metrological and technical characteristics of total internal reflection refractometers

7

Click here to load reader

Upload: m-a-karabegov

Post on 15-Jul-2016

215 views

Category:

Documents


1 download

TRANSCRIPT

Page 1: Metrological and technical characteristics of total internal reflection refractometers

Metrological and technical characteristics and diagrams of automatic total internal reflection refractometers

are considered. Measurement of the refractive index of a substance from the affected total internal reflection

spectrum is also considered.

Key words:refractive index, refractometer, total internal reflection, measuring prism.

Total internal reflection refractometers are used extensively in different branches by production and scientific enterpris-

es in order to determine refractive index, dry substance concentration, and other quality characteristics of thick suspensions,

opaque production liquids, juices, syrups, milk, fats, oils, petroleum products, pharmacological materials, biotechnical liquids, etc.

The main components of a total internal reflection refractometer are the optical system, including an illuminator, a

measurement prism with refractive index N and refraction angle α; an angle measuring device with an optical arm Rand pho-

toreceiver with a measurement system. The substance being monitored with refractive index n < N is placed on the flat sur-

face of the measurement prism. In measuring refractive index n, the cut-off beam at the output of the measurement prism

deviates by angle β proportional to n. Correspondingly, there is a shift in the beam projection at the photoreceiver surface.

With rotation of the angle measuring device, the shift in the beam is recorded (or balanced) and the value of the rotation angle

is proportional to n.

The dependence of the exit angle β for the cut-off beam on the determined refractive index n is expressed by the

equation [1]

(1)

By differentiating (1) with respect to n, we obtain an equation for sensitivity ∆β/∆n:

Sensitivity ∆β/∆n increases with an increase in angle α from 0 to 50° and almost remains constant with 50 ≤ α ≤ 90°.

With α = 90°, the sensitivity will be

(2)∆∆

=− − −

βn

n

N n N n( )[ ( )].

2 2 2 21

∆∆

=+ −

− − −

βα α

α αn

n N n

n N n

cos sin /

cos sin

.

2 2

2 22

1

β α α= − −

arcsin cos sin .n N n2 2

Measurement Techniques, Vol. 47, No. 11, 2004

METROLOGICAL AND TECHNICAL

CHARACTERISTICS OF TOTAL INTERNAL

REFLECTION REFRACTOMETERS

PHYSICOCHEMICAL MEASUREMENTS

M. A. Karabegov UDC 535.32

Translated from Izmeritel’naya Tekhnika, No. 11, pp. 50–54, November, 2004. Original article submitted August 9,

2004.

0543-1972/04/4711-1106©2004 Springer Science+Business Media, Inc.1106

Page 2: Metrological and technical characteristics of total internal reflection refractometers

Measurement of angle β is normally accomplished by determining the illumination intensity E for the photoreceiv-

er. For this,the photoreceiver is placed in the light field of the beam emerging from the prism and a narrow band of light with

width L, including the light and dark zones of the light field, is cut out by a diaphragm. The change ∆E in illumination inten-

sity for the photoreceiver is a function of the change in exit angle for the cut-off beam β and the optical arm R of the mea-

suring device. With an identical width of the light and dark zones assuming that tan∆β ≈ ∆β, and taking account of (2),∆E

may be determined as

(3)

By placing construction values R= 200 mm and L = 4 mm in (3),we obtain with ∆n = 0.0001 the change ∆E/E ≈ 3%,

and with ∆n = 0.00001 we have ∆E/E ≈ 0.3% [2].

A variety of realizing the total internal reflection method is based on Fresnel regularities. A diagram of the mea-

surement prism for a refractometer and the beam path is given in Fig. 1.

A parallel beam is directed at the glass–monitored substance interface at angle of incidence ϕ close to the cut-off

angle ϕlim for the prescribed ratio n0/N, where n0 is the initial refractive index of the substance being monitored.

With a change in refractive index n for the substance being monitored intensity Φ of reflected light changes in pro-

portion to n.

The intensity of the reflected beam is determined by the equation [3]

Φ = (1/2)Φ0{[sin2(ϕ – γ) /sin2(ϕ + γ)] + [tan2(ϕ – γ) / tan2(ϕ + γ)]}, (4)

where Φ0 is initial intensity corresponding to n0; ϕ is the angle of incidence; γ is refraction angle, γ = arcsinn0/n, n > n0.

