NATL INST. OF STAND & TECH R.I.C.

AlllDM t.S7TbM

I P!

NISI

PUBLICATIONS ^Wm'M.

'»,?r'/'; « '!';«> ^,

. ed States Department of Commerce

Technology Administration

National Institute of Standards and Technology

NIST Technical Note 1410

Measuring Long Gage Blocl<s With the

NIST Line Scale Interferometer

John S. Beers

2995

I
7he National Institute of Standards and Technology was established in 1988 by Congress to "assist industry in the development of technology . . . needed to improve product quality, to modernize manufacturing processes, to ensure product reliability ... and to facilitate rapid commercialization ... of products based on new scientific discoveries." NIST, originally founded as the National Bureau of Standards in 1901, works to strengthen U.S. industry's

competitiveness; advance science and engineering; and improve public health, safety, and the environment. One of the agency's basic functions is to develop, maintain, and retain custody of the national standards of measurement, and

provide the means and methods for comparing standards used in science, engineering, manufacturing, commerce,

industry, and education with the standards adopted or recognized by the Federal Government.

As an agency of the U.S. Commerce Department's Technology Administration, NIST conducts basic and applied

research in the physical sciences and engineering, and develops measurement techniques, test methods, standards,

and related services. The Institute does generic and precompetitive work on new and advanced technologies. NIST's

research facilities are located at Gaithersburg, MD 20899, and at Boulder, CO 80303. Major technical operating units and their principal activities are listed below. For more information contact the Public Inquiries Desk, 301-975-3058.

Office of the Director

• Advanced Technology Program

• Quality Programs

• International and Academic Affairs

Technology Services

• Manufacturing Extension Partnership

• Standards Services

• Technology Commercialization

• Measurement Services

• Technology Evaluation and Assessment

• Information Services

Materials Science and Engineering

Laboratory

• Intelligent Processing of Materials

• Ceramics

• Materials Reliability'

• Polymers

• Metallurgy

• Reactor Radiation

Chemical Science and Technology

Laboratory

• Biotechnology

• Chemical Kinetics and Thermodynamics

• Analytical Chemical Research

• Process Measurements^

• Surface and Microanalysis Science

• Thermophysics^

Physics Laboratory

• Electron and Optical Physics

• Atomic Physics

• Molecular Physics

• Radiometric Physics

• Quantum Metrology

• Ionizing Radiation

• Time and Frequency'

• Quantum Physics'

Manufacturing Engineering Laboratory

• Precision Engineering

• Automated Production Technology

• Intelligent Systems

• Manufacturing Systems Integration

• Fabrication Technology

Electronics and Electrical Engineering

Laboratory

• Microelectronics

• Law Enforcement Standards

• Electricity

• Semiconductor Electronics

• Electromagnetic Fields'

• Electromagnetic Technology'

• Optoelectronics'

Building and Fire Research Laboratory

• structures

• Building Materials

• Building Environment

• Fire Safety

• Fire Science

Computer Systems Laboratory

• Office of Enterprise Integration

• Information Systems Engineering

• Systems and Software Technology

• Computer Security

• Systems and Network Architecture

• Advanced Systems

Computing and Applied Mathematics

Laboratory

• Applied and Computational Mathematics^

• Statistical Engineering^

• Scientific Computing Environments^

• Computer Services

• Computer Systems and Communications^

• Information Systems

'At Boulder, CO 80303. 'Some elements at Boulder, CO 80303.
NIST Technical Note 1410

Measuring Long Gage Blocks With the

NIST Line Scale Interferometer

John S. Beers

Precision Engineering Division

Manufacturing Engineering Laboratory

National Institute of Standards and Technology

Gaithersburg, MD 20899-0001

May 1995

^^ATES o*

U.S. Department of Commerce

Ronald H. Brown, Secretary

Technology Administration

Mary L. Good, Under Secretary for Technology

National Institute of Standards and Technology

Arati Prabhakar, Director
National Institute of Standards U.S. Government Printing Office For sale by the Superintendent of and Technology Washington: 1995 Documents

Technical Note 1410 U.S. Government Printing Office

Natl. Inst. Stand. Techno!. Washington, DC 20402

Tech. Note 1410

20 pages (May 1995)

CODEN: NTNOEF

I

I
Measuring Long Gage Blocks with the NIST Line Scale Interferometer

CONTENTS

Page

1. Introduction 1

2

History of conversion blocks 3

3. The need for end standard to line standard conversion 3

4. A new conversion block design 4

5

Measurement methods 5

5.1 Static interferometry 5

5.2 Dynamic interferometry 6

6

Sources of differences in results 8

6.1 Geometry of the selected block 8

6.2 Geometric and graduation quality

of the conversion blocks 9

6.3 The second wringing film 9

6.4 Length change from horizontal to vertical 9

7. Experimental tests 10

7.1 Objectives 10

7.2 Equipment 10

7.3 Procedure 10

7.4 Results 11

7.5 Additional measurements 14

8

Measurement uncertainty 14

9. Conclusions 16

10. References 16

Acknowledgments 17

lU

Measuring Long Gage Blocks with the NIST Line Scale Interferometer

By John S . Beers

An improved method for temporarily converting long gage blocks

into line scales is described. The new process employs fused

silica rather than previously used steel conversion gage

blocks. Conversion blocks are pairs of small (13 mm) gage

blocks with graduation lines on their side faces. When the

pair is wrung to a long gage block, one at each end with the

graduated faces upward, the long block becomes a line scale.

