comparison of the measurement of the phase change on reflection...

EUROMET Project 413: Inter-laboratory comparison of measurements of the phase

correction in the field of gauge block interferometry

Richard K. Leach, Anne Hart

National Physical Laboratory

Queens Road, Teddington

Middlesex TW11 0LW, UK

[email protected]

Abstract

A set of eight gauge blocks, two steel platens and two quartz platens have been circulated to ten

European laboratories, plus laboratories in the USA and Australia, in order to compare methods

for measuring a phase correction when obtaining the interferometric length of a gauge block.

Measurements were made of the central length and a phase correction for each gauge block.

The participants were free to use any method to measure a phase correction. The four methods

used to measure a phase correction were: the phase stack technique, optical scattering methods,

stylus profilometry and a mechanical contacting technique. The results for the central length

measurements showed a linear secular decrease in length as the project progressed - the total

change in length being about 30 to 40 nm. Within a 95% confidence level, the central length

measurements all agree, but the phase correction results vary by as much as 30 nm in the worst

case. Significant changes to the surface were recorded as the project progressed - the scratch

content increased and there was evidence of a reaction of the gauge block surfaces with the box

in which they were housed.

1. Introduction

The most accurate method for calibrating the length of a gauge block is to use optical

interferometry. However, interferometry measures the optical length rather than the mechanical

length of the gauge and an error in the length measurement may be introduced because of the

different bulk and surface characteristics of the gauge and the platen to which the gauge has

been wrung. These different characteristics, such as the surface roughness and the bulk optical

constants, will give rise to a difference between the length measured in an interferometer and

that measured using a mechanical, contacting technique. ISO 3650 (1998) states that a correction

must be applied to the measured length of the gauge to account for the differences in surface

characteristics and this correction is known as the ‘phase correction’.

The measuring instructions for this comparison, which involved ten European National

Measurement Institutes (NMIs) plus one laboratory in the USA and one in Australia, required

each participating laboratory to measure the deviation from nominal length and a phase

correction for eight gauges and four platens. This project is, therefore, a comparison of both

central length measurements and phase correction measurements. This paper presents a

summary of the results of this comparison.

2. Participants and timetable

2.1 The participants

The comparison was undertaken within the framework of EUROMET (project number 413)

with the National Physical Laboratory (NPL, UK) acting as the pilot laboratory. Table 1 lists, in

alphabetical order, the twelve laboratories which participated.

1 Bureau National de Métrologie - Laboratoire National d’Essais, 1 Rue Gaston Boissier, F-75015 Paris, France (BNM - LNE).

2 Centro Español de Metrologia, C/ del Afar 2, 28760 Tres Cantos, Madrid, Spain (CEM).

3 Commonwealth Scientific and Industrial Research Organisation, PO Box 218, Lindfield, NSW 2070, Australia (CSIRO).

4 Centre for Metrology and Accreditation, PO Box 239, FIN-00181, Helsinki, Finland (CMA

5 Danish Institute of Fundamental Metrology, Building 307, Anker Engelunds Vej 1, DK-2800 Lyngby, Denmark (DFM).

6 Instituto di Metrologia “G. Colonetti”, Strada della Cacce 73, 10135 - Torino, Italy (IMGC).

7 Justervesenet, Norwegian Metrology and Accreditation Service, Fetveien 99, N2007, Norway (JV).

8 National Institute of Standards and Technology, Metrology Building, Room B113, Gaithersburg, Maryland 20899-0001, USA (NIST).

9 National Physical Laboratory, Teddington, Middlesex TW11 0LW, United Kingdom (NPL).

10 Physikalisch-Technische Bundesanstalt, Bundesallee 100, 38116 Braunschweig, Germany (PTB).

11 Portuguese Institute for Quality, Rua C à Avedida dos Trés Vales, 2825 Monte da Caparica, Portugal (IPQ).

12 Swiss Federal Office of Metrology, Lindenweg 50, CH-3003 Bern-Wabern, Switzerland (OFMET).

Table 1. Participating laboratories

2.2 Timetable

Each participant was given six weeks to carry out the measurements. The pilot laboratory

measured the gauges at the beginning, middle and end of the project. Table 2 shows the

timetable of the project.