After transforming (4),the dependence of intensity Φ for reflected light on refractive index n for a substance being

monitored is described by the expression

(5)

where A = (N/n)sinϕ.

According to (5),the dependence of beam intensity Φ on refractive index n is not linear, and therefore with an

increase in refractive index n measurement accuracy and sensitivity decrease.

Φ Φ= −

− + + −

+ −

2 1

1 1 1 2

1 2 2 10

2 22

2

A A A A

A A

sin cos sin

( / ) sin,

ϕ ϕ ϕ

ϕ

∆ = ∆ − − −E REn n L N n N n2 12 2 2 2( / ) ( )[ ( )] .

1107

Fig. 1. Beam path and measurement prism for the total internal

reflection method:ϕ is beam angle of incidence; N is refractive

index for the measurement prism; n is test substance refractive

index.

Page 3: Metrological and technical characteristics of total internal reflection refractometers

In order to measure the cut-off angle, a compensation scheme is effective for the refractometer within which angle

of incidence ϕ for the beam is reduced to the value ϕ = ϕlim and the refractive index n is found from the equation

ϕlim = arcsin(n/N). (6)

The sensitivity of the scheme ∆ϕlim/∆n is determined from the expression

The relationship Φ = ƒ(ϕ) with different ϕlim and n is also not linear. With measurements of refractive index n, the

initial value of angle ϕ is determined by the lower limit of measurement n0. For values n > n0, there is a change (increase) in

angle ϕ up to a derived beam intensity to Φ = 1. A change in n0 by ∆n = 0.00001 corresponds to a change in cut-off angle by

∆ϕlim = 0.0005° and a reduction in beam intensity (and correspondingly photoreceiver illumination intensity) by ∆Φ ≈ 3%

that is an order of magnitude greater than with the method of recording for the light-shadow boundary. Sensitivity increases

by a factor of two with two-fold beam reflection.

On the basis of new instrument developments,an automatic total internal reflection refractometer has been worked

out with a system for linearizing the statistical (graduated) characteristic ∆ϕlim = ƒ(n) and a scale correction mechanism has

been developed with a change in refractive index N for the glass measurement prism, for example with relacement of it.

The total internal reflection refractometer with increased sensitivity makes it possible to record a change in illumi-

nation intensity of the order of 0.05%. The information signal of the refractometer forms in the cell unit including two iden-

tical glass total internal reflection semicylinders, i.e., a stationary “standard” and a measuring cylinder fitted with a rotary

mechanism [4]. A diagram of the instrument is given in Fig. 2.

By means of a condenser 2 and a diaphragm 3, the emission source 1 is formed into a narrow parallel beam and mod-

ulated by means of a shutter 4 made in the form of a cylinder with two pairs of slits arranged over the height of the cylinder

and displaced with respect to each other by 90°. Then the beam passes one of the optical wedges 5 or 6 depending on how

∆ ∆ = +ϕlim / / ( / ) .n n N1 1 2 2

1108

1

23

4

5

6

7

8 9

10

11 13

12

1920

21

2324

15

14

16

17

18

22

Fig. 2. Diagram of a total internal reflection refractometer. 1, 14) Emission sources; 2, 16) condensers;

3, 17) diaphragms; 4) shutter; 5, 6) optical wedges; 7) semitransparent mirror; 8) planoconcave cylindrical

lens; 9) “standard” and 10) measurement identical glass total internal reflection semicylinders; 11, 12) mir-

rors; 13) rocker arm; 15) micrometer screw; 18) disk with slits; 19) lens; 20, 22) photoreceivers; 21) zero

indicator; 23) amplifier; 24) reversible pulse counter.

Page 4: Metrological and technical characteristics of total internal reflection refractometers

part of the beam is overlapped by the shutter and the semitransparent mirror 7, and it is directed into the cell unit. A “stan-

dard” glass semicylinder 9 of the cell unit is kept stationary, and the measurement glass semicylinder 10 is kept rotating

around the cylinder axis. The semicylinders are arranged so that the beam covers the corresponding semicylinder and passes

into it from the direction of the cylindrical surface at an angle close to critical (glass–distillate) to the plane of the boundary

passing through the cylinder axis. In order to obtain parallelism of the beam within the semicylinder at the entrance for the

beam close to the semicylinder, a planoconcave cylindrical lens 8 is installed whose material and radius of curvature are sim-

ilar to the material and radius of the semicylinders.

