Report on the measurements of the refractive index of air, using interference refractometers

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Report on the measurements of the refractive index of air,

using interference refractometers

Citation for published version (APA):

Schellekens, P. H. J. (1983). Report on the measurements of the refractive index of air, using interference refractometers. (TH Eindhoven. Afd. Werktuigbouwkunde, Vakgroep Produktietechnologie : WPB; Vol. WPB0063). Technische Hogeschool Eindhoven.

Document status and date: Published: 01/01/1983

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Editor:

P. Schellekens

Metroloqy Labaratory THE

Participating Laboratories:

-1-REPORT ON THE MEASUREMENTS OF THE REFRACTIVE INDEX OF AIR,

USING INTERFERENCE REFRACTOMETERS.

- National Physical Labaratory (NPL), Teddington, United Kingdom.

(M. Downs, K.P. Birch).

- Physikalisch Technische Bundesanstalt (PTB), Braunschweig, West-Germany.

(G. Wilkening, F. Reinboth).

-Dienst van het IJkwezen, VanSwinden Labaratory (VSL), Delft, Netherlands.

(J. Spronck).

-Eindhoven University of Technology (THE), Metroloqy Laboratory,

Eindhoven, Netherlands. (P. Schellekens).

This work was organised and partially funded by the Community Bureau of Reference, Commission of the European Communities, Brussels, Belgium.

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CONTENTS:

1 . Introduetion. . . 3

2. Description of the comparison set-up ... 5

3. Measurements and results ... 19

4. Analysis and conclusions ... 35

5. Recommendations and acknowledgements ... 37

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-3-Chapter 1.

INTRODUCTION.

For about 15 years laser interferometers have been commercially available and the use of this measuring instrument becomes more and more important,

especially in industrial practice. Today most of the metrology laboratorles own one or more of these instruments and they are used for the accurate measurement of length and angle and for calibration of measuring machines. In length measurements the length is calculated from: L

=

(K * Àv}/N. Here K is the number of counted fringes over L divided by a constant, generally two or four. Ày is the vacuum wavelengthand N the refractive index of the

medium, mostly air. As the use of the laser interferometer outside the

laboratories, in uncontrolled environments is increasing, the composition of the air plays an important role during measurements.

In a careful analysis Edlén [1] has shown which variables determine the refractive index of air. Recently Jones [2] has revised this work but the results are the same for all practical purposes. Edlén bas given values for the dependenee of N on wavelength, pressure, temperature, humidity, carbon-dioxide and carbon-hydragen contents. For a wavelength of 633 nm the formula of Edlén can be written in the following useful farm:

-4

N-1

=

D

*

0,104127

*

10

*

p- 0,42063 * 10-9

*

F 1 + 0,3671

*

10-2* T

with D

=

0,27651756

*

10-J* (1+0,54*10- 6*(C-300})

P is the pressure in Pa, T the temperature in °C, F the water vapour-pressure in Pa and C the

co

_{2-content in ppm. Most commercially available}

interferometers use the measurement of pressure, temperature and humidity to calculate N, either electronically ar by means of tables prepared for this purpose. The influence of other parameters like variations of

co

_{2 content}

are neglected. Since the accuracy needed is increasing this is nat always permitted and one has to measure the refractive index directly.

Also for the calibration of laser measurement systems a high accuracy of the refractive index value is needed, so in this case it is better to measure N directly and to campare this value with the value used by the

interferometer. Ta get a better understanding of the accuracy achievable for the measurement of Nat a level of 1 part in 107, BCR has initiated an

international project on comparison of refractometers, constructed in different laboratorles of EC-countries. Partielpants are mentioned on page

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The project has a dual role:

First: a comparison of measured val~es of the refractometers with calculated values using Edléns formula,

Second: a direct comparison of refractometers to get an understanding of instrumental accuracy.

Two meetings of specialists were organised to prepare the experiments, they were held at PTB and Eindhoven University. The experiments were carried out in the Metrology Labaratory of Eindhoven University in June, 1983.

After the comparison each participating laboratory was asked to write a small report on their own measurements and send it to the Eindhoven

participant who had to prepare the final report. Due to technica! problems it was impossible for one of the intended participants to take part in the measurements so on the last moment THE and VSL decided to built a second set-up for measuring the refractive index. The laser interferometer to be used in this experiment was kindly lent to us by the metrology lab of Rank Xerox Holland, Venray.

Chapter 2 of this report contains in the first place a description of the measurement facilities available for the comparison and next a short

description of each refractometer. In chapter 3 are presented the results of the individual measurements compared to the calculated values according to Edlen. Also the results of direct comparison between NPL and PTB and between NPL and THE are given. After a calculation of systematic and random errors results are discussed in chapter 4 and some suggestions for impravement arepresented. In chapter 5 some recommendations for further research are given. Most of the results are listed in chapter 6.

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-5-Chapter 2.

DESCRIPTION OF THE COMPARISON SET-UP.

During the second specialists meeting held at Eindhoven details of the comparison set-up were discussed. On a stable table a large thermally insulated cabinet should be placed containing the refractometers of the participating laboratories. Facilities for the measurement of

temperature,pressure, humidity and

co

₂content should be present to such a level that the calculation of N from Edlens formula could be carried out with sufficient accuracy. Each participant laboratory should put in a refractometer with, if possible, instruments for measurement of pressure, temperature and humidity.

The following is a detailed description of the facilities used in the set-up.

2.1. Measuring table and insulated cabinet.

From the discusslons it was clear that a surface of 1*2 metre was just sufficient to contain all refractometers without light sourees and vacuum pumps. In the metrology laboratory of THE rather heavy table tops, made of stone at a size of 0,75*1,5 metre, were available soit was decided to use four of these slabs and mount them on a steel frame. Thus a table surface of 1,5*3 metre was available. The insulated cabinet, sizes 2,5*0,75*0,50 metre, was constructed of 50 mm polystyrene covered on both sides by a layer of 5 mm pressed paper. Holes for feed through of cables, tubes and light beams were prepared during building the comparison set-up. Also optica! windows were mounted later, as needed.

2.2. Facilities for the measurement of temperature, pressure, humidity and carbon-dioxide content at THE.

2.2.1. Pressure measurement.

Usually two types of pressure measurement are in use at the metrology lab of THE. One is a metal-barometer - system Paulin - with a resolution of 5 Pa and a systematic error less than 20 Pa. The other instrument is a Fortin-type mercury-barometer with a resolution of 10 Pa and a systematic error less then 20 Pa. The VSL instrument was based on a quartz-pressure sensor (Paro-Scientific) with a resolution of 1 Pa and a systematic error less then 20 Pa. This instrument consists of a calculation unit and display coupled to the sensor by a flexible wire so the sensor can be placed near to the

air sample-place. A comparison of values measured by the different

instruments available, on 6-6, showed maximum errors of 10 Pa from a mean value so a systematic error less than 10 Pa would be obtained.

