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A liquid refractometer based on a digital autocollimator is described. The results of an investigation, estimates of the errors in measuring the refractive index of liquids, and an example of its use to determine the concentration of aqueous solutions of sodium chloride are presented. Key words: digital autocollimator, refractometer, refractive index, concentration of a solution. Refractometric methods of investigating the composition and properties of chemical materials are widely used in different areas of industry. Recently, these methods have been used to determine the composition and properties of solutions in the technological lines for purifying and synthesizing different types of materials. To carry out these investigations, labo- ratory refractometers are employed, as well as automatic industrial continuous-flow refractometers, which, as regards the accuracy of measurements of refractive index (refractive-index differences), are not always suitable to the problem in hand. For high-accuracy measurements, interference refractometers have been developed and introduced into chemical production [1, 2]. However, these technical and constructive solutions (the complex construction and the difficulties involved in making measurements, requiring highly qualified personnel) limit the practical possibilities of these refractometers and make it dif- ficult to employ them in industrial analytical laboratories, as well as in the technological production lines for the constant monitoring of chemical processes. Below we propose a refractometer with a differential cuvette, in which the angle of refrac- tion of a light beam from a system of two adjacent prisms, filled with liquids with different refractive indices, is measured. High accuracy in measuring the angle of refraction is achieved using a recently developed [3] digital autocollimation system. The optical arrangement of the instrument is shown in Fig. 1. An optical marker 7, in the form of cross wires, is illuminated using a light-emitting diode 9 and a condenser lens 8. By means of a beam-splitting cube 5 and an objective 4, these cross wires are projected onto a differential cuvette 2. The light beam is incident normally on the input face of a liq- uid prism with a refractive index N, is refracted at the interface of the prism and traverses the liquid with refractive index n. Then, at the exit face of the prism it is once again refracted and, on being reflected from the plane mirror 1, again passes through the cuvette 2. Using the objective lens 4 of the autocollimator 3, the beam is projected onto the light-sensitive area of the charge-coupled device chamber 10, which is placed in the focal plane of the objective lens. The signals from the charge-coupled device chamber are applied to the input of the plate of a video pickup, con- nected to a personal computer. Further processing of the signals is carried out in the personal computer using a specially developed program. The angle of refraction of the beam is determined by the digital autocollimator, using the relation 2β = arctan X /ƒ, (1) where ƒ is the focal length of the objective lens, and X is the coordinate of the center of the image of the marker. Measurement Techniques, Vol. 49, No. 8, 2006 A LIQUID AUTOCOLLIMATION REFRACTOMETER OPTOPHYSICAL MEASUREMENTS V. L. Shur, A. S. Naidenov, A. Ya. Lukin, and G. I. Leibengardt UDC 535.32 Mendeleev All-Russia Metrology Research Institute; e-mail: [email protected]. Translated from Izmeritel’naya Tekhnika, No. 8, pp. 50–53, August, 2006. Original article submitted February 22, 2006. 0543-1972/06/4908-0815 © 2006 Springer Science+Business Media, Inc. 815

A liquid autocollimation refractometer

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A liquid refractometer based on a digital autocollimator is described. The results of an investigation,

estimates of the errors in measuring the refractive index of liquids, and an example of its use to determine

the concentration of aqueous solutions of sodium chloride are presented.

Key words: digital autocollimator, refractometer, refractive index, concentration of a solution.

Refractometric methods of investigating the composition and properties of chemical materials are widely used in

different areas of industry. Recently, these methods have been used to determine the composition and properties of solutions

in the technological lines for purifying and synthesizing different types of materials. To carry out these investigations, labo-

ratory refractometers are employed, as well as automatic industrial continuous-flow refractometers, which, as regards the

accuracy of measurements of refractive index (refractive-index differences), are not always suitable to the problem in hand.

For high-accuracy measurements, interference refractometers have been developed and introduced into chemical production

[1, 2]. However, these technical and constructive solutions (the complex construction and the difficulties involved in making

measurements, requiring highly qualified personnel) limit the practical possibilities of these refractometers and make it dif-

ficult to employ them in industrial analytical laboratories, as well as in the technological production lines for the constant

monitoring of chemical processes. Below we propose a refractometer with a differential cuvette, in which the angle of refrac-

tion of a light beam from a system of two adjacent prisms, filled with liquids with different refractive indices, is measured.