At the outlet of the beam adjacent to the semicylinders, there are two planoconcave mirrors 11 and 12 whose mate-

rial and radius of curvature correspond to those of the semicylinders. The mirror coating is applied from the direction of the

flat surface. Mirror 12 is stationary, mirror 11 rotates around the axis of the measurement cylinder. The mirror angle of rota-

tion is twice as great as the rotation angle for the semicylinder.

The substance being monitored is placed on the reflecting surface of the measurement semicylinder, and the sub-

stance with which it is compared is placed on the surface of the “standard” semicylinder.

The beam,depending on the position of the shutter having passed into one of the semicylinders, is reflected from its

surface and falls on one of the mirrors 11or 12, and being reflected from it falls again on the semicylinder surface. The twice-

reflected emerging beam propagates over a path analogous to the path of the entry beam. Depending on the position of the

shutter the emerging beam is reflected from the semitransparent mirror 7, it is concentrated by lens 19 and falls on the pho-

toreceiver 20. The signal from the photoreceiver 20enters the zero indicator 21whose zero value is only recorded in the case

of setting up the measurement semicylinder at a critical cut-off angle corresponding to the refractive index of the substance

being monitored. For a given substance being monitored, measurement of the critical, i.e., cut-off angle ϕlim, is accomplished

by rotating the measurement cylinder 10by means of a mechanism including a micrometer screw 15connected with the semi-

cylinder by means of a rocker arm 13.

The statistical characteristic of the instrument in the form of a dependence of the output value, i.e., the cut-off angle

ϕlim, on the input value, i.e., the refractive index of the substance being monitored n, is determined by (6), where N is the

refractive index of the measurement semicylinder glass.

A disk 18 is fastened to the micrometer screw within which slit tracks are arranged concentrically whose scale cor-

responds to the chosen unit of measurement. A change-over from one track to another in order to select a unit of measure-

ment (refractive index, concentration,etc.) is accomplished by controlling the reciprocal position of the disk axis and the opti-

cal axis of the subsidiary optical channel formed by emission source 14, condenser 16, and diaphragm 17. The beam of the

subsidiary channel illuminates the corresponding track of the disk 18, falls on photoreceiver 22, whose emerging signal is

amplified in amplifier 23, and enters the reversible pulse counter 24. Recording of the measured result is accomplished by

counter 24 with entry of pulses from amplifier 23 and the signal from the zero indicator 21.

The value of cut-off angle ϕlim depends on the refractive index of the glass of measurement semicylinder N. The scat-

ter of values of N causes a change in characteristics of the instrument scale and requires adjustment of the scale with a change

in N, for example with a change in measurement prism. A correction system has been developed providing retention of scale

parameters for the refractometer with different values of refractive index N for the glass of the measurement semicylinder [5].

The system has been realized in the form of a rotary mechanism for the measurement semicylinder including a

micrometer screw connected with the measurement semicylinder by means of a rocker arm fitted to a regulating unit. The

length of the rocker arm is changed by means of the regulating device in proportion to the change in refractive index of the

semicylinder glass so that the ratio of the rocker arm length l to the semicylinder glass refractive index N is a constant value:

l /N = const. If the refractive index of the semicylinder glass changes by ∆N with respect to the nominal value N0, the length

of the rocker arm should be changed by ∆l in order to observe the condition

(l0 + ∆l) / (N0 + ∆N) = l /N,

where l0 is the nominal rocker arm length; ∆l is the change in rocker arm length during correction; N0 is the nominal semi-

cylinder glass refractive index; ∆N is deviation of measurement semicylinder glass refractive index from a nominal value.

1109

Page 5: Metrological and technical characteristics of total internal reflection refractometers

In order to accomplish correction for the substance being monitored, it is placed on the flat surface of the measure-

ment semicylinder. If the refractive index of the substance being monitored n is greater than the refractive index of the zero

solution (for example distillate) n0, then beam intensity Φ0 in the measurement channel decreases. In order to arrive at the

initial beam intensity for the measurement cylinder, it is rotated by means of the micrometer screw by angle ∆ϕ that with a

nominal value of the measurement semicylinder glass refractive index N0 is clearly connected with the refractive index of the

substance being monitored n.

