was spring loaded in the translation stage and was driven
by a 40 turns-per-in micrometer which in turn could be stepped in
4acrements of 1/19200 in by a 480 steps-per-revolution stepping motor.
The detector was a 30 mm diameter end-on photomultiplier tube
with S-13 spectral response, and it was operated at 750-1000 V. The
photoanode current was amplified by a current-to-voltage converter and
measured by a lock-in amplifier, which was tuned to the phase and
frequency of the chopper described in Chapter III. The output of the
lock-in amplifier was directed to the analog input of the PDP-11
'computer (see Appendix If for a description of the computer system).
A block diagram of the complete HTS system is shown in Figure 4. The
components used in the system are listed in Table 3.
COMPONENTS OF THE HADAMARD TRANSFORM SPECTROMETERa
509 Total Slot
255 Cyclic Code
Dynamic Research Corp.,
Wilmington, MA 01887
Under license from
Benton Harbor, MI 49022
Plainview, NY 11803
Wakefield, MA 01880
Benton Harbor, MI 49022
Cleveland, OH 44139
aNote: Other components (excitation source, flame, computer system)
are listed in Tables 1 and 12.
The Fast Hadamard Transform (FHT)
The process of accumulating data in an orthogonal fashion in
order to form a set of linearly independent simultaneous equations is
begun when the atomic fluorescence system, including the light source
and flame cell described in Chapter III, and the spectrometer and
electronics described in the last section, is aligned and adjusted.
The monochromator is set so that the center of the desired 25 nm span
is displayed on the wavelength counter. The computer program is loaded
and started with the command "G". The computer steps the mask to the
first position and takes a series of 255 readings from the lock-in
amplifier by means of the analog-to-digital converter (ADC). These
readings are averaged, and the average is added to or subtracted from
a double precision (two 16 bit words) 255 point data buffer storage
array according the following scheme. The first eight coefficients,
corresponding to the first eight slots of the mask as it is currently
positioned, are determined in the same manner as the coefficients for
the mask were calculated in the previous section. For example, for the
first mask position, the first eight coefficients are 10001110. These
binary digits are designated b0 to b The double precision accumulators
are numbered 1 to 255 and are determined as eight bit binary numbers
a0 to a7 (00000001 for the first accumulator number). Corresponding
bits are added, mod 2, according to (a0 + b ) + (al + bI) +...+ (a7 + b7);
the sum determined will be 1 if the number of matching set (1) bits in
these two eight bit words is odd, and the average signal at this slot
position is then added to the respective accumulator. If, on the other
hand, the number of matching set bits is even (0), then the average
signal is subtracted from the patricular accumulator. It can be seen
that for the first code word (10001110), there are no matching l's for
the first storage location (00000001), and so the signal is subtracted
from the first accumulator.
The accumulator is then incremented by one and the new set of
bits, representing the new accumulator number, is matched with the code
word; the average signal is then added to or subtracted from the next
accumulator (10001110 has 1 matching set bit with 00000010 so the first
signal is added to the second accumulator). The code word remains the
same (until the mask is stepped to the next location), the accumulator
number is increased by one and the add/subtract process is repeated
until the average signal at this mask position has been added to or
subtracted from each of the 255 accumulators.
At this point, the code word describing the first eight slots of
the next mask position is determined in the same manner as used to
determine the coefficients in the last section. Briefly, the bits
b0 + b2 + b + b are added, modulo 2, and the result is used as bg.
A shift, one to the right results in the eight bit word b1 to b8.
These bits are used as the new code word. The mask is then stepped one
slot width to the new mask position, and the data gathering and
kaddition/subtraction process is repeated.
After 255 mask steps, the spectral signal values are stored as
Double precision, octal (base 8) integers with any noise portion of the
signal resulting in a baseline fluctuation about zero. To eliminate
problems caused by negative numbers being routed to a unipolar digital-
to-analog converter (DAC), each signal value is digitally offset until
no negative numbers remain in the data buffer.
A final permutation is needed to obtain the actual signal versus
wavelength spectrum. The real channel in a monotonically increasing
spectrum (denoted by X ; i = 1 to 255) is related to the stored
channel (Sk) by an eight bit binary number which can be found according
to the following procedure.
The intensities of the first eight spectral elements (Xi; i = 1
to 8) are contained in the storage channels (accumulators) Sk as follows:
Xi = Sk
where; k = 2 and i = 1 to 8.
