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/NBS monograph QC100 .U556 \/152;1975 C.1 NBS-PUB-C 1959

NBS MONOGRAPH 1 52

U.S. DEPARTMENT OF COMMERCE / National Bureau of Standards

A Gage Block Measurement

Process Using Single

Wavelength Interferometry

lOO
NATIONAL BUREAU OF STANDARDS

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- Located at Boulder, Colorado 80302,
A Gage Block Measurement Process

Using Single Wavelength interferometry

ATIOHAL BUARitU

DEC 3 1 1975

) o — -

John S. Beers

Institute for Basic Standards

National Bureau of Standards

Washington, D.C. 20234

U.S. DEPARTMENT OF COMMERCE, Rogers C. B. Morton, Secreiary

James A. Baker, III, Under Secreiary

Dr. Betsy Ancker-Johnson, Assisfanf Secreiary for Science and Technology

U.SiNATIONAL BUREAU OF STANDARDS, Ernest Ambler, Aciing Direcfor

III Issued December 1975
Library of Congress Cataloging in Publication Data

Beers. John S. A Gage Block Measurement Process Using Single Wavelength

Interferometry.

(National Bureau of Standards Monograph; 152) Bibliography: p. Supt. of Docs. No.: 013.44:152

1. Gage Blocks—Calibration. 2. Interferometer. I. Title. II. Series: United States. National Bureau of Standards. Monograph; 152. QC100.U556 No. 152 [TJ1166] 602'.ls [530'.8] 75-619353

National Bureau of Standards Monograph 152

Nat. Bur. Stand. (U.S.). Monogr. 152, 34 pages (Dec. 1975) CODEN: NBSMA6

U.S. GOVERNMENT PRINTING OFFICE

WASHINGTON: 1975

For sale bv the Superintendent of Documents, U.S. Government Printing Office, Washington, D.C. 20402 (Order by SD Catalog No. C13.44:152). Price 85 cents. (Add 25 percent additional for other than U.S. mailing).
Contents

Page

1. Introduction 1 2. The Interferometer. 2 2.1. Interferometer Corrections 4 3. The Laser Light Source 5 4. Environmental Conditions and Their Measurement 6

4.1. Temperature 6

4.2. Atmospheric Pressure 8

4.3. Water Vapor 8

5. Gage Block Measurement Procedure 8

6. Computation of Gage Block Length 11

6.1. Calculation of Wavelength 11

6.2. Calculation of the Whole Number of Fringes 12

6.3. Calculation of Block Length from the Observed Data . . 12

7. Systematic and Random Errors 13

8. Process Evaluation 14

8.1. Control Standards 15

8.2. Determining Process Characteristics 15

8.3. The Search for Systematic Errors «... 16

8.4. The Study of Random Errors 25

8.5. Summary 27

References 28

Appendix 29

Figures

1. Gage block interferometer. . 3

2. Typical gage block fringe pattern 3

3. Fringe patterns on a master optical flat 3

4. Temperature measuring system schematic 7 5. Fringe fraction measurement 10

6. Control chart on the 0.129 inch control standard .... 16

7. Control charts on the 10 inch steel and 10 inch glassceramic control standards 20

8. Control charts on the 0.129 and 0.150 inch control

standards showing secular changes 20

9. Correlation chart, length vs vapor pressure 21

10. Control chart on the 10 inch glass-ceramic block

measured with an iodine stabilized laser 24

11. Control chart on the 10 inch steel block measured

with an iodine stabilized laser 24

Tables

1. Length dependent errors resulting from systematic

errors in measurement parameters 14

2. Summary of control standard measurements 17

3. Analysis of 28 measurements of the 0.129 inch

control block 25

iii

A Gage Block Measurement Process Using

Single Wavelength Interferometry

John S. Beers

The int erferome trie transfer of the length unit from its

defined wavelength to NBS reference standard gage blocks is

basic to the gage block calibration program at NBS. The interferometric measurement process using a laser light source and

a Kosters type gage block interferometer is described here.

Continuous evaluation and refinement of the process is aided

by statistical treatment and control chart techniques. All error sources, both random and systematic, are evaluated and

the process is maintained in a state of statistical control.

Key words: Calibration; gage blocks; interferometry; laser;

length; measurement process; uncertainty.

1. INTRODUCTION

Gage block calibration at NBS depends on the interferometric measurements by which the unit of length is transferred from its defined wavelength of light to the NBS gage block reference standards used for the

intercomparison process [1, 2]-^.

Although the interferometric process has undergone changes, the new

process does not differ fundamentally from previous gage block interferometry at NBS except for using a laser light source. It employs some new

techniques and some techniques successfully used in the past coupled with

an analysis program designed to reveal random and systematic errors. The

analysis program fosters refinements aimed at reducing these errors. A

practical limit is eventually reached in making refinements, but the analysis program is continued to assure the reliability of the measurement

process

.

Briefly, static interferometry is employed to compare NBS gage block

reference standards with a laser wavelength. The blocks are wrung to a platen and mounted in an interferometer maintained in a temperature con- trolled environment. The fringe pattern is photographed and at the same moment those ambient conditions are measured which influence block length

and wavelength. A block length computed from these data is a single point

in a collection of measurements. By least squares fitting, this collection gives an estimate of process precision, a rate of change of length

with time and an accepted value for the correction to the block length at

any given t ime

.

1. Figures in brackets indicate the references at the end of this paper.
/ Gage block length in this measurement process is defined as the perpendicular distance from a gaging point on the top face of the block to the

plane surface of identical material and finish wrung to the bottom face.

This definition has two advantages. First, specifying a platen identical

to the block in material and surface finish minimizes phase shift effects

which may occur in interferometry . Second, it duplicates practical usage

where blocks of identical material and finish (from the same set) are wrung together to produce a desired length.

The NBS gage block reference standards are commercially produced gage

blocks and possess no unusual qualities except that they do have a history

of calibration from frequent and systematic comparison with wavelengths of

light. Although this description is for blocks from 5 to 20 inches long,

a similar process is being applied to blocks less than 5 inches in length.

2. THE INTERFEROMETER

A Kosters type gage block interferometer, shown schematically in

figure 1, is used.