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2.2.2. Temperature measurement.

For the measurement of temperature bath resistance thermometers and semiconductors devices {PTB) were employed. THE bas 100 Q {Pt-100)

resistance thermometers coupled to a measuring set-up (TI) according to Dauphinee [3]. In this bridge the resistance of the thermometer is coupled

to a Diesselhorst-comparator by means of electric null-detection. Besides the Dauphinee-set-up, a conventional two-circuit set-up (TII) using a Diesselhorst-comparator used with precision 10 Q (Pt-10) resistance

thermometers was present. These thermometers were used as standards for calibration of PT-100 thermometers. Systematic errors of this temperature measurement were less than 10- 2K, random errors were a few mK. The

systematic errors in Pt-100 measurements are about 10-2K, random errors less than 10-2K, in the semiconductor devices these are less then 4

*

10-2K. 2.2.3. Measurement of humidity.

Measurement of this quantity was in principle possible with two types of instruments: a wet and dry bulb psychrometer and a dewpoint measuring instrument (humidity analyzer 911 EG and G). Systematic errors were within

1\ relative humidity or 30 Pa absolute pressure as claimed by the

manufacturer. A comparison over several days between the two instruments has shown a discrepancy of absolute pressures within 20 Pa. Random errors were within 10 Pa (0,1 Kin dewpoint reading).

2.2.4.

co

_{2 measurement.}

The

co

_{2 content was measured by gaschromatographic techniques and was} carried out by the Chemistry Department of Eindhoven University. For this measurement air samples were taken at regular times during the day and at the end of the day these samples were analyzed. A maximum relative

systematic error of 6\ was calculated. At a maximum measured

co

_{2 content of} 950 ppm this corresponded to an absolute error of 75 ppm which was

acceptable. Analyses on other contaminants were also carried out by gaschromatographic techniques have shown insignificant values. 2.3. The comparison set-up.

The refractometers were situated parallel to each other and in the centre a sample-place was arranged containing all the inlets of the refractometers. Also the sensors of pressure and temperature measurement and the inlets for humidity and

co

_{2-content were connected to this place. By means of this} arrangement each individual measurement of N could be recalculated to the conditions measured at the sample-place. Figure 2.3.a gives a schematic diagram of the comparison set-up and in figure 2.3.b the real situation is shown with an opened cabinet. The temperature measurement set-up TI, was used in the refractometers I, II and IV with a total of eight thermometers.

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V / / V /

/ / / / / / / V / / / / / / / / / /

V / /

V

~

.

s

:,.../-~

I

n

m

N:

~

/ P-10 P-10 P-10 lUC

~

~>---

iel

I

11 ~

~///////////////////////7//

J2:.F

~~

I

j_

--3000

1''ig.2.3.a.~chemat~c d~agram of comparison set-up._

I IV :refractometers PI ...

Prv=

pumping systems

IF ... IVF:air inletsystem p-10 resistance thermometers IL ... IVL:laser lightsouree

and counting system Tr ... T₁₁₁:temperature measurement system p D

s

pressure measurement humidity measurement sample-place 0

g

... I -.] I

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Fig. 2.3.b Open cabinet with refractometers and laser systems.

The thermometers used in I and II were calibrated against presision PT-10 THE thermometers. Those used in IV were calibrated at NPL. Set-up T

11 is

connected to four Pt-10 precision thermometers Three of these thermometers were located near the refractometers I, II and III while the fottrth measures the temperature of the sampleplace.

2.4. Briefdescription of the refractometers used tn the comparison.

2.4. 1. The NPL refractometer.

The refractometer consisted of a double passed Jamin beam-splitter1 an air

sample cell and a single retro-reflector consisting of a lens and mirror combination - Fig. 2.4.a. Bath surfaces of the beam-splitter block are coated with an aluminium film; the rear surface is fully reflecting and the front partially reflecting. The beam-splitter coatings produced equal

intertering intensities for s and p polarisations in the refractometer and this results in maximum fringe contrast. This system does nat require the use of a stabilized laser, and its 'common path' optical contiguration is insensitive to variations in path length resulting from mechanical changes.

The input light beam is split into two laterally separated beams at the beamsplitter. One beam passes twice through the outer light path of the

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-9-refractometer cell while the other, reflected from the back surface of the beam-splitter, passes twice through the central campartment of the cell. The two beams are recombined at the beam-splitter and interfere with each other. A À/4 mica phase retardation plate with its axis suitably oriented is

located in one of the outer beams; this produces a phase difference of 90° between the two orthogonally polarized components of the interferogram, which are then examined by means of a polarizing beam-splitter and two photo-detectors. A third polarized and photo-detector are used to examine the single beam output from the system which provides a de signal directly proportional to the energy of the beam after transmission through the system.

An 80 mm focal length achromatle doublet was employed for the

retro-reflector. The retro-reflector mirror is mounted on a loudspeaker motion and the distance between the mirror/lens combination must be maintained to

better than 1 ~m in order to achleve an absolute measurement of accuracy of 1 part in 108 of air refractive index. This was realised by designing a retro-reflector mount compensated for thermal expansion.

The ends of the glass tubes were cement.ed into channels ground into the cell windows, the spacing of the windows being controlled during fabrication using end bars. The inner and outer cell chambers were accessed through single glass tubes from which pvc tubes connected the cell chambers to a control manifold. This consisted of four valves (V1 - V4) which could be used either for admitting air intoor evacuating either cell chamber. A gauge was mounted on the manifold for the measurement of vacuum pressure. Inserted into the refractometer cell outer chamber were two NPL calibrated platinum resistance thermometer bulbs which were 8 mrn long* 1.6 mm in diameter. These were seperated with respect to the cell centre by 150 mm along its length. With the polarised heliurn neon laser souree emitting 633 nm radiation and a sample cell lengthof 31.64 cm one electronic count corresponds to a path length change of À/8 and a refractive index change of 2.5 partsin 107 .

To obtain reliable bi-directional fringe counting, two electrical signals must be generated from the photo detectors in the interferometer, with constant average de levels and sinusoidal components related to the optical path difference and in phase-quadrature. The counter logic is set to trigger each time one of the signals passed through its average values.

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detector

CD

Polarising beam splitter Laser beam Semi-reftecting surface ~

/

Fully reflecting surface ~.:..Po;:;.lariser Photo

®

detector detector

@

Single beam output ln\erferometer beam splitter enelosure wall

I'A\

@

©

Plotinurn resistance

'Cl thermometers

®

+

Vacuum gauge

To

Vacuum pump

Fig. 2.4.a. Principles of NPL-refractometer.

Lens

t

Phose plate

®

End view I

....