Thus X1 = S;
X = S 2;
x8 = S128'
Subsequent spectral intensities (Xi; 9 < i < 255) may then be found in
storage locations calculated from the binary representations of the
previous eight storage locations. Spectral intensity Xi(9 i 255),
with binary representation (x.i, x1,2 x.3 x,4 x, x.6 x., x. 8)
1,1 x2 i,3 i,4 x,5 i,6 i 7 ,8
will be found in accumulator Sk where the binary representation of
k Is (s1 s2 s3 s s5 s 7 s8) and where,
< (mod 2)
s. = x + x + x + x
s = i+j-9, + xi+j-9,3 + i+j-9,4 i+j-9,5
where s. is the value of the first binary bit of the Sk accumulator and
x + 1 s the value of the first binary bit of the (i+j-9)'th spectral
interval and the other x-terms are correspondingly defined. For example,
for X9 (the ninth spectral) interval, the eight pervious accumulators
in binary notation are
X1 = 00000001, i.e. X1 = x1,1 x1,2 x1,3 x1,4 x1,5 x1,6 xl,7 x1,8'
X2 = 00000010,
X3 = 00000100,
X .= 00001000,
X = 00010000,
X = 00100000,
X7 = 01000000,
X8 10000000, i.e. X = x8,1 x8,2 x x x8,5 8,6 x8,7 x8,8'
Thus for i = 9
s x +x + x + x = x +x1 +xI +x1
1 X9+1-9,1 +9+1-9,3 9+1-9,4 9+1-9,5 1,1 +1,3 1,4 +X1,
s1 0 +0 + 00+ 0 0
s2 x 2,1 + x2,3 + x2,4 + x2,5 0+0 +0 + 0= 0,
s x3,1 + 3 + ,4 + 3,5 0 + 0 + 0 +
s 54 +X +X +X = 0+0+0+1=1,
s4 4,1 *4,3 4,4 4,5
s5 = x +x +x +x = 0 + 0 + 1 + 0 = 1,
5 5,1 5,3 5,4 5,5
s = x +6,1 x + x + x = 0+1 +0 +0= 1,
s = x +x +x +x = 0+0+0+0=0,
7 7,1 7,3 7,4 7,5
s8 x8,1 + x8,3 + x8,4 + 8,5 1+ + 0 + 0 =1.
Therefore, k = (00011101) = 358 = 2910 so X9 = S29 and so the ninth
spectral element is found in the 29th sequential storage location.
Each subsequent location can therefore be determined from the eight
binary words describing the eight previous storage locations.
The storage locations are determined, and each stored value is
divided by (N+1)/2 or 128 in the present case (N = 255). These final
values are stored in a sequential (increasing with wavelength) data
buffer area of the computer. At this time, the transform is complete,
and the digital data are available for processing.
It can be seen that the FHT can be accomplished in this way with
N x N additions (or subtractions), and N simple divisions. For this
reason, the FHT can be programmed on any computer without the need for
a hardware multiply/divide or a slow, software multiply/divide package.
This one-step arithmetic process is the basis for the order of magnitude
Increase in speed of the FHT (56) compared with the fast Fourier
transform (FFT) which requires N log2 N multiplications (or divisions)(57).
Because the spectral intensity values are stored, they are
available for digital manipulation. The data can be read out on an
oscilloscope or an x-y plotter. Alternatively, the entire set of
signals can be punched on paper tape for storage. Also, the data can be
smoothed, and the baseline averaged. Peaks can be located and integrated,
and comparisons with calibration standards or previous spectra can be
made. Multiple scans can be generated and added or subtracted.
Analytical Procedure with the HTS System
Stock aqueous solutions of 1000 pg ml of the metals listed in
Table 4 were prepared from reagent grade chemicals. Appropriate serial
dilutions of the combinations of elements were made in-the concentrations
shown. The spectrometer was manually scanned to the center wavelength
shown In Table 4 for the wavelength range desired.
The system was then energized. The illuminator was started and
allowed to stabilize, the flame was ignited and adjusted, and the
ELEMENTS INVESTIGATED WITH THE
HADAMARD TRANSFORM SPECTROMETER SYSTEM
Ni, Co, Fe
g9 mi -1
- 500 jg ml"1
- 200 pg ml-
- 200 mg mli-
- 200 jig ml-1
Wavelength setting of grating spectrometer.
computer program was loaded and readied. Solutions, including a blank
and the standards, were aspirated each in turn and the data gathering
process was initiated by means of software (the keyboard). The current
amplifier and lock-in were set to give 10 volts per amp and 30 mV full
scale, respectively. Thus, the current measured and amplified by the
lock-in was about 3 nA. The settings were adjusted if necessary on a
subsequent run if the readings during a run exceeded full scale out
from the lock-in or if no reading during a run exceeded 10% full scale
out. The maximum S/N in the output resulted when there was a maximum
difference in the reading obtained as the mask was stepped across the
exit plane. All of the adjustments to the electronics were performed
to maximize this difference in readings. The photomultiplier tube
dc voltage was initially set at 800 V but was also adjusted in the range
750 V to 850 V to maximize the difference in readings. The results from
the FHT were available about 30 s after the start of a scan via the
oscilloscope display. The results were typed out as intensity vs.
channel number and also were plotted via the x-y recorder.
Results and Discussion
It was intended that analytical curves (log intensity vs. log
analyte concentration) be obtained by gathering digital data from the
printout of the intensity of the channels as a function of the
concentration of analyte introduced into the flame. After an exhaustive
study of this possibility it was determined that this was not feasible for
two reasons; (i) the concentrations which allowed signal-to-noise ratios
of greater than about 10 were found to be on the non-linear portions of
an analytical curve; lower concentrations of analyte, which would fall
in the linear portion of the working curve would not give S/N ratios
-greater than about 2 or 3; (ii) all variations in electronic parameters,
in-order to increase differences in the readings as the mask was
stepped, resulted in vastly different background noise levels. For
these reasons, the x-y plots of the spectra were used to estimate the
limits of detection for the elements of interest.
One problem became evident during the preliminary operation of
the system. With the electronic sensitivity used in these studies,
i.e., about 3 nA current and 100 ms time constant with the lock-in, a
blank solution resulted in considerable noise in the baseline as
depicted in Figure 5. The background, which is reproducible in peak-to-
peak noise intensity but not in spectral distribution, was probably due
to slight fluctuations in scattered radiation in the flame. Since about
-oe-half of the mask slots are transparent, a total spectral region of
approximately 12.5 nm of the background is passed at each mask position.
