A procedure and structural-correction diagrams for increasing the accuracy of analytical instruments are

considered.

Key words: analytical instruments, procedure and structural correction diagrams, increase in accuracy.

The development of new technologies, the diversification of the economy, modernization of traditional technological

systems, the complexity of monitored technological and natural media, and difficult and often extreme operating conditions

raise new problems in the development of analytical instrument construction and require new approaches to ensure the relia-

bility and invariance of the results of measurements.

The basic problem of analytical measurements is to determine the concentration (quantity) of dissolved or suspend-

ed material with a specified accuracy. When monitoring technological and natural liquid media, this determination is carried

out in laboratories using measurement procedures, in automatic online mode using analytical instruments, built in to techno-

logical lines, or even in a complex way. Automatic monitoring is the most modern, and the values of the concentration of

material obtained in this way are often the basic primary information for controlling processes, ensuring the quality and safe-

ty of production, systems functioning, and protecting the environment. When making analytical measurements, particularly

automatically, the most important problem is to ensure the required accuracy of the results of the measurements under pro-

longed use without the participation of an operator, when there are various destabilizing factors present.

For automatic analytical instruments, interference due to fluctuations of the parameters of the various parts of the

instruments (F1), the media being monitored (F2), and external conditions (F3) is the most significant. The interferences F1,

F2, and F3 depend on various influencing factors, namely:

1) internal noise of the circuit and structural components, contamination, modes of operation and length of service,

external conditions, etc.;

2) the quality of the raw material, including the composition and concentration of impurities, the parameters of the

technological process etc. (they manifest themselves as noninformative parameters); and

3) variations of the ambient temperature, pressure, humidity, the voltage and frequency of the supply and mechani-

cal effects.

Taking the effect of interference into account, the static characteristic of an instrument has the form

Y = ƒ(X, F1, F2, F3),

where X and Y are the input and output quantities.

Measurement Techniques, Vol. 52, No. 10, 2009

A METHOD OF INCREASING THE ACCURACY

OF ANALYTICAL INSTRUMENTS BY

STRUCTURAL CORRECTION

PHYSICOCHEMICAL MEASUREMENTS

M. A. Karabegov UDC 621.753.1

Central Research Institute of Machine Construction Technology, Moscow, Russia; e-mail: karabegov@rambler.ru.

Translated from Izmeritel’naya Tekhnika, No. 10, pp. 68–72, October, 2009. Original article submitted May 7, 2009.

0543-1972/09/5210-1126 ©2009 Springer Science+Business Media, Inc.1126

There is a variety of analytical measuring problems which can be differentiated depending on the composition, the

state and other parameters of the media being monitored and the influencing factors. In general, the result of a measure Y is

produced under the action of the above-mentioned forms of interference, in which case additive and multiplicative errors

arise. Invariance to the effect of interference is obtained by using different methods and algorithms for automatic correction,

among which, in continuous automatic measurements, the structural correction method is one of the most effective.

The procedural basis of structural correction is the basic propositions of the structural analysis of measuring cir-

cuits, obtained using logical constructions, mathematical models and algorithms of the structural circuits. The principle of

“two-channel” measurements, widely used when a correction channel is formed in the circuit of the analytical instruments,

the signal of which Yc and the informative signal Yi are converted by a special algorithm, forming the output signal Y,

which is invariant to the effect of interference, is considered. Multichannel, compensation, feedback, etc., measuring cir-

cuits are also used.

In the “two-channel” scheme, information may be contained in the correction signal Yc, which is generated by a

deterministic value of the measured quantity X1 and the interferences F1, F2, and F3 or solely by these forms of interference:

Yc = ƒ(X1)ƒ(F1, F2, F3) or Yc = ƒ(F1, F2, F3).

The informative signal Yi includes information obtained by converting the measured quantity X and the interferences

F1, F2, and F3:

Yi = ƒ(X)ƒ(F1, F2, F3).

The output signal of the instrument represents the result of a conversion of Yi and Yc using the algorithms of sub-

traction, division and other processes, which enable the effect of different kinds of interference to be eliminated (minimized)

and enable a result of the measurement Y to be obtained that is invariant to them:

Y = F(Yi, Yc) = ƒ(X).