Converted blocks can be measured by fringe counting (dynamic)

interf erometry in the NIST line scale interferometer. This

measurement can serve as an independent long block

measurement, or it can be used to establish the order of

interference for measuring a long block by single wavelength

static interferometry . The new conversion blocks have several

advantages as shown by experimental evidence . Measurement

uncertainties of the static and dynamic interf erometric

processes are compared.

Key Words: Length; gage blocks; line scales; interf erometry;

uncertainty.

1. Introduction

Gage blocks are linear dimensional standards where the length

interval is defined as the distance between opposing, optically

flat and parallel, end faces. Line scales are linear standards

using graduations to define lengths (e.g., meter bars and

microscope magnification standards) . Both these forms are widely

used in industry to maintain dimensional control in manufacturing

processes ranging from micro-miniature electronic circuits to

aircraft. The key to their utility lies in the ability to relate

them precisely to the international standard of length [1] by

interferometry using laser light of known frequency. At NIST,

static interf erometry [2] (stationary optical components and

stationary interference fringe pattern) is used to measure gage

blocks and dynamic interf erometry [3] (fringe counting with a moving

reflector) is used for measuring line scales.

A method will be described here for temporarily converting gage

blocks into line scales so they can be measured by the dynamic

process. There are advantages and needs for occasional use of this

method to measure blocks over 100 mm long.

Long gage blocks are made of steel and have flat and parallel

opposing faces. These optically lapped gaging faces can be "wrung",

i.e., they can be brought into such close contact that they will

adhere tightly together, separated only by an oil or light grease

wringing film usually less than 0.025 jim thick. This property makes

it possible to combine gage blocks into nearly any length up to 250

1
length up to 250 mm from a standard set of 88 blocks in scaled

lengths from 0.5 mm to 100 mm. Supplementing these sets with longblock sets of 8 scaled lengths from 125 mm to 500 mm greatly

extends the range

Precision line scales come in many forms. Some are metal, usually

steel or Invar, where the lines are machine ruled with diamond

points. Others are transparent materials such as glass or fused

silica with deposited chromium rulings. Line widths from less than

1 /im to 10 /zm or more and spacings (line center to line center)

from 1 fim up to 1 m or more are available.

Converting a selected gage block into a line scale is accomplished

with a pair of small conversion gage blocks having graduations on

their non-gaging faces as shown in Figure 1. The two conversion

blocks are wrung to the selected block, one at each end, with the

ruled faces in the neutral plane of the selected block, as shown in

Figure 2 . An interf erometric measurement of the combined length is

then made, i.e., the interval from center to center of the two

graduations. The conversion blocks are then removed and wrung

together in the same orientation as when wrung to the selected

block, and the interval between graduations is measured by

interf erometry. This conversion interval length is subtracted from

the combined length to obtain the selected block length:

Lc = L„ - L^n

where Lg is the selected block length, L^ is the measured combined

length, and L^ is the measured conversion interval length.

-Graduations and

alignment lines

mrrfl l ®\®

13

mm

>k13

mm

'Gaging face

(two opposing

faces on each

block)

Figure 1. Photo and schematic of conversion blocks.

Figure 2 . Conversion block wrung to selected block,
2. History of Conversion Blocks

Measuring gage blocks by this method is not new. Conversion blocks

were first used at NBS in the late 1950 's in preparation for the

approaching change in the international definition of the meter

from the prototype platinum- iridium meter bar to the wavelength of

a specific ^^Kr spectral line. This was several years before lasers

and dynamic interferometry were invented.

A plan was devised to convert several long gage blocks into line

scales with conversion blocks made from commercial blocks modified

with rulings at NBS. These long blocks were then measured by

comparing them with a group of NBS laboratory standard line scales.

By virtue of their known lengths relative to the international

prototype meter bar, these laboratory standards were the national

length standard at that time. Once the long block lengths were

determined, they were used to measure the krypton wavelength by

static interferometry . Thus, the krypton wavelength was indirectly

measured with the meter as then defined. The meter could then be

redefined as a specific number of wavelengths.