0 I

(12)

-11-In this refractometer, the required electronic counting signals are obtained by subtracting from each of the two sinusoidal path-difference signals the de signa! generated at the non-interterenee output. Using this technique,

two sinusoidal signals can be obtained, having an average signa! level of zero volts and in phase-quadrature; any de components unrelated to the optica! path are automatically removed. The two sinusoidal path difference signals were matebed by adjusting the energy balance between the two

orthogonally polarised components by rotating the plane of vibration of the incident beam, and the level of the de signa! output was controlled by

rotating a polarizer in front of the photo-detector. The two counting signals are used to drive a bi-directional counter that displays a count every time one of the signals crosses the zero voltage level, each count representing an optica! path difference of À/8. The measurement sensitivity this represents in terms of refractive index is depent upon the wavelength of the light souree and the length of the refractometer cell employed. The two counting signals were then used to drive the x and y inputs of an

oscilloscope. When the optica! path length was changed this resulted in a circular lissajous figure being displayed centred about zero volts. Under static conditions the resultant vector maintained a fixed angular

orientation relative to zero volts and since one complete vector revolution represented one fringe of path length change, fringe fractions could be easily estimated.

The refractometer system was mounted on a box section aluminium support with the laser souree mounted remotely. The wall of the isothermal enelosure was slotted over the refractometer such that the laser was outside the

enclosure. A piece of pvc tube was connected from the centre of the

enelosure to valve V1. Attached to the end of the pvc tube was a platinum resistance thermometer {C).

Measurement Procedure.

The refractometer system was allowed to stabilise in the isothermal chamber for about 18 hours before any measurements were taken. Both chambers of the refractometer cell were pumped out and left under vacuum.

With the cell under vacuum and the system stabilised the reversible fringe counter was set to zero and the fringe fraction determined from the angular orientation of the voltage vector as displayed on the oscilloscope. Valve V2 was then closed and V1 was openend to leak air into the outer chamber of the cell. When the air in the cell had reached atmospheric pressure the

resistance of the platinum resistance thermometers was measured on an bridge T_{1 .} The measurement sequence was A-B-C with a repeat on A to check for drift. Whilst the resistance was being measured the new fringe count, angular orientation of the voltage vector and the barometic pressure were all noted. The atmospheric pressure was determined using an aneroid (NPL) barometer outside the isothermal chamber. The dew point of the air in the

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chamber was measured by continuously cycling this a1r through a humidity sensor. Finally the

co

_{2 content was measured as described}in 2.2.4.

Valve V1 was then c]osed and V2 opened to re-evacuate t.he outer chamber of the cell and the angular orientation of the voltage vector was remeasured. The measured value of refractive index could therefore be determined from the fringe count and measured fractions. These were then compared with the value determined from t.he Edlen equation.

Accuracy of the measurements.

As given in detail in appendix 6.2 there has been calculated a random error of 1.6x10-8 (95% confidence interval} and an unknown systematic error of up to 1.4*10-8 (shown by experience, 95% confidence interval) for the measured values of the refractive index of air. Quadratic addition of these errors gives a total uncertainty of 2.2*10- 8 (95% confidence interval). For the calculated value of N1 based on Edlens relations, a total uncertainty of ± 8*10- 8 (95% confidence interval) has been determined (Chapter 4).

2.4.2. PTB-refractometer~

The refractometer consists of a Mach-Zehnder interfetameter with an

integrated block with two bores and optical windows which serve as measuring chambers (see Fig. 2.4.b). The lengthof the chambers is 160.044 mm (20°C). The interferometer is driven by a stabilized two-mode HeNe-laser (beat

frequency ~ 600 MHz). Changes of the optical lengthof one of the armsof the interferometer produce phase shifts of the beat oscillation. These shifts are measured relative to the phase of a reference path. Complete fringes (= 360° of phase) are counted by a fringe counter, whereas the high-resolving evaluation of the fringe patterns is done by tracing back phase shifts to the rotation of a polarizing filter. Thus, fraction of complete fringes are detected by measuring a rotation angle:

180° of rotatien (ex) = 360° of phase

=

1 complete fringe.

Fringe fraction and amount of complete fringes are added to calculate the refractive index. The resolution of the interferometer is about i 1*10-9, the uncertainty is about ± 1*10-B in terms of N. The temperature of the air probe in the measuring chamber equals t.he block temperature, as the heat capacity of the probe volume is very small compared to that of the rather solid aluminium block. The block temperature is measured at the surface (03 ). A small difference between probe temperature and block temperature is likely to occur in case the surrounding temperature becomes different from the block temperature. The contribution of the temperature measurement to the uncertainty is

i±

4*10- 8 in terms of N for

e

₃

-e

₂

i±

0.5 R.

For the experiments carried out this means an overall uncertainty of the refractometer of ± 5*10- 8while for the calculated values, using Edlêns formula, a total uncertainty of i 8

*

10-8 has been determinated (Chapter 4) .

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r - - · - ·

I

_.

I

.

_I

_{nterferometer}

I

llnsuloted

box

·-·,

_.

I

'

I

Photo-diode PoL fitter

(rotary)

Fig. 2.4.b. PTB-refractometer.

I

9()0 Cf>

ffJ

!QQ_QJ

Oivider

Mixer

Fring? counter

oo

_ffJ

[>

Servo drive

Rotation angle

Laser ~---~

V

Vacuummeter

Throttle

Vocuum

pump

I _,. w I

(15)

Metbod of measurement.

The individual measurements had been carried out with both measuring

chambers tilled as reference. After pumping down one chamber and allowing a certain time for settling of temperature, bath counters were registrated (complete fringes, fringe-fraction) and the chamber filled again to continue measurements. Thus an interval of about 4 min was reached. The speed of pumping and flooding was about 1 bar/30 sec. The temperature of the block (=

measuring temperature 93) was taken tagether with the counter readings.In addition, air temperatures at several points _{in the cabinet ( PTB (92),} common air inlet (91), THE} were taken every 20 min tagether with the

pressure. Measurements of the.dew point and of the co_{2-content were made at} several times, spread over the whole day.

Calculation.

The readings for complete fringes and for fringe-fractions were taken to calculate the refractive index (N-1} of the air in the measuring chamber at the temperature of 93 . In order to be able to campare the results of all groups these results were transformed to the temperature at the common air inlet {91), or to the air temperature near the PTB refractometer (92), respectively with 91, a_{2 lineary extrapolated with time. As the change of} refractive index with time is no linear function no mean values have been calculated.