The circuits of analytical devices, in which structural correction is carried out, include sections based on electron-

ic-logic components, physical and physicochemical and other modules, depending on the physical principle on which the

instrument is based. The main requirement imposed on the construction of a correction channel is maximum saturation of

the channel with information on the interferences F1, F2, and F3, according to the conversion algorithm. The principal prob-

lem when constructing a structural-correction circuit is to ensure complex optimization of the structural circuit, the infor-

mative and correction channels and the conversion algorithm. The solution must correspond to the requirements of the

cost–efficiency criterion. Below we present automatic analyzer systems in which structural correction is obtained.

An automatic analyzer for measuring radiation absorption based on the Bouguer–Lambert–Beer law, solves

the problem of determining the concentration of a substance x, which is in a solvent r, the parameters of which vary due to

the presence in it of a residue from previous measurements of the material x, the concentration of which also changes. The

problem of structural correction, under continuous conditions, eliminates the effect of the varying parameters of the solvent

on the results of the measurements. The basis of the solution is a double-beam arrangement with modulation of the radiation,

formed using two flow cells, each of which includes a basic and additional cavity with the same optical bases l1 and l2 [1].

The first cell is situated in the informative channel while the second is placed in the correction channel, and they are con-

nected by liquid-flow devices.

The solvent r with the material x to be determined flows through the cavity l1 of the first cell and l2 of the second

cell, but only the solvent r flows through the cavity l1 of the second cell and l2 of the first cell. The solvent contains a certain

material x, which is the residue from previous measurements. Radiations of intensities I1 and I2, passing through the main

additional cavity of the first and second cells, is incident on a photoreceiver:

I I I Ixl

rl

rl

xl

rl

rl

1 0 2 01 1 2 2 2 1= =τ τ τ τ τ τ τ τ τ τ τ τ τ τ τ τopt g con con g opt g con con g; ,

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where I0 is the initial intensity of the radiation; τopt, τg, and τcon are the transmission coefficients of the optical components,

the glass of the cells and the contamination of the inner surfaces of the cell glass; and τx and τr are the transmission coeffi-

cients of the material to be determined x and of the solvent r.

The output signals of the photoreceiver y1 and y2, which are proportional to the values of I1 and I2, enter the mea-

suring instrument, which operates using a division algorithm. Its output signal is

where K is a coefficient of proportionality.

The output signal is a function of the transmission coefficient (the concentration) of the substance x to be determined,

the constant constructional parameters of the instrument l1 and l2 and is invariant to any changes in the parameters of the sol-

vent with the residual material, the radiation intensity, the contamination of the optical components and the glass of the cells,

and low-frequency fluctuations of the parameters of the various sections of the instrument.

Structural correction eliminates the effect of the composition of the samples (chemical impurities) when measuring

the concentration of elements using atomic-absorption spectrometers. This is particularly important when determining the

microconcentrations of elements, for example, less than 10–6%, in media of complex chemical composition – sewage waters,

run-offs from soils, and geological, hydrometallurgical, biological and other technological and natural samples. Highly sen-

sitive atomic-absorption determinations are carried out using an intensive electrothermal atomization method. Chemical

impurities are not atomized and their effect manifests itself in the form of an additional “nonatomic” absorption, which is one

of the main components of the error of this form of measurement.

In atomic-absorption spectrometers, any invariance to the effect of impurities is solved using double-beam (λ1, λ2)

optical arrangements, where λ1 is the spectral resonance line of the informative channel and λ2 is the wide spectral line of

the correction channel. Atoms of a specific element only absorb the radiation λ1, and the chemical impurities absorb radia-

tion at λ1 and λ2. For the λ1 channel, the main radiators are hollow-cathode lamps, while for channel λ2 deuterium radiators

are often used. In contrAA (Analytik Jena) spectrometers, a high-pressure continuous-spectrum xenon lamp and a high-res-

olution monochromator, which separates the λ1 and λ2 lines, are used.

A structural correction system based on the Zeeman effect – the phenomenon of the splitting of spectral lines in a

magnetic field – is effective. In the electrothermal atomic-absorption spectrometer, alternating-current electromagnets are

placed in the atomizer zone – a graphite tube. In their magnetic field, the resonance spectral lines λ1 are split into compo-

nents, equally spaced from the unsplit absorption line. As the magnetic induction E is increased the splitting increases and

the atomic absorption uat decreases. For the amplitude (maximum) value of the magnetic induction, the atomic absorption

approaches zero:

Nonatomic absorption is independent of the magnetic induction (of the line splitting): unonat → const. For zero E0and an amplitude Emax of the values of the magnetic induction, the following signals are generated

where k1, k2, and k3 are coefficients of proportionality.