Any noise (due to the source) on the background is passed to the detector.
This effect, which is a direct consequence of the multiplexing effort,
ams a major cause of-the poor performance of the HTS.
Iieiesolution capability of the HTS system is demonstrated by
the ultielement AFS spectra shown in Figure 6. 200 pg ml-1 each of Mn
sand Mg were aspirated. Entrance slit widths of 200 pm and 50 jur resulted
-in the spectra shown. In each case, a digita) filtering technique was
used to average the noise on the baseline in order to better demonstrate
.the resolution possible. The Mn triplet at 279.5, 279.8 and 280.1 shows
baseline resolution with 50 jim entrances it width, and the spectral
bandpass is less than 0.3 nm per channel with this slit width.
In Figures 7 to 10 results are given of Hadamard scans of
wavelength centered as listed in Table 4. In Figure 7 the AFS spectrum
..---AIISN3INI 3AIl V73b
------ ALS vM31M 3AaIIV73
-- -- --
S---- ,AISN31NI B3AI V73I
AWlSIlt 3Ali V7n38 -
<-- A ISN31NI 3AI VY73U
is given for 300 Pg ml"1 Ni, 200 jug mll Co and 200 ug ml"1 Fe; in
Figure 8 the AFS spectrum is for 10 jg ml'" each of Mn and Mg; in
Figure 9 the AFS spectrum is for 100 ag ml- each of Cu and Ag; in
Figure 10 the AFS spectrum is for the Cr triplet from 100 ug ml"1 Cr.
Each of the spectra was scanned in 28 s with an entrance slit of
100 jm. From results such as these, estimates of limits of detection
for these eight elements were made and are given in Table 5. Also
listed there are the detection limits found for those elements using
a single channel system in a stationary mode, and the same type of
150 W xenon continuum source (53).
A comparison of these results show that the HTS system results
in detection.1imits some orders of magnitude less than for a stationary,
single channel system. It can be estimated that the loss in S/N due to
the extremely wide spectral region for the background scatter is at
least one order of magnitude. This result was estimated from the
background noise levels in a single channel scanning system with
similar time constant and sensitivity. The root-mean-square (rms)
noise ratio is aboutTO for the HTS/single channel system.
All of the detection limits listed in Table 5 are for similar
signal levels from all fluorescent lines in the wavelength region under
investigation. This situation would not normally occur in real samples
where vastly differing concentrations of elements could lead to large
differences in signal levels. To investigate potential problems in
multiplex systems for the analysis of mixtures of different concentrations,
the Mg-Mn mixture shown in Figure 11, i.e., a mixture of 50 jg ml"1 Mg
and 25 jug ml Mn, was measured. The Mn signal is clearly evident.
When the ratio is increased from 2:1 to 3:1 (60 jig ml-1 Mg and
LIMITS OF DETECTION (LOD)a FOR THE ELEMENTS
ANALYZED BY THE HADAMARD TRANSFORM SPECTROMETER SYSTEM
j9 ml 1
The limit of detection is defined as the concentration of
analyte which gives a signal twice the rms noise observed
when a blank is measured.
----- Al ISN31NI 3A11 V73
4-- AUSN31 I 3AllV73H
20 pg ml-1 Mn), the noise level increased, and the signal from the Mn
was no longer clearly visible. (Figure 12). This effect of the
multiplex disadvantage is certainly a major limitation of this type of
SINGLE CHANNEL SCANNING SPECTROMETER (SCSS) SYSTEM
Most conventional spectrometric systems are able to scan the
wavelength which is presented to the detector. In order to be able to
scan at speeds greater than about 0.2 nm/s all that is needed is a
means of rapid data handling and some method to determine the wavelength
accurately and reproducibly during the scan. These functions are easily
performed by means of a computer, and so, with a computer available,
the scanning technique is easily implemented.
Because only one spectral interval is measured at a time, only
conventional problems of spectral interference are encountered. The
spectral bandpass of the instrument must be chosen so that possible
spectral interference will be of low probability. At the same time,
the dispersion of the instrument should be chosen such that the time
necessary for scanning the grating is as short as possible.
An obvious advantage to a single slit scanning system is that the
range of wavelength which can be covered during a scan is only limited
by the data handling capability of the system. However, in order to
compare this system with the HTS only 25 nm wavelength scans are
Description of SCSS Experimental Setup
The AFS excitation source and atomization flame cell described
in Chapter III were used in the SCSS experimental setup as well as in
the HTS setup. Only the dispersion device and detection system are
changed from the HTS system.
A 0.3 m, f/5.3 modified Czerny-Turner mount monochromator with
a 50 mm x 50 mm, 600 grooves/mm grating was used as a dispersion device.
This monochromator has individual bilaterally adjustable straight slits
variable in width from 5 um to 2000 um and in height from 0 to 20 mm.
The reciprocal linear dispersion with the specified grating was 5.41 nm/mm
and the resolution with 10 um wide 4 mm high slits was 0.12 nm.
Throughout this work, the slits were set at 75 jum wide and 10 mm high
to correspond closely to the HTS system bandpass. With these conditions
the bandpass was approximately 0.3 nm.