The light beam from laser A passes through polarization isolator B

and spatial filter B', is diverged by lens C, converged by lens D through

aperture E, where it diverges again to fill the field of the interferometer and is collimated by lens F. Entrance aperture E is at the principle

focus of lenses D and F. The collimated beam is directed by constant deviation prism G* to beam splitter H where the beam is divided into two

beams of equal intensity by the semi -reflecting upper surface. One beam

(the measuring beam) continues through to gage block surface K, and optical flat L, and the other beam (reference beam) is reflected through com- pensating plate I to plane mirror J. Now the beams are reflected by mirror J, gage block surface K, and optical flat L, and are recombined at

the beamsplitter. The remaining portions of these beams (some light is

lost at each reflection) are visible through lens M and aperture N as an interference pattern created by the phase relationships of the wavefronts

in the recombined beams.

Interference in this instrument is most readily explained by assuming that an image of reference mirror J is formed at J' by the beamsplitter. A small angle, controlled by adjustment screws on table P, between

the image and the gage block-platen combination creates a Fizeau fringe

pattern. When this wedge angle is properly adjusted for reading a gage

block length, the interference pattern will appear as in figure 2.

Table P has its center offset from the optical axis and is rotatable

by remote control. Several blocks can be wrung to individual small platens or a single large platen and placed on the table to be moved, one at

a time, into the interferometer axis for measurement.

* This prism separates the spectral lines of quasi-monochromatic light sources such as Hg.. q„ for multiple wavelength interferometry

2
Figure 1. Gage block interferometer.

Figure 2. Typical gage block fringe pattern.

Figure 3. Fringe patterns on a master optical flat.
Two criteria must be met to minimize systematic errors originating

in the interferometer: (1) the optical components must be precisely

aligned and rigidly mounted and (2) the optical components must be of

high quality, i.e. the reference mirror and beam splitter must be plane

and the lenses free of aberrations.

Alignment is attained when the entrance aperture, exit aperture and

laser beam are on a common axis normal to, and centered on, the reference

mirror. This is accomplished with a Gaussian eyepiece, having a vertical

and a horizontal crosshair, temporarily mounted in place of the exit aperture, and a vertical and a horizontal crosshair permanently mounted on the

reference mirror and intersecting at its center. Through a process of

autocollimation with illumination at both entrance aperture and Gaussian

eyepiece, the reference mirror is set perpendicular to an axis through

the intersections of the two sets of crosshairs and the entrance and exit

apertures are set coincident with this axis. In addition, the laser beam

is aligned coincident with the axis and the prism adjusted so the laser

light coming through the entrance aperture is aligned precisely with the

exit aperture. Having an exact 90° angle between the measuring leg and

the reference leg is not essential as can be seen from instrument geometry. This angle is governed by the beam splitter mounting. All adjustments are checked regularly to assure their permanence. The gage block

and its platen are easily aligned by autocollimation at the time of measurement and no fringes are seen until this is done. Final adjustment is

made while observing the fringe pattern, producing the configuration of

figure 2.

Overall optical quality is tested by evaluating the fringe pattern

produced on a master optical flat mounted on support table P. Photographs

showing fringes oriented vertically and horizontally are shown in fig- ure 3. Measurements of the fringe pattern indicate a total distortion of

0.10 fringe vertically in the field. A correction factor proportional to

the section of field used can be computed and applied. This correction

is relatively small because the field section used in fringe fraction measurement is small. Alternatively, the most likely source of distortion,

reference mirror J, can be replaced or reworked, and this course will be

taken

.

Temperature stability of the interferometer and especially of the

gage block being measured is important to precise measurement. For this reason an insulated housing encloses the entire interferometer to reduce

the effects of normal cyclic laboratory air temperature • changes , radiated

heat from associated equipment, operator, and other sources. A box of

3/4 inch plywood with a hinged access door forms a rigid structure which

is lined with 1 inch thick foam plastic. Reflective aluminum foil covers

the housing both inside and outside.

2.1. Interferometer Corrections

In some interferometers, the entrance and exit apertures are off the

optic axis so light falls obliquely on the gage block. Gage block length

is then a cosine function of the obliquity angle. In this interferometer

4
the apertures are precisely on the optic axis, the obliquity angle 'is zero,

and thus no correction is needed. Periodic interferometer alignment in- sures that the obliquity angle remains zero.

In most interferometers, the entrance aperture is of finite size,

therefore ideal collimation does not occur and oblique incidence effects

arise from the resultant of all rays from the aperture area. A laser as used with this interferometer is almost a point source because the aperture is at the common focal point of lens D, and collimating lens E, and

at this point the beam diameter is the effective aperture.

In two papers, one by Bruce [3] and one by Thornton [4], the authors

developed aperture correction equations which consider obliquity of rays

from a finite aperture and fringe intensity distribution. Correction factor 62, for a gage block of length Jl, measured with wavelength X, using a circular aperture is

. ^ S(v)- - S(v)dv

A ^ -1 V O

0 =7— tan z C(v) / C(v)dv

V 1 4I a where ^ T X 2f

for aperture of diameter a, and collimating lens of focal length f. S (v)

and C(v) are Fresnel integrals. As aperture diameter aproaches zero, the

correction approaches zero. In this interferometer the correction is very

small because the laser beam diameter is small at the aperture.

3. THE LASER LIGHT SOURCE

The advantage of a laser light source lies in its unequalled coherence. Conventional spectral light sources have such low coherence that

gage blocks longer than 10 inches have in the past been measured by stepping up from shorter blocks. Laser fringe patterns in this interferometer compared with patterns from other spectral lamps are of superior

contrast and definition throughout the length range.

The disadvantage stems from the somewhat unstable wavelength of Lamb

dip stabilized lasers. Variations can approach 1 part in 10^ both short

term and long term. This is not serious for most metrological applications but this study required better stability as will be seen later.

Commercial Lamb dip stabilized helium neon lasers of nominal .6328 micrometer wavelength were used for most of the measurements described in this

paper and their performance was monitored by periodic calibrations. Lamb

dip laser calibration and stability has been described by Mielenz, et

al [5].

Toward the end of these gage block measurements the newly developed

iodine stabilized l^ser was used. Its stability exceeds that of Lamb dip

lasers by at least two orders of magnitude and even exceeds the stability

of Krypton 86, the present international length standard. Schweitzer, et

al [6] describe this laser and its calibration in detail.

5
Single wavelength static interferometry in contrast with multiple

wavelength interferometry requires that the gage block length be known

to within +1/4 wavelength (+1/2 fringe) either from. its history or from

another measurement process. This is no problem for NBS reference blocks.