The algorithm for the generation of the output signal has the form

where k4 is a generalized coefficient of proportionality.

Hence, in a simple single-beam atomic-absorption spectrometer two-beam measurements are carried out, and the output

signal depends on the absorption of the radiation by the atoms of the element being determined and their concentration, and in

this way one obtains invariance to the effect of nonatomic absorption and low-frequency fluctuations of the circuit components.

Y Y Y k u k u k u k uE E= − = + − =0 1 2 3 4max

,at nonat nonat at

Y k u k u Y k uE E0 1 2 3= + =at nonat nonat; ,max

E E u→ → →max, , .λ λ1 2 0at

Y y y K xl l= = −

1 21 2/ ,τ

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Differential-prism type automatic refractometers with a flow cell are widely used for the continuous monitoring

of technical liquids [2]. The cell consists of two cavities: one with a flow volume of 8–10 cm3, through which the monitored

liquid with a refractive index nx flows, and a closed volume of 2–5 cm3, filled with a comparison liquid with known refrac-

tive index ncom. The closed cavity is placed inside the flow and is immersed in the flowing liquid being monitored. A change

in the determined concentration of the liquid being monitored is related to the change in its refractive index. When nx ≠ ncom,

the beam emerging from the cell is deflected by an angle β, proportional to the difference ∆n = nx – ncom, and the result of

the measurement isY = ƒ1(α1, ∆n) = ƒ2(α2, β),

where α1 and α2 are the refracting angles of the flow and closed cavities.

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Fig. 1. Sketch of an automatic refractometer with a difference cell with two closed

cavities: 1) radiation source; 2, 5) slits; 3, 4) mirrors; 6) difference cell with two

closed cavities; 7, 14) photoreceivers; 8–13) amplifiers; 9) adder; 10) recorder;

11) correcting section; 12) subtracter.

Fig. 2. Sketch of the automatic refractometer with beam reversal: 1) radiator; 2) condenser

lens; 3) adjusting slit; 4) objective lens; 5, 10, 11, 15) mirrors; 6, 7) the difference cell;

8, 9) plane-parallel glass plates; 12) shaded optical wedge; 13) Dove prism; 14, 17) photore-

ceivers; 16) separating prism; 18) amplifier; 19) recorder.

The geometry of the cavities and the positioning of the closed cavity inside the flow facilitate the formation of the

angles of deflection of the exit beam for a specified sensitiviy and the establishment of thermal balance between the liquids.

When the temperature of the liquid being monitored changes, its refractive index changes, the temperature and refractive

index of the comparison liquid in the closed cavity also changes, with a certain inertia, and an error ε occurs.

The problem of structural correction – the minimization of the error ε – is solved using a double-beam arrangement,

in which the informative and correction channels are formed using different cells with two independent closed cavities with

different volumes of the comparison liquid and a common flow cavity for the liquid being monitored (Fig. 1).

When the temperature θ of the liquid being monitored changes, heat exchange with the comparison liquid in the

closed cavity of the cell occurs with an inertia, and the following dynamic error occurs:

εθ(p) = [bT0(p) /Tcom(p) + 1)(Tx(p) + 1)]θ(p),

where p is the Laplace operator, Tcom and Tx are the time constants of the closed and flow cavities with the comparison liq-

uid and with the liquid being monitored, and b is the temperature gradient of the refractive index of the monitored liquid.

When θ changes due to the difference in the masses and rates of equalization of the temperatures of the comparison

liquids in the informative and correction channels, signals yθ1 and yθ2 are generated, the difference between which is

described by the function

yθ(p) = k1[yθ1(p) – yθ2(p)] = [k1bp(Tcom1 – Tcom2)/(Tx(p) + 1)(Tcom1(p) + 1)(Tcom2(p) + 1)]θ(p),

where k1 is a coefficient of proportionality.

The result of a measurement, proportional to the value of the measured refractive index and invariant to a change in

the temperature of the monitored liquid, is formed in accordance with the algorithm

Y(p) = εθ(p) /yθ(p).

In the automatic refractometer arrangement (Fig. 2), the low-frequency drift of the output signal, which mani-

fests itself in the form of an error in the values of the measured quantity, is compensated. The problem is solved using a

double-beam arrangement with an informative channel containing components of the arrangement and the cell, and a cor-

rection channel, formed when part of the beam before the cell is separated out. The channel correction beam then passes

through the components of the system and a Dove prism, in which it is turned through 180°, and the other components of

the system and is then combined with the informative-channel beam. The correction channel is not connected with the cell

– its signal is a function of the interference.