The normal scanning motor/gear system for this monochromator was
disengaged, and a stepping motor was coupled directly to the shaft of the
precision screw which rotates the grating. The stepping motor, which
makes 480 steps per revolution (0.750 per step) can be driven at speeds
to about 1200 steps second-1. Because one revolution of the precision
screw scans the monochromator 10.0 nm, the resolution capability of the
monochromator/stepping motor system was 480 steps/10 nm = 4.8 steps/0.1 nm
or about 0.02 nm per step. Maximum stepping speed used in this
application was about 1000 steps s" so that the maximum slewing rate
was about 20 nm s
A high gain, low dark current photomultiplier tube with S (Q)
spectral response (EMI 6256S) was used in a photon counting mode within
a magnetically and electrostatically shielded housing at the exit slit.
The tube was operated at -1450 V from the photon counting ratemeter/power
supply described later. The dark count with this system was 70-100
counts per second (cps).
The photon counting system consisted of a fast amplifier/discriminator,
ratemeter/power supply, and a digital synchronous computer. The
amplifier/discriminator was powered by the ratemeter/power supply low
voltage power out. Output from the discriminator was sent through the
ratemeter to the digital synchronous computer. The ratemeter was used
as an intermediate analog output device and power supply for the
photomultiplier tube and the amplifier/discriminator. These components
were operated according to the manufacturers instructions.
The digital synchronous computer (DSC) is essentially a photon
counter with two high speed 8 digit scalers, an arithmetic processing
unit and timing and control signals and functions. In a mode called
CHOP, It is able to function as a "lock-in photon counter" by use of
the two scalers in conjunction with a mechanical chopper. When a
synchronizing signal indicates that the data signal to be measured is
-present at the photomultiplier tube, the DSC uses a scaler designated
as "DATA". Switches and a clock are available for setting the
:observation time, in microseconds, for which the DATA scaler is to be
used. After that observation time, the scaler is shut down and the
-DATA is stored. The synchronizing signal next indicates that the
background signal is present and the counts from the background are
-routed to a scaler designated "BACKGROUND". This scaler accumulates
counts for the same observation time as the DATA scaler. The DSC has
thumb-wheel switches on which the operator can set a "preset number" of
chopper cycles. After each DATA-BACKGROUND cycle, the preset N counter
is checked to see if the number of chopper cycles set there has been
finished. If not, further cycles are started and the total of DATA
and BACKGROUND are stored in the appropriate scaler. If the preset N
counter has been accomplished then the results are displayed on light
emitting diodes on the control panel of the instrument in floating point
notation (3 significant digits and an exponent). The information displayed
can be either the DATA, the BACKGROUND, or the sum or difference of
these two counts. At the same time, a "ready" light is lighted, and
If the instrument is in the automatic cycle mode, the process is
started again (see Figure 13 for a timing diagram of this process).
The components of the SCSS are listed in Table 6 and a block diagram of
the system is shown in Figure 14.
The DSC is Ideally suited to computer control because two
connectors at the rear of the Instrument allow all of the functions of
the DSC to be controlled by TTL level signals from a computer interface.
Also, the data is available as TTL levels in binary coded decimal (BCD)
notation. Synchronization signal lines are provided to allow communication
between the DSC and a laboratory computer. For a more detailed
description of the DSC/computer interface, see Appendix II.
The software for the SCSS is designed for simple control/data
acquisition. Briefly, the computer steps the grating 0.1 nm and then
counts for 4 chopper cycles. The fluorescence information (difference
between the DATA and BACKGROUND scalers) is picked up after each cycle,
and, at the end of 4 cycles, the sum is stored in a data buffer. The
computer steps the grating 0.1 nm again and the data gathering is
repeated until a wavelength scan of 25.6 nm is complete. The data can
be displayed or printed or normalized to values between 0 and 1023 for
plotting by means of an x-y recorder. The routines are quite easily
I I I I I
I I I I I I
I I I I I I
II IIS I
I I I I I I
I I I I I I
i t I I
I I I I I
Timing diagram showing when the DATA and
BACKGROUND registers of the Digital Synchronous
Computer are open with respect to the source
0 0 C.
T 8 pi
COMPONENTS OF THE SINGLE CHANNEL SCANNING SPECTROMETERa
Photomult Ipl ier
Digital Synchronous Computer
EM I 6256S
GCA/McPherson Instr. Co.,
Acton, MA 01720
Plainview, NY 11803
SSR Instrument Co.,
Santa Monica, CA 90404
Wakefield, MA 01880
Other components (excitation source, flame, computer system)
are listed in Tables I and 12.
written and, since no transformation is necessary, almost all the computer
time is used in data acquisition.
Operation of the SCSS System
When the system is in operation (flame and optics aligned and
adjusted, chopper and electronics energized and computer program
loaded), the monochromator is initially positioned at 190.0 nm. The
wavelength region to be scanned can be approached by slewing. The
keyboard command "F" will accept an octal (base 8) number at 0.1 nm
steps to be slewed forward from 190.0 nm. The digital display will
show thewavelength at all times during all operations. When the
starting wavelength is reached, a "G" keyboard command will initiate
the scan. The scan time is 31 s for a 25.6 nm scan. Upon completion
of the scan the TTY will type "READY", and the fluorescence intensity
vs. wavelength will be displayed on the oscilloscope. This may be
plotted on the x-y recorder by typing "P", or the set of intensities
may be printed with the command "W". Plot time on the x-y recorder is
65 s and printing. timeon the high speed printer is 28 s. Also, the
data may be normalized so that the intensities are between 0 and 1023
for the 10-bit digital-to-analog converter. This routine, on an "A"
command, will divide or multiply the entire data buffer by 2 as many
times as necessary until the data points all have a magnitude of 1023
or less. The normalized data are stored in a separate data buffer
(number 1) and a further buffer (number 2) can be used to save ("S"
command) whichever data buffer is currently displayed. The buffer on
the display can be changed by the commands 0, 1 or 2 corresponding to
the data buffer of interest. The plot and print commands operate on the
buffer which is currently displayed.
