NBSIR 87-3625

NEW NIST PUBLICATION

June 12, 1989

Length Scale Measurement

Procedures at the National

1 Bureau of Standards

John S. Beers, Guest Worker

U.S. DEPARTMENT OF COMMERCE

National Bureau of Standards

National Engineering Laboratory

Precision Engineering Division

Gaithersburg, MD 20899

September 1987

U.S. DEPARTMENT OF COMMERCE
NBSIR 87-3625

LENGTH SCALE MEASUREMENT

PROCEDURES AT THE NATIONAL

BUREAU OF STANDARDS

John S. Beers, Guest Worker

U.S. DEPARTMENT OF COMMERCE

National Bureau of Standards

National Engineering Laboratory

Precision Engineering Division

Gaithersburg, MD 20899

September 1987

U.S. DEPARTMENT OF COMMERCE, Clarence J. Brown, Acting Secretary

NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Director

LENGTH SCALE MEASUREMENT PROCEDURES AT NBS

CONTENTS

Introduction

1.1 Purpose

1.2 Line scales of length

1.3 Line scale calibration and measurement

assurance at NBS

The NBS Line Scale Interferometer

2.1 Evolution of the instrument

2.2 Original design and operation

2.3 Present form and operation

2.3.1 Microscope system electronics

2.3.2 Interferometer

2.3.3 Computer control and automation

2.4 Environmental measurements

2.4.1 Temperature measurement and control

2.4.2 Atmospheric pressure measurement

2.4.3 Water vapor measurement and control

2.5 Length computations

2.5.1 Fringe multiplier

2.5.2 Analysis of redundant measurements

3. Measurement procedure

Page No

1

1

1

2

2

2

3

8

8

9

11

11

13

15

15

15

16

17

18

18

18

19

20

20

Planning and preparation

Evaluation of the scale

Calibration plan

Comparator preparation

Scale preparation, mounting and alignment

Microscope magnification, illumination, focus

and adjustment 22

Interferometer preparation and alignment 23

Temperature equilization and the measurement

of environmental parameters 24

Instrument operation 27

Turning on the apparatus 27

Controls, adjustments and displays 27

Computer/controller operation 31

Reading initial environmental conditions 32

Starting a run with scale normal 32

Reading intermediate and final environmental

conditions 32

Reversing the scale 33

Setting controls for the reversed scale 33

Temperature stabilization 33

Starting the reversed scale run 33

3.2.11 Combining data from normal and reversed runs 33

3.2.12 Operational check list 33

Measurement results 34

4.1 Evaluation 34

4.2 Scale calibration report 38

Measurement assurance 39

5.1 Definition and principles 39

5.2 NBS control standards 40

1

1

2

2

2

2

2

2.5

2.6

7

8

9

10

1
5.2.1 Invar meter bar No. 5727 40

5.2.2 Twenty inch steel bar No. 6495 41

5.2.3 Twelve centimeter quartz scale No. 5541 41

5.3 Monitoring the measurement process with control

standards 41

5.3.1 Measurement of meter bar No. 5727 41

5.3.2 Measurement of 20 inch bar No. 6495 42

5.3.3 Measurement of 12 centimeter scale No. 5541 42

5.4 Measurement assurance data and its evaluation 42

5.4.1 Evaluation scope 42

5.4.2 No. 5727 data evaluation 43

5.4.3 No. 6495 data evaluation 53

5.4.4 No. 5541 data evaluation 53

5.4.5 Data from very short intervals 54

5.4.6 Summary and conclusions 54

5.5 Error sources and error analysis 55

5.6 Minimizing errors 57

6. Appendices - Detailed procedures 58

A. Temperature system calibration 58

B. Barometer calibration 59

C. Hygrometer calibration 60

D. Interferometer alignment 60

E. Operational check list 61

F. Microscope angle adjustment 62

7. References 65

ii
LENGTH SCALE MEASUREMENT PROCEDURES AT THE NATIONAL BUREAU OF

STANDARDS

John S. Beers

ABSTRACT

Precision graduated length scales have been measured by

interferometry at NBS since 1965. An instrument called the

Line Scale Interferometer was designed for this purpose. The history, development, improvement, operation and evaluation

of the line scale interferometer are described here. Special emphasis is given to detailed operating procedures to provide guidance in the use of the instrument. Evaluating

performance through a measurement assurance program is also

emphasized.

Key words: Length; graduated scales; interferometry;

measurement assurance; uncertainty.

1 . INTRODUCTION

1 . 1 Purpose

This publication is primarily a documentation of current

measurement procedures for calibrating graduated length scales, and, as such, it will serve as an operating manual for the NBS line scale interferometer. Its secondary purposes are to record the history of the instrument and to describe the measurement

assurance program that provides continuous surveillance of the line scale measurement process.

There are five main sections: (1) "Introduction", which is general in nature, (2) "The NBS Line Scale Interferometer", which describes the instrument and traces its development from conception to the present and is partially adapted from a previous paper (reference 1) , (3) "Measurement Procedure", which detailed instructions for operating the instrument,

(4) "Measurement Results", which describes the analysis of measurement data and the writing of calibration reports, and (5) Measurement Assurance", which explains the principles and details the practice of monitoring measurement process performance.

1.2 Line scales of length

Graduated length scales probably surpass any other measuring device in the variety of its forms. They are made in lengths trom a few micrometers to over a meter (longer ones are made, but they are usually classified as measuring tapes or rods) . Many materials are used including steel. Invar, brass, glass, silicon and quartz. Cross sectional shape can be rectangular, "H", "U" or

1

'
a modified "X". Graduations are cut by diamond, photo-etched or

deposited by metal evaporation. Width of graduations can be

anywhere from sub-micrometer on up, and graduation spacing can be

from one micrometer on up. Their lack of standardization can

often make calibration a real challenge, and almost every scale

presents a different measurement problem.

1.3 Line scale calibration and measurement assurance at NBS

In the industrial and technological worlds, length scales have

always been important. One of the basic objectives of the

National Bureau of Standards when it was established in 19.01 was

to maintain the national standard of length and provide a length

scale calibration service. This service was the only means for

disseminating the standard of length throughout the economy.

Measurement assurance, although it was not called that at the

time, was practiced in a simplified form from the beginning. By

1928 it had reached an advanced form employing incomplete block

designs and least squares data reduction (ref. 2, 3) for making

intercomparisons of length standards. These statistical

techniques were used until 1964. The measurement assurance

program used since 1964 is described in section 5 of this paper.

2. THE NBS LINE SCALE INTERFEROMETER

2 . 1 Evolution of the instrument

From 1889 until 1960, the international prototype length standard

and the national length standards were graduated platinum-iridium

meter bars. Calibrations of all other scales were accomplished

in comparators employing filar microscopes for measuring length

differences between the standard and the scale being calibrated.

Subintervals were determined by a lengthy process of

intercomparison by subdivision (ref. 4) . In 1958, a committee of NBS scientists* chaired by I. C. Gardner,

Chief of the Optics and Metrology Division, started planning for

an interferometric line scale comparator in preparation for a

proposed change in the definition of the meter. By international

agreement in 1960, the meter was redefined as the length equal to

1,650,763.73 wavelengths in vacuum of the orange-red spectral

line of the krypton 86 atom. A new era of length measurement by

interferometry was opened by this change and the developement of

high speed fringe counters in the preceding decade.

Prior to 1960, wavelengths from selected light sources were

internationally sanctioned as secondary definitions of the meter

* Committee members were H. D. Cook, L. A. Marzetta and M. L.

Kuder of the Electronic Instrumentation Section, K. G. Kessler of

the Spectroscopy Section, T. R. Young and J. B. Saunders of the

Engineering Metrology Section, and B. L. Page of the Length

Section.

2
to serve, among other uses, in measuring end standards of length.

End standards have been measured by static interferometry since

early in this century. Their optically plane and parallel

measuring faces are ideally suited to this method because they

can serve as mirrors in the measuring legs of interferometers.

Line scales cannot be measured efficiently by the static method

for a number of reasons including the multiplicity of intervals.

They are best measured by dynamic (fringe counting)

interferometry

.

By 1961, an experimental fringe-counting interferometer (ref. 5)

was operational using a mercury 198 light source as a length

standard. Development of a final version proceeded, by good

fortune, in parallel with the development of the laser (ref. 6) . In 1964, the two activities converged and a successful

measurement of a one-meter scale with helium-neon laser

wavelengths was accomplished (ref. 7)

.

Refinements in the NBS

line scale interferometer were made and laser wavelength

stability was improved until in 1966, a semi-automated line scale

calibration system was in routine operation (ref. 8)

.

Much of

the credit for the success of this project belongs to Herbert D.