Laser light must not be allowed to reflect back into its own cavity

from interferometer optical components because this will disturb the

lasing action and may cause a wavelength shift, wavelength dithering or

it may stop the lasing altogether. The reflected light is prevented from

re-entering the laser by a polarization isolator consisting of a Glan

Thompson prism and a quarter wave plate in the beam as it emerges from

the cavity (see B, fig. 1). This assembly is tilted just enough to deflect reflections from its faces to the side of the laser exit aperture.

The isolator linearly polarizes the highly elliptical laser output

with the G.T. prism, then circularly polarizes it by phase displacement

with the quarter wave plate. Light returning to this assembly from dielectric surfaces in the interferometer is reversed in polarization direction

by the 180° phase shift at reflection. Thus, light emerging from the isolator polarized in a clockwise direction returns after reflection polarized counterclockwise. It is then linearly polarized by the quarter wave

plate at 90° to the polarization plane of the G.T. prism and is diverted

away from the laser cavity by the prism's action.

4. ENVIRONMENTAL CONDITIONS AND THEIR MEASUREMENT

Environmental control of the laboratory holds temperature at 20°+.05°C

and water vapor content below 50% relative humidity. Temperature variations

within the interferometer housing are attenuated by a factor of about 10

from those in the room thus insuring stability of both interferometer and

blocks

Temperature, atmospheric pressure, and water vapor content of the

ambient air in the interferometer light path must be measured at the time

the gage block is measured. From these properties the refractive index

of the air is calculated and, in turn, the laser wavelength. Gage block

temperature is measured so that the length of the block at 20°C, or any

other temperature, can be computed.

4.1. Temperature

The measuring system for air and block temperature' consists of copperconstantan thermocouples referenced to a platinum resistance thermometer.

Figure 4 is a schematic diagram of the system.

A solid copper cube provides a stable reference temperature measured

by a Standard Platinum Resistance Thermometer (SPRT) and a Mueller resistance bridge. A well in the cube' holds the thermometer stem, the reference

thermocouple junction and a liquid of high heat conductivity but low electrical conductivity. There is also a second well whose function will be

described later. An enclosed thermocouple selector switch connects the

measuring junctions, one at a time, to the reference junction and the

6
RESISTANCE

THERMOMETER

BRIDGE

PLATINUM RESISTA^\ICE

THERMOMETER

NANOVOLTMETER

-o i oREFERENCE

THERMOCOUPLE

JUNCTION

REFERENCE

TEMPERATURE

DPDT SWITCH

THERMOCOUPLE

SELECTOR

SWITCH

MEASURING

THERMOCOUPLE

JUNCTIONS

Figure 4. Temperature measuring system schematic.

thermal emfs generated by the temperature differences between measuring

junction and reference junction are indicated on a nanovoltmeter . ^ The

nanovoltmeter is shared with the bridge where it is used as a nullmeter.

To keep the copper block in a stable state and to minimize thermal emfs

in the selector switch, both block and switch are enclosed in an insulated box. The switch is operated through a fiber shaft ^extending to

the exterior and the protruding part of the thermometer is protected by an insulated tube

.

Thermocouples generate emfs proportional to the temperature gradient

along the wire:

where T^ and T2 aire the temperatures of the reference and measuring junctions respectively

(j) is the thermocouple constant.

Minimizing this gradient reduces uncertainties.

Relating the system to the International Practical Temperature Scale

of 1968 (IPTS '68) is a three step procedure. First, the SPRT is calibrated using methods described in NBS Monograph 126 [7] . Second, the

bridge is calibrated as described in the same Monograph. The third step

is the calibration of the thermocouples which is accomplished with a sec- ond SPRT and insulated copper cube. The second cube has an extra well

for thermocouples being calibrated and is heated one or two degrees to

equilibrium. Measured thermal emfs generated by the temperature difference between the two cubes together with the temperatures of the cubes

allow computation of a calibration factor for each junction.

7
Integrity is maintained by periodic redeterminations of the SPRT

ice point with a triple point cell, checking the bridge against a calibrated standard resistor and checking the thermocouples for equality when

they are all at the same temperature in a well of an insulated copper

cube.

4.2. Atmospheric Pressure

The interferometer housing is not airtight and pressure inside it is

the same as laboratory pressure. An aneroid barometer is located adjacent to and on the same elevation as the interferometer. Aneroid barometers can be read much faster than mercury barometers and this is an important characteristic in interferometric length measurements. The aneroid used for gage block measurements has good stability, and frequent

comparisons with NBS reference barometers insure its reliability.

4.3. Water Vapor

A commercially available Dunmore type hygrometer is used. This type

has a sensing element whose electrical resistance changes with moisture

content of the air. Periodically calibrated, it has an uncertainty of

about 1.5% relative humidity [8, 9]. The sensing element was originally

mounted adjacent to the interferometer, but was later moved inside the

interferometer housing (see section on process evaluation)

5 . GAGE BLOCK MEASUREMENT PROCEDURE

In preparation for measurement, the gaging faces of the NBS standards

are cleaned with trichloroethylene and ethyl alcohol. Wiping the alcoholrinsed gaging faces is done with paper tissue or a clean cotton towel.

Lint or dust is removed with a camel's hair brush.

The gaging faces are examined for burrs and, if present, these are removed with a deburring stone. The bottom end is tested for wringability

with a quartz optical flat. The transparency of the flat makes possible

a judgment of the wring. A uniform grey color at the interface indicates

a good wring. Any colored or light areas indicate a gap of several microinches between the faces in that area, and such a gap may result in an erroneous length measurement. Deburring and cleaning is continued until

a good wring is achieved. The quartz flat is left wrung to the gaging

face to keep it clean until preparations are completed for wringing the

block to the steel optical flat (platen)

Preparation of the steel platen is similar. Trichloroethylene and

ethyl alcohol rinses are used, then deburring if necessary, followed by

more rinsing and drying. After sweeping with a camel's hair brush, a thin

uniform film of light grease is applied to the wringing surface with a bit

of tissue. This film is rubbed and finally polished with tissue or towel

until the film appears to be gone. After carefully sweeping the platen

with the brush, it is ready for wringing.