The purpose of this exercise was to minimize the change in the

actual length of the meter when changing to the new definition.

These were difficult procedures: line standard measurements,

because of the skill required to make time consuming comparisons

using filar eyepiece microscopes and a massive, temperature

sensitive, comparator; interf erometry, because limited coherence of

atomic light sources necessitated stepping up in increments of 200

mm or less to longer lengths.

Based on measurement data from BIPM and several national

laboratories, including NBS, the ®^Kr wavelength was determined and

the number of wavelengths in vacuum was computed for a one meter

length. The change in the actual length of the meter has been

estimated to be less than 0.2 ixm, a worthy achievement for that

time [4]

.

In 1960, the ^^Kr wavelength definition of the meter was adopted [4]

and interferometry became the official international method of

reproducing the meter.

3

.

The Need for End Standard to Line Standard Conversion

Since 1975, NBS/NIST has used static, single wavelength, laser

interferometry to measure its master gage blocks [2] . Single

wavelength dynamic laser interf erometry has been used to measure

line scales since 1964 [3] . The HeNe frequency stabilized lasers

emit a single wavelength at a nominal 0.633 jim. In static interferometry only the last fraction (called the fringe fraction) of a half -wavelength is observed, as shown in Figure 3. The whole number

of half wavelengths (fringes) must be determined by other methods.

This means that the length of a gage block must be known to better

than 1/4 wavelength (0.16 ^m) before it can be measured. Nearly all

commercially produced blocks of 100 mm or less are within this
tolerance at the standard temperature of 2 °C. Furtherrnore, the

lengths of NIST master blocks from 100 mm up to and including

500 mm, with many years of history, are known to better than 0.13

^m.

Most unknown blocks can be measured by mechanical comparison [5]

with NIST masters to determine the order of interference, as the

whole number of fringes is called. Problems arise in some cases,

however. For example, in determining the order of interference for

odd length blocks and blocks longer than 500 mm having no

equivalent master, or even an occasional NIST long block master

that gets out of control from rapid secular change or accidental

damage. There is also a size limitation because the longest NIST

static interferometer is 750 mm. It is in these problem areas that

the conversion technique is needed. Measurements up to 102 mm can

be made in the line scale interferometer.

4. A New Conversion Block Design

Previous conversion blocks were commercial 12.7 mm (0.5 inch) gage

blocks modified by polishing a side face and machine -ruling

graduations on the polished area with a diamond tipped stylus. For

the present study, new fused silica conversion blocks were designed

with prospects for improved performance.

Fused silica was selected for four reasons: (1) Being transparent,

the wringing interface between the selected block and the

conversion blocks is visible, thus making it easy to evaluate. (2)

High quality chromium lines can be deposited on the side faces for

improved measurement precision. (3) Optically lapped fused silica

surfaces are very smooth and wring very tightly. This is an

important characteristic because the wringing area is small when

conversion blocks are wrung crosswise on rectangular selected

blocks (steel conversion blocks can be insecure under these

conditions) . (4) They are lightweight and produce a minimum change

in the Airy point support positions.

In a perfect wringing with transparent conversion blocks, the

interface will appear as a uniform grey color. Defects in the wring

will appear as light areas or, in the worst case, colored areas.

These defects can result in errors of 0.025 ^m or more.

Steel conversion blocks are wrung with only the "feel" of the wring

to judge its quality. Ruling quality on steel conversion blocks,

while good, does not match the edge definition, straightness, and

contrast of modern chromium lines on a transparent substrate. Two

pairs of steel conversion blocks in fairly good condition from the

1950' s are extant at NIST. One of these pairs is used in the

experiments of section 6.

The fused silica gage blocks used in this study were fabricated by

an optical company to NIST specifications for flatness and

parallelism of the gaging faces, and for clearness and smoothness

of the ruling area. High-quality chrome graduations were added by
a photolithography firm.

5 . Measurement methods

5.1 Static Interf erometry

One of the long-block interferometers used in the NIST gage block

measurement process is shown schematically in Figure 3 . A photo of

a static interf erometric fringe pattern as seen through the exit

aperture is also shown. The block is wrung to the steel optical

flat (platen) . Gage blocks are particularly suited to this

measurement technique because the optically finished upper face and

the optical flat that forms the extension of the lower face serve

as mirrors in the interferometer. Together, with the reference

mirror in the diagram, these surfaces form an interferometer that

makes the interference phenomenon possible. A length measurement is

made from the plane of the optical flat to the gage point on the

top face. This length includes the wringing film that exists

between the block and the platen. Blocks are frequently used in

wrung combinations (stacks) . When combined, each block in a stack

includes one wringing film. Gage block length is defined [6, 7] as

the distance from the gage point to the plane of the optical flat

to which the block is wrung. The definition fits both the widely

used stacked condition and the interferometric measurement

technique

DISPERSION MISM f^^Q-Q-EB-C

LASER

SUPPORTING TABLE

Figure 3 . Gage block interferometer schematic with photo of

a fringe pattern as seen through exit aperture.