High accuracy in measuring the angle of refraction is achieved using a recently developed [3] digital autocollimation system.

The optical arrangement of the instrument is shown in Fig. 1. An optical marker 7, in the form of cross wires, is

illuminated using a light-emitting diode 9 and a condenser lens 8. By means of a beam-splitting cube 5 and an objective 4,

these cross wires are projected onto a differential cuvette 2. The light beam is incident normally on the input face of a liq-

uid prism with a refractive index N, is refracted at the interface of the prism and traverses the liquid with refractive index n.

Then, at the exit face of the prism it is once again refracted and, on being reflected from the plane mirror 1, again passes

through the cuvette 2. Using the objective lens 4 of the autocollimator 3, the beam is projected onto the light-sensitive area

of the charge-coupled device chamber 10, which is placed in the focal plane of the objective lens.

The signals from the charge-coupled device chamber are applied to the input of the plate of a video pickup, con-

nected to a personal computer. Further processing of the signals is carried out in the personal computer using a specially

developed program.

The angle of refraction of the beam is determined by the digital autocollimator, using the relation

2β = arctanX /ƒ, (1)

where ƒ is the focal length of the objective lens, and X is the coordinate of the center of the image of the marker.

Measurement Techniques, Vol. 49, No. 8, 2006

A LIQUID AUTOCOLLIMATION REFRACTOMETER

OPTOPHYSICAL MEASUREMENTS

V. L. Shur, A. S. Naidenov, A. Ya. Lukin,and G. I. Leibengardt

UDC 535.32

Mendeleev All-Russia Metrology Research Institute; e-mail: [email protected]. Translated from Izmeritel’naya

Tekhnika, No. 8, pp. 50–53, August, 2006. Original article submitted February 22, 2006.

0543-1972/06/4908-0815 ©2006 Springer Science+Business Media, Inc. 815

The refractive index of the liquid n is calculated from the well-known relations [1] (Fig. 2):

sinα1/sinα = N /n; n /na = sinβ /sin(α1 – α), (2)

where N is the refractive index of a standard liquid; na is the refractive index of the air during the measurements; α is the

angle of incidence of the beam onto the boundary of the liquid media; α1 is the angle of refraction of the beam in a medium

with refractive index n; and β is the angle of refraction of the beam on emerging from the cuvette.

Hence, by measuring the angle of refraction β using the differential cuvette, one can calculate the refractive index

of the liquid N using relation (2).

When measurements are made over a long period, zero drift of the instrument occurs, due, for example, to drift of

the coordinate system of the charge-coupled device matrix, which considerably reduces the accuracy with which n can be

measured. In this case, it is better to use a differential cuvette, in two of the three parts of which there is a reference liquid

(see Fig. 2b).

If one alternately switches the left and right parts of the cuvette, one can periodically “zero” and make measurements

of n with respect to a new zero. Moreover, one can determine and take into account the constant error which arises due to

residual aberrations of the objective lens and focusing inaccuracy (in this case, all parts of the cuvette are filled with the stan-

dard liquid).

In view of the fact that the refractive index of the liquid depends on the temperature, the instrument is supplied with

a system for measuring it, which consists of a platinum resistance thermometer and an electronic unit with a microprocessor

and a digital display. The platinum resistance thermometer is calibrated against standard thermometric equipment, and the

calibration equation is written into the memory of the microprocessor. The error in measruing the temperature does not

exceed 0.02°C. The value of the temperature is automatically transmitted to the computer with the aim of converting the mea-

sured value of the refractive index to 20°C.

We developed a computer program with the following capabilities to aid the functioning and investigation of the

refractometer:

• visualization of the image of the cross wires and of the measuring fields, control of the parameters of the image of

the cross wires – contrast and brightness – and its additional filtering;

• control of the parameters of the storage and computation cycles;

• calculation of the X (and also the Y) coordinate of the centers of the cross wires and the center of the cross. Here

we used the method of sections based on gradations of the brightness of the image with a determination of the cen-

ter of gravity of the darkness profile of the lines and of the error in measuring the coordinate;

• calculation of the refractive index (the difference in the refractive indices) and the standard uncertainty of a mea-

surement;

• storage of the results of a measurement and the copying of these measurements into other programs, for example,

MS Exel for constructing graphs, etc.