When the operation is finished with the data from the current
scan, a scan from the present location can be achieved with commands
"C" (continue) followed by "G". The next 25.6 nm wavelength region will
then be scanned. Alternatively, the operation can begin the same scan
over again with "B" to rewind and "G". The rewind time is 1.3 s.
A "control R" command at any time will slew the monochromator to the
original starting wavelength (190.0 nm).
Because of the limited dynamic range of the DAC-display system,
the most useful results are obtained from printing the original results
(data buffer 0). If the display is normalized, then the ratio between
lines in the wavelength region is maintained, and this ratio can readily
be observed. The printed data may be corrected for off-wavelength
background and plotted in an intensity vs. concentration analytical curve.
Analytical Procedure with the SCSS System
Stock aqueous solutions of 1000 jig ml-1 of the metals listed in
Table 7 were prepared from reagent grade chemicals. Appropriate serial
4dilutions of the combination of elements shown in Table 7 were made in
the range 0.1 jg ml-1 to 100 g ml-1m
When the system was energized, the command was given to slew
rapidly to the starting wavelength for the particular element combination
as-given in Table 7. A blank solution deionizedd water) was aspirated,
-and the scan was initiated with the "G" command. After the scan was
complete, both a plot of fluorescence intensity vs. wavelength, and a
digital printout was requested. After this was accomplished, the
nxmoochromator was slewed back to the starting position, and a standard
-solution was aspirated; the intensity values were plotted and printed
each in turn. Three replicate analyses of each standard solution were
ELEMENTS ANALYZED BY THE SINGLE CHANNEL SCANNING
SPECTROMETER BY GROUPS WITH WAVELENGTH RANGE AND
RANGE (pg ml"')
Mn, Pb, Sn, Mg
performed. The printed results were used in the preparation of
analytical curves. The average, off-wavelength background was subtracted
from the peak intensity, and the average of the three replicates was
plotted vs. the concentration of the analyte.
Results and Discussion
Some of the results from the SCSS system are shown in Figures
15 to 20. In Figure 15 the background (obtained in 31 s) is given
for the wavelength range from 265.0 nm to 290.5 nm while aspirating
deionized water into the flame. In Figure 16, the spectrum is given
for 1 jug ml each of Zn and Cd. This figure shows the effect of
normalization on small peaks (of less than one-half full scale) as each
of the readings is multiplied until at least one spectral interval is
more than one-half full scale. In Figure 17, the AF spectrum for
10 jig ml each of Ni, Co and Fe is given. Five elements can be
w-easured in the wavelength range 265.0 nm to 290.5 nm as shown in
Figure 18; 30 pg ml- each of Au, Mn, Pb, Sn and Mg give discernable
signals with the SCSS-. The signals from Mn and Mg are extremely large
-t 30 jug ml" and they cannot be plotted on the same scale with Au, Pb
and Sn at this same concentration. Also, 1 jg ml-1 each of Cu and Ag
givealarge S/N ratios as seen in Figure 19. The resolution of this
-system is demonstrated in the slight separation of the 327.4 nm line
of Cu and the 328.1 nm strong line of Ag. The signal at approximately
336-um appears in the spectra in this region and has tentatively been
assigned to the molecular fluorescence of NH in the flame (58). Finally,
the Cr triplet and the resonance line of TI are shown at a concentration
of 1 jug ml in Figure 20. This figure has also been scale expanded by
a factor of 2 for clarity.
----- ISN31NI 3A1 V73
- 4- AISN31JI 3A11 V73&
-f AIISN31NI 3AII V73
---- AISNH31NI 3AJV73H
4- AIISN31NI 3AIIVY738I
- ,IAJISN31It 3AIl l73
The analytical working curves for the 14 elements studied with
the SCSS system are shown in Figure 21 and Figure 22. The shapes of
the curves are expected for AFS with a continuum source (59). The
curves for Pb (measured at 283.3 nm) and Sn (measured at 284.0 nm) do
not have the characteristic slope of 1, probably because of the strong
Influence of the Mg fluorescence (measured at 285.2 nm). The limits of
detection, defined as the concentration of analyte which would result
in a signal two times the rms noise on the background, for the 14
elements are listed in Table 8.
The background in the 230.0 nm to 255.6 nm wavelength region
was seen to contain significant flame fluorescence background (see
Figure 23). The effect of the background on elemental analysis in this
region is shown clearly in Figure 24, which gives the spectrum of
30 ug ml" each of Ni, Co and Fe. The molecular species involved in
this background is believed to be CO (58).
The S/N of any spectral interval of the SCSS should, according
to Chapter II, be independent, as far as the resolution and stray light
capability of the olptTcal system allows, of the signal in any other
spectral Interval. To check this premise, and as a comparison with the
HTS system, dissimilar concentrations of elements within a wavelength
scan were aspirated, and plots made of the intensity vs. wavelength.