2.4.3. THE-Refractometer.

This system is based on an ordinary double-beam interferometer using a commercially available laser-system (Hewlett-Packard 5526A}. Both beams are passing through 406 mm long cells which can both be evacuated. The

measurement-system uses the remote-interferometer and corner-cubes as usual; only an extra beam-bender is used so bath beams are parallel and close

together. Normally the counting system counts in~ or, if preferred, ~

units, but bere an extra 10 times extender is used so the least count equals

~· In a cell length of 406 mm this means about 70.000 counts at an

air-vacuum change so one count corresponds to a resolving power of 5*10- 9 in N. Both cells are made of invar, to decrease temperature sensitivity, and are closed by quartz windows. Temperature is measured on the vacuum-cell and inside the other cell, the measuring or sample-cel!, using Pt-100

thermometers as described before. The pressure in both the cells is checked by a Pirani-gauge befare starting the measurement. As the interferometer is essentially asymmetrie the corner-cubes are mounted in a steel block

staggered 50 mm to correct for asymmetry. Temperature of the block is

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Tl

VACUUM PUMP ~Fig. 2.4.c. Diagram of THE-refractometer.

D

p

o _________

'---~

-

_L

-

0'---1111111

0

E I

....

U"' I

RI: Remote Interferometer; T1, T2, T3: Temperature measurement; L: Laser; E: Extender; D: Display;

C: Corner-cubes; BB: Beambender; SC/VC: Sample-place/vacuum-cell; fS: Filling Station;

P: Pirani gage; AT: Adjustment Table; S: Sample valve; W: Quartz Windows; TI: Temperature measurement system.

(17)

The air sample is taken through a special needie valve so the filling can be controlled perfectly. Figure 2.4.c shows a.schematic diagram of the

apparatus. Pressure and humidity values, belonging to the air sample, were determined from the results measured on the sample-place while

co2

values were taken from the results of the analysis of air samples.

Measurement procedure.

First both cells were evacuated and temperature measurement of T1, T2 and T3 was carried out. Then an air sample was brought into the sample-cel! and after equilibrium the number of counts was taken and again the temperature of T1, T2 and T3 was measured. From the number of counts, corrected for small temp~~ature effects, actual cell length and vacuum-wavelength, the refractive index of air was calculated. Also the Edlén-value was calculated from the measured data of pressure, temperature, humidity and

co

_{2 content.} The filling of the sample-cel! takes only a few minutes; this is the real measuring time. Re-evacuation of the system takes around ten minutes due to relatively great length of pumping lines between cells and pumping system. Measurement accuracy.

As mentioned before resolving power of the refractometer _is one count

corresponding to 5*10-9 in N. Together with other influences a total unknown systematic error has been calculated as 2.5*10-8 (95\ confidence interval)

in N. If a result of measurement is recalculated to sample-piace conditlans due to temperature differences this value rises to 5*10-8 in N. Random errors will be within 2*10-8 in N. So a total error of 6*10-8 in N is expected. (95\ confidence interval). A specification of these errors is given in appendix 6.3. Total error in the calculated value from Edléns

formula will be less then 8*10-8 in N (95\ confidence interval). These errors are specified in Chapter 4.

2.4.4. VSL-Refractometer.

This refractometer is based on the same measurement-system as the THE

refractometer but the set-up and filling system are different, in fact this was the prototype THE-refractometer. One beam of the interferometer is passing through open air, the other beam passes the sample-cel! which is made of steel. The sample-cel! is closed by glass-plates extending in the air pathof the interferometer. As with the THE-refractometer the

corner-tubes are staggered over 50 mm to correct for asymmetry of the interferometer. The block containing the corner-cubes is made of aluminium.

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L 2 / 36*

-10* ~DISPLAY

I/

h 1/ HP- LASER

u

I/

1 4 9

.,..

_!=N_

___]

~~

(:::)

_/."

_J-

_u

r:

~~

I

PIRANI DIFF. PUMP ROTARY PUMP

Fig. 2.4.b. Diagram of VSL refractometer.

<

3

~

_V

v6

5./

'

/6

\

1 7 (P,T,H,C02)

..1..8

1. Beamsplitter 2. Beambender 3. Glass windows 4. Sample-cell

5. Aluminium mounting block for corner-cubes

6. Corner-cubes

7. Air inlet

8. Triple-valve for air inlet and pumping

Pr

9. ess ure measurement

T₁ Thermometer for sample-cell

T 2 Thermometer of the aluminium block T

3 Thermometer of the open air path

syst em

I

,_.

...,

(19)

First the measurement-cell is evacuated and then slowly filled with the air-sample to be measured. The least counts here is also

i

but a total extension of 360 times is used so one count equals ~· Since the sample-cel! has a length of 278 mm a vacuum to .air change in the cell gives around 170.000 counts. Temperature of sample-cel!, aluminium-block and air path are measured by Pt-100 thermometers so corrections for expansion and air path

changes during the measurement can be made using Edlens formula. A Pirani-gauge is used for checking the vacuum after evacuation. Figure 2.4.d gives a

schematic diagram of the apparatus. Temperature measurement was carried out by the Dauphine-setup T1 while pressure, humidity and

co

2 content were measured as described in 2.2.

Measurement procedure.

In principle there are two possibilities for the measurement of N. First it is possible to start with the sample-cel! filled with air to be measured and then pumping out slowly until a sufficient vacuum level (< SPa) is reached. Air conditions should be measured befare starting pumping. Second it is possible to start with an evacuated sample-cel! and fill it with air. The second methad has the advantage to be faster so corrections for expansion and changes in the open air pathare smaller. Better agreement with

calculated values, was achieved when the second methad was used so it was decided to use this metbod for the measurements. As the temperature of the air sample was measured by a thermometer on the outside of the cell

gradients could be present. Differences between measured and calculated values can be partly explained by this effect. On 10-6 the temperature of the inlet-place has been taken for calculation of N and no corrections have been carried out for drifts of the interferometer-system. In this case the real measuring time was only 2 minutes and the results show much better agreement with calculated values.

Accuracy of the measurements.

The usabie resolution during the measurement was determined to be 2 counts

(~). This gives an uncertainty of 3*10-9 in N. In appendix 6.4 a

specification of random and systematic errors has been given. An systematic error of 1.5*10-8 and a random error of 5.0*10-8has been determined (95\ confidence interval). Since the systematic error for the measurement of air temperature will be around 0.04K the total uncertainty increases to 6.6*10-S in N if one uses this temperature for recalculation of measured values of N to inletplace conditions. The uncertainty of results calculated from Edléns formula will be 8*10-8 in N as specified in 4.1 (95% confidence interval).

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-19-Chapter 3.

MEASUREMENTS AND RESULTS.

The measurementprogram can be split up in four parts: 3.1. Adjustments and tests.

3.2. Individual measurements.

3.3. Comparison of individual results by recalculation to sample-piace and conditions.

3.4. Direct comparison of pairs of refractometers using the same inlet-system.

3.5. Changes of

co

_{2-content during the measuring period.} 3.1. Adjustments and tests.

