Long gauge block measurements based on a Twyman-Greeninterferometer and three stabilized lasers

Han Haitjem&' and Gerard J. Kotteb

a Eindhoven University of Technology, Precision Engineering Section, 5600 MB EindhovenbNederlands Meetinstituut, Dimensional Metrology section, 2600 AR Deift

The Netherlands

ABSTRACT

An interferometer is realized, based on the Twyman-Green Interferometer principle for the calibration of long gaugeblocks and length bars in the 100 - 1000 mm range with an uncertainty ofO,02 jim + 0,1 pm/rn. Also the expansioncoefficient of gauge blocks and even of rod-shaped materials with non-optical flat faces can be calibrated in the I 8 -22 °C range with an uncertainty below 1107/K.The set-up basically follows the most commonly used interferometer arrangements for long gauge blocks as they aredescribed by Darnedde1, Ikonen2 and Lewis3 where the most similarities with the latter occur.The set-up has some peculiarities which make the measurement straightforward, accurate and reliable.These features are:- A Zeeman-stabilized laser (TESA, type SR), calibrated against a Iodine-stabilized laser, is used as the reference. Inaddition, two two-mode stabilized He-Ne lasers ('green' and 'yellow') are used. The wavelength of these two lasers iscalibrated with an uncertainty of 1.108 using gauge-block measurements in a step-up method.These three lasers can simultaneously be used for two more short-gauge block interferometers.- Temperatures are measured using 20 k thermistors calibrated in the 18 -22 °C range. Thermistors have a highertemperature-sensitivity, higher stability and a lower seift-heating when compared to e.g. Pt-100 elements.- The optical alignment is carried out with an autocollimator which is, after adapting the optics, used for viewing theinterference pattern in the same position.

The fraction is determined from a linearized voltage which is applied to a piezo system which can both tilt and movethe reference mirror parallel.- The temperature inside the interferometer is controlled by a thermostatic bath.- Special tools are applied to enable a calibration of the expansion coefficient of any rod-shaped material; reflectingand optical quality surfaces are not necessary.

Keywords: long gauge blocks, length bars, interferometry, dilatometry

a Further author information -H.H.(correspondence): Email: H.Haitjema@wtb.tue.nI; Telephone +31 40 2473715; Fax +31 40 2465330G.J.K.: Email: gkotte@nmi.nl; Telephone +31 15 2691642; Fax +31 15 2972557

Part of the SPIE Conference on Recent DeveIoments in Optical Gauge Block MetrolociySan Diego. California • July 1998 25

SPIE Vol. 3477 • 0277-786X/981$10.00

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1. INTRODUCTION

Long gauge blocks up to a length of 1 m and, in cylindrical form, length bars, are used as secondary length standardsin industry and in calibration laboratories in the field of dimensional metrology. These standards are used to transferthe unit of length to other length standards and instruments. Especially the use for the verifications of coordinatemeasuring machines (CMMs) requires a gauge block calibration with an uncertainty less than 0,5im for the highestgrade CMMs.As the demands for such high-level calibration normally have to be satisfied by national metrology institutes, anumber a calibration facilities have been developed in several countries. Several authors have describedinterferometer set-ups where the gauge block length is calibrated in terms of light wavelengths which are traceable toa primary length standard: an Iodine-stabilized He-Ne laser. Darnedde' has described the PTB-set-up which uses aKösters interferometer and three Iodine-stabilized lasers. Ikonen2 uses a method in which the gauge-block-optical flatcombination is moved and a reference point in space is established using a white-light interferometer so that only one(laser) wavelength is needed in order to determine a displacement instead of an absolute length. This method is alsoused at OFMET (Wabern, Switzerland) and IMGC (Torino, Italy). Lewis3 and Noguchi4 use multiple wavelength in a