In Figure 25, the lack of any interelement effects of a mixture of
10 jig ml"1 Zn plus 1 ug ml"1 Cd and a further mixture of 10 jug ml"
Zn and 0.3 jg ml"1 Cd is shown. The results for Cd are unchanged and
are also the same as if equal concentrations of Zn and Cd were used.
If 700 jag ml"1 Co is combined with 10 jpg ml1 each Fe and Ni, the Co
fluorescence lines are extremely intense (Figure 26) but, except for a
rise in the baseline, the Ni and Fe signals remain the same as when
C C 0
-- W S
SI I I -
( U t 1mO
(Scuno^3) 7VNWS 33N33S3,J~l73
LIMITS OF DETECTION (LOD'S) FOR THE ELEMENTS
ANALYZED BY THE SCSS SYSTEM
---- A ISN3JNI 3A I1V73BU
----- AJJSNM.Ll 3AUYT73
S o^ g
---- Al ISN31NI 3AIIV.73,
4--- U ISN31NI B3AIJY?3I
---- AIISN31NI 3AI YV73b
- AIISN31NI 3AII V73b
the concentrations of all three were the same. In Figure 27, 800 jug ml"'
TI has essentially no effect on the signal from 3 Jg ml- Cr. However,
100 pg mil Cu raised the background substantially in the vicinity of
the 327.4 nm Cu line and the 328.1 nm Ag line. Even here, as shown in
Figure 28, no effect on even the 328.1 nm Ag line is noticed if the
Increase in background is taken into account. It is apparent that,
within the limits of the dispersive system, no adverse effects of
spectral interference are noticed with the SCSS system.
COMPARISON OF MULTIPLEX AND SCANNING TECHNIQUES
The Hadamard transform spectrometer (HTS) and the single channel
scanning spectrometer (SCSS) share almost every hardware feature and the
design and construction of these two instruments is similar with respect
to time and costs. The HTS system does require a relatively expensive,
precision mask for coding the spectral interval intensities. Furthermore,
the multiplex method requires.some mask alignment precautions to assure
that the mask is in the correct optical position. Otherwise, the
complete systems are similar in operating characteristics. Because the
4TS system used a shorter dynamic range analog lock-in amplifier, it
mas necessary to change scales to obtain the optimum S/N benefit from
:the system. However, a photon counting system could eliminate the problem
4n the HTS system as it did in the SCSS.
Software considerations show that the HTS system software is
somewhat more complex than the SCSS software. Because some logical
functions and comparisons must be performed to determine the addition/
subtraction process and further decisions are necessary to complete the
final permutation of the stored values, so that a monotonically increasing
.spectrum results (see Chapter IV), the HTS software requires both
-moderate assembly programming effort and some time during the scan.
The SCSS, on the other hand, is essentially straightforward data
accumulation and stepping functions. In each case, the final data are
stored in digital form within the computer, and are available for
various filtering, integration or comparison purposes.
The wavelength range of the HTS is determined by the dimensions
of the mask and the dispersion of the grating. Likewise, the resolution
is limited to one point for each channel determined and in this study.
The wavelength range was about 25.0 nm with maximum resolution of about
0.1 nm per channel. If more than one wavelength region is to be
studied, the grating must be manually slewed from one region to the
next. Indeed, this function could be incorporated under computer
control, but this would involve more hardware and software considerations.
The SCSS is essentially limited only by computer memory storage
locations and in the present case more than 4000 data points could be
stored. The total number of points accumulated in a scan is software
controlled. Also, the resolution capabilities of the SCSS are limited
to 48 points per nm, a factor of about 4.8 more than with the HTS. The
number of points per nm is also under software control, and so, in the
SCSS, both the wavelength range and the resolution can be controlled by
From these considerations, it can be noted that the HTS system
is essentially a SCSS with a few more problems and complexities added
on and a little less versatility. The use of the multiplex HTS system
in the area of multielement atomic fluorescence analysis can only be
Justified if this method can improve on the sensitivity of rapid AFS
A comparison of the results of the two methods shown in
Chapters IV and V is probably best seen in the limits of detection (LOD's)
obtained for similar elements by the two methods. Because the analysis
time was almost the same for the two techniques, the ratiasof LOD's are
.good estimates of the S/N ratios of the analytical lines determined in
a multiplex compared to a single channel mode. The HTS resulted in
LOD's worse by a factor of 50 to 500 in the eight elements common to
the two systems as seen in Table 9. The other 6 elements, studied with
the SCSS, could not be determined with the HTS (except for TI which was
not attempted with the multiplex method) because the noise in the
multiplex method severely limited the sensitivity of that system.
Because the systems were designed to maintain as many similarities
-as possible as far as excitation source, flame cell, optics and
4monochromator speed are concerned, it may be assumed that instrumental
influence can account only for a factor of 2 to 5 in the S/N ratios of
the two systems. The S/N considerations, described in Chapter II,
expect at most a degradation of S/N by a factor of 0.7 in the HTS system
if the background is large, and only shot noise is considered. The last
part of Chapter II considers. the effect of proportional noise
(fluctuation or scintillation noise (52)) in multiplex.systems. It can
dteA determined that if the noise due to scatter from the flame
or wolecular fluorescence from the flame is the major source of noise
in the tfTS system used in this study, then the S/N ratio of the HTS
system may be degraded by as much as 16 (the square root of the increase
of the number of spectral intervals measured) when compared with the
-SCSS. This, combined with other small factors, may account for the
4-atios in the LOD's found in the two systems.