After arrival the refractometers were set-up as described in 2.3. The cabinet was prepared for the measurements and glass windows were fitted to admit the laser-beams into the cabinet. Figure 3.1.a shows the measuring

table containing the cabinet and part of the instrumentation. The NPL-temperature-measurements were performed by connecting the NPL-thermometers to the THE-T₁ temperature-measurement-system. After the preliminary tests it was decided to use the THE-dewpoint hygrometer for humidity measurements while the

co

_{2 correction was to be calculated from the THE measurements of} the

co

_{2-content. The first}

co

_{2 measurements gave contents of 970 and 980 ppm} against a normal content of 300 ppm [1]. Soit was decided to take air-samples spread over the whole day and to use interpolated values from the

co

_{2 analysis in the determination of Edlens-refractivity values. THE and VSL} used the Edlens formula as given in the introduction. Comparison of results from this formula with PTB and NPL results of N shows differences smaller than 5*10-9 in N.

3.2. Results of individual measurements.

As mentioned before it was decided to carry out first individual

measurements of N and to compare these results with calculated values. Since some of the participants have carried out a great number of

measurements complete results are given in appendices. In the following paragraphs the results of each of the refractometers are surveyed by showing up the differences between measured and calculated (Edlén) values, taking the latter ones as a reference. It should be pointed out that, by doing this, systematic and random errors of the calculated values are - at least optically - transfered to the measured values. This procedure was taken only

(21)

3.2.1. NPL results.

The NPL results of individual measurements are listed in appendix 6.1. The differences between measured and calculated (Edlén) values are given in graphic farm in figure 3.2.a. Part of the results on 10-6 were influenced somewhat by the Eindhoven filling system since some of these values are taken from the comparison measurements between NPL and THE. Also a few of the measurements on 9-6 may be influenced by the NPL-PTB comparison (3.3). Since the calculated values have a total uncertainty of 8*10-B in N, as shown in 4.1., nobetter results can be expected.

(22)

16 12 IA.

~

..I. t.Z..

if

~

~ '~

$

...-t

~-t

~

0

~

11

_'po

J

~

13

Po

14f

~

't

~

1---U 8 4 0 4 8 12 16

.

Fig. 3.2.a. NPL measurements.

A

~

_"

I. \

"

~

h/

...

,

__

~

~b-.

1'1 17

Po

/'[

_t'n

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(23)

3.2.2. PTB - Results.

Complete PTB-results are listed in appendix 6.2. Results of 7-6 are

recalculated to temperature

a

_{2 outside the refractometer while the results} from 8-6 to 10-6 are recalculated to the temperature of the sample-place. No differences in pressure and humidity between sample-cel! and sample-piace have been supposed.Figure 3.2.b shows graphs of the differences between measured and calculated values. The results of 9-6 and 10-6 show good agreement with calculated values but some of the results of 7-6 and 8-6 differ considerably from the calculated values. The apparatus then was

checked and the arrangement of the temperature sensors was altered to remave unwanted thermal effects. After that the temperature of the air probe in the refractometer was measured with a smaller systematic error and from then on the results show a good agreement with Edléns values. From the results of 9-6 and 10-6 it can be concluded that results of the measurements are within ±1*10-7 of the calculated values which is the aim of these camparisen

measurements as given in the task description of BCR. 3.2.3. THE - Results.

These results are listed in appendix 6.3. Since the complete

measuring-procedure, due to the pumping duration, took more time than with the ether refractometers, less results are available. Also the preparatien of the air-sample for co_{2 analysis and the modification of the filling} station, for direct camparisen measurements with NPL, taak some extra time. The THE-results are graphically represented in figure 3.2.c. Here again the differences between measured and calculated values are given. They show a goed reproducibility of the measurements but there is a mean offset of +1,1*10- 7 from the calculated values. The analysis given in paragraph 3.4 will explain, at least for a part, this offset.

3.2.4. VSL - Results.

After the replacement of the valves preliminary measurements were carried out on 8-6. Results of measurements on 9-6 and 10-6 are given in appendix 6.4. The results of 9~6 show relatively large differences with calculated values which may be explained, at least partly, by a temperature difference between wall and air-sample in the sample-cel!. On 10-6 this problem was evereome by using the temperature measured at the sample-place, considering that the temperature of the air-sample changes only slightly. The results are represented graphically in figure 3.2.d and show better results for the measurements on 10-6. It was concluded that a temperature measurement inside the sample-cell would imprave the results.

(24)

32 A~ .. 1)11o8 2 8

l

24 20 16 12

}

_~

lol I

1'\

V

"r

J

~

I

'!-I

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_~

/.

'

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4 0 4

~~

..J. ~

1~

~

"

l..

V·

11 00~ !)_ 1~ 13 ....,( "---'t ~

-...

<

tf"'

'-V 8 12 16 Fig. 3.2.b. PTB measuréments.

rV

~

<r>--.

p

~

t.

'

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I

L

l

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_I

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)

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18 h ~

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00 I me 19

oo

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7-6 0 8-6 Ä 9-6 <>10..6 I I'.) w I

(25)

A(n-1)lt108

l

20 18 16 12 8 i.

~

I ...{ ' \ ~ _!,...~

~

--

r--I"'

~

;s

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~ 4 0 1000 1100 1200 1300 1400

Fig. 3.2.c. THE measurements.

( _~

-

-A

1.,...1

"03

~

'1! .

....,.__,

~

(

1500 1600

~

j -'

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1700 1800 .. Time 19 00 [] : 8-6

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:10-6 I N ~ I

(26)

40

1

30 Q....

-V

....

'

f\

V

20

\

~

mi

1\

10 IL..- ..

V

110~ 1200 1300 1400 0 Fig. 3.2.d. VSL measurements.

r--~I

\

_~

,V

...

.

1500 1600

~

~ 1700 11 18 00 T I me 8 : 9-6

BI

1o-6 I N IJt I

(27)

3.3. Comparison of individual resuits by recalculation to sample-piace conditions.

To make a direct comparison of the measured values of N possible, some results are re-calculated to sample-piace conditions. Since on 7-6 no temperatures for the sample-piace were available the temperature condition on the outside of the PTB-refractometer was taken as reference. On the other days information about the inlet conditions was available so the results are then referred to conditions at the sample-place. Since only a limited number of measurements coincide in time only these values are taken for

re-calculation. In appendix 6.5 these values are given whiie these are shown graphicaliy in figures 3.3.a to 3.3.d. If different values of pressure and humidity were measured, compared to sample-piace conditions, the measured value of N was aiso corrected for this differences. As explained befare the measured results of PTB at 7-6 and 8-6 are probably influenced by a

systematic error in the temperature measurement. After 11.00 h on 10-6 the NPL-refractometer was connected to the THE inletsystem, so the results were altered compared to values measured before 11.00 h.

The results show no large differences when compared to the individual measurements but there seems to be a smal! tendency to higher values of refractive index compared to the calcuiated (Edlên) values as seen from the graphs.