Two fringe patterns are formed in this interferometer: one on the

platen and the other on the gage block upper face. The offset

between the two patterns is called the fringe fraction, and it is

the ratio a/b in Figure 3 . It is always measured with the

interferometer adjusted so that one gage block fringe passes

through the gage point to ensure that the defined length from the

platen face to the gage point is measured. On a rectangular block
the gage point is at the center of the face. On a Hoke type block,

it is halfway between the center hole and the side of the block

where the size is marked.

In the NIST measurement process, a stabilized and calibrated laser

is the wavelength source. The fringe fraction is the last part of

a half wavelength in the block length. It must be added to the

whole number of half wavelengths (fringes) in the block length.

This whole number, called the order of interference, must be

determined by a secondary method, i.e., by mechanical comparison

with a calibrated master block or by gage block to line scale

conversion. To visualize the fringe fraction origin, imagine that

the gage block is infinitely compressible and the upper face can be

pressed down to the plane of the platen. At this point the block

and platen fringes are coincident. Then imagine that the block face

slowly grows to its original height and that the fringes that flow

past the gage point as it grows are counted while the platen

fringes remain fixed. This count is the whole number of half

wavelengths. The fraction is added to the count to get the actual

total length. The total is converted to millimeters or inches by

multiplying it by a "fringe multiplier." This multiplier is

composed of one-half the wavelength corrected to observed air

ambient conditions of temperature, pressure, CO2 content and

humidity. A factor is also included to correct block length to

2 °C from observed temperature using the block thermal expansion

coefficient

.

5 . 2 Dynamic Interf erometry

In preparing a selected block for the line scale measurement, the

conversion blocks are wrung to its end faces. The conversion blocks

are precisely positioned, both horizontally and vertically, so that

the graduations are on the central axis of the selected block. The

wringing interface is examined for flaws and re-wrung until a minimum of flaws are seen. Deburring the gaging faces with a

deburring stone may be necessary to improve surface conditions.

A schematic of the NIST line scale interferometer and a photograph

of a gage block mounted for measurement is shown in Figure 4 . A

converted gage block is mounted horizontally on the carriage and

the graduations focused in the photoelectric microscope field.

Airy point support is used because it maintains the gage block end

faces parallel to the degree that they are parallel in the vertical

position. The Airy points of the gage block are, for practical

purposes, the same with or without the fused silica conversion

blocks attached because of their light weight. When steel

conversion blocks are used. Airy points must be recomputed. Once

temperature has stabilized, the distance between the graduations on

the conversion blocks is measured by fringe counting. Both the

whole number and the interpolated fractional fringe are accumulated

in the counter. This count is converted into length units

(millimeters or inches) by the computer-controller in a similar

manner to static interf erometry . Several passes are made up and

back. These are averaged to produce a length value at the standard
temperature of 20 °C. Conversion blocks are re-wrung on the selected

block two or more times and repeat measurements made. The average

of all values is the combined length.

The conversion blocks are wrung together, precisely aligned and

mounted in the line scale interferometer for measurement in the

same manner as the combined length. Repeat wringings and measurements are made and averaged to give the conversion interval length.

Subtracting conversion interval length from combined length yields

the selected block length.

Remote

interferometer

tubtzms tm nBifM» a naksn- raon Mar

Long gage

block

Conversion

block

Retroref lector

^

Remote -^^M v interferometer ^^. ^

Figure 4. Schematic diagram of the NIST line scale

interferometer and a photo of a long rectangular

gage block mounted for measurement.
6. Sources of Differences in Results

There are differences in the principles of these two measurement

methods that will inevitably produce small differences in results.

Five factors that can affect the degree of agreement between the

two methods are: (1) flatness of the gaging faces, (2) parallelism

of the gaging faces, (3) conversion block alignment, (4) the

presence of two wringing films in the conversion process and onlyone in the static interf erometric measurement, and (5) static

measurements are vertical and dynamic measurements are horizontal

so the influence of gravity on the block length is different.

Corrections for most of these factors can be derived and applied.

6.1 Geometry of the Selected Block

If a block of rectangular cross section deviates in flatness across

its width at both ends as in Figure 5 (left) the effect will be

negligible. This is because the gage point is at the center where

the static measurement is made and coincident with the graduations

in the conversion method. Gaging faces are generally symmetrically

convex in all but very thin blocks where warping is present.