The block is removed from the quartz flat and the exposed gaging face

8
is immediately wrung by carefully sliding it onto the edge of the steel

platen, maintaining perpendicularity by feel. Sliding is continued until

wringing resistance is felt, and then with slight downward pressure the

block is slowly worked into its final position. Square style blocks, such

as the NBS reference standards, are positioned so that the gage point* is

at the right in the viewing field of the interferometer. One to four

blocks can be wrung to the platen for measurement

.

The platen with its wrung blocks is placed in the interferometer and

two thermocouples are fed down the center hole of each block, one about

three quarters down and one about one quarter down the length of the block.

A small wad of polyurethane is pushed into the hole to seal and hold the

wires.

A preliminary alignment by autocollimation with the Gaussian eyepiece

as the support table is adjusted, will produce fringes. Rapid changes in

the fringe pattern occur as the block cools from handling.

It is convenient to wring the blocks in late afternoon and allow

overnight temperature stabilization. No effort has been made to determine

minimum stabilization time. Two length observations are made several hours

apart, but the first measurement is not taken until the laser is in equilibrium. Leaving the laser on continuously when observations are being

made over several days eliminates delays. The laser beam is blocked from

entering the interferometer except when measuring.

Final fringe pattern adjustment is made so that the platen fringes

are parallel to the top and bottom edges of the block and one fringe on the block goes through its defined gage point. The direction of increasing fringe order is verified by pressing down on the eyepiece and observing fringe flow. A photograph is taken of the pattern. Block temperature,

air temperature, barometric pressure, and humidity are measured immediately

before and after the photograph and then averaged.

The photograph can be either a positive or a negative and image size

is determined by th,e distance between the film plane of the lensless camera and the viewing aperture of the interferometer. A compromise is made

between image size antT^^^posure time, but short exposure is desirable be- cause the fringe pattern m^y shift. Further image magnification takes

place in the fringe measuring instrument. A compromise is also made between magnification in the photograph and magnification in the measuring

instrument. Too much total magnification degrades image sharpness.

*NBS reference standards in the 5 to 20 inch size range are of the square

type with a^Kaxial hole, and the gage point is on the measuring face midway between the^-edge of the hole and the edge of the block nearest the

size marking. In figure 2 the right hand edge is the reference edge and

the gage point is midway between it and the right hand edge of the hole.

In sizes below 5 inches the reference standards are of the rectangular type

with the gage point at the center of the measuring face as in figure 5.

9
Fringe fractions are taken from the photograph with a coordinate com- parator which has a fixed stage in the focal plane of a microscope movable

on X-Y slides by precision screws having drum readouts. Four measurements

of distances "a" and "b" are recorded and averaged to obtain fringe fraction f, figure 5. Settings on the block fringe to obtain "a" are made at

the point where the fringe intersects the gage point. Settings on the

platsn fringes to obtain "a" and "b" are made as close as practical to

the edges of the block because it is here that the platen best represents

an extension of the bottom face of the block. Parallelism between gage

block and platen is also read from the photo because this information is

useful in detecting a defective wring. Poor wringing contact is indicated if the parallelism is different from its usual value and this is sufficient cause to discard a particular length measurement.

FIELD OF VIEW

Figure 5. Fringe fraction measurement.

Photographing fringe patterns has several advantages. The photograph is a permanent record which can be reinterpreted at any time with

the same or other techniques. Changes in block geometry are readily

seen by comparing photographs in time sequence. The coordinate comparator is superior to the common practice of fringe fraction estimation

by eye because it is more objective, lends itself to multiple measurements and averaging, and is more ' precise . Finally, photography is fast

and thus permits readings of the ambient conditions to closely bracket

the fringe recording. This is especially important because atmospheric

pressure is usually in a state of flux.

10
6. COMPUTATION OF GAGE BLOCK LENGTH

Calculating gage block length from the data is done in 3 steps:

(1) Calculation of wavelength,

^j-pf observed ambient conditions

(2) Calculation of the whole number of fringes in the gage block

length from its predicted length and the laser wavelength in ambient air.

(3) Calculation of the gage block length from the whole number of

fringes, the observed fringe fraction, wavelength in ambient air, gage

block temperature, and interf erometric correction factors.

6.1. Calculation of Wavelength

Edlen's 1966 formula [10] for the refractive index of air is used to

calculate the wavelength from the relationship

" tpf tpf as follows

X = = Xo [1+A-B-C]

where

_ P[8342.13 + 2406030 (130-0^)"-*-+ 15997 (38

. ""^j 10~^ ^ -720.775

1 + (0.817-0. 0133t) 10"^

1 + 0.003661t

C = f (5. 7224-0. Q457a2) 10

Sjmibols:

Aq = Vacuum wavelength in ym

X ^ = Wavelength at observed conditions t,p,f

t,P,f

n ^ = Index of refraction of air at t,p,f

t,p,f

p = Atmospheric pressure in mm of Hg

t = Temperature in degrees Celsius

f = Water vapor pressure in mm of Hg

a = I/Xq in ym

^

11
6.2. Calculation of the Whole Number of Fringes

...This method for determining the whole number of fringes is valid only

If the block length is known to better than +1/2 fringe (1 fringe =si 12yin.

for helium neon laser light) from either its history or from an independent measurement process. The calculation is as follows:

2 L [1+C(t'-20°)J

where F is the number of interference fringes in the length of the block

at temperature t*, and in air of temperature t, pressure p, and

vapor pressure f.

L is the predicted block lergth at 20°C taken from an independent

^ measurement or from the block's history.

C is the linear thermal expansion coefficient per degree Celsius of

the block.

t' is the block temperature at the time of measurement.

X , is the wavelength in the ambient air at the time of measurement,

tpf

The fractional part of F is retained temporarily for the reason explained

below.

6.3 Calculation of Block Length from the Observed Data

Generally, the observed fringe fraction <^ is simply substituted for

the fractional part of F, but there are cases where the last digit in

whole number F must be raised or lowered by one. For example if the re- tained fractional part of F is .98 and the observed fraction is .03, obviously the last whole number in F must be raised by one before substituting the observed fraction.