Laboratory Time schedule Date of

measurement Receipt of results

NPL 1/5/97 30/5/97 - OFMET 30/6/97 3/7/97 14/10/97 DFM 11/8/97 18/8/97 11/11/97 CEM 22/9/97 23/10/97 12/12/97 BNM - LNE 3/11/97 5/12/97 5/1/98 IPQ 15/12/97 30/1/98 12/2/98 NPL 2/2/98 19/2/98 - NIST 16/3/98 15/4/98 1/9/98 CMA 27/4/98 2/6/98 1/7/98 JV 8/6/98 16/6/98 -

3/7/98 9/7/98

IMGC 20/7/98 4/9/98 1/2/99 PTB 12/10/98 Not known 3/5/99 CSIRO 1/3/99 16/3/99 -

20/4/99 5/5/99

NPL 1/4/99 20/5/99 -

Table 2 The timetable

3. The gauge blocks and platens

The eight grade K steel gauge blocks were supplied with nominal lengths of 2,5 mm, 3,0 mm,

3,5 mm, 4,0 mm, 4,5 mm, 5,0 mm, 5,5 mm and 6,0 mm. The gauge blocks fulfilled the

requirements of the relevant specification standard (ISO 3650: 1998). Also supplied were two 50

mm diameter quartz platens and two 60 mm diameter steel platens, together with an adjustable

mount to be used for obtaining the correct orientation for the wedged quartz platens in an

interferometer. All the gauges were marked with their respective nominal lengths and the serial

number C289. The gauges were manufactured by Alan Browne Gauges Ltd and were

approximately six months old at the start of the comparison. When measured at NPL, all the

gauge surfaces wrung readily. The coefficient of thermal expansion was given by the

manufacturer as 10,6 x 10-6 K-1 and all participants used this value. Provided the gauges were

measured on the steel platens, no correction for the different optical constants was requested

(although PTB did make a correction). Where the quartz platen was used, a correction for the

optical constant was used (see equation 2.1 in Leach [1998]). The values for the optical constants

of the gauges and platens, n and k, were obtained at Southampton University using

ellipsometry (PTB also used an ellipsometer to measure n and k).

The steel platens were labelled PLBI7 and PLBI8 and the quartz platens were labelled A and B.

The quartz platens were polished so that their optical axes were perpendicular to their polished

faces in order to minimise the difference in thermal expansion coefficient between quartz and

steel.

4. The measurements

Measurements were made of the central length of each gauge block according to ISO 3650. A

phase correction was also measured for each gauge using any method desired. Length

measurements were carried out at 20 ºC ± 0,3 ºC. Instructions for handling and measuring the

gauges as well as for data reporting were distributed to all the participants. Only combined

standard uncertainties (k = 1) have been quoted in the results section.

5. Instrumentation

Table 3 lists the instruments used to measure both central length and a phase correction. NIST

did not measure central length. To determine a correction for the refractive index of the air, all

participants, with the exception of NIST who did not make interferometric measurements, used

the modified Edlèn formula (Birch and Downs 1993, Bönsch and Potulski 1998) along with

measurements of the temperature, pressure and humidity of the air. PTB and NPL also used

interference and phase contrast microscopy to examine some of the surfaces. Details of the

instruments are not presented here but can be found in the references provided.

Laboratory Interferometer used to measure central length/manufacturer

Methods used to measure phase correction

NPL Twyman Green/NPL, TESA (Pugh,

Jackson 1986)

Phase stack technique (Hume K J

1963), Total integrated scatter (TIS)

(Leach 1998)

OFMET Twyman Green/NPL, TESA Phase stack technique

CEM Twyman Green/NPL, TESA Phase stack technique

BNM-LNE Twyman Green/NPL, TESA Phase stack technique

IPQ Twyman Green/NPL, TESA Phase stack technique

NIST Not measured Spherical contact technique (Stoup,

Faust, Doiron 1998)

CMA Twyman Green/CMA (Ikonen, Riski

1993)

Phase stack technique,

Integrating sphere (TIS) (Ikonen, Riski

1993)