Michelson/Twyman-Green type interferometer.The latter set-up is also used at the NMi and is described in detail in this paper. The instrument is an adaptation of aninstrument which was designed to operate in vacuum as a wavelength comparator. It will be shown that a use as awavelength comparator is still highly useful. The first test measurements, which will be partly described in this paper,were on 600 and 1000 mm gauge blocks in the framework of EUROMET project #254, organized by the PTB. Theresults of this international comparison are already described by Darnedde and Helmcke5. Since then, the instrumentwas used for calibrations for the industry and accredited laboratories. Also, reference measurements were carried outfor a comparison of long gauge block calibration facilities which were accredited by the Dutch laboratoryaccreditation organization (RvA/NKO). Recently a special tool was added to enable the calibration of expansioncoefficient of rod-shaped materials, even if they do not have optical refecting surfaces.

2. INTERFEROMETER DESIGN

The interferometer is basically of the Michelson/Twyman-Green design6. Additional focusing and path-folding mirrorsare used to limit the physical size of the instrument. The interferometer is laid out horizontally inside a chamber, seefigure 1. The original evacuation capability is dropped to enable temperature-controlled water flow through tubesinside the interferometer which now can be temperature-controlled up to a stability of 0.01 °C over a day in a 18-22oc range in the 20 °C laboratory environment.The light enters through the entrance slit E which is in the focus of convex mirror F which has a focal distance of 900mm. The collimated beam is reflected by mirrors Ml and M2 and split by beamsplitter BS. One part passes throughthe compensator C and is reflected by the reference mirror M4. The other part is reflected via M3 by the gauge blockGB which is wrung on the reflecting optical flat OF. The interference pattern is viewed through theautocollimator/telescope AC. This autocollimator is also used in the alignment of all mirrors: in the autocollimatoritself the parallelism between M4 and OF can be observed. Also the autocollimator beam can be followed in thereverse direction and it can be checked whether it is focused in E. The course adjustment of the gauge blockorientation and all mirrors is carried out using micrometer screws. The fine adjustment of M4 takes place using a 3-segment piezo translator (Burleigh) which generates a displacement of 2 Mm/I000 V.

MlIl —---II —.------- — EF Ii —--.----------I I — --- — - -II -.-- —III IIIIt - — — —— .—— — _I - — --- — — ——— —

—-. #-

AC

(:oii

Figure 1 . Schematic optical lay-out of the interferometer

3. SPECTRAL ILLUMINATION SYSTEM

The spectral light sources are three He-Ne frequency stabilized lasers: Tesa type SR (red, Zeeman stabilization), Tesatype SG (green, 2-mode stabilization) and Tesa type SY (yellow, 2-mode stabilization). With these 3 wavelengths:632.99 nm, 543.51 nm and 593.9 nm respectively, a measured length needs to be pre-determined with an absoluteuncertainty smaller than 4.7 tim. Note that the use of a 4thHe-Ne laser with a wavelength of 612 nm does not improvethis, as also this wavelength almost fits an integer number oftimes in 18.98 pm. To distinguish between 2 successivefraction intersections of the red and the green wavelength, the fraction determination must be better than 8% (22 nm).A more extensive treatment of these considerations is given by Lewis3.

The illumination system is sketched in figure 2: the 3 wavelengths are mixed in a 3-to-3 fiber coupler. Each outputfiber contains all 3 wavelength. One output is used for the long gauge block interferometer. A fiber shaker removesthe speckle. With a lens which fits the apertures of the fiber output to the focusing mirror F in the interferometer, thefiber output is imaged on the entrance slit E of the interferometer. The wavelength is selected by opening theelectromechanical shutter of the selected laser.The two other fiber outputs are used for two Kosters-type interferometers which are used for gauge blocks <100 mm7.

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M4

Piezo

M3I

9 OF

28

To

Figure 2. Sketch of optical fiber delivery system

4. FRACTION DETERMINATION

As already mentioned, the reference mirror can be adjusted using piezo elements. These elements can also be used togenerate a parallel displacement of the mirror. A parallel displacement shifts the interference lines which are observedvisually in the telescope. In the telescope is a vertical reference line. The fraction is now determined as following:1 . An interference fringe on the baseplate is made to coincide with the reference line in the telescope. The voltage on

the piezos, Vi, is recorded.2. The voltage is increased until an interference fringe on the gauge block center coincides with the reference line in

the telescope. The voltage on the piezos, V2, is recorded.3. The voltage is further increased until the next interference fringe on the base plate coincides with the reference

line in the telescope. The voltage on the piezos, V3, is recorded.This is illustrated in figure 3.