Cook who worked virtually alone for several years designing and

constructing the final instrument. The mechanical and optical

structures are shown in figure 1.

Development work has continued on both the line scale

interferometer and on lasers (ref. 9)

.

The principle changes

made in recent years are (1) rigid coupling and kinematic

mounting of the microscope and the interferometer in 1970, (2)

replacement of the Michelson interferometer with a commercial

interferometer in 1979, (3) modernization of the microscope

electronics in 1981, and (4) addition of a computer/controller in

1981 to completely automate instrument operation.

2.2 Original design and operation

In this section the instrument is described as it stood in 1966,

but with the 1970 modification (kinematic mounting of the optical

components) . It is important to describe the instrument as it

then stood to aid in understanding its present form because its

design principles and much of its structure remain unchanged.

For this reason the present tense is used here. Changes in the

system are described in the next section.

Six principal elements comprise the instrument: (1) a waybed and

carriage for mounting the measuring apparatus and translating the

scale, (2) an interferometer with a laser light source to

establish a length standard, (3) a photoelectric microscope with

a servo system for scale graduation positioning, (4) a

temperature controlled enclosure for environmental isolation, (5) devices for measuring temperature, barometric pressure and

humidity and (6) data recording and processing equipment. The

first three elements are shown in figures 1 and 2, and element

(4) is shown in figure 9.

3
moving mirror

^FOCUSING COKIBOtS

<AT .EACH END)

45* MIRROR

^; X.£AO SCR?

' <r,"A-Zi^ .- , MAIN carriage

SOBCARRIAGE 0« WHICH LINE SCALE AND MIRROR ARE MOUNTED

Figure 1. The line scale interferometer mechanical and optical

components with the Michelson type interferometer

Kinematically Mounted

Frame for Mlcroscopo,

Beam Splitter,45* Mirror

and Retarding Plates

Plane

Reference

Mirror

Stabilized Laser

Diverging LensCollimating Lena

Polaroid Filter 45“ Mirror

Vertical

Photoelectric

Microscope — Four

I Photomultiplier

'"^==CZQ lubes

L

Lead Screw

Waybed

Main Carriage

Sub*Carriage Servo

Controlled With

Respect to Main

Carriage for Fine

Motion and Mirror

Parrallelism

Split Lens

45“ Mirror

Four

Retarding

Plates

Aperture Plate

Figure 2. Schematic diagram of the line scale interferometer

4
The two-meter waybed and its carriage are the mechanical foundation of the instrument. A line scale is mounted on the

3.nd the carriage is moved on the ways by a motor driven lead screw. A modified Michelson interferometer is located at

one end of the waybed with its moving mirror attached to the carriage, coaxially with the scale. The stationary reference mirror is mounted along the side of the waybed on the microscope support structure. The photoelectric microscope is mounted vertically above the carriage at the midpoint of the waybed, and

IS focused on the scale graduations. All stationary components interferometer together with the microscope are attached to a rigid mounting frame which, in turn, is kinematically

s^PPo^ted on the waybed structure* . Interferometer components include the beam splitter and 45 degree mirror, the reference mirror and the retarding plates. It is vital that the microscope and stationary interferometer components remain dimensionally fixed during a scale measurement because any relative motion

among these parts will be seen as part of the measured scale length, thus obviously resulting in errors.

The entire apparatus is housed in a vibration isolated enclosure held at 20 degrees C ±0.01 degree by a thermostatically controlled circulating water bath. All heat producing components such as the laser, microscope lamp, drive motor and electronic circuits are externally mounted. Laboratory temperature is maintained at 20 degrees C ±0.05 degree.

Fringes formed by the laser light in the interferometer are detected, counted and interpolated to 0.01 fringe, giving a continuous indication of carriage position. Four retarding plates divide the 50 mm diameter collimated laser beam into quadrants, each quadrant acting as a separate interferometer, when the carriage moves, a sinusoidal voltage is simultaneously obtained from each of four photomultipliers monitoring the fringe patterns in their respective quadrants. A 0, 90, 180, and 270 degree simultaneous phase relationship between the four interference patterns is obtained by initial adjustment of the retarding plates . Direction of fringe counting, fringe interpolation and servo control - • parallelism deviations between

result from waybed straightness

four related signals.

of mirror parallelism (mirror

the fixed and moving mirrors

errors) are derived from these

Fringe interpolation and counting direction are displayed by applying the sine and cosine voltages from the photomultipliers cathode ray tube, the two voltages being applied to separate deflection axes. The resulting display spot follows a circular Clockwise or counterclockwise path coinciding with the forward or

Kinematic mounting of the optical system was completed in 1970. optical components were attached to the waybed caused by the shifting weight of the carriage was duced by a steel beam connecting the upper body of the microscope to the upper frame of the beam splitter assembly

5
reverse direction of the fringe patterns. One revolution of the

spot equals one fringe and the fringe fraction is the polar angle

of the spot. Digital interpolation is done by a built-in analog

computer

Mirror parallelism deviations caused by waybed straightness

errors are detected, and two error voltages generated, by

comparing the phase of the fringes in diagonally opposite

interferometer quadrants, one error signal from each diagonal.

These error signals actuate a dual hydraulic system which imparts

corrective motions to the mirror as described below.

Referring to figure 1, the scale and moving mirror are on a

subcarriage which, in turn, is mounted on top of the main

carriage. This subcarriage is movable relative to the main

carriage and it provides the mechanism for three functions: (1)

maintaining mirror parallelism without changing the relative

position of scale and mirror, (2) centering the scale graduations

and (3) focusing the scale. Except for focusing, these functions

are performed as parts of servo loops. The subcarriage is

supported on flexure springs near the mirror end to permit

longitudinal motion for line centering. Movement is imparted by

hydraulic pressure generated from the line centering error signal

working through a solenoid and piston arrangement. The springs

also serve as a fulcrum for rotational motion imparted to the

opposite end of the subcarriage by two hydraulic actuators.

Error signals from diagonal quadrants A and C operate one

hydraulic actuator and the error signals from B and D operate the

other. The hydraulic actuators on the subcarriage are at right

angles to one another and can, therefore, create the necessary

motion to keep the moving mirror parallel to the fixed reference

mirror while the carriage is travelling. Using plane mirrors in

this way has the advantage of reducing potentially serious

measurement errors caused by geometric errors in the waybed.

Detailed descriptions of the circuits and logic used to perform

the fringe counting, fringe interpolation and mirror parallelism

control can be found in reference 5.

Various helium-neon lasers have been used over the years starting

with a manually stabilized version in 1964, then progressing to a

commercial Lamb-dip stabilized model (ref. 10), and in 1977, to

an NBS-developed iodine-stabilized laser, stable to a few parts

in 10** (ref. 9)

High-contrast fringes are easily maintained

over the one-meter path because of the extreme coherence of laser

light.

Line scales are calibrated by making carriage displacement, as

measured by the interferometer, correspond exactly to scale

interval length. This correspondence is accomplished by the

servo and nulling action of the photoelectric microscope when the

carriage is stopped and a scale graduation is in view. As

illustrated in figure 3, a vibrating mirror in the microscope

sweeps a magnified image of the vertically illuminated graduation

across a slit located in front of a photomuliplier . Electronic

6
Figure 3. Schematic diagram of the photoelectric microscope

Rack-Mounted

Oscilloscope

Figure 4. Schematic diagram of the microscope servo system

7
circuits process the resulting signal and generate an output

voltage (error signal) proportional to the deviation between line

center and microscope optical center. This error signal operates

through a solenoid-piston assembly to apply a longitudinal

adjustment to the subcarriage holding the scale and

interferometer mirror. The graduation is centered when the error

signal is nulled and the fringe count reading is then recorded.

Proceeding up the scale in this manner produces a set of recorded

fringe count readings corresponding to the interval lengths on

the scale. These fringe counts are converted into length units

by multiplying them by a factor which encorporates the vacuum

wavelength, the refractive index of the ambient air and the

thermal expansion of the scale to 20 degrees C. Several passes

up and down the scale are made with the scale in both normal and

reversed orientation to generate redundant data for averaging and

statistical analysis. Length values are reported for a 20 degree

C scale temperature, the internationally accepted temperature for

dimensional measurements.

Data are recorded on punched paper tape, transferred to cards and

processed in the NBS central computer.

2 . 3 Present form and operation

2.3.1 Microscope system electronics

Obsolescence and gradual deterioration of the original electronic

systems made it desirable to bring them up to modern standards.

The photoelectric microscope, and its associated servo system,

was originally constructed with an electronic vacuum tube and

early solid state technology. It has been totally redesigned

with solid state integrated circuits and provisions for computer

control. The present system is shown in figure 4.