JV Twyman Green/NPL, TESA Phase stack technique

IMGC Twyman Green/NPL, TESA Phase stack technique

PTB Twyman Green/PTB Phase stack technique

Integrating sphere (TIS) (Bönsch 1998)

CSIRO Kösters interferometer Mechanical stylus technique (Thwaite

1977)

Table 3 Methods used by the participants to measure central length and phase correction

6. Results and discussion

6.1 Deviation form nominal length

The reference values which served for the comparison of length measurements were calculated

as the non-weighted mean over all measurements for each gauge block. The pilot laboratory,

which measured the length of the gauge blocks three times, thus contributes three times to this

average. Figures 1(a) and 1(b) show the deviations from the nominal lengths for each gauge

block. All the methods for measuring a phase correction have been included in this figure and

the standard deviations for all the results are quoted.

Time (days)

-50-40-30-20-10

01020304050

0 100 200 300 400 500 600 700 800

2.5 mm gauge block

Mean deviation = 2.6 nmStandard deviation = 15 nm

-50-40-30-20-10

01020304050

mea

sure

d

leng

th /

nm

Mean deviation = -32.0 nmStandard deviation =15 nm

3.0 mm gauge block

-50-40-30-20-10

01020304050

Dev

iatio

n

from

m

ean

3.5 mm gauge block


-50-40-30-20-10

01020304050

4.0 mm gauge block

Mean deviation = 16.3 nmStandard deviation =17 nm

NPL1

OFM

ETD

FM

CEM

BNM

-LNE

IPQN

PL2

CM

AJV IM

GC

PTB

CSIR

O

NPL3

Figure 1(a). Deviations from mean measured length for 2.5 mm to 4.0 mm gauge blocks where � and � denote gauges measured on steel platens and quartz platens respectively, using stack method for phase correction, ∆ denotes gauges measured on steel platens using TIS for phase correction and � and � denotes gauges measured on steel platens and quartz platens respectively using surface roughness for phase correction.

Time (days)

-50-40-30-20-10

01020304050

0 100 200 300 400 500 600 700 800

4.5 mm gauge block


-50-40-30-20-10

01020304050

mea

sure

d l

engt

h /

nm

5.0 mm gauge block


-50-40-30-20-10

01020304050

Dev

iatio

n f

rom

m

ean

5.5 mm gauge block

Mean deviation = 23.8 nmStandard deviation = 14 nm

-50-40-30-20-10

01020304050 6.0 mm gauge block

Mean deviation = -39.8 nmStandard deviation = 19 nm

NPL1

OFM

ETD

FM

CEM

BNM

-LNE

IPQN

PL2

CM

AJV

IMG

C

PTB

CSIR

O

NPL3

Figure 1(b). Deviations from mean measured length for 4.5 mm to 6.0 mm gauge blocks where � and � denote gauges measured on steel platens and quartz platens respectively, using stack method for phase correction, ∆ denotes gauges measured on steel platens using TIS for phase correction and � and �denotes gauges measured on steel platens and quartz platens respectively using surface roughness for phase correction.

It is clear from figures 1(a) and 1(b) that there has been a secular change in length for each

gauge block of approximately 30 to 40 nm. A linear fit could be removed from the data to take

account of this secular change in length. However, at this stage of the analysis only the raw

results are considered.

It is impossible to say whether the secular length change is due to chemical and physical

changes in the bulk material, i.e. ageing, or due to wear during handling and repeated

wringing. The condition of the gauges was measured at NPL at the start of the project using

Nomarski phase contrast microscopy. Figure 2 shows a micrograph of a typical gauge surface

before the start of the project.

Figure 2. Nomarski micrograph of a gauge surface before the project began (NPL).

Figure 3. Interference micrograph of a gauge surface during the project (PTB).