Figure 3. Positioning of interference patterns for determining the fraction

Entrance slit

optical fibers

vi V2 V3

Now the fraction f follows from

V2—V1

3—1 (1)

The voltage resolution corresponds to 2 nm. The voltage is linearized by calibrating the piezos as above, point 1, 3etc. over multiple fringes. The uncertainty in a fraction determination is about 2% which corresponds to 10 nm.

5. TEMPERATURE AND ENVIRONMENTAL CONDITION MEASUREMENT

The temperature of the air and the gauge block are measured using aged 20 k thermistors which are read-out by amultimeter (PREMA type 6000) equipped with a scanner for 10 4-wire channals. The sensitivity of the sensors is 1WmK which is easily measured by the multimeter. The self-heating of the sensors in air was determined to be about0,5 °C/mW. The multimeter current is 7 iA; this makes the self-heat of the thermistors smaller than 1 mK.For the gauge block temperature and the air temperature each 4 sensors are used. The sensors for the air temperatureare positioned near the supporting positions (about the Airy points) in air. The sensors for the gauge blocktemperature are positioned on the gauge block, equally spaced at upper and lower side.The temperature sensors are calibrated together with the multimeter at the temperature section of NMi-VSL. Themaximum uncertainty of each sensor after calibration is 6 mK in a 16-25 °C range. At annual calibrations, nosignificant changes are found. Any drift of the multimeter is monitored using a standard resistor.

The refractive index of air is derived from the air temperature, pressure, humidity and the CO2 content. A modifiedEdlen-equation is used, as proposed by Birch and Downs8 based on accurate measurements such as those bySchellekens9, with a correction for the C02-content according to Muijlwijk'°. The pressure is measured using a digitalbarometer (Druck DPI 140) with an uncertainty after calibration of 0,09 mbar. The humidity is measured using apsychrometer and a Nova-Sina type humidat IC, uncertainty 4 %Rh.. The C02-meter is a Riken Keiki; type: RI-411A,uncertainty 1 80 ppm.

6. LASER CALIBRATION

The red laser frequency is calibrated against an iodine-stabilized He-Ne laser. This primary standard is developed atthe Precision Engineering section of the Eindhoven university of Technology according to the Mise en Pratique" andacts as the Dutch national and primary length standard. The relative uncertainty of the red Tesa laser after calibrationis 61O. As the original calibration data of the yellow and green laser caused some problems we decided to derivethese wavelengths from gauge block measurements thus using the interferometer as a wavelength comparator.The requirements for the accuracy of the yellow and green laser are rather demanding: in order to achieve a uniquelength determination from the fraction measurements, the fraction must be determined correctly within 20 nm.For a 1 m gauge block this requires a knowledge of the frequency within 2 parts in 108. As soon as the frequencydeviates 26.1O8, the determined length will be one integer half wavelength in error, being 31O. On the other hand,when a gauge block length is known, the wavelength of the unknown radiation can be derived from the measuredfraction, but this wavelength has a number of solutions, being relative 0,3 Mm/i (1 is gauge block length) apart.

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As an example we take the calibration of a 100 mm gauge block with a known deviation of -(0.10 0.05) rim. Thevacuum wavelengths are 632.89908 nm for red (known) and 543.51596 nm for green (first estimate). From thefraction measurements, a length deviation of -0.12 im is derived for the red; the closest solution for green is -0.05rim. To achieve a same result for both the red and green wavelength, we must multiply the green wavelength with (1-0.07 im/100 mm); this gives green 5435 1559 nm. Using the latter wavelength, for the gauge block a deviation of -0.12 im is found for both the red and the green wavelength using the same fraction measurements.By measuring shorter gauge blocks, the derived wavelength becomes proportionally less accurate, but the solutions forthe possible wavelength become wider apart until they can be excluded on physical grounds.We have calibrated the green and yellow laser against the calibrated red laser by measuring gauge blocks withincreasing sizes, using for the larger gauge block the wavelength as derived by the smaller, thus increasing theaccuracy with each step while keeping a unique solution for the wavelength. As an example we take the re-calibrationof the green laser after one of its repairs.