A high speed stepping motor and a preset indexer interfaced with

a microcomputer replaces the original dc-motor/cam-drive system

for moving the carriage predetermined distances corresponding to

nominal line spacings. The indexer can be operated either under

manual or computer control. Except for the photomultiplier

signal conditioning circuit, all of the microscope electronics

are built into five circuit board modules housed in a single 483

mm chasis. These modules consist of the mirror drive oscillator,

optical signal processor and line center error detector, indexer

control interface and proportional-integral (PI) servo driver.

The line signal derived from the photomultiplier is displayed on

an oscilloscope operating in the XY plot mode. The horizontal

input of the scope is driven by a sinusoidal signal from the

mirror drive oscillator circuit. Hence, a signal is displayed on

the screen showing the line position relative to the microscope

center.

The purpose of the optical signal processor and the line center

error detector is to transform the signal into a means for

centering the line in the microscope field. The optical signal

processor consists mainly of a pair of positive and negative peak

8
detectors. The difference between the positive and negative peak

voltage is used to scale the amplitude of the line signal and to

generate the peak-present signal. The peak-present signal is

used to disable the lead screw drive circuit and to activate the

electro-hydraulic servo circuit for fine centering of the line.

A threshold voltage derived from the scaled amplitude of the line

signal is displayed on the oscilloscope as a horizontal line

intersecting the line signal pattern (figure 4) and is used in

the line centering error detector to produce a dc signal

proportional to the distance of the line from the optical center.

The sign of this signal reflects the direction of the line from

the center. The threshold voltage can be adjusted with a

potentiometer to select the optimum level (usually 50% of the

amplitude) for triggering the centering-error detector. Using

the two points where the threshold voltage intersects the line

signal, the line centering error detector generates a bipolar dc

voltage corresponding to the direction, and proportional to the

distance, of the line from the optical center. This voltage is

used as an error signal to run the PI servo driver which, in

turn, moves the upper carriage through electro-hydraulic means to

center the line with the optical center. This servo system loop

will continuously and dynamically lock a line onto the optical

center. The two point criteria for line centering was chosen

because it closely resembles what an operator does when centering

with a bifilar eyepiece. Centering can also be achieved using

one point on either the right or left edge of the line for

special measurement needs.

2.3.2 Interferometer

A Hewlett Packard* interferometer system has replaced the

original Michelson type interferometer. It can be readily

integrated into an automated, computer controlled system. The

new interferometer, shown in figure 5, is mounted at the opposite

end of the waybed from the Michelson. When the HP system is used

alone, the parallelism control feature of the Michelson is lost

and the straightness errors in the waybed are uncompensated.

Under these conditions, great care must be taken to avoid Abbe

offset by adjusting the scale axis to coincide with the

interferometer axis so that measurement errors caused by carriage

pitching are minimized. The interferometer has a helium-neon

laser producing a continuous red beam. The cavity of the laser

is stabilized by using an internal zero thermal expansion

coefficient structure combined with a servo loop for automatic

tuning. This laser interferometer system has a resolution of

0.025 wavelength. Measurement units can be displayed in either

millimeters, inches or quarter wavelengths. Atmospheric

*Certain trade names and company products are mentioned in the

! text in order to specify adequately the equipment and procedures

[ used. In no case does such identification imply recommendation

I or endorsement by the National Bureau of Standards, nor does it

I imply that the products are necessarily the best available for

I the purpose.

9
Figure 5. The line scale interferometer with the commercial interferometer in place

Figure 6. Block diagram of the interfaces in the automated measurement system

10
parameters and workpiece temperature can be compensated by

dial-in switches when working in the millimeter or inch display

modes. At NBS it is used exclusively in the quarter wavelength

mode which is uncompensated. This ensures better compensation

through the use of NBS calibrated temperature, pressure and

humidity measuring instruments and computer generated

computations

.

2.3.3 Computer control and automation

The system has been completely automated using a Hewlett Packard

9845B microcomputer equipped with a crt display, two 2 56 k-byte

cassette tape drives and various parallel and serial interfaces.

The automated line scale measurement system is shown in figure 6.

Operation and control of the microscope servo, data acquisition

from the interferometer outputs, and statistical analysis on the

raw data can all be performed under computer program control. A

clock module adds a real-time reference and time related control

to the computer. It also enables the computer to keep track of

the time of day to interpolate environmental effects. The

indexer/controller is interfaced with the computer through two

16-bit parallel I/O interfaces. The interface connections allow

the computer to command the indexer to perform jogging, indexing

and running operations at both low and high speed.

A computer program (figure 7) operates the computer and calls for

scale intervals, number of passes, coefficient of thermal

expansion and other parameters to be entered as required. Once a

scale is aligned, the microscope focused, and the temperature

stabilized, operations in the automatic mode occur as follows:

(1) the microscope servo centers the zero scale graduation, (2)

the interferometer count is read when line centering criteria are

met, (3) the stepping motor advances the scale to the next

graduation, (4) the centering, reading and advancing sequences

repeat at each selected interval until the terminal graduation is

reached, (5) the selected number of passes up and down the scale

are made, (6) air temperature, scale temperature, barometric

pressure and humidity are measured and entered in the data file

at the end of each pass, and, (7) when all data are recorded, the

computer calculates, analyzes and tabulates the measurement

results and prints the calibration report tables.

Increased efficiency has resulted from the improved and

modernized automation. Scale calibration time from the reading

of the first graduation to the final print-out has been reduced

by factors ranging from five to ten.

2 . 4 Environmental measurement and control

Temperature, barometric pressure, humidity and carbon dioxide

content influence the refractive index of air and, thus, the

wavelength of light; temperature also affects the length of the

scale being measured. Air temperature, scale temperature,

barometric pressure and humidity are measured during every line

11
Enter Environmental Data

Record Readings and Input Data into a File

( Start j

I Enter Parametric Values and Environmental Data

Calculate Standard Deviations and Corrections

Print Output Tables

Perform Graphics

Stop

GED

Convert Distance Between Lines into Indexing Steps

J = 1 \ T / —

J>Nread-f 1 J=J + 1 "T“

Output the Index Command

{ Read Laser 10 Times and Calculate Average

Convert Difference into Indexing Steps

Index in Negative Direction

Convert Difference into Indexing Steps

1 Index in Positive Direction

1 Read the Servo Current

Reading

Rar'Se

|jog in Negative Direction

Reading < Preset Range ]

- Jog in Positive Direction

Read Laser 100 Times and Calculate Average

Figure 7. Flow chart for the automated measurement system

12

4
scale calibration. An average value is used for carbon dioxide

content because it stays relatively constant and has a small

effect on the refractive index.

2.4.1 Temperature measurement and control

Interferometer air path temperature and scale temperature are

measured with copper-constantan thermocouples in combination with

a standard platinum resistance thermometer (SPRT) . A

thermostatically controlled cell provides a stable 20.000 degree

C temperature which is measured by the SPRT, and serves as a reference temperature for the thermocouples (figure 8) . Thermocouples are used rather than thermistors because the long

term stability of thermocouples is superior and because they can

be easily referenced to the International Practical Temperature

Scale through the SPRT.

Three concentric copper tubes comprise the reference cell. A

thermoelectric cooler is attached to the outer tube and the fins

of the cooler are exposed to air flow from a fan. Resistance

heating^ wire is wrapped uniformly around the second tube and

these windings are fed by a current controller. The inner tube

is wound with platinum wire which constitutes one leg of a bridge

oircuit. A null detector in the bridge circuit feeds its error signal into the current controller. The platinum winding thus

acts as a resistance thermometer with its null detector forming the feedback loop by controlling current through the heating coil. Constant cooling is therefore offset by modulated heating

to produce the desired temperature. Cell temperature is monitored with the sprt. When cell temperature drifts away from

20 degrees C an adjustment is made by hand to a controller circuit potentiometer. Stability of the system is such that a daily adjustment will keep the cell temperature at a constant 2 0 degrees C to better than a millidegree.

Laboratory temperature is controlled at 20 degrees C ±0.05 degree by a special air conditioning system but, in addition, the interferometer enclosure is also controlled to give maximum

temperature stability to the interferometer and the scale under calibration. The housing is constructed of 19 mm thick plywood and IS lined with 1 mm thick copper. The 60 mm space between the pl^ood and the copper lining is completely filled by expanded polystyrene insulation and copper tubing soldered to the lining. A multibladed, 0.5 m diameter, slow— speed fan sits horizontally

on the bottom of the enclosure. It is driven by an external and it gently stirs the air to reduce temperature gradients. Themostatically controlled water circulated through the copper tubing produces the desired temperature within the enclosure.

The temperature of the circulating water is controlled by heating and cooling elements in the reservoir. A constant rate of cooling IS achieved by circulating 14 degree C water from the laboratory chilled water supply system through a heat exchanger.