When the beam in the correction channel is turned through 180°, the vectors of the informative and correction sig-

nals become opposite in sign. The conversion algorithm with signal subtraction generates an output signal proportional to the

value of the measured refractive index, and eliminates low-frequency drift of the instrument readings:

Y = k1(∆x∆n + ∆xint) – k2∆xint = k1 + (k1 – k2)∆xint or Y = k∆n,

where ∆x∆n and ∆xint are the deflections of the beam due to the difference ∆n and the interference, respectively, and k1 and k2are conversion coefficients; when channel regulation is obtained k1 = k2 = k.

Structural correction is obtained in an automatic organic analyzer of materials in stagnant and natural waters

(Fig. 3). The operating principle of the instrument is based on the heating and evaporation of the water, separation of the

gaseous carbon dioxide and a determination of the carbon concentration by an optical-acoustic analyzer. Carbon dioxide is

liberated when organic and inorganic materials, situated in water, are burnt. The purpose of the instrument is to determine the

concentration of organic materials in water, and hence the informative parameter is the concentration of carbon liberated

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when only organic materials are burnt (“organic carbon”). The structural correction problem is to eliminate the effect of “inor-

ganic carbon” on the result of a measurement.

A sample of water is selected, poured into combustion tubes filled with catalysts, and evaporated and oxidized to

carbon dioxide. The total carbon from organic and inorganic materials xΣC is oxidized in the high-temperature tube at

950–1000°C, producing the informative signal. In the low-temperature tube (at 140–180°C), only the carbon from the inor-

ganic materials xnonorg is oxidized, producing a correction signal. The products of the reactions xΣC and xnonorg in gaseous

form are fed into the measuring instrument, which is basically a two-channel optical-acoustic gas analyzer. Here they are con-

verted into proportional electric signals, and, using the subtraction algorithm, an output signal Yx is generated proportional to

the content of organic materials in the water xorg, invariant to the content of inorganic materials:

Yx = ƒ(xΣC) – ƒ(xnonorg) = ƒ(xorg).

For spectrum analyzers, operating in the flame-emission mode, the structural-correction problem is to ensure that

the results of measurements are invariant to the effect of low-frequency fluctuations (instability) of the flame – the emission

source. This interference is fundamental in determining the quality of the measurements. The problem is solved using a two-

beam system (Fig. 4), in which the emission signals are formed from two flame zones – a main high-temperature and a sub-

sidiary zone [3]. The flame temperature is different along its height. The signal strength of the emission from the sample with

a certain material also varies along the height of the flame and will be greatest in the zone of maximum flame temperature.

This zone is used to form the informative emission signal. The emission signal for correction is formed from the same sam-

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Fig. 3. System for analyzing organic materials in water: 1) gas-carrier preparation device (6 – tank with oxygen;

7, 9, 10 – manometers; 8 – reduction gear; 11, 12 – valves; 13, 14 – rotameters); 2) synchronous sample feed

device (15, 16 – pulsed dosers; 17 – sample intake; 18 – programmed regulator); 3) burner (19, 20 – high- and

low-temperature combustion tubes; 21, 22 – heating ovens; 23, 24 – temperature regulators; 25, 26 – coolers),

4) external recorder; 5) measuring instrument based on a two-channel optical-acoustic gas analayzer (27 – primary

converters; 28 – amplifier; 29 – integrator; 30, 31 – indicator and a recorder).

ple in another (subsidiary) flame zone and differs from the informative signal in its intensity. At the same time, fluctuations

of the flame (instability) are practically independent of the flame zone.

The liquid being monitored, in the form of an aerosol, is introduced into the burner flame 1, the material to be deter-

mined is atomized, and radiation is emitted. The radiation passes through an aperture in the opaque screen 2, the lens 3, the

shutter 4 and the interference filter 5 and is incident on the photoreceiver 6 (see Fig. 4). The opaque screen 2 is constructed

in the form of two movable plates with openings, superimposed on one another, which act as regulated diaphragms.