'\\, The new measured block vdlue, in fringes, is

F' = F + (J)

Finally, the interferometer aperture correction, ,62, is added, the

block is normalized to 20°C, and a conversion to length units is made to

arrive at the final value at 20°C as follows:

X _

L200 = F'[l+C<20°-t')] + 62

12
7. SYSTEMATIC AND RANDOM ERRORS

Potential sources of systematic errors are as follows:

(1) Wavelength

a. Vacuum wavelength of laser

b. Refractive index of air equation

c. Refractive ind ex determination

1. Air temperature measurement

2. Atmospheric pressure measurement

3. Humidity measurement

(2) Interferometer

a. Alignment

b. Aperture correction

c. Obliquity angle correction

(3) Gage Block

a. Gage block temperature measurement

b. Thermal expansion coefficient

c. Phase shift difference between block and its platen.

Length proportional errors are potentially the most serious in long

block measurement. Their relative influence is illustrated in table 1.

One example will help explain the table: if air temperature measurement

is in error by 0.1°C a systematic error of 1 microinch (1 part in 10^)

results in the value of a 10 inch gage block.

Every practical means, as previously discussed, was used to reduce

these errors to a minimum and, at worst, errors in measuring the parameters

listed in the table did not exceed those listed in column 1 (1 yin. or 1

part in 10^), and most are undoubtedly in the column 2 category. Further

evaluation of these errors is described in the section on process evaluation .

A few error sources in the first list but not in the table have not

been completely discussed. The first of these is phase shift difference

between block and platen. As indicated earlier, the present solution is

to closely match the optical characteristics of block and platen. This

undoubtedly reduces the phase shift difference to a point where it becomes

13
TABLE 1. LENGTH DEPENDENT ERRORS RESULTING FROM SYSTEMATIC ERRORS IN

MEASUREMENT PARAMETERS

ERROR IN A 10 INCH GAGE BLOCK

1 microinch 0.1 microinch

(1 part in 10 ) (1 part in 10 )

1 part in lO'

1 part in lO'

0.1°C

0.30 mm

12% R.H.

1 part in 10

1 part in 10^

0.01°C

0.03 mm

1.2% R.H.

0.45 mm/m 0.14 mm/m

0.01°C 0.001°C

PARAMETER

Wavelength

Vacuum wavelength

Refractive index formula

Air temperature

Atmospheric pressure

Relative humidity

Interferometer

Alignment

Gage block

Steel gage block temperature

smaller than measurement process precision and, therefore, difficult to

detect. Future studies will deal with the problem of phase shift, especially those cases where block and platen properties cannot be matched.

Thermal expansion coefficients of gage blocks have an uncertainty

that is to a large extent nullified by measuring at temperatures very

close to^the 20°C reporting temperature. Gage block manufacturers give

11.5X10^ /°C for steel blocks. This average value may be uncertain by 5%

(.6X10 /°C) for individual blocks. The manufacturer's value was used for

the 10 inch steel control block described in the next section and for all

NBS steel reference standards. A program is now in progress to measure

coefficients at NBS.

Random errors arise from variability in any parameter in table 1,

and in addition, they can arise in the fringe fraction measurement and

wringing variability.

8. PROCESS EVALUATION

A collection of values from repetitive measurements of stable control

standards can be characterized by (1) the limiting mean value, (2) process

precision, (3) systematic error and (4) process uncertainty. Furthermore,

these values can be plotted against a time base to produce a control chart

showing the limiting mean and process precision. The basic assumption in

most statistical techniques is that the data are a random sample from a stable probability distribution, and in most cases that they have a normal

(Gaussian) frequency distribution. This assumption can be tested by the

14
control chart method and if it meets the test, the process is said to be

in a state of statistical control.

These are powerful tools for process evaluation because the effects

of planned process changes are visible on the control chart and are quantified by the statistics. If measurements of the control standards made

after each process change are analyzed as a subgroup the effect, if any, on process precision and limiting mean will be revealed. These methods

were used for tracking down error sources, evaluating precision, and indicating the way to improved measurement techniques.

8.1. Control Standards

Four gage blocks were selected as control standards to evaluate and

improve thig interferometric measurement process. The blocks and their

purposes are as follows:

(1) A 0.150 inch chrome-carbide gage block. This block is short

enough to minimize the influence of variations and uncertainties in wavelength, temperature, pressure and humidity. Repeated measurements tend

to show the best precision attainable with this process.

(2) A 0.129 inch steel gage block selected for the same reasons as above, but in addition because it had slightly superior geometric and sur- face finish characteristics. It is an alternate control block and was not

available at the beginning of the experiment.

(3) A 10 inch glass-ceramic gage block stack consisting of two 3

inch and one 4 inch block wrung together (a single 10 inch block of this

material was not available) . This block has a very low thermal expansion coefficient thus minimizing the influence of block temperature un- certainties but accentuating, by virtue of its relatively long length,

uncertainties in wavelength, air temperature, pressure, and humidity.

(4) A 10 inch steel gage block. This block is equally affected by

all the parameters that contribute to the uncertainties of the 10 inch

glass-ceramic block, and in addition, by the uncertainties of temperature

and thermal expansivity.

Each of the four blocks was wrung to its own steel optical flat and

remained wrung throughout the evaluation so that wringing variability

would not obscure the investigation of other parameters. The 0.129 inch

block was wrung to a steel flat of matching surface finish. A 0.150 inch

steel block was wrung to the upper gaging face of the glass-ceramic block

to make fringe contrast and definition comparable to the other control

blocks. Thermal expansion of this steel auxiliary block was included in

computations of the length.

8.2. Determining Process Characteristics

The first step was to determine process characteristics existing

during prior measurements of the NBS long block reference standards by

15
single wavelength interferometry . Data for the first control standard

measurement subgroup was therefore obtained before making any planned

process changes.

CO

o •=o o

QC

>LLI a

r , , ^ > , ^ > A ^.-

+ 3a ^

-3a

^

OBSERVATION NUMBER

MEAN VALUE

N

= 1.67 MICROINCHES

= 38 a = 0.09 MICROINCH

3a = 0.27 MICROINCH

MEAN

Figure 6. Control chart on the 0.129 inch control standard.

Figure 6, a typical control chart, is for the 0.129 inch block and

it shows individual measurement values expressed as deviations from nominal length (corrections) at 20°C plotted against observation number. The

solid line is the mean value for the set and the dashed boundary lines are located +3 standard deviations (+3t7) about the mean. The two 10 inch blocks

have many more points taken over a long time period so, for convenience,

figure 7 shows only averages of subgroups with their +3a bandwidths and

plotted against a time scale. Figure 8 is a similar chart for the 0.150 and

0.129 inch blocks. Table 2 summarizes process characteristics and lists

process changes for each subgroup.