(28)

380 370

~~

(N-1) ,1(108

I

360 350 340

')q

·~

_~~

)

~

330

"

320

~

'\. A 310

"\

ffi

27300

\

~

290 1f400 1 sOO 1 eOO 1700\

~1

8~

1 gOO 280 --...,_

'{

270

~

' - -

--Fig. 3.3.a. Results on 6-7 near the PTB-refractometer.

Cl:

NPL 0: PTB

6.:

THE

x:

Edlén 2 ooo 7 10-Time I ('.,) -...I I

(29)

(N-1~10

l

380 370 360 350 340 330 320 310 27300 290 280 270 200 250 240 230 $: [B:

&:

x:

10

Fig. 3.3.b. 19830608 Results at sample-place conditions.

PTB NPL THE Edlén I N Q) I

(30)

360

&

(N-1} *108 ₃₅₅

•

• l

350 345 340 i

m

~

L:~ A 335

1\

...a ~~ 330

l

~

kei

325 ~

~

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27320 ~ 315

'\

15 .. 11 1 2 1 3

~

1 6 310

\

305

\

300

\

~ A 295

f

1\

!V ....,

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_4~ 290 Î\ 285

\

280

)e

Fig. 3.3.c. 19830609 Results at sample-place conditions.

$: G):

&:

<5>:

x:

10-7 Time

-17

~

PTB NPL THE VSL Edlén I

""

IJ) I

(31)

365

**(N-Y*1os**

t

360 355 350 345 340 27335 330 325 320 315 310 Cl.

~

6

\ 0

_\

₀

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...,.A IA

\

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tl

\

~0~

: 1000 1100

\i>

30 J ~ i\ ~

\~~

! I

\

(~~

Fig. 3.3.d. 19830610 Results at sample-place conditions.

NPL-THE same air inlet after 11.00 h.

o:

0:

6.

~·

x

10-7 PTB NPL THE VSL Edlén Time

(32)

-31-3.4: Direct comparison of NPL-PTB and NPL-THE refractometers.

For a more direct comparison between the refractometers it was decided to couple two refractometers to one inlet-system. In this way the same

air-sample was sent to both refractometers so the performance of the refractometers could be measured, undisturbed by possible differences in the inlet-systems. The results were corrected for any temperature gradients. On 9-6 the measurements between NPL and PTB were carried out. In this case

the PTB system was connected to the NPL filling system. In figure 3.4.a the results of the intercomparison are tabulated while they are graphically represented in figure 3.4.b. Time (N-1 )x108 {N-1 )x108 (N-1)x108 ANx10 8 Edlén NPL PTB (NPL-PTB) 11.20 27345.3 27346.3 27346.5 -0.2 12~00 27337.1 27335.0 27334.0 1.0 14.00 27319.6 27318.8 27318.5 0.3 15.00 27300.6 27297.5 27293.7 3.8 -15.30 27294.1 27293.8 27292.0 1.8

(33)

(N-1) H108 345

~

0 .

.

NP L 0

.

PT

1

340 : ~·

\

I

)(

.