I Current through an electric heating element is modulated by a

13
Figure 8. Schematic diagram of the temperature measuring system

Enclosure

Figure 9 . Schematic diagram of the temperature control system

14
timing circuit controlled by feedback from a thermocouple in the

temperature measuring system (figure 9)

.

There are ten thermocouple junctions inside the enclosure. Two

are in the interferometer air path, three are on the scale being

measured and, the rest are on various parts of the instrument

where they are used to detect gradients and stability. A motor

driven selector switch allows temperatures to be read

sequentially and displayed on a strip chart recorder. There are

two operating modes for the system: control and measurement. In

the control mode, the selector switch is locked on one

thermocouple in the interferometer air path. Since the reference

point for the thermocouples is at 20.000 degrees C, any

measurable thermal emf indicates a deviation from 2 0 degrees in

the air path and is used as an error signal to adjust the water

bath temperature and complete the loop back to air temperature.

Null voltage is the 20 degree mark at the center of the recorder

scale. Graduations in millidegrees extend for 50 divisions (0.05

degrees C) on each side of the center for use in the measurement

mode. Periodically during a scale calibration the measurement

mode is used by unlocking the selector switch and reading air

path and scale temperatures for use in computing scale length.

The system is calibrated and related to the International

Practical Temperature Scale of 1968 (ref. 11) using the

procedures described in appendix A.

2.4.2 Atmospheric pressure measurement

Barometric readings are taken with an electro-mechanical pressure

transducer. The transducer has a sealed chamber with a low

stress diaphragm in one wall. As the diaphragm moves with

changes in pressure its position is detected with a capacitance

probe and an output voltage proportional to the atmospheric

pressure is displayed. An NBS calibration establishes the exact

relationship between pressure and voltage. See appendix B for

calibration and verification procedures.

2.4.3 Water vapor measurement and control

Relative humidity is measured with a Dunmore type hygrometer.

Electrical resistance of the sensing element in this instrument

changes with air moisture content and, with periodic

calibrations, uncertainties can be held to 1.5% relative humidity

(ref. 12 and 13)

.

See appendix C for calibration methods.

In order to reduce the possibility of rust forming on steel

parts, laboratory relative humidity is held below 50%.

2 . 5 Length computations

Data from the line scale measuring system are in the form of

fringe counts recorded at each observed scale graduation. These

data must be converted into scale interval lengths at 20 degrees

C. To accomplish this, the fringe count recorded at the zero

15
graduation is subtracted from each succeeding fringe count. This

results in interval lengths from zero expressed in

half-wavelength units (quarter wavelength units for the HP

interferometer) . Conversion to length units is accomplished with

the fringe multiplier.

2.5.1 Fringe multiplier

Three elements are combined in the fringe multiplier: (1) vacuum

wavelength, Xo , of the laser light, (2) refractive index of

ambient air in the interferometer, n^^ , and (3) scale expansion,

a , from observed temperature to 20 degrees C.

Vacuum wavelengths for the iodine-stabilized laser are taken from

CCDM recommended values (ref. 14) . Vacuum wavelengths for other

lasers are taken from NBS calibrations or other appropriate

sources.

The refractive index of air is computed from Edlen's 1966 formula

(ref. 15) (Note: the key to the symbols used below is on the next

page) :

ntpf = 1 + AB - C (1)

where

A = ( p [ 8342.13 + 2406030 (130 - ) + 15997 (38.9 - )"'

] lO’® ) / 720.775 (2)

1 + p (0.817 - 0.0133ta) 10*‘

B (3)

1 + 0.003661ta

C = f (5.7224 - 0.0457 ) 10 (4)

Wavelength in ambient air can then be determined from the

fundamental relationship

(5)

Scale expansion to 20 degrees C is expressed by

AL = aL (20° - ts ) (6)

The wavelength in ambient air and the scale expansion are

combined to form the fringe multiplier, M. For the Michelson

interferometer which counts fringes (half wavelengths), it is

M, = 0.5 X^^^ [1 + a(20°- ts)] (7)

16
- 12 -

and for the HP interferometer which counts quarter wavelengths,

it is

Mj. = 0.25 Xtp^ [1 + a (20*^- tj)] (8)

All units are metric (millimeters) . When a scale is graduated in

inches, the fringe multiplier is divided by 2 5.4 (1 inch = 2 5.4

mm, exactly)

.

KEY TO SYMBOLS

f Water vapor pressure, mm Hg

L Nominal scale interval, mm

p Atmospheric pressure, mm Hg

tg Air temperature, degrees C

tg Scale temperature, degrees C

a Linear thermal expansion coefficient for

the scale, ppm/degree C

n^pf Refractive index of air at observed t,p,f

Vacuum wavelength, /im

a l/x„, m

2.5.2 Analysis of redundant measurements

Assigning uncertainties to measured length values requires

statistical analysis to determine the random error component.

Redundancy is built into the measurement process to provide

sufficient data for this analysis. At least four and as many as

fifty measurement passes are made for a scale calibration. Half

of the passes are made with the scale mounted in the normal

orientation (scale zero at the left) and half are made with the

scale reversed (zero at the right). This reversal not only

provides needed redundancy but also tends, when averaged, to

cancel effects caused by possible machine distortions,

photoelectric microscope bias and scale mounting distortions.

Data analysis for each measured interval includes determining

mean length, standard deviation of the mean and measurement

uncertainty. Uncertainty, U, is the sum of random error and

estimated systematic error, se:

U = 3s^ + se (9)

where random error is taken as three times the standard deviation

of the mean:

yJxd^/N-i

3s„ = 3 -zr (10)

yjN

and d is the deviation of a single measurement from the mean of N

measurements. Variations resulting from differences between

normal and reversed scale orientations are treated as random

errors

.

17
3.

MEASUREMENT PROCEDURE

3 . 1 Planning and preparation

3.1.1 Evaluation of the scale

- Inspect for graduation quality: are they smooth, uniform, of

good contrast, free from imperfections or blemishes? Graduations

with sharp, smooth edges, free from imperfections, and having

high contrast are the ideal. Although imperfect graduations may

give good measurement precision, systematic errors can arise when

the graduation viewing system is changed. There is a high

probability that other viewing systems will find a different line

center depending on the nature of the imperfections and the

operating principle of the viewing system.

” Estimate the graduation width because it may be necessary to

change the microscope objective lens if the graduations are very

narrow or very wide. Table 1 is a guide to the selection of

objective lenses.

Table 1. Objective lens guide

Graduation Width Microscope Objective

2 ;um or less

2 to 5 /im

5 to 25 /im

25 /im or more

4 mm (40X) or 8 mm (20X)

8 mm (20X) or 16 mm (lOX)

16 mm (lOX) or 32 mm (5X)

48 mm (3.3X)

Other factors must also be considered in lens selection. High

magnification will make focusing difficult, especially if the

scale is not flat to within the depth of focus of the lens. Low

magnification will reduce reading sensitivity. Close graduation

spacing may also be a factor because the microscope display

screen must show only one line signal at a time and the signal

must be spread out until this condition is met. When discussing

calibrations with customers always emphasize that optimum

graduation width is 5 to 10 urn. “ Evaluate other scale characteristics with questions such as:

1. Is the graduated face flat enough to avoid focusing

problems?

2. Are there longitudinal alignment marks on the scale?

3 . Are the graduations long enough to produce a good

signal?

4. Is the substrate material stable and is the thermal

expansion coefficient known?

5. Will the scale fit in the interferometer? (maximum width 150

mm, maximum length 1000 mm)

6. Can the scale be supported at 2 points, or 3 points in the

case of a grid plate?

7. Is the scale rigid enough ? Scales that are thin or lack

rigidity cannot be supported at 2 points and will require tedious

shimming to make the top surface flat and in focus.

18
Once the scale is examined, the potential calibration accuracy

can be estimated. If all scale characteristics are optimum then

the highest accuracy can be attained if the customer needs it.

Table 2 is a guide to accuracy ranges:

Table 2 . Accuracy level guide

Scale

Length

Accuracy level

Low Medium High

(mm) im) (jum) (PM)

1 .25 .10 .01

10 .50 .25 .05

100 .50 .25 .05

500 1.00 .50 . 10

1000 1.50 .75 .20

3.1.2 Calibration plan

Once the accuracy potential of the scale is estimated either by

examination or from the customer's description, the accuracy

required and the intervals to be calibrated must be obtained from

the customer. The instrument will run in the automatic mode only

on groups of equal subdivisions. Calibrating more than 5 0 equal

subintervals in one group should be avoided because of the

magnitude of the work and because calibration of larger groups is

generally not needed. For example, an entirely adequate

calibration of a one meter scale graduated in millimeters is as

follows

Group 1. The 5 centimeter intervals (0 , 5 , 10 , 15 , . . . 100 cm): 20

Group 2. The millimeters in the first 5 centimeters: 50

Total: 70

This scheme provides a calibrated interval for any length from 1

to 1000 millimeters by measuring 70 intervals. Similar schemes

can be devised for other scales.