8.3. The Search for Systematic Errors

Time period A on the chart (fig. 7) and in table 2 shows representative

process characteristics for the "as it was" evaluation. Once these were es- tablished, the next steps were devoted to searching for systematic errors.

First, an analysis was made on data from period Ai Coefficients of

linear dependence were computed for control block values against air temperature, barometric pressure, relative humidity, and gage block temperature. The analysis revealed significant dependence (see fig. 9) between

the 10 inch control block values and relative humidity. Humidity cor- rections were apparently incorrect. Two causes were possible: an error

in the vapor pressure term in the refractive index equation or an error

in humidity measurement. After verifying that the correct equation was

used, a measurement error was investigated by using two hygrometers; one inside and one outside the interferometer housing. It was discovered that

16
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Figure 7. Control charts on the 10 inch steel and 10 inch glass-ceramic

control standards,^

T

oo

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c

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1—

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1

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showing secular changes.

20
28

27

CO03

I 26

E

<

25

24

5 6 7

VAPOR PRESSURE (mm of Hg)

Figure 9. Correlation chart, length vs vapor pressure.

although both instruments gave the same reading with the interferometer

door open, a difference developed once the door was closed. Hygroscopic

material in the housing is the probable explanation.

The hygrometer sensing element was then mounted inside the housing (a

process change) and control block measurements were resumed for period B. A marked improvement in precision was obvious on the control charts (fig. 7)

but no significant change in mean values occurred.

Period B measurements, no longer masked by imprecise humidity measurements, indicated the steel block values to be less precise than the

glass ceramic values. Temperature was the only parameter likely to affect

steel more than glass-ceramic, therefore, it was possible that temperature

measurement variability was causing the difference in precision. This

theory was tested by attempting to improve the temperature measuring system. New thermocouples were assembled using higher grade copper and con- stantan wire and the lead length was reduced by moving the reference tempperature enclosure from a position several feet away to a position in contact with the interferometer housing. The leads do not pass through open

air, but go directly into the housing with a consequent improvement in

thermal environment for the thermocouple system. Finally, one measuring

junction was attached to the stem adjacent to the resistance coil of the

SPRT . This allows verification of temperature equality between reference

21
junction and thermometer coil and checks for the presence of parasitic

thermal emfs. The new temperature system was then recalibrated by the

method previously described.

Control standard measurements were resumed and results plotted on the

control charts, periods C and E. Points taken in period D were omitted

from this subgroup for cause.* It seemed apparent from the control chart

that no improvement in precision resulted from rebuilding the temperature

system, in fact precision was degraded slightly.

In rebuilding the temperature system, the nanovoltmeter was moved

close to the interferometer from a location several feet away. Even

though circuitry is solid state, the small amount of heat generated by

this instrument could introduce perturbations effecting precision. Evidence such as a faster rise in interferometer air temperature when power was supplied to the nanovoltmeter plus the metrological axiom against

heat sources being near measurement areas led to moving the meter.

Again the effect of this change was visible on the control chart,

period F, with a statistically significant improvement in precision for

the 10 inch steel control standard, the one most influenced by temperature. Temperature system rebuilding had indeed improved precision. A

small systematic error probably not exceeding 0.001°C may be indicated

by the change in mean value of the 10 inch steel block but the evidence

for this conclusion is marginal.

Measurement precision on the 10 inch blocks (a=0.18 and 0.21 yin.)

now approached that of the 0.150 inch control block (a=0.10 yin.) suggesting that length dependent random errors were very small. Until factors causing this variability are discovered it is unlikely that process

precision can be improved.

Another round, G, was started with no process changes. Only four measurements were made before laser No. 109 broke down, requiring a new plasma

tube. Unfortunately this occurred just before a planned laser calibration

which would have allowed evaluation of wavelength, the last source of systematic error remaining to be studied. Judgment of long term stability of

this laser must be based mainly on three calibrations: one at the beginning of this study and two about 18 months before. Vacuum wavelength variations of approximately 1 part in 10^ were observed. Extrapolation of this

evidence is not advisable although the control block data seems to reinforce the picture of a well behaved laser.

At this point measurement precision (3a) of the process was about 5

^During this period, the aneroid barometer was carried back and forth

between two laboratory rooms. A periodic barometer check indicated a calibration change, probably from mechanical shock. Pinpointing the

exact date of the calibration shift was impossible so all values were omitted

.

**Further tests of temperature measurement effectiveness are given in the

Appendix, item 4.

22
parts in 10° for the 10 inch control blocks. Variations in vacuum' wave.- length of a few parts in 10^ became significant at this level. Laser

No. 184, newly calibrated, was installed shortly after the demise of

No. 109 and periods H, I, J, L, N, and Q (plotted with symbol "A" in fig- ure 7) were measurements made with No. 184. The somewhat erratic nature

of these measurements led to expending much time and effort on an error search that revealed nothing until an iodine stabilized laser became available .

The iodine stabilized laser was used in periods K, M, 0, P, and R

(plotted with sjmibol "•" in figure 7) . This helium-neon laser slaved to

a saturated absorption line of iodine is far more stable than any light source in the visible range now in use including krypton 86, the international standard. The measured vacuum wavelength of the iodine stabilized laser must carry with it the uncertainty in krypton 86, but since

this uncertainty is only a few parts in 10^ it is of no consequence in

these gage block measurements.

The differences between the two lasers shows up well in figure 7.

Period Q measurements with No. 184 were made immediately after t.he laser was recalibrated and shows a significant reduction in the systematic difference. Recalibration indicated a change of 13 parts in 10^ in vacuum

wavelength over an 18 month period. This laser was apparently atypical

and the measurements made with it were of little value for this study.

The remarkable stability of the iodine stabilized laser is apparent

from the data in table 2 and the control charts of figures 7, 10, and 11.

Selecting all iodine stabilized laser values from periods K through R,

the process precision is 0.66 microinch for the 10 inch steel block, whereas for the comparable periods J- through Q it is 0.93 microinch for laser

No. 184. Comparable figures for the 10 inch glass ceramic block are 0.60 microinch and 1.11 microinch.

In figures 10 and 11 all iodine stabilized laser values are plotted

vs observation number. The analysis of this data for linear dependence

against air temperature, barometric pressure, relative humidity, and gage

block temperature failed to show significant correlations.