In a Hoke type block with a flatness deviation across the width at

both ends as in Figure 5 (right) there will be a difference because

the gage point is not at the point of maximum length where the

conversion measurement is made. It is offset to a point halfway

between the hole and the block edge. This can be compensated by

measuring the difference in elevation between the two points and

subtracting it from the conversion measurement . At the end opposite

the gage point there will be no difference between the two methods

because both conversion block and platen will be wrung to the area

of maximum length.

Gage

/

point

^

) ;

_ Figure 5 . The effect of flatness deviations on the

measurement of rectangular (left) and Hoke

(right) types of selected blocks.

Figure 6. The effect of parallelism deviation on the measurement of

a rectangular selected block.
Figures 5 and 6 show flatness and parallelism deviations which are

greatly exaggerated for illustrative purposes.

Small (0.05 fim or less) deviations in parallelism of the gaging

faces will create only a very minor problem as shown in Figure 6

A parallelism error, either across or along, will produce a

lengthening in the distance from the gaging face of the selected

block to the graduation on the conversion block. The amount of

lengthening is the difference, h - a, and this difference is very

small because side a is short (6.5 mm) and angle 9 is small (0.02

s) for an 0.05 jim parallelism deviation.

Large flatness and parallelism errors, of 0.10 /im or more, add to

measurement uncertainty in mechanical intercomparisons and static

interf erometry . These errors also add to the uncertainty in using

gage blocks by affecting the geometry of stacks. Blocks with poor

geometry should be replaced.

6.2 Geometric and Graduation Quality of the Conversion Blocks

The fused silica conversion blocks were required to meet close

tolerances for flatness and parallelism: 0.025 /im across the width

and 0.050 ptm along the length of the faces. When received from the

manufacturer these blocks were even better than this. Such close

tolerances will not cause significant measurement errors. In

addition, the high quality chrome graduations ensure excellent line

setting precision and the longitudinal alignment tracks running to

the edges of the graduated faces make aligning the blocks

relatively easy.

6.3 The Second Wringing Film

Wringing film thickness is difficult to measure and can vary from

block to block and wring to wring by as much as 0.064 /im. The

accepted average wringing film thickness value of 0.025 fim is used

here to correct the conversion method measurements.

6.4 Length Change from Horizontal to Vertical

Gravitational force will shorten a block when changed from a horizontal to a vertical position. Gage block lengths are reported

in the vertical position so a negative correction must be made to

the horizontal length value. The equation for this correction is:

cjL^

6 =

2 AE

where 6 = amount of shortening

00 = weight per unit length of the block

L = total length of the block

A = cross sectional area

e = Young's modulus of elasticity
7 . Experimental tests

7.1 Objectives

The general objective is to test the theoretical advantages of the

new fused silica conversion blocks. There are three subdivisions to

the general objective: (1) determine the degree of agreement

between the fundamental interferometric method (static interferometry) and each of the two conversion block methods, (2)

determine the measurement precision of each method and (3) judge

the relative ease of use and durability of the conversion blocks.

7 .Equipment

SELECTED BLOCK

Nominal size: 10 inches (254 mm)

Identification No. 2306

Material : steel

Coefficient of thermal expansion: 10.6 x 10"^ m/m/°C

Flatness and parallelism deviations: 0.050 jum or less

INTERFEROMETERS

Static: Kosters type, gage block interferometer

Dynamic: NIST Line Scale Interferometer

CONVERSION BLOCKS:

Fused silica pair: A and B

Steel pair: K and M

7 .

Procedure

The first step is to measure the interval between the graduations

on the steel and fused silica conversion blocks. This requires

careful wringing and alignment of each pair. Alignment is done on

a bench microscope having a crosshair in the eyepiece and a

moveable stage. The interval is then measured in the line scale

interferometer. This process is repeated several times to generate

redundant data for statistical analysis. The mean value for each

pair is subtracted from the total length each time a selected block

is measured with the conversion blocks attached.

A single high quality gage block was selected for measurement by

conversion and static interf erometry. Measurement data on this

block will determine comparability of the methods. The block chosen

is a 254 mm (10 inch) Hoke type steel block. It has excellent

flatness and parallelism of the gaging surfaces, fine surface

finish and a square cross section which provides a large wringing

area for attaching conversion blocks.

Wringing conversion blocks to the selected block must be carefully

done to ensure that the graduations and their alignment marks are

coincident with the central axis of the selected block. This is

accomplished on a surface plate by using a straight edge and gage

block spacers as shown in Figure 7

10
p Spacer ..^ Straight edge

Conversion

block

Spacer

Surface plate

Figure 7. Aligning a conversion block with gage block spacers,

using a horizontal surface plate and a straight edge.

In addition to data on the 254 mm block, data on two special end

standards are included to illustrate typical conversion measurement

esults from the NIST gage block calibration program. These two

ars were measured to establish the interference order for static

interferometry measurement. They are:

A "16 inch" (406.4 mm) bar with a round cross section.