The redundancy required to achieve the various accuracy levels is

shown in table 3

.

Table 3 . Measurement redundancy guide

Accuracy

Level

Total Number of

Passes Required

Normal and

Reversed Orient.

Required?

Low

Medium

High

2

4

8 (minimum)

No

Yes

Yes

I Actual measurement uncertainty is determined by the statistical

analysis performed by the computer and displayed on the

: print-out.

19
3.1.3 Comparator preparation

- Clean and oil the ways, the lead screw and its bearings, the

carriage rollers, the drive gears at the left end of the way bed,

and the drive shaft where it passes through the housing. This

maintenance should be done at least every 4 months. Heavy oil

designated "Mobil Gear Oil C" is used on the gears. On all other

parts use "Mobil Velocite CA" . A large can of each of these oils

is on hand.

- Add distilled water to maintain the reservoir level about one

inch above the pump intake hole. Make sure that all return lines

are flowing. Oil the pump motor every 3 months.

- Adjust the air circulating fan speed to give adequate air

movement inside the housing. The fan drive motor should operate

at about 100 rpm.

- Add fluid to the servo systems (line centering and parallelism)

as needed. Add oil with the power off so there is no pressure on

the fluid.

- Adjust the housing covers so they do not touch the microscope.

Any pressure on the microscope will cause measurement errors.

- Center the two optical system support balls located under the

microscope by tightening the collars, then loosen them so the

balls are free to roll.

3.1.4 Scale preparation, mounting and alignment

- Cleaning. All scales, with a few exceptions, should be cleaned

before calibration. Grease, dust, and finger prints on the

graduations can seriously alter calibration results. If a steel

scale has been greased for rust protection it must be degreased

with mineral spirits then flushed with ethanol using clean

surgical cotton to wipe it dry. Remove lint with a clean camel

hair brush. Most scales will require only the ethanol, cotton and

camel hair brush cleaning. Some grid plates come sealed in

polypropelene cases and do not need cleaning. Always inspect a

scale for cleanliness with a bench microscope or the comparator

microscope.

- Scale mounting - general principles. (1) The method of

supporting a scale influences its length except for very short

scales. (2) The support method must be the same for calibrating

and using a scale. (3) Many scales have markings indicating the

points of support. (4) Whatever support method is used it should

be easy to duplicate.

-Scale support methods.

(a) Bessel points

These points are symmetrically located 0.544L apart where L is

the length of the scale body. Bessel points will minimize scale

sag. One of the supports should be cylindrical or have an

20
inverted V cross section and should be fixed in position while

the second support should be constructed so it allows freedom for

expansion or contraction of the scale without imparting a

twisting force. A ball in a longitudinal groove will provide

this freedom, or it can be attained with crossed cylinders; the

lower one fixed longitudinally under the scale and the other with

an annular groove at its center so it can roll along the lower

cylinder and support the scale. This latter support system is an

integral part of the line scale interferometer carriage.

(b) Airy points

These points are located symmetrically 0.577L apart where L is

the length of the scale body. Airy point support points are

sometimes used for line scales although their best use is for

long gage blocks because these points are designed to keep the

end faces parallel. The support precautions stated in (a) above

should be observed.

(c) Flat support

This type of support is unavoidable for long thin scales, but it

requires tedious shimming and repeated flatness measurement. If

there is any choice in the matter, flat support should be

avoided.

(d) Other support points

Points other than Airy and Bessel are permissible but avoid point

spacings that will cause excessive sag in the scale with

consequent focusing problems.

- Support of grid plates

Plates measured in this apparatus are limited in size to 12 5 mm

square. A three point support with the points forming an

equilateral triangle is best. The points should be from 25 to 50

mm from the edge of the glass with two points parallel to one

edge and the third in the middle of the opposite edge. Adhesive

coding dots, about 1/4 inch in diameter, make good support pads.

A 150 X 225 mm aluminum support plate is available for attachment

to the carriage as a platform for grid plates.

- Scale alignment

Place the scale on the carriage mount with the zero graduation at

the left (this is called "normal” orientation) . The scale will

be remounted later with the zero graduation at the right for

measurement in the "reversed" orientation. Once the scale is

mounted and focused in the microscope it should be aligned parallel to the ways. Most scales have alignment marks

consisting of short longitudinal lines at each end of the

rulings, some have continuous lines running through the rulings,

and some have no marks (see figure 10)

.

0/234 0/234 c5 2. 3 A

Figure 10. Typical alignment marks

21
Move the carriage back and forth and observe the alignment marks

at each end. Make adjustments by hand at first, then with the

knurled control knobs to bring the scale into good alignment. If

no alignment marks are present use the tips of the graduations as

a reference. Misalignment will cause length dependent errors

proportional to the cosine of the misalignment angle.

3.1.5 Microscope magnification, illumination, focus and

adjustment

- Magnification

The choice of magnification depends mainly on the graduation

width, but it also depends on graduation spacing in finely

divided scales, and on sag in long scales. Too high a

magnification may make it difficult to maintain sharp focus

throughout the length. On the other hand high magnification is

needed to give enough separation of closely spaced graduations.

Too low a magnification results in a loss of sensitivity.

However, the 16mm(10X) or the 32mm(5X) objective lenses will

provide optimum magnification for most scales. The table in

section 3.1.1 is a guide for selecting objective lenses.

- Illumination

The illuminator lamp is powered by a d.c. source to ensure a

smooth signal from the microscope detector (photomultiplier

tube) . Lamp voltage should not be raised above 12 volts to avoid

burning out the filament. Position the lamp to give uniform

illumination over the field of view. To achieve this, center a

graduation in the field and observe the signal on the microscope

monitor. Move the lamp around in its holder until a maximum line

signal is seen and the background signal (straight part of the

signal on each side of the graduation) is horizontal.

- Focus

Sharp focusing is very important in high precision measurements

and should be done with great care. Coarse adjustments are made

by releasing the two knurled screws locking the microscope tube

and moving the microscope up or down. Always lock the kinematic

support balls before making coarse adjustments (and remember to

unlock them when finished) . The microscope is heavy and a firm

grip is needed to prevent it from slipping down through its full

travel and causing damage. A lab jack is located under the

microscope body to provide some control. Only an approximate

focus is attempted by this procedure. Fine focusing is done by

raising or lowering the subcarriage with the controls located at

each end. Once the scale is in approximate alignment and focus

the carriage should be moved back and forth to view alternately

the terminal scale graduations. At each end check the focus by

pressing down and lifting up on the carriage "U" channel which

holds the scale. Note the effect on the monitor signal. The

signal should be of maximum height when no pressure is applied

and it should shrink in height when either upward or downward

pressure is applied. Adjust focus carefully until this condition

is met at both ends of the scale. Maintain alignment during this

procedure. Check focus at the scale center. If the scale is not

22
flat, the focus will not be sharp at the center. Serious

degradation of focus can be remedied only by changing to a lower

power objective or by changing the scale support method to reduce

sag.

- Adjustments

Two additional mechanical adjustments must be made on the

microscope itself (electronic adjustments are covered under 3.2,

"Instrument Operation") . The first is to align the slit parallel

to the graduations. This is done by swinging the photomultiplier

housing, which contains the slit and is located at the top of

the microscope, back and forth while watching the monitor signal.

Alignment is achieved when the signal is at minimum width. The

second adjustment is to mask the graduation to provide the

correct line segment. Two black masking rectangles are visible

in the microscope viewing eyepiece; one comes down from the top

of the field and the other comes up from the bottom. They are

independently controlled by adjustment screws on the left side of

the microscope. The microscope does not operate on the full

visible height of the field. The operational part of the

field can be determined by moving one mask toward the center of

the field until a barely perceptible change in signal height is

seen then move the other mask until it also produces a change in

signal height. These mask settings define the operational field.

Further adjustments can then be made, if necessary, to limit the

graduation segment to the desired length and location. Be sure

to maintain alignment and focus during adjustment.

3.1.6 Interferometer preparation and alignment

- Preparation

If the compensating system for carriage pitch and yaw is not

operating, the interferometer axis must be coincident with the

scale graduation axis. Coincidence is achieved by changing the

position of the retroreflector on the carriage until the center

of the retroref lector , as indicated by the protruding pin, is

coincident with the scale axis both vertically and laterally.