Stability of the two 10 inch control standards is of interest and it can be stated with reasonable certainty that they changed less than 2 microinches (2 parts in lO'') in the 33 months covered in this report. But

the nature of systematic errors discovered during this process study makes

it impossible to express the change more precisely or to define the trend

of the change. A length change, of course, was not unexpected.

It is significant that all subsequent measurements fell within the

approximate +2 microinch 3a bandwidth of group A in spite of the random

and systematic errors discovered and remedied in the process analysis.

The 0.150 and 0.129 inch control standards also exhibited time dependent length changes as shown in figure 8. Rates of -0.19 yin./year

and -0.28 yin./year for the 0.150 and 0.129 inch block respectively were

23
CO M

28 -

>

' •• •

• • • «

27

• • •

o

o

I—

26

__._L

MEAN VALUE = 27.4 MICROINCHES

IM = 74 o = 0.20 MICROINCH

3a = 0.60 MICROINCH

16 32 48

OBSERVATION NUMBER

64

Figure 10, Control chart on the 10 inch glass-ceramic block measured with

an iodine stabilized laser. ^C/5 20

1CD +—

'

(UEo

CD 19

<

z

1 18 o

17

—^

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M :AN VALUE = 18.7 MICROINCHES

N = 74

a,= 0.22 MICROINCH

3a = 0.66 MICROINCH

1 1 1 1 16 32 48

OBSERVATION NUMBER

64

Figure 11. Control chart on the 10 inch steel block measured with an iodine stabilized laser.

24
determined

.

During the search for systematic errors the parametric measuring

devices and sources were calibrated and checked. Some were mentioned

in this section, others not, but all are summarized in the Appendix.

8.4. The Study of Random Errors

The 0.150 and 0.129 inch blocks were selected as controls because

their short lengths reduced length dependent random and systematic errors

to insignificance. Thus, the control charts on these blocks demonstrate

a nearly minimum random variability that must originate in the only nonlength dependent variable, fringe fraction measurement. Knowledge of the

minimum variability can be useful in long block error analysis

.

Twenty-eight measurements of the 0.129 inch block were studied for

clues to minimum random variability. Each photograph was remeasured and

the lengths recomputed to create a second set, called Round 2, based on

the remeasured fringe fraction. The precisions of the four submeasurements made on each photograph were also computed and pooled. The results

are in table 3

.

TABLE 3. ANALYSIS OF 28 MEASUREMENTS OF THE 0.129 INCH CONTROL BtOCK

Round 1 Round 2

Mean deviation from nominal length 2.06 yln. 2.06 yin,

Standard deviation, S^, of a length value

from a single photograph

2 Variance, S

.097 .096

.00941 .00922

Standard deviation, S , of the difference

between Round 1 and Round 2

Variance , Sm

Pooled standard deviation, S , of the mean

g of 4 fringe fraction submeasurements of a photograph

2 Variance, S

.067

.00449

.013

.00017

Mean length values for Rounds 1 and 2 agree exactly (2.06 yin.) and

the total random errors (S =.097 yin. and .096 yin.) agree closely. Two

principal components contribute to total random error: fringe fraction

measurement error, S , coming from the process, and photographic image

error, S , coming from sources described below. The magnitude of the

fringe fraction measurement process error is the standard deviation of

the differences between Rounds 1 and 2 (S =.067 yin.) and since this is m

25
not as large as there must be a contribution from image variations

from photograph to photograph which are not related to the control block

length. S is computed as follows:

= - = (.097)^ - (.067)^ = .00492, S = .070 yin.

p t - m p

2 2 2 Comparing variances and with shows that approximately one-half

the total random error comes from the fringe measuring process and the

other half from photographic image variations. Image variations from one photograph to the next probably result from several factors such as vibration, surface roughness effects and incomplete spatial filtering of

the laser light.

There is a relatively small random error (S = .013yin.) in the four

s submeasurements on a photograph. Thus, the observer tends to interpret

the fringes consistently at a given time, but image ambiguities cause the

observer to interpret the fringes in a slightly different manner at a later time as indicated by the magnitude of (.070 uin.).

Analyses of variance can also shed light on length dependent random

errors. Only data taken with the iodine stabilized laser, where wavelength uncertainties drop out, are used in the following analysis.

Combined pressure and humidity measurement variabilities are determined by comparing the variances of the 0.129 and 0.150 inch blocks with

the variance of the 10 inch glass-ceramic block with its maximization of

pressure an^ humidity effects and minimization of temperature effects.

Variance, S , caused by pressure and humidity is

2 2 2

pf max min

2 2 where S and S . are variances of the 10 inch glass-ceramic and the max mm

0.150 inch blocks respectively. Then

S^^ = 0.040 ~ 0.009 = 0.031 yin.^

pf

S - = 0.176 yin. pf

3S - = 0.53 yin. pf

The 0.53 yin. is equivalent to 0.16 mm of pressure or 6.4% RH for a 10

inch block. The relative influence of the two parameters based on experience is approximately 1.5% RH variability and 0.13 mm pressure variability.

The effect of temperature measurement variability is maximized in the

10 inch steel block and minimized in the 10 inch glass-ceramic block. The

difference in variance between these two blocks is 0.008 yin.^ (0.048 - 0.040). attributable primarily to temperature, variability and this is

26
equivalent to 0.002°C in a 10 inch steel block at the 3a level.

This analysis shows the largest source of length dependent random

error to be in the measurement of atmospheric pressure.

8.5. Summary

Application of single wavelength laser interf erometry to reference

standard gage blocks at NBS has proven valuable in several respects:

(1) the extreme coherence of the light simplifies interferometry on blocks, especially those longer than 10 inches, (2) the bright, high

contrast fringe patterns facilitate photographic recording and objective

measurement, (3) the advent of ultra stable lasers reduces wavelength

uncertainties, and (4) the special requirements in monitoring reference

standard gage blocks make the process especially useful. The necessity

for prior knowledge of gage block length to within 1/4 wavelength is the one drawback, although a minor one at NBS.

During this study of the long gage block process each random and

systematic error source was minimized by improving equipment and techniques. A new process now exists because of these improvements and this

new process will continue to be monitored. Performance during the last

8 months with the iodine stabilized laser indicates a measurement process in a state of statistical control (see fig. 10 and 11). The data

show no statistically significant dependence on parameters which are potential systematic error sources indicating that systematic errors can be regarded as negligible relative to the random errors.