816

1 2 4 5 10

6 7 8 9

3

Fig. 1. Optical arrangement of the instrument: 1) reflector; 2) differential

cuvette; 3) digital autocollimator; 4) objective lens; 5) beam-splitting

cube; 6) mirror; 7) marker; 8) condenser lens; 9) light-emitting diode;

10) charge-coupled device chamber.

The program has three windows: Start, Measurement, and Protocol, successive switching between which is carried

out using appropriate knobs on the display.

The Start window is designed for inputting the initial data and for choosing the standard liquid and the liquid being

measured from the drop-down lists. In the Measurement mode the program takes averaged readouts of the angles of refrac-

tion and calculates the values of the refractive index and the concentration of the solution.

The Protocol window is the concluding part of the program. The protocol can be printed or stored on the disc of the

personal computer in the form of a test file, and can also be imported into MS Word or MS Exel.

Before starting a measurement, the zero of the instrument is set. To do this, both sections of the cuvette are filled

with a standard liquid, for example, distilled water, and the coordinates of the light marker are measured. The Calibration

button is then pressed to set the zero reading.

The refractometer is calibrated for the value of the refractive index using an aqueous solution of sucrose, as recom-

mended by international organizations, and the readings of the refractive index are written in a table of reference data, tak-

ing into account the dispersion correction for the wavelength of the light-emitting diode. In the calibration, the values of the

constructive parameters of the liquid cuvette, including the partition angle α in the cuvette (see Fig. 2a) are refined and the

program for calculating the result of measurements for this instrument is corrected. Moreover, for a more accurate determi-

nation of the concentration of solution one can calibrate the instrument against a solution of known concentration, in which

case the value of N is recorded and used to calculate the concentrations of the solutions being analyzed.

Using this instrument, we measured the refractive indices of solutions of sodium chloride with concentrations of

0.01, 0.1, and 1 g/100 ml.

Below we present the protocol for measuring the refractive index and concentration of a solution of 0.1 g/100 ml.

Protocol of the Measurement of Refractive Index and ConcentrationLiquid investigated: aqueous solution of sodium chloride

Standard liquid: distilled water

Date of measurement: November 3, 2005

Values of the refractive index reduced to 20°C

Measurement results:

Temperature, °C Angle, ″ Refractive index

1. 20.125 25.95 1.3322481

2. 20.145 25.93 1.3322480

3. 20.150 26.10 1.3322490

4. 20.150 26.30 1.3322502

5. 20.160 26.16 1.3322494

6. 20.160 26.13 1.3322492

7. 20.170 26.27 1.3322501

8. 20.175 26.44 1.3322511

9. 20.175 26.40 1.3322509

10. 20.185 26.45 1.3322512

817

a b

Fig 2. Liquid differential cuvettes: a) two-section; b) three-section.

The mean value of the refractive index is 1.3322497, and the root mean square deviation of the mean value of the

refractive index is 0.0000004. The mean value of the concentration is 0.0976 and the root mean square deviation of the mean

value of the concentration is 0.0002.

In Fig. 3, we show graphs of the errors of the measurements obtained based on the experimental data.

It is worth noting that the random errors of the autocollimation refractometer are considerably less than the errors

of the interference liquid refractometer described in [2]. This is particularly the case when analyzing binary solutions of small

mass concentration (0.01% or less).

Using the autocollimation refractometer, we also analyzed the impurity content in the organic compound isopropy-

lbenzene, used, in particular, in the production of phenol and acetone. This material has a high average dispersion, and hence

satisfactory results were obtained when the mark was illuminated with a coherent light source – a semiconductor laser.

We will consider the main sources of systematic error when making measurements with the refractometer.

The error in measuring the angle of refraction by a digital autocollimator. As stated in [4], the overall error of a

digital autocollimation system does not exceed 0.05″. Calculations using (1) have shown that the corresponding error in mea-

suring the difference in refractive indices does not exceed 2.5·10–7.