Make this adjustment only after the scale is in focus throughout

its length so that the scale elevation will not have to be

changed except for fine focusing. Once the retroreflector is set

on this axis the rest of the interferometer system is brought

into alignment with it. Coincidence of 1 mm or better should be

attained, and the longer the scale the more critical is the need

for precise coincidence. Various methods can be used to project

the scale axis to the retroreflector pin. One that works well is

to lay a plastic ruler (to prevent scratching) on the scale face

and extend its end to the retroref lector pin. When making

adjustments on the microscope or the interferometer the kinematic

support balls beneath the microscope should be locked with the

knurled collars. Release the collars when adjustments are

completed or serious measurement errors can occur. Readjustment

of coincidence is needed only when a change is made in the

location of the scale graduation axis relative to the

retroreflector axis.

23
- Alignment

A complete alignment procedure is given in the appendix D . Most

of the time it is only necessary to check the alignment and make

fine adjustments. There is always a risk that alignment can be

disturbed by visitors or others who touch the machine. The

following procedure should be performed daily when high accuracy

measurements are being made:

(a) Turn the laser head face plate so the two return beams show

on the face plate target. Bring the small aperture into the beam

with the lever on the face plate. Move the carriage all the way

to the left.

(b) Check the coincidence of the measuring beam and the reference

beam by alternately inserting and withdrawing a piece of paper in

the measuring beam while watching the beam spots on the target.

(c) Move the carriage all the way to the right and repeat (b)

(d) If any misalignment is indicated by a lack of beam

coincidence, follow the procedure in the appendix starting with

step 8

3.1.7 Temperature equalization and the measurement of

environmental parameters

- Temperature equalization

The interferometer chamber is under automatic temperature control

whenever the control circuits are turned on manually or by the

timer. Thermocouple #5 is the sensor used to maintain control.

See parts (c) and (d) in this section for the procedure to lock

the system onto #5. Mounting, aligning, and focusing a scale

changes the temperature of the chamber, the mechanical structure

and the scale. Sufficient time must be allowed for these

temperatures to stabilize and reach equality. The dynamics of

thermal disturbances in this system are such that all parts must

be in equilibrium before measurements are made.

The most practical schedule is to make all preparations for a

calibration in the afternoon and set the timer to start the

control system at about 3 a.m. The potentiometer on top of the

reference temperature cell should be set to the value

anticipated from experience to be the equilibrium point. Thermal

conditions in the chamber will be sufficiently stable to start

measurements the next morning.

An accelerated schedule can be used when short lengths are being

measured or when repetitious measurements are being made and the

chamber is opened for only a short time to make the preparations.

For example, in calibrating grid plates where changes from one

scale to another on the same plate are being made, and in

calibrating short scales such as stage micrometers which require

short preparation times. A judgment of the readiness of the

system must be based on the temperatures at various critical

points inside the chamber such as the three scale mount points,

24
the air path, and the optical system support tube (thermocouples

1 , 2 , 3 , 4 , 5 and 8 )

.

- Temperature measurement

Two systems are involved in measuring temperature: the

temperature reference system which maintains a constant

20.000 degrees C temperature in a cell and the measuring system

which employs ten thermocouples placed at various points

throughout the chamber as shown in the table 4. The reference

thermocouple for the measuring system is in the 20 degree cell so

that the measuring thermocouples can be read directly without

correcting for reference temperature. See 2.4.1 for a detailed

description.

The reference temperature is maintained at 20.000 degrees C

automatically for the short term (one day)

.

A daily check and

adjustment is necessary to compensate for slow drift. The

reference temperature check and adjustment are performed at the

beginning of each day as follows:

(1) Turn on the galvanometer illuminator and adjust the glass

scale so the galvanometer cursor reads zero. (It may occasionally

be necessary to adjust the mirror angle using the knob at the top

of the galvanometer to get the cursor approximately centered on

the glass scale.)

(2) Depress and lock the Rq switch on the Mueller bridge and

adjust the Rq knob to give 2.0 ma through the SPRT. After

approximately four minutes the SPRT current heating effect will

stabilize and the galvanometer can be read.

(3) Adjust the potentiometer on the temperature controller until

the galvanometer reading is zero. This must be done in steps

with three or four minutes between to allow the thermometer to

stabilize after each change. Turning the pot clockwise

(increasing numbers) will move the galvanometer cursor to the

right, and turning it counterclockwise will have the opposite

Table 4 . Thermocouple locations

Thermocouple

Number

(switch position)

Location

1

2

3

4

5

6

7

8

9

10

11

Scale mount, right end

Scale mount, center

Scale mount, left end

Air in interferometer path, right end

Air in interferometer path, left end

Waybed , right end

Waybed, left end

Remote interferometer support beam

Chamber lining at water exit

Chamber lining at water entrance

Zero volts for nulling voltmeter

25
effect.

(4) When a zero galvanometer reading is achieved, release the Rq

switch to verify that the zero has not shifted. If no shift has

occurred, depress and lock Rq again and leave it locked. The

system is calibrated for use with thermometer current flowing.

(5) DO NOT CHANGE ANY BRIDGE SETTINGS OR CONTROLS. The bridge is

set at the 20.000 degrees C resistance of the SPRT so that when

the galvanometer null reading is reached, the temperature in the

reference cell is correct. The only controls on the bridge that

should be operated are the Rq switch and the Ro current

adjusting knob. A calibration report inside the bridge cover

gives the value for the bridge resistance setting.

Temperature readings with the thermocouples can be made when

the reference temperature stabilizes at 2 0 degrees C. Readings

are made as follows:

(a) Normally, the system will be under control from the automatic

operation of the timer switch, but if it isn't, activate the

system with the timer switch.

(b) Set the Model 148 nanovoltmeter on the 3/iv range. (For

controlling chamber temperature, either the lOuv or the 3;uv range

can be used.

)

(c) Swing the strip chart recorder out of its housing and grasp

the chain at the upper left side. Pull this chain along to

change the thermocouple numbers in the illuminated window until

#5 appears. The system is locked on this thermocouple for

chamber temperature control. Turn the rotary switch located to

the left of the illuminated numbers from 11 to 10. When it is on

11 the chamber temperature is controlled continuously, but when

it is on any other number control only occurs when that number is

illuminated in the window. Unlock the control system from #5 by

snapping upward the toggle switch on the left side of the

recorder housing. Proceed to #11 by pulling the chain. Number

11 provides a null voltage and when this is reached the

nanovoltmeter "zero suppress" controls must be adjusted to make

the recorder pointer read exactly 20.000. The thermocouples can

now be read in sequence as the chain is pulled along. Readings

are taken directly from the chart recorder scale. Twenty degrees

Celsius is at the center and the scale extends .05 degree in each

direction. Scanning once through all the thermocouples will show

the temperature condition in the chamber. Generally, after

sufficient equalization time, the temperatures should not deviate

from 20 degrees C by more than 0.01 degree except for #9 and #10

which are indicators of circulating bath temperature.

(d) When a scale is being measured, adjust the "zero suppress" at

#11, record readings of #1, #2, #3, #4 and #5, and then lock it

on #5 by snapping the toggle switch down. Temperature control is

maintained using the thermocouple displayed in the window at the

time the toggle switch is snapped down. Return the rotary switch

26
to 11 to put the system in the continuous temperature control

mode.

- Atmospheric pressure measurement

The electronic pressure transducer used to measure barometric

pressure displays a voltage proportional to the atmospheric

pressure (see 2.4.2). An NBS calibration establishes the exact

relationship between pressure and voltage and this relationship

is programmed the computer. It is important to locate the

pressure transducer at the same elevation as the interferometer

because pressure varies with elevation. A 30 cm change in

elevation will result in a .03 mm change in pressure.

- Humidity measurement

A Dunmore type electronic hygrometer is used to measure relative

humidity and the manufacturer's calibration graph is used to

convert the meter reading to percent relative humidity (see

2.4.3). Exposure of the sensing element to organic solvents or

their vapors can ruin the element.

3 . 2 Instrument operation

The following discussion assumes that a scale is mounted,

aligned, and focused on the carriage in the NORMAL orientation

(zero graduation at the left) and that the chamber temperature is

under control and equalized.

3.2.1 Turning on the apparatus

There are two racks of electronic equipment. One has the

interferometer, microscope, and carriage drive controls and

displays. The other has the pressure and humidity transducer

electronics plus the carriage pitch and yaw correction

electronics. Each rack has a multiple outlet box that serves as

a main switch. The microscope illuminator power supply is

located on the elevated walkway behind the machine. Turn it on

with the voltage selector switch on the 0 to 8 volt position then

switch to the 0 to 16 volt position. Do not set the rheostat

above the 12 volts indicated by the red marker on the dial.

These procedures protect the lamp filament. Check the switches

on the individual units to ensure that they are all turned on.