Evidence from the short control block measurements sets a probable

limit on precision for this process at about 3a=0.3 microinch. A possibility exists that using photo scanning techniques in fringe interpretation can improve precision, but the benefits will probably be small.

Length dependent random errors can best be improved with better pressure

measuring devices.

The one random error source not studied here, wringing variability,

is now under analysis. In all probability it will be the largest single

source of random error.

27
REFERENCES

[1] Pontius, P. E., The measurement assurance program - a case

study, part I, short gage blocks (0.1 to 4 Inches), Nat.

Bur. Stand. (U.S.), Monogr. 149 (1975) in print.

[2] Pontius, P. E., The measurement assurance program - a case

study, Part II, long gage blocks (5 to 20 inches), Nat.

Bur. Stand. (U.S.), Monogr. (in process).

[3] Bruce, C. F., Australian J. Phys . 8:224 (1955).

[4] Thornton, B. S., Australian J. Phys. 8:241 (1955).

[5] Mielenz, K. D., et al, Appl. Opt. Vol. 7, No. 2:289 (1968).

[6] Schweitzer, W. G., et al, Appl. Opt. Vol. 12, No. 12:2927 (1973).

[7] Riddle, J. L., et al , Platinum resistance thermometry, Nat.

Bur. Stand. (U.S.), Monogr. 126 (1973).

[8] Handegord, G .. 0., et al, Humidity and Moisture, Vol. I,

Reinhold Publ. Corp., N.Y., 265 (1963).

[9] Hedlin, C. P., Humidity and Moisture, Vol. I, Reinhold Publ.

Corp., N.Y., 273 (1963).

[10] Edlen, B. , Metroiogia, Vol. 2, No. 2, 71 (1966).

[11] Wexler, A. and Hasegawa, S., Relative humidity - temperature

relationships of some saturated salt solutions, J. Res. Nat.

Bur. Stand. (U.S.), Vol. 53, No. 1:19 (1954).

28
APPENDIX

Calibration Schedule

The apparatus used in the measurement of gage blocks during the period

covered by this paper were calibrated and verified as follows:

1. Lasers

Laser No. 109 : Ag was determined just before period A. Two previous

determinations were made 19 and 18 months, respectively, before the

start of this study. Variations in Xq of 1 part in 10^ were observed

among the three calibrations. The plasma tube in this laser failed

during period G.

Laser No. 184 : Aq was determined just before period H and again

before period Q. A change of 13 parts in 10^ occurred between calibrations .

Iodine stabilized laser : Aq was taken from published results [6]

.

The Aq of this laser will not change from the published value and

its stated uncertainty as long as it is stabilized to the selected

absorption line of iodine.

2 . Hygrometer

The unit was calibrated by the manufacturer to within +1*5% RH just

before period A and again in period H. No significant change was

observed. At the end of this study the unit was tested against four

saturated salt solutions [11] covering a range from 12% to 75% RH

and the instrument readings agreed with the published values within

2% RH.

3. Aneroid barometer

Biweekly comparisons were made with a reference aneroid barometer

maintained by the Pressure and Vacuum Section of NBS until period E. After period E comparisons were made with the reference barometer

each time the control standard gage blocks were measured. During

periods P and R several comparisons were also made with a fixed

cistern mercury barometer. The accumulated data were used to calculate a mean correction to the aneroid. Only once (period D) did

the mean correction change significantly.

29
Temperature measuring system

The SPRT, bridge, and thermocouples were calibrated just before period A. After rebuilding the system between B and C the bridge, thermocouples, and SPRT ice point were calibrated. Between G and H, and

between P and Q, the SPRT ice point was redetemined , and the bridge

was checked against a standard resistor. No significant changes were

observed

At the end of the study a further verification of the system was made.

Two resistance bridges were used to measure temperature t of the insulated copper block with the SPRT. Th6 first was the system Mueller

bridge and the second was a high resolution a.c. bridge provided by

the NBS Temperature Section. The procedure used was to measure R^ of

the SPRT with both bridges (called A and B) in an A B B A sequence to

compensate for the effect of temperature drift. Then the SPRT was placed in a triple point of water cell and R was measured with both

bridges. Resistance ratio R /R and temperature t were computed from

both sets of data and the SPRT constants. The average difference was 0.0004°C and the values had a range of 0.0003°C.

A test was also conducted to determine thermocouple effectiveness.

Thermocouples were inserted into the holes of several blocks as described in Section 5 and, in addition, thermocouples were attached

to the outside of the blocks with magnets. After overnight stabilization in the interferometer, the maximum difference observed between inside and outside block temperature was 0.0002°C and this

value was not exceeded during three days of observation. Under ad- verse conditions, however, thermal contact between the thermocouples

and the wall of the hole might need improving.

30
NBS-114A (REV. 7-73)

U.S. DEPT. OF COMM. BtBLIOGRAPHIC DATA

SHEET

1. FUHLK A I ION OK 1<1-,P()K I' NO. NBS MN-152

2. ( i()v 't Ac( e .s s i (jn No.

3. K( ( ipK.iii's Alccssioij No.

4. TITLE AND SUBTITLL:

A Gage Block Measurement Process Using Single

Wavelength Interferometry

5. Publication Date December 1975

6. Performing Organization f-ode

7.AUTH0R(S) j^^^ 3^ g^^^^ 8. Performing Organ. Report No.

9. PERFORMING ORGANIZATION NAME AND ADDRESS

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

10. Project/Task/VCork Unit No. 2321125

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Same

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15. SUPPLEMENTARY NOTES

Library of Congress Catalog Card Number: 75- 619353

16. ABSTRACT (A 200-word or less factual summary ol most significant information. If document includes a significant a bibliography or literature survey, mention it here.)

The interferometric transfer of the length unit from its

defined wavelength to NBS reference standard gage blocks is

basic to the gage block calibration program at NBS. The interferometric measurement process using a laser light source and

a Kosters type gage block interferometer is described here.

Continuous evaluation and refinement of the process is aided

by statistical treatment and control chart techniques. All error sources, both random and systematic, are evaluated and

the process is maintained in a state of statistical control.

17. KEY WORDS (six to twelve entries; alphabetical order; capitalize only the first letter of the first key word unless a proper name; separated by semicolons

)

Calibration; gage blocks; interf erometry ; laser; length; measurement process;

uncertainty

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