B én Edl 335

~

330 I

~~~

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""'

"

10-? 325

""'

1 ... 27320

""

315 11 00 1200 1 300

~

~0

₁₅₀₀ •1 6

oo

310

\

305

1\

300

\

295 [

~

290

0 _f

~

Fig. 3.4.b Direct comparison NPL-PTB.

The direct comparison between NPL and THE refractometers was carried out on 10-6. The NPL-inlet-system in this case was coupled to the THE filling system. For this experiment an extra outlet-valve was mounted on the THE-filling-system so the NPL inlet-system could be connected to this valve. Results of the experiments are tabulated in figure 3.4.c and shown

graphically in figure 3.4.d. The intercomparisen shows a good agreement between NPL and THE results, the THE results being consistently slightly higher (àN<5*10- 8 ). In addition both the NPL and THE results show an offset of+ 7.6*10-8 when compared to the calculated values. Since earlier

measurements of NPL show good agreement with calculated values this difference can be attributed to some property of the THE inlet-system. Analysis of Edléns formula show that a lower humidity value of the air in

the sample-cel! would cause the measured difference.

(34)

-33-Time (N-1)x108 (N-1)x1o8 (N-1)x10

8

ANx10 8

Edlén NPL THE NPL-THE

11.10 27332.4 27341.2 27346.0 -4.8

11.35 27325.9 27332.5 27336.1 -3.6

11.55 27319.8 27327.5 27331.1 -3.6

12.30 27310.2 27317.5 27320.4 -2.9

Fig. 3.4.c Results of direct comparison NPL-THE.

1

₃₃₅340 330

0

(\. 1Ö7

"

tJ

_{L_} 325

"'

~ [

"

27320

""'

315 1 00 ₁₁30 _1~

~

1~

~

13 310

"'

305

"'

300

Fig. 3.4.d Direct comparison NPL-THE.

(Off-sets discussed insection 3.4).

C::,.

0 x

bo

.

T THE NPL Edlén I me

(35)

3.5. Changes of co 2-content durinq the measurinq period.

As explained before each day the co2-content of the air was measured several times. The results show rouqhly the same behaviour each day as may be seen in fiqure 3.5.a. There is a considerable increase of co₂-content over the day; which can be related to the number of people {7-8) taking part in the experiments in a 300 m3 volume room which was air controlled by a closed circuit. The influence of the co 2-content increase can be calculated from the formula given in paragraph 1. This gives in increase in N of 1.4 parts in 108 for a 100 ppm increase in co2-content.

800 .I. ~

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t:::=-J

~

v

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(A

400 300 900 1000 11 00 1200 1300 1400 1500

1a00

1~ 1800 Time

(36)

-35-Chapter 4.

UNCERTAINTY ANALYSIS AND CONCLUSIONS.

In the preceding chapters experiments and measurements are described as they have been carried out in June 1983. Now an analysis of uncertainty of the calculated values of N will be given as well as a survey of the uncertainty of the results of each refractometer. Details about random and systematic

uncertainty are represented in the appendices. Some conclusions about the measurements and results are given in the second part of this chapter. 4.1. Uncertainty of calculated values of refractive index of air. In chapter 1. the formula has been given for the calculation of N from measured values of P, T, H and co2-content. From literature, [1] and [2], a maximum systematic uncertainty of ~ 5*10-8 is given for the calculated value of N without taken in account any uncertainty in P, T, H and

co

_2-content. Uncertainties in P, T, H and co 2 cause additional uncertainty in the calculated value of N. This influence can be calculated by partial differentlation of N = _{F(P,T,H,co2} and gives the following relations:} dN/dP = 2.67

*

10-9 ,dP in Pa

dN/dT = -9.20

*

10-7 ,dT in I{

dN/dF = -4.21

_*

10-10 ,dF in Pa dN/dC = 1. 45

*

10-10 ,de in ppm

Systematic uncertainty in pressure-measurement will be within 20 Pa while random uncertainty is estimated as less then 10 Pa. Total uncertainty in N due tothese uncertainties will be ± 6*10-8 . Systematic part in temperature-measurement will be 10- 2K maximum while the random part is estimated as

10-2K. So the uncertainty in N due to temperature uncertainty will be ±1.3*10-8 . Systematic uncertainty in the measurement of absolute humidity has been estimated earlier as ±30 Pa while the random uncertainty as

calculated, is small compared to this value. From this an uncertainty in N of ±1.3*10-8 can be calculated. For the co2-content only an overall relative uncertainty of ~6\ was available which results in 57 ppm for the maximum measured

co

_{2-content. This uncertainty causes an uncertainty in N of}

±0.8*10-8. Quadratic addition of partlal uncertainties described here give a total uncertainty in N of ~8*10-8. All uncertainties given correspond to 95\ confidence interval (2o). Uncertainties of the measured values were

calculated by the partielpants and depend, of course, on the refractometer principle used. The partleipants have calculated their total uncertalnty in the measured values of N as:

(37)

NPL: ~ 2.2

_*

10-8 PTB: ~ 1.0

*

10-8 THE: ~ 4.0

*

10-8 VSL: ~ 6.0

_*

10-8

These are instrumental uncertainties and additional uncertainties will occur when the differential temperature measurement is used.The magnitude of these errors will be at least 3*10-8 and will be dependent upon the measurement

situation. The uncertainties of THE and VSL are somewhat higher than the values calculated by PTB and NPL because their results had to be corrected

for the expansion of the interferometer-path. This correction was calculated from the measured temperatures.

4.2. Conclusions.

The intercomparisen has provided the information required for the

development of instruments for use in industrial applications were a length accuracy of 1

*

10-7 is required.

From the results presented here it may be concluded that most measured values covered the aim of the project being a maximum uncertainty of

1

*

10-7 in the measurement of the refractive index of air.

The direct comparison of PTB, NPL and THE refractometers showed an agreement of better than 5

*

10-8 and thus significantly better than the aim of the project.

In addition the comparison of measured and calculated values proved that the model uncertainty of Edléns formula is better than 5

*

10-8 provided that the correction is carried out for

co

_2-content.

The measurements in some cases indicated some imperfections of the set-up which required modification. Special attention has to be paid to the

measurement of temperature which is the most limiting factor with respect to the deviations of a comparison (see chap. 4.1 for the dN/dT value). Impraper temperature measurements caused most of the troubles during our measurement. It is worth noting that during the experiments the atmosphere was not

contaminated to any extend. However the

co

_{2-production of around eight} people caused an increase of up to three times the normal content (3 in

104). In industrial environments much larger disturbance of

co

_2-content tagether with organic vapours might be expected and large errors are possible if these factors are neglected as in the usual procedure in

commercially availably laser interferometers. It might be concluded that to achieve an absolute accuracy of 1

*

10-7 it is essential to measure the

refractive index directly with a refractometer, these measurements having no dependenee on variations of the constituentsof the air.