The laser should be emitting light as indicated by the beam

alignment meter. One hour warm-up is sufficient for measurement

of a long scale, one-half hour for short scales. Laser stability

is the principle concern in warm up. If measurements are being

made every day it is best to leave the system on all the time

except perhaps for weekends. At night, turn off the line servo,

turn down the oscilloscope intensity and reduce the microscope

illumination.

3.2.2 Controls, adjustments and displays

The following list of controls, displays and their functions is

I keyed to figure 11. Some of the obvious controls and displays

are left out for the sake of brevity.

27
a. Interferometer display panel

"Prints - Plots/Min." switch should be set to MAX. "Print"

switch should be set to TIMED. "Smooth" button should be ON.

"Direction sense" switch should be set according to instructions

displayed on the computer screen during entry of preliminary data

(R for scale in normal orientation and F for scale in reversed

orientation) . Units switch should be on A/4

In this mode the

automatic wavelength compensation is inoperative and the computer

performs the compensation.

b. Resolution extender, line centering meter and servo current

meter panel

The switch on the resolution extender should remain in the

"extended" position to increase the interferometer resolution by

a factor of 10. Least count is then 0.025 wavelength. The

decimal point on the interferometer display is actually one place

to the left of its indication when the extended mode is used with

millimeter or inch units. The mode has no decimal point.

The line centering meter is one of two displays of the

line-centering error signal, the other one being on the

oscilloscope. The graduation is centered in the microscope field

when there is a null reading on this meter.

The line-centering servo current, indicated on the last meter on

this panel, is controlled at 0.4 ±.02 ampere by a computer

programmed jogging procedure. When the retroreflector is mounted

on the scale support the program should be changed to control at

0.4 ±.10 ampere.

c. Line display oscilloscope panel

Press the CHI and CH2 switches and set the CHI and CH2 dials to

.1 volt /div. on the dual trace amplifier. On the time base

amplifier press the CHOP, AC COUPL, and EXT switches and set the

VOLTS/DIV. dial to 50 mv. Adjustment for the trace displays is

made by pressing the two GND switches and adjusting the two

POSITION controls so that two horizontal trace lines coincide

at two squares down from the top for a dark graduation on a

bright background and two squares up from the bottom for a bright

graduation on a dark background. Left to right centering is done

with the position control. Release the two GND switches and,

with a graduation in view, control the width and height of the

line signal as described below. See figure 4 for a view of the

line signal trace.

d and f . Line signal processor and line servo panel (d)

,

and the

high voltage power supply panel (f). (These two panels are described together because they interact.)

A number of important adjustments are made from these panels:

(1) Line signal width is set by dual operation of the SCAN WIDTH

control on panel d and the red CAL control on the time base

amplifier on panel c. As one control is raised the other is

reduced to change the signal width while keeping the total trace

28
Figure 11. Controls and displays

29
out to the edges of the screen. Ideal width is about two grid

divisions at the half height of the signal. When a scale with

very small graduation intervals is being calibrated, the signal

width must be widened so that only one graduation at a time is

showing on the screen. The system will tend to servo on the

space between graduations if more than one is present. This is

the most difficult calibration to do, but it can usually be

accomplished with the combination of a high magnification

objective lens and careful adjustment of signal width.

(2) Line signal height is adjusted by the high voltage control on

panel f, and by the gain control on the separate microscope

chassis located on the back shelf of the interferometer housing.

Both controls should be adjusted to obtain the cleanest line

signal. Signal height should be about 3/4 of the screen height.

(3) The BRIGHT/DARK selector switch refers to the reflectivity of

the graduations. It should be on BRIGHT when the graduations are

bright on a dark background, and it should be on DARK when the

graduations are dark on a bright background.

(4) The LINE PRESENT indicator should be lit only when a line

signal is present on the screen. Turn the control knob clockwise

1/4 turn and then slowly turn it counterclockwise until the light

just comes on with a steady glow.

(5) The THRESHOLD LEVEL should be set at 1/2 the line signal

height in most cases. Set the selector switch on THRESHOLD and

adjust the THRESHOLD LEVEL control until the half-height point is

reached. This control works only when the line-present

indicator light is on.

(6) The SERVO REVERSAL serves to correct the occasional tendency

of the servo to repel the line rather than center it. The

repelling condition only occurs when the servo switch is first

turned on.

(7) The PROPORTIONAL-INTEGRAL controls influence the damping rate

of the line centering process. Operate these two controls in

tandem, that is, they should both be set at about the same angle.

Start with the controls set at the center then apply one jog to

the lead screw drive motor. The error signal on the screen

should damp out within 9 to 11 seconds. Turning the controls

clockwise will increase the damping counterclockwise will

decrease it. Too much damping will cause imprecision from

hysteresis and too little damping will cause imprecision because

interferometer readings will be taken by the computer before the

line is centered.

(8) The LASER DISPLAY switch permits a choice of laser display

modes. In the AUTO mode changes in count are displayed only when

the computer is taking data and this is often advantageous. In

the MANUAL mode the display registers changes continuously. The

manual mode should be used to set the counter near zero at the

first scale graduation.

e. Indexer panel

The indexer controls the stepping motor driving the lead screw.

It is under computer control when the switch is set to EXT, and

under manual control in the UP and D positions. The SELECT switch

is only operative under manual control and has JOG and RUN

options. The UP position will cause the carriage to move to the

30
left when the FUNCTION EXECUTE switch is moved downward and the D

position will cause the carriage to move to the right. The SPEED

control affects only high speed operation. If the speed is set

too high the motor will falter and lose count. Faltering can be

detected from the sound of the motor.

3.2.3 Computer/controller operation

Load the "SCALE 1" program into the computer from back-up tape #2

by using the GET "SCALE 1" command. Remove the back-up tape and

substitute a data tape. The RUN key will start the program.

Questions automatically appearing on the screen will lead the

operator through the process of entering preliminary information

and starting the run. Some of the questions require explanation:

- Data file name - this is a six place (max.) alpha-numeric

identifier for the data.

- Indexing speed - high speed indexing is generally

used for intervals of 1 mm or more, low speed for intervals less

than 1 mm.

- Lamp - wavelength source: use 1 to indicate the HP laser.

- Scale - scale length units: 0 for millimeters, and 1 for

inches.

- Low - starting graduation for the measurement, generally 0. - High - ending graduation for the measurement in inches or

millimeters.

- Step - nominal distance between calibration points.

- Coeff - thermal expansion coefficient for the scale expressed

in ppm/degree C. (e.g. 11.5E-6 for a steel scale).

- System - systematic error to be used for the calibration

expressed in ppm, e.g. 0.2E-6. See section 5.5 for a discussion

of systematic error.

- N pass - number of measurement passes to be made on the scale,

e.g. 2 means one pass up the scale and one pass down the scale,

returning to the starting point. It must always be an even number

of passes so that closure is achieved.

- Tempi - initial temperature of air in degrees C (read to

thousandths of a degree)

.

- Stempl - initial scale temperature in degrees C (read to

thousandths of a degree)

Note: Pressure and humidity are read automatically by the

computer/controller at this point.

31
- N Read - the number of intervals to be measured. This equals

the length of the scale divided by the interval length.

- Graduation tolerance - a length limit applied to the measured

position of the graduation to ensure that the correct graduation

is in view. The computer/controller must decide if the right

graduation is in view when it makes each stop. It does this by

computing the length to that point from the fringe count and

comparing it to the nominal length plus or minus the tolerance.

The tolerance must be small enough to prevent setting on the

wrong graduation but not so small that the natural errors in the

scale will preclude an acceptance. For example, if the spacing

is 0.1 mm between lines and scale errors of 0.005 mm probably

exist, the tolerance should be 0.010 mm. If the tolerance is set

too small the system will not read but will continue to jog back

and forth looking in vain for the line.

- Date - expressed as month/day/year.

- Start - time of day pass is started using the 24 hour clock,

e.g., 1300 for 1:00 pm.

- Direction - measurement direction: use 1 for going up

the scale and -1 for going down the scale.

- N group - always use 1. This input has no meaning at present.

3.2.4 Reading initial environmental conditions

Read and enter the values for air and scale temperature when

asked to do so by the computer. Following the procedures in

3.1.7, read thermocouples 1, 2, and 3 for scale temperature, and

4 and 5 for air temperature. Enter the mean values. Pressure

and humidity are read automatically by the computer/controller.

3.2.5 Starting a run with the scale in the normal position (0

graduation at left)

Before answering the last question on the screen and pushing the

CONT key to start the first pass, the laser display should be

adjusted to read a small positive number. This is done by

setting the LASER DISPLAY switch to MANUAL on the line signal

processor and then pushing the RESET button on the laser display

until the display reads a small positive number (under 100).