The error due to instability of the wavelength of the radiation source. The wavelength of the light-emitting diode

varies when it heats up, when there is instability of the voltage supply and when the temperature of the surroundings changes.

We will present some of the estimates obtained. It is well known that the change in the wavelength of a light-emitting diode,

corresponding to the maximum intensity distribution, is about 0.2 nm per 1°C. Calculations show that for aqueous solutions

of low concentration, due to dispersion the change in the refractive index amounts to about 6·10–6. It is obvious that to obtain

a higher measurement accuracy one must stabilize the working temperature of the light-emitting diode and use a stabilized

power supply.

The error in measuring the temperature and its instability had the greatest effect on the error of a liquid refrac-

tometer. This can be explained by the considerable temperature-dependence of the refractive index of liquids, in particular,

for distilled water and aqueous solutions of low concentration n /∆n = 1·10–4.

In the refractometer described above, the error in measuring the temperature is 0.02°C. Here the error in reducing

the value of the refractive index to 20°C amounts to approximately 2·10–6. When measuring low concentrations, the differ-

ence in the temperatures of the standard liquid and the liquid being analyzed has the main effect. A difference of 0.02°C leads

to an error in measuring mass concentration of 0.001%.

The error due to a change in the external pressure is related to the compressibility K = ∂d /d∂p, where d is the den-

sity and p is the pressure. The compressibility of liquids is small, so an increase in the pressure by 0.1 MPa produces an

818

RMSD

ρ, g/100 ml

1

2

Fig. 3. Measurement errors (RMSD): 1) concentration;

2) refractive index n = 10–6.

increase in n by 1·10–5. It is obvious that a change in the pressure, likely under laboratory conditions, leads to a change in n

by a few units in the seventh place, which must be taken into account when making measurements at the standard level of

accuracy.

The error in determining the refractive index of air na, according to (1) leads to an approximately similar error in

measuring n. The refractive index of air can be calculated from dispersion formulas, presented, for example, in [5], from

which it follows that an error in measuring the temperature of 0.1°C leads to an error in calculating the refractive index of air

of about 1·10–7. The error in determining the pressure has a similar effect when it changes by 8.3 Pa.

Hence, the liquid refractometer with a digital autocollimation device for measuring the angle of refraction, described

above, has the following metrological characteristics:

Range of measurement of refractive index n . . . . . . . . . . . . . . . . 1.3–1.7

Range of measurement of difference of refractive indices

(depending on the modification) ∆n . . . . . . . . . . . . . . . . . . . . . 3·10–3–3·10–2

Resolving power of a measurement of refractive index ∆n . . . . . . 1·10–7

Resolving power of a measurement of the concentration

of aqueous solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0.001 g/100 ml

Limit of absolute error in measuring n . . . . . . . . . . . . . . . . . . . . . (1–3)·10–6

Duration of one measurement cycle . . . . . . . . . . . . . . . . . . . . . . . 20 sec

Operating mode in one measurement cycle . . . . . . . . . . . . . . . . . . atomatic

It should be noted that this range of measurement of refractive indices is achieved if one uses liquids from the set of

State Standard Samples as the sample liquids [3].

The instrument can be employed to measure the difference in the refractive indices of liquids or the difference in the

refractive indices with respect to standard samples, to determine the concentration of solutions in analytical laboratories, and

in chemical production to determine the presence of impurities as well as for scientific research.

The considerable advantage of the autocollimation refractometer is the simplicity with which the dispersion charac-

teristics of liquid media can be measured by employing a light-emitting diode of appropriate wavelength.

REFERENCES

1. B. V. Ioffe, Refractometric Methods in Chemistry [in Russian], Khimiya, Moscow (1971).

2. G. I. Leibengardt, A. S. Naidenov, and V. L. Shur, Izmer. Tekh., No. 12, 58 (2004).

3. A. S. Naidenov and O. Yu. Nikolaeva, Izv. Vyssh. Ucheb. Zaved. Priborostroenie, 45, No. 6, 49 (2002).

4. V. L. Shur et al., Izmer. Tekh., No.9, 45 (2005).

5. L. Yu. Abramova, V. M. Baratov, and V. L. Shur, Izmer. Tekh., No. 6, 16 (1992).

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