The increase in the intensities measured with a multiplex
method is fundamental in the expected increase in S/N. When this
increase in signal is enough to allow noise, proportional to a high
COMPARISON OF LIMITS OF DETECTION (LOD'S)
WITH THE HTS AND SCSS SYSTEMS.
background level, to prevail over the random, photon noise of lower
signal levels, then the multiplex method has serious disadvantages
compared with a single channel system. This seems to be the case with
multielement atomic fluorescence flame spectrometry.
It is appropriate to consider the premise that a wavelength
scan is actually necessary in multielement analysis. Measuring the
intensity at wavelengths where no analytical line can appear is
certainly a waste of analysis time (unless an off-wavelength intensity
is desired) which could be put to better use by increasing the
measurement time (and thereby the S/N ratio) at spectral intervals of
interest. Overcoming the analyst's preference for an intensity vs.
wavelength spectrum is of primary importance to rapid multielement
PROGRAMMED SLEW SPECTROMETER (PSS) SYSTEM
The conclusion of Chapter VI leads naturally to the suggestion
that analysis time can be reduced substantially if intensities are
measured only at the wavelengths of interest in multielement atomic
fluorescence. Such a programmable slewing system would rapidly and
accurately slew to specific wavelengths, make measurements for some
time and then slew to another wavelength. In this way, little time
would be wasted between spectral intervals of interest. The
signal-to-noise relationships for the single channel scanning spectrometer
would still hold for the individual spectral intervals. If the time
spent slewing to the wavelength is considerably shorter than the
measurement time, their S/N ratios can be increased by spending more
time with useful measurements. For the shot noise limited ce, the
S/N is proportional to the square root of the measurement time. Now, if
there are five spectral intervals of interest in a 25.0 nm wavelength
region and the slewing rate is 20 nm s1, the intensities at the five
wavelengths can be measured for 5 s each, and the total analysis time
would be.about 26 s. The S/N of each of the spectral intervals would
Increase by a factor of (5/0.1) or about 7, as compared to the
scanning system where the spectral intervals are measured for 0.1 s each.
The equipment for such a programmable monochromator is
completely contained in the single channel scanning spectrometer. The
computer is able to slew the grating at 20 nm s by use of the stepper
motor. All that is necessary is additional software for the computer.
Description of Software
An assembly language program was developed to accept a list of
elements from the teletype and convert these atomic symbols to stepper
motor steps necessary to slew from 190.0 nm to the analytical wavelength.
The element symbols can be typed in any order the computer sorts them
according to increasing wavelength. After the elements are specified,
the computer .asks if a background scan should be performed and if
desired the computer will store the background intensities at each
analytical wavelength while a blank solution is being aspirated. This
background will be subtracted during subsequent cycles. At each spectral
interval, the computer gathers the DATA, BACKGROUND, SUM and DIFFERENCE
for each chopper cycle (see Chapter V) and sums them individually for
255 chopper cycles (*about 5 s ). At that time, each of these readings
is printed out, with the atomic symbol of the element at that wavelength,
by a high speed printer. If a background had been stored, it is
subtracted before printing, and if no background subtraction is made,
a symbol is printed denoting that the reading is uncorrected. The
monochromator is slewed to the next spectral interval, and the process
is continued. Alternatively, a command will allow the computer to wait
at the wavelength and take more readings, continuing only on command
from the keyboard.
A separate routine is used in conjunction with a mercury penlight
for al Ignment of the monochromator/stepper/computer system. The penlight
is placed in the monochromator optical path and the slits are closed to
5 jim. On command, the computer slews the wavelength to within 5 nm of
the 253.7 nm line of mercury. It then scans rapidly until the intensity
reading reaches a peak and starts to fall off. The computer then
considers this point to be one step beyond the mercury line and proceeds
backwards until it has set the monochromator at exactly 190.0 nm. This
procedure takes only a few minutes and allows excellent alignment of
Analytical Procedure with the PSS System
A solution of 50 ug ml"1 each (and listed in Table 10) of the
elements analyzed by the SCSS was prepared from 1000 ug ml" stock
solutions. Silver was not included because AgCI precipitate was formed
by the reaction of Ag+ with the chloride from HCI used in preparing
stock solutions of some elements. Serial dilutions were prepared from
the mixture until the least concentrated solution contained 0.01 jg ml"1
of each element.
The programmed slew spectrometer (PSS) was initialized, the
source started and allowed to warm-up, the electronics energized and
the computer program was loaded and started. Before the analysis, an
alignment procedure, described in the previous section, was performed
with a mercury penlight. Then, the 13 elements were entered on the
keyboard and the analysis was begun.
A background run was stored while aspirating deionized water.
Then each of the standard solutions was aspirated, and the system slewed
the spectrometer, measured the intensities and printed the results for
each element of interest. Ten complete replicates of the above
procedure were done for the entire range of standards. The analysis
LIMITS OF DETECTION (LOD'S) WITH THE PSS
atmits of detection are measured in pg ml-1
time for each of the solutions was 86 s. The wavelengths used for each
of the elements of interest are listed in Table 10.
Results and Discussion
The printed results were analyzed and growth curves from the
averages of results are depicted in Figures 29 and 30. As expected,
the results are very similar to the results obtained for the SCSS with
some additional extension towards lower limits. The limits of detection
for the 13 elements are listed in Table 10.