Nominal gauge blocklength I mm

derived green vacuum wavelengthI nm

relative uncertainty relative deviation ofnext solution

20 543.514 804 1.10.6 1.5 1050 543.515 616 4•10 6.106100 543.515586 210 3.106150 543.515 502 1.310 2.106

250 543.515 472 8.108 1.2.106

500 543.515488 4.108 6101000 543.515 480 2.108 310

Note that all environmental influences cancel as long as they are stable between two fraction measurements (usuallysome 20 seconds). Only the dispersive term in the Edlen equations may lead to an erroneously derived vacuumwavelength. Even this is compensated in the later use of the derived wavelength when the same Edlen equations areused. We end up with 3 wavelengths which are calibrated traceable to the primary length standard.

7. THERMAL EXPANSIVITY MEASUREMENTS

The thermal expansion coefficient is determined from the length measurements between, in general, 19 °C and 21 °C.From the length, not reduced to 20 °C, as a function of the temperature, the thermal expansion coefficient is calculatedfrom:

1Ltlltt (2)

where a is the expansion coefficient, I the length, Al the measured length difference and At the measured temperaturedifference. As can be observed in equation (2), the expansion coefficient will be equally sensitive to the relativeuncertainty in the length as to the relative uncertainty in the length difference and the relative uncertainty in the

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temperature difference. This rather low sensitivity to the exact length is exploited in a special tool which enable thecalibration of the expansion coefficient around 20 °C of arbitrary rod-shaped objects.

A picture of the whole assembly. this time attached to a 150 mm gauge block. is shown in figure 4. On one side of theobject, a 5 mm gauge block is positioned in a holder (5) with a flat side facing towards the observer (M3), while atthe other side a partial ball is attached which rests on the bar to be measured. The holder is attached to a ring (I

which is fixed to the bar. At the other side, the optical flat rests against the bar. The optical flat rests in a holder (2).which is attached to the bar via the ring (I ) and pre-loaded by springs (3). For the gauge block, the tilt and the pre-load can be adjusted by screws (6.7.8) in the holder: the optical flat is aligned h' moving the two cylinders on whichthe assembly rests. as which any gauge block.. Now the length of the whole assembly is measured at variousiciuperatures. The length must be corrected for the additional gauge block length and for the probing element length aswell as for the expansion of the gauge block. The length of the bar is sufficiently accurately determined using a CMM.

31

Figure 4. Assembly for expansion measurements

8. MEASUREMENT UNCERTAINTIES

Considering the contributions mentioned in section 5, an uncertainty budget can be made for the length of any gaugeblock of length 1. As a gauge block is calibrated just above and just below 20 °C, the uncertainty in the expansioncoefficient cancels. The example given below is for a steel gauge block on a steel wringing plate. A more extensivetreatment of most contributions is given by Decker and Pekelsky'2.

Source of uncertainty standard uncertainty(is)

sensitivity factor uncertainty in length I

Laser freQuency 3•109f 1/f 3•lOlrepeatability 0.01 m 1 0.01 im

wringing on base plate 0.01 im 1 0.01 imphase correction 0.01 m 1 0.01 pm

aperture correction 1 .5 . 108.l 1 1 .5 . 1 08.1

gauge temperature 3 mK 11.5.106.1 3.2.108.l

airtemperature l2mK 1.106.l 1.2.108.1

air pressure 0.03 mb 2.7•1O1 O.8.108.1

air humidity 2 % 8O1 1.7.108.l

C02-content 90 ppm 1 .3 . 10'°.l 1 .2 1 08.l

Edlen-eguation 1 .8 108•n 1/n 1 .8 108.1

Totalsquared sum of length-dependent and length-

independent_terms

2 -8 7 11'((0.017 pm) + (4.510 •l)}

With a coverage factor k=2 the uncertainty can be approximated, without any significant deviations in any aspect, as

u(k=2) = 0.03 pm + 7.108.l for a steel gauge block with length I � 1000 mm

For the expahsion coefficient a, the uncertainty &x can be derived from equation (2) as:

(a2 (öl2 (&12 (6At2) = T) J +For a 500 mm bar or gauge block, measured between 19 and 21 °C with a 11.5.106 /K this gives as an uncertainty

budget:

(3)

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source of uncertainty standard uncertainty (is) sensitivity factor relative uncertainty in c1 5 pm 1/500mm i•i0

Al 0,02tm 1/11,5tm 21OAT 6mK 3iO

total uncertainty 410

Here, some simplifications are used such as a constant air pressure, humidity and C02-content between themeasurements at 19 °C and 20 °C, and no change in the air temperature calibration error. Some contribution of thesefactors is implicitly included in &\1. The uncertainty in a, using a coverage factor k=2, thus becomesu(k=2) = 9108/K.

9. RESULTS

In the framework of Euromet project #254 the length and expansion coefficient of a steel 600 mm and 1000 mm steelblock were determined. Both values deviated less than the uncertainties as stated above from the reference values5.In the framework of Euromet project #390 the expansion coefficients of some bars with non-optical end surfaces weredetermined. As an illustration, figure 5 gives the deviations from the length at 20 °C of a 543 mm steel bar at differenttemperatures. The measured lengths as a function of temperature are all on a straight line within 20 nm. The derivedexpansion coefficient of x = (1 1.40 0.09).106/K illustrates the accuracy of the method, despite the smalltemperature range used.

Figure 5. Length deviation of a 538 mm steel bar as a function of temperature

86-

6

1 9.0 19.4 19.8 20.2 20.6Temperature in OC

21 .0

33

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10. REFERENCES

1 . H. Darnedde, "High-precision Calibration of Long Gauge Blocks Using the Vacuum Wavelength Comparator",Metrologia 22, pp 349-359. 1992.

2. E. Ikonen and K. Riski, "Gauge-block Interferometer Based on One Stabilized Laser and a White-light Source"Metrologia 29 pp 95-104. 1993.

3 . A. Lewis,"Measurement of Length, surface form and thermal expansion coefficient of length bars up to 1 ,5 m

using multiple-wavelength phase stepping interferometry" Meas. Sci. Technol 5 pp 694-703, 1994.4. H. Noguchi and S.Shuto, "Development of an interferometer for the Calibration of Long Gauge Blocks",

Mitutoyo Technical Bulletin 2 pp 1-7, 1987.5. H. Darnedde and J. Helmcke, "European comparison of long gauge blocks", Metrologia 33 pp 485-491, 1996.6. F. Twyman and A. Green, British Patent 103832, 1916.7. G.J.Kotte and H.Haitjema, "Ball diameter measurements in a Kösters interferometer", this conference.8. K.P. Birch and M.J. Downs, "Correction to the updated Edlen equation for the Refractive index of

air",Metrologia 31 pp 315-316, 1994.9. P.Schellekens, G. Wilkening, F. Reinboth, M.J. Downs, K.P.Birch and J. Spronck, "Measurements of the

refractive index of air using interference refractometers", Metrologia 25 pp 279-287, 1986.10. R.Muijlwijk,"Update of the Edlen formulae for the refractive index of air", Metrologia 25 p 189, 1988.11. T.J.Quinn,"Mise en Pratique of the Definition of the Metre (1992),Metrologia 30, pp 523-54 1, 1993/1994.12. J.E Decker and J.R. Pekelsky, "Uncertainty evaluation for the measurement of gauge blocks by optical

interferometry", Metrologia 34, pp 479-493, 1997.