The polishing and lapping marks can just be made out in this figure, but the main structures are

the bubbly marks that appear to be topographic features above the mean plane. PTB used

differential interference microscopy and Mirau microscopy to observe a gauge surface towards

the end of the project and noticed the dominant topographical features shown in figure 3 which

now appear to be valleys in the surface. However, measurements using the NPL stylus

instrument, NanoSurf IV, prove that these apparently topographical structures are in fact

crystal grains, having different phase changes on reflection, embedded in the bulk material. The

difference between the condition of the gauges in figures 2 and 3 illustrates that, as would be

expected, they have been scratched during use. Note that the micrographs presented in this

paper are for qualitative information only.

Figure 4 shows the surface of the 3,5 mm gauge at the end of the project measured using the

Nomarski microscope. A new structure is now apparent in the form of the lighter bubbly marks

shown in the figure. Repeated cleaning of the gauge surface did not clear these marks. It was

also noted that only half of the gauge was covered with this structure. To date, the only

explanation of this phenomenon is that the gauges have reacted with either the wooden

material of their box or its treatment process (wood varnish). This structure is not visible to the

un-aided eye. Other gauges also display this effect to a lesser extent.

Figure 4 Nomarski micrograph of the 3,5 mm gauge surface at the end of the project (NPL).

6.2 Phase correction

The results for the phase corrections for the steel gauges on steel platens are presented in figure

5(a) and 5(b). The reference values which served for the comparison of phase correction

measurements were calculated as the non-weighted mean over all measurements for each

gauge block. Note that the guidelines stated that the 2,5, 3,5, 4,5 and 5,5 mm gauges should be

used on platen PLBI7 (or quartz platen A) for one phase stack and the 3,0, 4,0, 5,0 and 6,0 mm

gauges should be used on platen PLBI8 (or quartz platen B). For this reason if the phase stack

method has been used the values for a phase correction will be the same for each gauge in the

stack. This is clearly shown figures 5(a) and 5(b) where the relative dispositions of the results

are the same for all gauges measured on the same platen.

-25-20-15-10

-505

10152025

phas

e c

orre

ctio

n /

nm

3.5 mm gauge block - steel platen PLBI7

Mean phase correction = -12.6 nmStandard deviation = 8 nm

-25-20-15-10

-505

10152025

Dev

iatio

n f

rom

m

ean



-25-20-15-10-505

10152025 5.5 mm gauge block - steel platen PLBI7

NPL1

OFM

ETD

FM

CEM

BNM

-LNE

IPQ

NPL2

CM

A

JV IMG

C

PTB

CSIR

O

NPL3


Time (days)

-25-20-15-10-505

10152025

0 200 400 600 800



Figure 5(a) Deviations from mean phase correction for gauge blocks measured on steel platen PLBI7 where � denotes the stack method for measuring phase correction, ∆ denotes the TIS method for measuring phase correction and � denotes the stylus method for measuring phase correction.

Time (days)

-25-20-15-10

-505

10152025

0 200 400 600 800



-25-20-15-10-505

10152025

phas

e c

orre

ctio

n /

nm



-25-20-15-10-505

10152025

Devi

atio

n f

rom

m

ean



-25-20-15-10

-505

10152025


NPL1

OFM

ET

DFM

CEM

BNM

-LNE

IPQN

PL2

CM

AJV IM

GC

PTB

CSIR

O

NPL3


Figure 5(b) Deviations from mean phase correction for gauge blocks measured on steel platen PLBI8 where � denotes the stack method for measuring phase correction, ∆ denotes the TIS method for measuring phase correction and � denotes the stylus method for measuring phase correction.

The results for the phase corrections for the gauges on quartz platens are shown in figures 6(a)

and 6(b).

Time (days)

-30-25-20-15-10-505

10152025

0 100 200 300 400 500 600 700 800

2.5 mm gauge block - quartz platen A

Mean phase correction = 32.6 nmStandard deviation = 10 nm

-30-25-20-15-10-505

10152025

phas

e c

orre

ctio

n /

nm



-30-25-20-15-10

-505

10152025

Dev

iatio

n f

rom

m

ean



-30-25-20-15-10-505

10152025 5.5 mm gauge block - quartz platen A

NPL1

CEM

IPQ

NIST

CM

AJV IM

GC

CSIR

O

NPL3


Figure 6(a) Deviations from mean phase correction for gauge blocks measured on quartz platen A where � denotes the stack method for measuring phase correction, � denotes the NIST method for measuring phase correction and � denotes the stylus method for measuring phase correction.