(38)

-37-Chapter 5.

RECOMMENDATIONS AND ACKNOWLEDGEMENTS.

The value of the direct comparison of different refractometers was underlined by the results in this report which made the isolation of a

number of minor instrumentation differences between individual instruments possible, and higher accuracies to be achieved in the measurements by the examination of an indentical sample of the surrounding air.

A second intercomparison between these instruments, when they have been improved, in 1985 would culminate this essential standardisation work. If by these experiments a good agreement can be reached, information about the accuracy of Edlens formula can be obtained giving more information about possible systematic effects.

We like to thank the Community Bureau of Reference (BCR) of the European Commission for the organisation, the financlal support and the stimulating enthusiasm contributed to this intercomparison exercise which was done within the Applied Metrology Programmof BCR under the supervision of Dr. K. Hoffmann. Last but not least we like to thank Prof.Drs. J. Koning of the Metrology Labaratory of Eindhoven University for his hospitality and support

before and during the experiments and for reading the draft report.

REFERENCES.

[1] Bengt Edlén.

The Refractive Index of Air. Metrologia, 1966.

Vol.2, No 2. [2] Frank E. Jones.

The Refractivity of Air.

Journal of Research of National Bureau of Standards 1980. Vol.86, No 1.

[3] T.M. Dauphinee.

Potentiometric Methods of Resistance Measurement.

Temperature. lts Measurement and Control in Science and Industry. Ed. C.M. Herzfeld. Vol. III. 1962.

(39)

Chapter 6. APPENDICES. 6.1. NPL- Results. 6.2. PTB - Results. 6.3. THE - Results. 6.4. VSL - Results.

6.5. Results of recalculation of individual measurements to sample-place conditions.

(40)

-39-6.1. NPL- Results.

The results are presented in the original form as the were supplied by the NPL-participants.

(41)

EINDilOVEN UNIVERSlTY

(JUNE 1983)

CELL All! DEW C02 (PPM) AIR REFRACtlVITY MEASURED- co2 co2 CORRECTED HEASIJRF.Il

PRESSUIIE (n-1) x 10 8 VA!.IJF.S

TIME _(PASCALS) TEMPERAfURE •c POINT TIME EXTRAPOLATED CAt.CULATED CORRECTION MEASURED VAt.UE

KB4 KB6 •c VA LUES CALCULATED (EDLEN) _x_10-8 - CALCULATEO CORRF.C'I'F.ll '1'0

MEASURED (EOLEN) _-8 VALUE (EOLF.N) NPI, 1'F.HPF.RA'I'IIRF.

'! 1o-8 Tuesday 7th 1130 680 - 5.6 1<100 101930 19.320 325 9.1 721 27365.0 27356.0

..

9.0 - 6,2 + 2.8 1420 101926 19.331 335 9.2 727 27360.0 27353.6 t 6,4 - 6.3 • 0.1 1430 730 1450 101890 19,319 329 9.4 733 27348.8 27344.1

_•

<1.7 - 6.4 - l. 7 1510 101887 19.345 355 9.4 736 27343.7 27340.9 + 2.8 - 6.4 - 3.6 1525 101885 19.377 387 9.5 739 27342.5 27337.0

•

5.5 - 6.5 - 1.0 1535 101877 19.400 409 9.6 741 27340.0 27332.4 + 7,6 - 6.5 + 1.1 I 1555 101857 19.1176 488 9.9 744 27330,0 27318.7 + 11.3 - 6.6 t 4.7 ,j:l. 0 1600 745 I 1615 101842 19.500 508 10.2 750 27325.0 27311.6 + 13.4 - 6.6 + 6.8 1645 101844 19.553 564 10.4 758 27321.2 27306.4 + 14.8 - 6.8 • 8.0 1705 101830 19.552 564 10.6 764 27312.5 27301.9 + 10.6 - 6.9 + 3.7 1735 101001 19.682 695 10.7 769 27292.5 27281.6 + 10.9 - 6.9 + 4.0 1755 101781 19.692 707 10.7 1111 27283.8 27275.0 + 8.8 - 7,0 + 1.8 1800 780 1810 101785 19.717 735 u.o 703 27285.0 27272.6 + 12.4 - 7.1 + 5.3 Wednesday 8th 0900 380 0950 101688 18.604 596 8.6 490 27361.3 27360.5

_•

0.8 - 2.9 - 2.1 1010 101?1<1 18.586 583 8.1 545 27368.8 27366.6 + 0.2 - 3.6 - 3.-1 1030 101705 18.639 641 8.8 596 27358.8 27360.6

-

1.8 - 4.4 - 6.2 1100 668 1115 101782 18.775 781 9.0 673 27368.8 27367.7 + 1.1 - 5.5 - 4.4 1130 101776 tl.a35 849 9.0 678 27365.0 27360.1

_•

4.9 - 5.6 - 0.7 1200 101700 J.8.958 972 9.3 688 27330.0 27327.0 + 3.0 - 5.7 - 2.7 1230 :t01675 19.099 116 9.3 698 27313.7 27306.9 + 6.0 - 5.9 + 0.9 1330 101634 19.341 353 9.35 719 27281.3 27?.73.4 + 7,9 - 6.2 + I, 7

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WedneRday continue~! 8t.h 1440 1500 1530 1600 lf\30 1715 'l'hurRrllty 9 th Friday 1110 1120 11::10 1200 1230 1245 1345 1400 1500 1530 1600 1615 1630 1645 lOth 1000 1015 1030 1110 1135 1155 1230 121\5 101728 101720 101679 101685 101652 101711 102130 102132 102132 102127 102135 1021<15 102137 102132 102120 102107 102095 102089 102095 102100 101992 101984 101976 101970 101955 101950 101942 101930 19.504 19.626 19.709 604 646 731 19.760 779 19.915 933 19.972 983 20.045 047 20.032 036 20.035 041 20.108 114 20.121 131 20.169 180 20.304 311 20,316 322 20.482 482 20.516 526 20,561 5?2 20.601 608 20.585 593 20.642 652 19.603 595 19.574 570 19.574 572 19.696 19.?42 19.786 j9.872 697 748 801 882 19.895 909 9.6 9.6 9.6 9.7 9.8 9.8 9.8 10.0 9.9 10.0 10.0 10.1 10.1 10.0 10.3 10.2 10.2 10.2 10.3 10.5 9.5 9.5 9.5 9.!! 9.5 9.7 9.9 10.0 1600 743 750 760 770 772 776 1800 780 0900 1130 1400 1600 0900 410 609 625 640 649 656 662 660 690 730 750 770 780 785 788 430 470 460 490 1100 510 1240 510 576 614 661 700 710 27276.2 27275.0 27256.3 27252.5 27233.7 27242.5 27346.3 27346.3 27346.3 27335.0 27340.0 27336.2 27322.5 27318.8 27297.5 27293.8 27287.5 27280.0 27262.5 27276.3 27343.8 27347,5 27346.3 27341.2 27332.5 27327.5 27317.5 273f?7.5 27274.6 27266.5 27249.6 27246.2 27222.6 27233.4 27339.5 27340.5 27340,5 27332.0 27332.7 27330.6 27315.8 27313.8 27294.3 27287.5 27280.2 27275.0 27277.6 27272.9 27345.4 27345.7 27343.5 27329.3 27321.6 27315.2 27304.6 27298.6 • 1.6 + 6.5 t 6.7 + 6.3 + 11.1 + 9.1 + 6.8 .. 5.8 + 5.8 .. 3.0 • 7.3 + 5.6 t 6.7 • s.o • 3.2 .. 6.3 • 7.3 + 5.0 + 4.9 + 3.4 - 1.6 • 1.8 + 2.6 + 11.9 + 10.7 • 12.3 + 12.8 • 6.9 - 6.5 - 6.6 - 6.0 - 6.9 - 7,0 - 7.0 - 4.6 - 4.8 - s.o - 5.1 - 5.3 - 5.4 - 5.6 - 5.8 - 6.3 - 6.6 - 6,9 - 7.1 - 7.2 - 7.2 - :!.5 - 2.6 - 2.6 - 3.1 - 4.1 - 4.6 - 5.6 - 6.1 - 4,9 - 0.1 - 0.1 - 0.6 • 4.1 • 2.1 + 2.2 • 1.0 • 0.8 - 2.1 • 2.0 + 0.2 + 1.1 - 0.8 - 3.1 - 0.3 + 0.4 - 2.1 - 2.3 - 3.8 - 4.1 - 0.6 0 Air smple • 8. 8 t:al<en~t Elrd-tlltm + 6 • 6 valve am filter + 7.7 • 7.2 + 2.8 1'1'11 i'7?.7R.8 R ( N!>I,-I"I'B -1 , f. x 10- ) I'"1'FI ?73411.5 -8 ( NPI-PI'Il - 0. 2 x 10 ) rrn i'73Y•·o R ( NPL-1'"1'FI 41.0 x 10- ) I

""'

PTB 2?318.5 8 (NPI~PTB +0., x 10- ) Pre 2?293·? ₈ (NPL-PTB +3~ x 10- ) Pt'B n. ::>.o -8 {NI'I-PTB 11, x 10 ) PTB 27~3·9 -8 (NPL-PTR -Ö.1 x 10 )

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Souree UNCERTAINTY IN CELL LENG TH UNCERTAINTY IN FRINGE COUNT DUE TO (1) ambient drift (1) (2) fringe count reading

Parameter uncertainty :t 14.5 J.IJil :t 0.045 counts :t 1.2s x

tö

8 ( 2) Uncertainty in (n-1) x toB Random systematic :t 1. 45 :t 1.12 :t 1.25

(1) refers to parameter drift during maasurement cycle.

(2) parameter uncertainty quoted in tenns of (n-1)

99\ Confidence interval (n-1) x toB :t 2.17 :t 2.07 ± 1.25 Tbtal uncertainties in (n-1) x 108 Random Systematic :t 2.42 :t 2.17 Total uncertainty in (n-1) x 108 for measured refractivities ± 3.25 I ~ N I

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-43-6.2. PTB - Results.

Original results as supplied by PTB-participants.

Summary of uncertainty calculations for measured values of N: Resolution of the interferometer: +1*10-9

Uncertainty in N due to the interf;rometer ~1*10-8.

Contribution of temperature measurement to uncertainty: ~4*10-8.

!e

₃

-e

_{2 Ji0.5K.}

Overall uncertainty of the refractometer used with temperature measurement: ±5*10-8

For the values of N, calculated from Edlens formula, an uncertainty of ±8*10-S has been claimed.