An "18 inch" (457.2 mm) bar with a round cross section.

Both bars have good geometry: 0.064 fim or less flatness and

parallelism errors.

7.4 Results

Three estimates of measurement repeatability are used in the

following tables of measurement results: (1) a, the standard

deviation, the usual measure of repeatability, (2) o^ , the

variance, which can be used in a statistical technique called the

analysis of variance to separate the sources of variability, and

(3) 2(1, which is an estimate at a 95% confidence level. The latter

predicts that, based on present performance, additional

measurements will agree 95% of the time with the current mean

within the limits of the ±20" value. Subscripts after o identify the

measurement being evaluated: g for the conversion block graduated

interval measurement (Table 1) , s for selected block measurement

(Table 2) , and w for measurements made with a single wringing

(Table 3) . A summary of the graduated interval measurements on the two pairs

of conversion blocks is shown in Table 1. In Table 2, measurement

results on the selected experimental block are summarized.

11
Table 1.

Graduated interval length and measurement precision

AB KM

Interval length at 20° C. 12.997482 mm 10.108339 mm

ffg 0.03 6 /im 0.066 fim

0-/ 0.0013 /xm^ 0.0044 jim^

2o-g 0.072 ^m 0.132 fim

Number of wrings, n 8 8

Table 2

.

Measurement results on the 254 mm selected gage block

Dynamic Interferometry Static Interf erometry

254 mm block 254 mm block 254 mm block

with A 5c B with K & M

MEASUREMENTS (lengths at 20° C.)

Mean length 254.000404 mm 254.000406 mm 254.000376 mm

0.020 jim

0.0004 /xm^

0.040 fim

0.376 /xm

(^s 0.030 fim

^s^ 0.0009 /xm^

2^3 0.060 ^m

n 8

CORRECTIONS

Dev. from nom. 0.404 ixva -one wring film -.025

Hori2: . to vert

.

- .012

0. 068 fxm

0046 fim^

136

8

liva

.406 jim

- .025

- .012

Corrected value 0.367 0.369 0.376

FINAL LENGTH 254.000367 mm 254.000369 mm 254.000376 mm

Table 3 shows precisions for repeated measurement of: (1) the

length, measured by static interf erometry, for a single wringing of

the 10 inch block, (2) the combined length, measured in the line

scale interferometer, for a single wringing of conversion blocks A

and B to the selected block, and (3) the same with conversion

blocks K and M.

12
Table 3

Measurement repeatability for a single wring

Dynamic Interf erometry Static Interf erometry

254 mm block 254 mm block 254 mm block

with AB with KM

ffw 0.005 ixm 0.007 jim 0.009 /;.m

oj" 0.00003 /xm' 0.00005 /xm' 0.00009 /im^

2cr„ 0.010 /im 0.014 /im 0.018 ptm

n 8 8 8

The first question in considering the data in these tables is how

well do the three measurement methods agree? They agree remarkably

well (within 0.009 jum) as shown in Table 2. But, as previously

mentioned, the correction for wringing film thickness could not be

directly measured so the generally accepted value of 0.025 /um is

used.

The second question is which of the two conversion block methods

produces the least measurement variability? An answer comes from

the statistical measures of repeatability which say that fused

quartz is the most precise. This is not only in the measurement of

the 254 mm block (Table 2) , but also in the measurement of the line

spacing in multiple wringings (Table 1) and in a single wringing

(Table 3) . The graduations on the fused silica can be read with

less variability and their gaging surfaces can be wrung with less

variability than the steel blocks.

Analysis of variance can reveal other characteristics of these

measurements. In the static interf erometric measurements of the 10

inch block, variance from the single wringing in Table 3 can be

subtracted from total variance in Table 2

:

a^' = 0^"" - oj" = 0.0004 - 0.00009 = 0.00031 fixn" Standard deviations in Table 3 reflect all measurement variability

except that from repeated wringing. By subtracting variance oj^ from

variance o/ in the computation above, the wringing variability is

separated. The wringing variability standard deviation, o^., and the

2o^ prediction of the bounds of this variability in additional

static interf erometry measurements of the 254 mm block become:

0^ = VO .00031 = 0.018 ptm, and 2(7,. = 0.036 ^m

The same computation, again using the data in Tables 2 and 3,

produces estimates of the variability of wringing blocks A and B to

the 254 mm block, and the variability of wringing blocks K and M to

the 254 mm block:

13
G^ = 0.029 ^m, and 2o^ = 0.058 ^m for A and B

a^ = 0.067 ^m, and 2a^ = 0.134 ^m for K and M

Some conversion block wringing variability is produced by gaging

surface conditions. The steel blocks have been used enough over the

years to roughen the surfaces so they do not wring as tightly or

consistently as they once did. Stoning the faces will no longer

restore them to optimum condition; only relapping them can do that.