Time (days)

-30-25-20-15-10-505

10152025

0 200 400 600 800

3.0 mm gauge block - quartz platen B


-30-25-20-15-10-505

10152025

phas

e c

orre

ctio

n /

nm



-30-25-20-15-10

-505

10152025

Dev

iatio

n f

rom

m

ean



-30-25-20-15-10-505

10152025 6.0 mm gauge block - quartz platen B

NPL

DFM

CEM

IPQ

NIST

CM

A

JV IMG

C

CSIR

O

NPL3


Figure 6(b) Deviations from mean phase correction for gauge blocks measured on quartz platen B where � denotes the stack method for measuring phase correction, � denotes the NIST method for measuring phase correction and � denotes the stylus method for measuring phase correction.

7 Conclusions

If the assumed linear secular change in length is removed from the results then, at 95%

confidence level, the deviations from nominal length are in agreement for all of the

measurement techniques used on all of the gauge blocks. It is reasonable to make this

assumption based on examination on figures 1(a) and 1(b). This shows that the choice of platen

material (quartz or steel) and surface roughness measurement method (stack, scattering or

mechanical stylus) does not appear to effect the overall result. The only exceptions to this

statement are one result for the 5,5 mm gauge block and the final result on the 3,5 mm gauge

block measured at NPL which shows clear evidence of significant changes to the surface that

have occurred during the project.

The largest difference between phase corrections determined by the participants was

approximately 30 nm. This is a relatively large figure compared to the interferometric length

measurement uncertainties which are usually quoted. There is no obvious difference in the

variability of the values for a phase correction for the quartz and steel platens.

In general the results obtained with scattering instruments are in good agreement with the

results obtained using the phase stack technique. The exceptions to this are the final NPL results

where surface changes invalidate this comparison and all NPL measurements on platen PLBI7.

The reason for this latter disagreement is not fully understood at this stage, but may be due to

the reliance of the NPL TIS method on the type of steel (or finishing technique) that is used

during its calibration.

Acknowledgements

The authors would like to thank all their colleagues in the participating laboratories: Kari Riski

(CMA), Joaquín Rodríguez (CEM), Nick Brown (CSIRO), Geneviève Lipinski (BNM-LNE), Jes

Henningsen (DFM), Maria Paola Sassi (IMGC), Helge Karlsson (JV), John Stoup (NIST),

Gerhard Bönsch (PTB), Fernanda Saraiva (IPQ) and Reudi Thalmann (OFMET) for performing

the measurements, supplying all the results and providing valuable comments. They would

also like to thank their colleagues in the Dimensional Metrology Section at NPL: Teresa

Grimshaw, Andrew Lewis and Keith Jackson.

References

ISO 3650: 1998 Geometrical product specifications (GPS) - Length standards - Gauge blocks

(ISO: Geneva)

Birch K P, Downs M J 1993 An updated Edlén equation for the refractive index of air Metrologia

30 155-162

Bönsch G 1998 Interferometric calibration of an integrating sphere for determination of the

roughness correction for gauge blocks Proc. SPIE 3477 152-160

Bönsch G, Potulski E 1998 Measurement of the refractive index of air and comparison with the

modified Edlén’s formulae Metrologia 35 133-139

Hume K J 1963 Engineering Metrology (Macdonald: London)

Ikonen E, Riski K 1993 Gauge block interferometer based on one stabilised laser and a white-

light source Metrologia 30 95-104

Leach R K 1998 Measurement of a correction for the phase change on reflection due to surface

roughness Proc. SPIE 3477 138-151

Pugh D J, Jackson K Automatic gauge block measurement using multiple wavelength

interferometry Proc. SPIE 656 244-250

Stoup J R, Faust B S, Doiron T D 1998 Minimising errors in phase change correction

measurements for gauge blocks using a spherical contact technique Proc. SPIE 3477 161-172

Thwaite E G 1977 Phase correction in the interferometric measurement of end standards

Metrologia 14 53-62

comparison of the measurement of the phase change on reflection...

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