The analysis time of 86 s represents a factor of 2 better than
If the SCSS were used to cover the wavelength range covered in the PSS.
(213.7 nm to 377.6 could be covered in 164 s at 1 nm s-1 with the SCSS.)
When the increase of sensitivity of about 7 is also considered, it can
be seen that the PSS is more than an order of magnitude better as far
as speed-sensitivity is concerned. If an intensity vs. wavelength
spectrum is not necessary then the PSS is the system of choice for
Normal precautions must be made with regard to spectral overlap
and precise background corrections. For example, the large signal from
Mg fluorescence at 285.2 nm affects the intensity observed for Sn at
284.0 nm and Pb at 283.3 nm. This is the probable cause of the non-unity
slope of the analytical curve observed in Figure 29 for Pb and in
Figure 30 for Sn. Alternative spectral lines should be considered if
this condition is evident in the real analytical situation. Also, it
may be more appropriate to sample an off-wavelength spectral interval
intensity rather than store a blank for the background correction.
These functions can be implemented with suitable software but have not
been considered in this study. The results for Au at 267.6 nm are
I l I I a.
(sjuno3) 7VN91S 33N33S3fOl7nd
somewhat poorer than the results obtained with the SCSS (2 ug ml vs.
1 ug ml-1 respectively). The mixture of elements, prepared for the
PSS, had some finely, divided metallic precipate after standing for a
-period and analysis of this precipate showed it to be Au. This type
of interference must be carefully avoided and a dedicated study of
multielement standard solution preparation is certainly needed.
The tabulated results, printed in digital form, are free from
operator bias and require no judgment as to baseline or peak values.
With further software refinements, it would be possible to have the
computer determine the analytical curves for each element of interest
and then calculate the concentrations of the elements in unknown
samples and present the results as a finished report. The assembly
language programming of this level of software sophistication is a
,matter best left to computer programmers.
COMPARISON OF THE THREE SYSTEMS
Three spectrometric systems have been constructed and evaluated
for the purpose of achieving rapid analysis of multielement samples.
In each case, the best equipment available was used for the construction.
This procedure resulted in the best possible devices, but unfortunately,
disallowed an accurate comparison of the techniques on their own merits.
Nevertheless, the experimental results lead to several conclusions.
First, Hadamard transform spectrometry in the UV-visible region is
very sensitive to the high backgrounds found in flame spectrometry and
to the time-varying fluctuations in the background. The single channel
scanning spectrometer and programmed slew spectrometer systems are not
as sensitive to this type of signal fluctuation, because only one channel
and one Instant in:time is used in the latter systems. Second, if HTS
systems are to function with the theoretical advantage in thb f"-visible
region, then every effort should be made to keep the background as low
as possible, and also the dynamic range and response of the detector
should be as large and as fast as is possible* The photon counting
system used in the SCSS would probably make an ideal detector for a
future HTS system. Finally, and most important, is the consideration of
the necessity of a wavelength scan. If a scan is not necessary, then a
system of slewing, stopping and measuring is more appropriate and
versatile than the SCSS for multielement atomic analysis. This approach
is only an extension of the original procedure of sequential analysis;
but with the same type of equipment as used in the scanning methods, it
is possible to devise a system which will determine elemental concentrations
at any desired wavelength and in less time than would be spent scanning
over informationless spectral regions. The limits of detection found
for the three systems studied in this work are tabulated in Table 11.
It is readily apparent that the PSS is faster and more sensitive than
either the HTS or the SCSS. The S/N relationships can even be programmed
so that the measurement phase of the cycle is a time-dependent function
of the counting rate. This would allow for more time to be spent
measuring low level signals while less time could be spent where the
signal level is high. Because of the versatility in wavelength
selection and S/N relationships, this slewing system is undoubtedly
Vhe most useful multielement measurement system available at the
LIMITS OF DETECTIONa (LOD'S)
FOR.THE THREE SYSTEMS STUDIED
IN THIS WORK
The limit of detection is defined as the concentration of
analyte which gives a signal twice the rms noise observed
when a blank is measured.
The PSS is two times faster than the HTS or the SCSS.
AVERAGE SIGNAL-TO-NOISE RATIOS
FOR THE UV-VISIBLE SPECTRAL REGION (39).
The Fellgett advantage (F is the gain in signal-to-noise (S/N)
ratio for equal analysis time) applies over the entire spectral region
of interest when a multiplex method is compared with a single channel
(SC) method in the IR spectral region. Consider the specific case of
4Hadamard transform spectrometry (HTS) measuring N spectral intervals
in T s analysis time. Each of the spectral interval intensities is
measured for one-half the total analysis time,e.g., T/2 s. A scanning
system measures each spectral interval for T/N s. Therefore, the
increase in measurement time for the HTS case is (T/2)/(T/N) = N/2.
For a signal with only random errors (as compared with systematic errors)
.an increase in measuring time is the same as an increase in the number
of independent measuring samples. The accuracy of such independent
-4mesurements is increased by the square root of the ratio of the
measurement times for the HTS and SC systems e.g., (N/2).
In-the IR region,the increase in precision is due to the fact
that the major source of noise is in the detector and is completely
independent of the signal level. At each spectral interval, there is
n-average gain in S/N of (N/2)2 in the HTS compared to the SC. In the
t~-visible region, low noise photomultipliers are used, and the major