The radiation passing through the opening is intercepted by the shutter 4 and converted into pulses. Electric pulses

U1 and U2, corresponding to pulses of radiation which have passed through the aperture in the screen, appear at the output

of the photoreceiver. These pulses are given by

U1 = k0k1I(h1)τ(λ)k3Cx + a; U2 = k0k2I(h2)τ(λ)k3Cx + a,

where k0 is a coefficient characterizing the gas in the flame, k1 and k2 are coefficients characterizing the temperature zones

of the flame at heights h1 and h2 from the plane of emission of the gases from the burner, I(h1) and I(h2) are the intensities

of the emission signals in zones h1 and h2, τ(λ) is the spectral characteristic coefficient of the interference filter, k3 is a coef-

ficient of proportionality, Cx is the concentration of the element being determined, and a are flame fluctuation parameters.

The signals U1 and U2 are converted in the measuring instrument 7 using the subtraction algorithm and an output

signal Y is generated proportional to the concentration of the element being determined and invariant to flame fluctuations:

Y = U1 – U2 = k0τ(λ)[k1I(h1) – k2I(h2)]k3Cx = k4Cx,

where k4 is a coefficient of proportionality, determined by calibration.

The results of optical monitoring of the particle size and numerical density of metal, silicate, organic and other par-

ticles of different origin suspended in the liquid often depend on the light-scattering properties, i.e., on the nature of the par-

ticles. The problem of structural correction is to ensure that the results of measurement are invariant to the effect of these

properties and is solved using a two-channel photometric-counter particle-size analyzer. Each of the channels contains a

radiator with a photoreceiver and forms a recording zone [4]. The recording zone of the second channel is spaced a distance

equal to the maximum particle size from the zone of the first channel. A flowing glass capillary cell of square cross section

is used. The recorder is a two-channel signal analyzer, the signals of which are correlated with the time pulses characteriz-

ing the passage of particles through the recording zone.

The velocity of motion v and the size d of the particles are related to the signal lengths and geometrical parameters

of the recording zones as follows:

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Fig. 4. Sketch of the flame analyzer with emission signals from two flame

zones: 1) atomizer-burner; 2) opaque screen with apertures; 3) lens; 4) shutter;

5) interference filter; 6) photoreceiver; 7) measuring instrument.

v = L / t; d = τv – l = τL / t ~ l,

where L is the distance between the first and second recording zones, t is the time interval between the leading edges of the

electric pulses, generated by particles during the motion when they intersect the first and second recording zones, τ is the

length of the electric signal at the output of the first-channel photoreceiver, and l is the length of the first recording zone.

The liquid being monitored flows through the flow cell. When particles intersect the recording zone, optical pulses

are formed which are fed to the photoreceiver channels. Quasi-trapezoidal electric pulses are generated at the photoreceiver

outputs, the time relations between which contain information on the velocity of motion and size of the particles. The infor-

mative parameter of the particle size is generated by converting the electric pulses, functionally related to the time pulses,

representing when a particle intersects the recording zone in the cell of the instrument. Hence, the output signal of the ana-

lyzer is a function proportional to the particle size and invariant to the light-scattering properties of the particles:

Y = ƒ(d) = C1τ / t – C2,

where C1 and C2 are constant quantities, proportional to the constructional parameters of the instrument (C1 = L and C2 = l).

The equipment and the algorithm for structural correction, obtained in the photometric-counter analyzer, enable one

to carry out particle-size monitoring of different dispersed systems, irrespective of their light-scattering properties and, cor-

respondingly, of the nature of the particles.

Structural correction is an effective method of increasing the accuracy of automatic analytical instruments and guar-

antees that their readings are invariant to the effect of instrument parameter fluctuations, the media being monitored, the

external conditions and other interference.

REFERENCES

1. M. A. Karabegov, “Algorithms and structural systems of liquid-media spectrophotometer analyzers,” Pribory,

No. 11, 66 (2006).

2. M. A. Karabegov, “Automatic differential prism refractometers for monitoring process liquids,” Izmer. Tekhn., No. 6,

31 (2007); Measur. Techn., 50, No. 6, 619 (2007).

3. M. A. Karabegov, G. Ya. Bragin, Yu. M. Sadagov, S. A. Khurshudyan, and D. A. Kodalashvili, Inventor’s Certificate

No. 1067417 SSSR, Otkr., Izobret., No. 2 (1984).

4. M. A. Karabegov, “Monitoring of the particle sizes of dispersed liquids,” Izmer. Tekhn., No. 7, 67 (2008); Measur.

Techn., 51, No. 7, 802 (2008).

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