With a glass refractive index N differing from the nominal value N0, the scale characteristics of the instrument

change. In order to retain constancy of the scale with glass refractive indices N = N0 ± ∆N correction of the rocker arm length

is performed. For this purpose, on the flat surface of the measurement semicylinder a “standard” glass plate or liquid speci-

men with a known “standard” refractive index ns is installed and measurement is performed. If the instrument reading n dif-

fers from ns, then the length of the rocker arm is changed so that the instrument reading coincides with the specimen refrac-

tive index. With values n > ns, the rocker arm length is reduced, and with n < ns it is increased.

The correction system increases measurement accuracy, it maintains constancy for the scale, and it simplifies adjust-

ment and regulation of the instrument. During experimental verif ication of the correction system the nominal refractive index

of the measurement semicylinder glass was N0 = 1.5163,and the nominal length of the rocker arm l0 = 25 mm.

The static (graduated) instrument characteristic determining the relationship between the output ϕlim and input n val-

ues is a nonlinear function:

ϕlim = arcsin(n/N) = ϕ0 + ∆ϕ = arcsin(n0 + ∆n) /N, (7)

where ϕ0 is the cut-off angle corresponding to n0; n0 is the refractive index of the zero solution (for example distillate);

∆ϕ = ϕ – ϕ0 and ∆n = n – n0 are increases in the cut-off angle and the refractive index respectively.

Linearization of the refractometer scale is accomplished by means of a system including a rotary mechanism with a

carrier and rocker arm with the possibility of rotation and movement connected with the measurement semicylinder. A test

substance, whose refractive index n is for determination, is placed on the flat surface of the measurement semicylinder. If the

refractive index of the test substance n is greater than n0 of the substance for comparison (“standard”) beam intensity Φ0 in

the measurement channel decreases. In order to reach the initial intensity Φ0, the measurement semicylinder is rotated by

angle ϕ proportional to the refractive index n of the test substance and determined according (7) as

ϕ = ∆ϕ + ϕ0 = arcsin(n0 + ∆n) /N.

Angle α between the rocker arm and the displacement direction of the carrier may be described by the equation

α = α0 + ∆α = arcsinl / l0 = arcsin(l0 + ∆l) / l, (8)

where α0 is the initial value of angle α; ∆α is the increase in angle α; l, l0 are structural dimensions connected with carrier

displacement; ∆l = l – l0 is the carrier displacement path length.

With the condition of parallelism for the carrier displacement direction and incident beam,we have

ϕ = α, ϕ0 = α0.

After transformation taking account of (7) and (8),the relationship between the increase in refractive index ∆n and

carrier displacement ∆l may be presented in the form

n0/N + ∆n/N = l0/ l + ∆l / l; n0/N = sinϕ0; l0/ l = sinα0; ∆n/N = ∆l / l; ∆n = (N/ l)∆l. (9)

Equation (9), representing function ∆n = ƒ(∆l), determines the linear connection between the increase in refractive

index for the substance being monitored ∆n and carrier displacement ∆l characterizing the linearization system for the refrac-

1110

Page 6: Metrological and technical characteristics of total internal reflection refractometers

tometer scale. The system makes it possible to improve the metrological characteristics of the refractometer, to carry out cor-

rection of the scale and “zero,” to accomplish scale calibration, and to use a simple system for transforming the input signal

into digital form.

Development of the method makes it possible to measure the refractive index for an absorbing material where an

affected total internal reflection (ATIR) is observed. A study has been made of the measurement of refractive index from the

ATIR spectrum distinguished by high accuracy and measurement reproducibility [6]. The refractive index is determined by

recording the ATIR of the “standard”–test specimen system with action on it of a flux of monochromatic emission. A speci-

men with a highly dispersed refractive index is used as the measurement standard. The ATIR spectrum is reproduced with a

constant initial angle of incidence and wavelength λmin is recorded corresponding to the minimum in the recorded spectrum.

The refractive index of the test specimen n is determined from the equality

n = ns(λmin),

where ns(λmin) is refractive index of the “standard” at wavelength λmin.

A diagram of the method is shown in Fig. 3.

The method is realized by means of a “standard” 1 with refractive index n1–test specimen 2 with refractive index

n2 system. A flux of monochromatic emission 3 is directed at a constant angle of incidence α at the interface of the test spec-

imen 2 and “standard” 1. The emission flux should be characterized by a high degree of collimation. The input flux is scanned

over the wavelength,and the ATIR is recorded.