On the other extreme, the fused silica blocks have such smooth

surfaces that they tend to wring together too tightly and must be

treated with extra wringing film material to prevent optical

contacting. This condition is gradually improving as they are used.

7.5 Additional measurements

In the course of this experiment two long gage blocks from private

sector customers were measured by conversion to establish the

interference order for a static interf erometric measurement.

Results of these measurements are shown in Table 4 as examples of

routine conversion measurements in the NIST gage block calibration

program. Each block was wrung twice for both conversion and static

interf erometry

.

Table 4

Results of routine calibration results for NIST customers

Block Description Conversion Static Interf. Difference

Measurement Measurement

Using A and B

(mm) (mm) (|Um)

"16 inch" (406.4 mm) 406.399322 406.399355 -0.033

"18 inch" (457.2 mm) 457.200048 457.200041 0.007

8 . Measurement uncertainty

The analysis presented here has stressed measurement repeatability,

the degree of agreement between the two types of conversion blocks,

and the degree of agreement between the dynamic and static

interferometry processes. Although this is sufficient to meet the

objectives of this paper, it is worthwhile to discuss measurement

uncertainty briefly.

The two measurement processes involved, static gage block

interf erometry and dynamic line scale interf erometry, are well

documented by long standing measurement assurance programs [5 , 8]

.

International and NIST policy requires expanded uncertainty, U, to

be stated as follows:

U = ku^

14
where k is the coverage factor, and combined standard uncertainty,

u.. is

u^ = V (Ui + u^ ) where u^ is the standard uncertainty arising from random effects

and Uj is the standard uncertainty arising from systematic effects

in the measurement process. Coverage factor k is assigned a value

of 2 which provides a confidence level of approximately 95% in the

expanded uncertainty.

Applying these rules to the data in this paper results in the

following evaluations of uncertainties:

Taking the random effects seen in the experiment (Table 2, aJ and

the systematic effects documented in reference [5] into account,

the uncertainties for the static interferometry measurements are:

and

u, = V0.020' + (0.05 X 0.254)^ = .02

[7=2 (0.024) = 0.048 /zm

4 /zm

Using the same analysis on the dynamic interferometry measurements,

with random effects in the measurements using conversion blocks K

and M (fused silica) , and systematic effects documented in

reference [8], the uncertainties are:

u^ = i (0.030^ + (0.05 X 0.254)' = 0.033 /im

and

[7=2 (0.033) = 0.066 /xm

The systematic component, 0.05 ^m (Uj), is a length dependent

factor expressed in parts in 10^. That is why it is multiplied by

the length measured, in this case 0.254 m, to scale it to this

measurement. Random error comes directly from analyzing the

measurement data and thus needs no scaling.

Another valid approach to estimating uncertainty is to measure a

quantity by two independent methods and compare the results. Static

and dynamic interf erometric methods are not fully independent,

because they share the same sources and magnitudes of systematic

error. This may explain, in part, why they agree so well in Table

2. The mean of the two dynamic values is 254.000368 mm while the

mean static value is 254.000376. This is a difference of only 8 nm

as contrasted with uncertainties of 48 and 65 nm by the first

method. The best values for uncertainty are probably between the

two methods, since both analyses are based on a relatively small

number of observations. However, this does not change any of the

conclusions in the next section.

15
9. Conclusions

Theoretical advantages of fused silica conversion blocks over the

steel variety have proved to be true in experiments presented here.

Advantages and one disadvantage are as follows:

(1) Chromium graduations on fused silica conversion

blocks yield better repeatability than the graduations on

the steel conversion blocks (see Table 3)

(2) Wringing repeatability is better for fused silica

blocks (see Table 1)

(3) Measurement repeatability on the 254 mm selected block is

better with fused silica blocks than with steel blocks

(see Table 2)

(4) Light weight, wringing interface visibility, superior

surface finish and excellent geometry (flatness and

parallelism) are judged to make fused silica blocks

easier to wring to the selected block. Light

weight also means that the effect on the Airy support

point positions is negligible.

(6) Durability is one potential disadvantage of

fused silica. Both steel and fused silica gaging

surfaces will become scratched with use, but the latter

tends to chip easily. Chips on the gaging faces may

leave sharp edges that can scratch other surfaces during

wringing. Edges of some chips can be rubbed with a

deburring stone to reduce sharpness. Block A

sustained a minor chip, but its sharp edge was

reducible

(7) Some of the fairly large wringing variability in both

pairs of conversion blocks is caused by the condition of

the gaging surfaces . The gaging faces of K and M show

signs of wear. One face of K (a face not used in these

experiments) will not wring, and stoning will not restore

it. On the other extreme, the faces of A and B are so

perfect that a heavier than normal grease film is needed

to prevent optical contacting when they are wrung

together.

It is noteworthy that all of the measurements of the 254 mm block

with both pairs of conversion blocks qualify for determining the

order of interference, i.e., they are within ^ fringe (0.16 jim) of

the actual block length. The 3a prediction, however, for the use of

K and M is that at some point in making additional measurements

there will be outlying values (see Table 2 where 3o^ = 0.204 /^m) .

10References

[1] "Documents Concerning the New Definition of the Meter,

Metrologia, 19, 1984

[2] Beers, J.S., "A Gage Block Measuring Process Using Single

Wavelength Interferometry, " NBS Monograph 152, Dec. 1975

16
[3] Penzes, W.B. and Beers, J.S., "Evolution of Automatic Line

Scale Measurement at NIST, " IMEKO TC Series No. 28, Sept. 1990

[4] Hart, K.H. and Baird, K.M., "On the Relation Between the Old

and the New Definition of the Metre, " Can J Phys v39 n6 June 1961

[5] Doiron, T. and Beers, J.S., "The Gage Block Handbook," NIST, in

process 1995

[6] Federal Specification: Gage Blocks and Accessories (Inch and

Metric) . Federal Specification GGG-G-15C, March 1975

[7] International Standard 3650, Gaucre Blocks , First Edition, 1978-

07-15, 1978

[8] Beers, J.S. and Penzes, W.B., "NIST Length Scale Interferometer

Measurement Assurance," NISTIR 4998, Dec. 1992

Acknowledgments: The author wishes to thank Group Leader Ralph

Veale for his support in this project, and to both Dr. Theodore

Doiron and William Penzes for very helpful discussions and ideas

that led to its successful completion.

17



NISTiTechnical Publications

Periodical

Journal of Research of the National Institute of Standards and Technology—Reports NISI research and

development in those disciplines of the physical and engineering sciences in which the Institute is active. These include physics, chemistry, engineering, mathematics, and computer sciences. Papers cover a broad

range of subjects, with major emphasis on measurement methodology and the basic technology underlying

standardization. Also included from time to time are survey articles on topics closely related to the Institute's technical and scientific programs. Issued six times a year.

Nonperiodicals

Monographs—Major contributions to the technical literature on various subjects related to the Institute's

scientific and technical activities. Handbooks—Recommended codes of engineering and industrial practice (including safety codes) developed

in cooperation with interested industries, professional organizations, and regulatory bodies.

Special Publications—Include proceedings of conferences sponsored by NIST, NIST annual reports, and

other special publications appropriate to this grouping such as wall charts, pocket cards, and bibliographies.

National Standard Reference Data Series—Provides quantitative data on the physical and chemical

properties of materials, compiled from the world's literature and critically evaluated. Developed under a

worldwide program coordinated by NIST under the authority of the National Standard Data Act (Public Law

90-396). NOTE: The Journal of Physical and Chemical Reference Data (JPCRD) is published bi-monthly for NIST by the American Chemical Society (ACS) and the American Institute of Physics (AlP). Subscriptions,

reprints, and supplements are available from ACS, 1155 Sixteenth St., NW, Washington, DC 20056.

Building Science Series—Disseminates technical information developed at the Institute on building

materials, components, systems, and whole structures. The series presents research results, test methods,

and performance criteria related to the structural and environmental functions and the durability and safety

characteristics of building elements and systems.

Technical Notes—Studies or reports which are complete In themselves but restrictive In their treatment of a

subject. Analogous to monographs but not so comprehensive in scope or definitive in treatment of the

subject area. Often serve as a vehicle for final reports of work performed at NIST under the sponsorship of other government agencies.

Voluntary Product Standards—Developed under procedures published by the Department of Commerce in Part 10, Title 15, of the Code of Federal Regulations. The standards establish nationally recognized

requirements for products, and provide all concerned interests with a basis for common understanding of the

characteristics of the products. NIST administers this program in support of the efforts of private-sector

standardizing organizations.

Order the following NIST publications—FIPS and NISTIRs—from the National Technical

Information Service, Springfield, VA 22161.

Federal Information Processing Standards Publications (FIPS PUB>—Publications in this series collectively constitute the Federal Information Processing Standards Register. The Register serves as the official source

of Information In the Federal Government regarding standards Issued by NIST pursuant to the Federal

Property and Administrative Services Act of 1949 as amended. Public Law 89-306 (79 Stat. 11 27), and as implemented by Executive Order 11717 (38 FR 12315, dated May 11, 1973) and Part 6 of Title 15 CFR

(Code of Federal Regulations).

NIST Interagency Reports (NISTIR)—A special series of interim or final reports on work performed by NIST

for outside sponsors (both government and nongovernment). In general, initial distribution is handled by the sponsor; public distribution is by the National Technical Information Service, Springfield. VA 22161, in paper

copy or microfiche form.