In order to provide high (not less than 1.5) dispersion of the refractive index, the “standard” should be prepared from

material that exhibits strong absorption in the range of the spectrum used, for example from fused quartz, ion-crystalline, and other

materials. Dispersion of the refractive index ns(λ) for fused quartz SiO2, ns(λ) = 0.4–3.5,for crystalline quartz α–SiO2,

ns(λ) = 0.2–7.9. High dispersion in the field of the main absorption band is exhibited by ionic crystals of MgO, Al2O3, NaCl,etc.

On reaching equality of the refractive index for the “standard” and specimen when the relative refractive index

n0 = n/ns = 1,a minimum (Fig. 4) appears in the recorded ATIR spectrum since in this case with approach to a low value of

the absorption coefficient the numerator in the Fresnel equations characterizing the dependence of reflection coefficient on

angle of incidence tends towards zero.

Then from the known value of refractive index for the “standard” at wavelength λmin corresponding to the minimum

in the ATIR spectrum for the “standard”–test specimen system the refractive index for the test specimen n = ns(λmin) is deter-

mined. In a number of works, the method has received the name “optical slit method.” If the specimen is transparent within

the wavelength range used the minimum in the ATIR spectrum will be unique (see Fig. 4),which it possible to determine eas-

ily the wavelength corresponding to the equality n = ns(λmin).

The value of the angle of incidence is selected in the range 65–87°. With large angles of incidence, it is difficult to

obtain the ATIR spectrum. With smaller angles of incidence there is broadening of the spectrum close to the point of the min-

imum that causes an increase in the error of determining λmin and consequently the refractive index of the test specimen n.

In determining refractive index n for a test specimen exhibiting considerable absorption an additional minimum aris-

es in the ATIR spectrum for the “standard”–test specimen system. In this case, apart from the ATIR spectrum the transmis-

sion spectrum is recorded for the test specimen and the value of n is determined from the known value of ns(λmin) at the

1111

1

2

Fig. 3. The “standard”–test specimen system with recording of the ATIR spectrum:

1) “standard” with refractive index n1; 2) test specimen with refractive index n2;

3) monochromatic emission flux; α is the constant emission flux angle of incidence.

Page 7: Metrological and technical characteristics of total internal reflection refractometers

wavelength of the minimum that is only observed in the ATIR spectrum. Thus,in this method in order to find the refractive

index for a specimen with a known dispersion of refractive index ns(λ) it is sufficient to determine the unique value, i.e.,

wavelength λmin corresponding to n = ns(λmin).

Use of the test method provides high accuracy and reproducibility for measurements. The refractive index is found

directly from the curve for dispersion of the “standard.” There is no requirement for measuring reflection coefficients,emis-

sion angles of incidence, and polarization with evaluation taking account of and considering the corresponding errors; in

determining coefficients that are in the calculation equation also taking account of and considering the corresponding errors;

in carrying out labor-consuming calculations. Use of “standards” with high dispersion of the refractive index provides the

possibility of direct determination of the refractive index of any test specimen without prior measurement of any subsidiary

values and it also increases the reproducibility of measurements. In addition, the method makes it possible to determine the

refractive index of both liquids and solid specimens over the whole spectral optical range.

REFERENCES

1. B. B. Ioffe, Refractometric Methods of Chemistry [in Russian],Goskhimizdat, Leningrad (1960).

2. M. A. Karabegov, Yu. I. Komrakov, and K. A. Mchedlishvili,Prib. Sist. Upravl., No. 10 (1980).

3. G. S. Landsberg, Optics [in Russian],Gostekhteorizdat (1957).

4. M. A. Karabegov et al.,Inventor’s Cert 657324 USSR,Byull. Izobret.,No. 14 (1979).

5. M. A. Karabegov et al.,Inventor’s Cert 792107 USSR,Byull. Izobret., No. 48 (1980).

6. V. M. Zolotarev et al.,“Analytical instrument building. Methods and instruments for analyzing liquid media. Optical

analytical instruments,” in: Proc. All-Union Sci.-Tech. Meeting, Tbilisi (1980).

1112

Fig. 4. ATIR spectrum for the “standard”–test specimen

system; R, % is reflection coefficient; λ is wavelength.