3.2.6 Reading intermediate and final environmental conditions

Repeat the reading procedure each time the environmental data is

requested by the computer. Keep a recording barograph in

operation so the trend of pressure can be observed. Weather

fronts or thunderstorms can cause such rapid pressure changes

that interferometric length measurements will lose precision and

the degree of loss is length dependent. Do not attempt to make

high precision measurements on lengths over one decimeter if the

pressure change approaches 1 mm/hour.

32
3.2.7 Reversing the scale

When the run is complete, and the data are judged to be

satisfactory, open the housing lid and reverse the scale so that

the zero graduation is at the right end. Align and focus the

scale then set the zero graduation under the microscope. While

the housing is open either turn the temperature control off at

the clock-timer or turn the thermocouple switch to No. 10 so the

system will not try to correct for the disturbance. Return the

system to full function when the housing is reclosed.

3.2.8 Setting controls for reversed scale orientation

Set the DIRECTION SENSE switch to F and, with the line servo on,

reset the interferometer display to a small positive number.

3.2.9 Temperature stabilization

The time necessary to stabilize and control the temperature to

20 degrees C depends on how much the temperature was perturbed

during scale reversal. The temperature can be monitored

periodically by observing all the thermocouples. On long scales

having high thermal expansion coefficients it may be necessary to

allow overnight for stabilization. On other scales it may be

possible to start measurements in an hour or two. Scale

temperature and the temperature of the beam holding the remote

interferometer are the most critical.

3.2.10 Starting the reversed scale run

The run may be started as soon as the temperature is acceptably

uniform and controlled, and the switches are properly set.

3.2.11 Combining the data from normal and reversed runs

Data combination is an option in the "SCALE" program. Follow the

instructions on the screen if both data sets are on the same

tape. If they are on separate tapes combination is accomplished

by using the pause key to stop the computer as soon as it

finishes processing the normal run. Substitute the data tape

with the reversed run and use the "CONT" key to resume the data

processing.

If there are several pairs of normal and reversed runs they can

be combined by using the "COMBIN" program which must be loaded

into the computer from another program tape.

3.2.12 Operational check list

The check list in appendix E is an important aid in making

reliable measurements. Review the list frequently to ensure that

nothing is being overlooked in the operation and maintenance of

the line scale interferometer.

33
4. MEASUREMENT RESULTS

4 . 1 Evaluation

Appraisal of calibrations must be made in conjunction with the

measurement assurance program in Section 5. The combined data

print-out contains information on which to base an evaluation.

Figure 12 shows an example of each of the tables in a print-out.

Each table has a letter designation (a through e) to correspond

with the discussion of important features given below.

a. Individual pass table

There is one table for each pass made in the measurement

procedure. They are not normally printed out unless, in trouble

shooting, one needs to search for possible mistakes in entering

data such as temperatures, pressures, etc. The means of air

temperature, pressure, humidity and scale temperature are

shown. The fringe multiplier is computed from the vacuum

wavelength and the ambient air conditions, using the Edlen

formula (see Appendix G) . In the column of fringe counts the

count at the zero line has been subtracted so the printed values

are the lengths of the intervals in fringes. The lengths in

millimeters are the result of multiplying the length in fringes

by the fringe multiplier.

b. Summary tables for normal and reversed scale orientations

This table lists the correction to each measured interval at 2 0

degrees C for each pass. A correction is the measured value for

the length minus the nominal value.

c. Comparison of mean normal and mean reversed corrections data

The difference column is particularly significant for long

scales. If the differences are large in the middle of the scale

and small at the ends it may mean that the microscope needs to be

adjusted so its optical axis is perpendicular to the scale

surface. This adjustment is described in appendix F. It also

means that the scale probably sags in the middle, resulting in

poor focus where the differences are large. It must be a matter

of judgment whether or not to make the tedious optical axis

adjustment since it may last only as long as the microscope

position and objective lens remain unchanged. The reduction in

measurement precision resulting from the poor focus reflects the

reality of poor scale quality and can, with considerable

justification, be allowed to stand. If the difference is

particularly large at a specific interval then the graduation

itself should be examined for asymmetry or for dirt near its

edges. The scale must be recleaned and remeasured if any such

condition is found.

d. Mean of normal and reversed data

Look at the uncertainty column in this table to see if it meets

the measurement requirements. If it does not, it may be

necessary to make more measurements (both noirmal and reversed) to

reduce the random error component of uncertainty. If the

uncertainty is unusually large for a particular interval the

34
SM HR CLASS SCALE

PASS 1 BATE START 94S GROUP AIR

TEHP

AIR PRESSVAPOR

PRESS EFFECTIVE NAVELENCTN

SCALE

TENP FRINGE NULTIPLIER

1 2B.RR3S 793.235 7.RI7 .C32821IC74 19.9948 3. 1C41899S847E-84

INTERVAL FRINGES LENCTN CORRECTION

8.888 TO 188.888 31S844. 19 99.99973 -.88827

8.888 TO 288.888 S32888.86 199.99936 -.88864

8.888 TO 388.888 948132.21 299.99988 -.88892

8.888 TO 488.888 12S417S.1S 399.99873 -.88127

8.888 TO 588.888 1988228.43 499.99849 -.88151 a

.

SRt NH GLASS SCALE

INTERVAL CORRECTION CORRECTION CORRECTION CORRECTION

<AILL1HETERS> <HH> (An> (AN) (HH> 8.888 TO 188.888 -.88827 -.88823 -.88826 -.88824

8.888 TO 288.888 -.88864 -.88857 -.88863 -.88861 8.888 TO 388.888 -.88892 -.88883 -.88898 -.88889

8.888 TO 488.888 -.88127 -.88116 -.88125 -.88128

8.888 TO 988.888 -.88151 -.88138 -.88147 -.88141 SSS24N^68S24R Ce*p4r4sen OF Hcan Nora*) And Avan Ravvraa Correct < on Bata

INTERVAL NEAN NORA. AEAN REV. BIFFERENCE

CORR. CORR. (NORA. -REV. <AILL1NETERS> (AA> <AA> <AA> 8.888 TO 188.888 -.88829 -.88827 .88882 8.888 TO 288.888 -.88861 -.88863 .88882 8.888 TO 388.888 -.88888 -.88898 .88882 8.888 TO 488.888 -.88122 -.88122 .88888 8.888 TO 988. 888 -.88149 -.88143 -.88882

SBS24N/SRR24R

Naan Of Neraal And Ravaraa Bata

SR6 nn CLASS SCALE

INTERVAL LENCTN CORRECTION RANBOA SYSTEAATIC UNCERT. (AILLIAETERS) (AA> (AA> (AA> (AA> (AA> 8.888 TO 188.888 99.99974 -.88826 .88882 .88881 .88883 8.888 TO 288.888 199.99938 -.88862 .88883 .88883 .88886 8.888 TO 388.888 299.99911 -.88889 .88883 .88884 .88888 8.888 TO 488.888 399.99878 -.88122 .88884 .88886 .88818 8.888 TO 588.888 499.99856 -.88144 .88885 .88887 .88812

41

Figure 12. One example of each table in a typical computer print-out

35
U.S. OIPANMCNT OP COMMCRCE

NATIONAL MMtAU OP tTANOANOO

•AfTMtnsaUNO. MAAYLANO 20—

REPORT OF CALIBRATION

S0055A a

b.

For: One Meter Steel Length Scale

SIP No. 15460 Suboitted by: . ...

C.

d.

e

f

gThis length scale was calibrated by interferometry using a stabilized

helium-neon laser as the length standard. The design and operation of the interferometer is described in Precision Engineering. Vol. 4, No. 4, October 1982, "Interferometric Measurement of Length Scales at the National Bureau

of Standards." Measurements were made of the last ten millimeters, the last ten centimeters, the ten decimeters, and the subdivided millimeters at each end of the scale. Results of the calibration are given on the following pages of this report. Each length value is the mean of 8 measurements and the uncertainty

in each value is

U - o_ S.E. « Random * Systematic

B Where is the standard deviation of the mean value and S.E. is the es- timated systematic error. Measurements were made using the segment of each graduation between the two longitudinal lines that run the full length of the scale. During measurement, the scale was supported at the two points indicated on the face of the bar. Normally, the millimeters and centimeters at the zero end of the scale are measured. On this bar the millimeters and centimeters at the one meter end

of the scale were measured because there is some corrosion in the area of the first 50 millimeters that makes a few of the graduations unusable. This corrosion was present when the bar was received here. No attempt should be made to remove the corrosion because of the danger of altering or destroying

graduations.

All lengths are reported at a temperature of 20* CelaiuSg(68" Fahrenheit).

A coefficient of linear thermal expansion of 11.7 x 10 /• Celsius was used

in normalizing the lengths to 20* Celsius.

Measurements were made

For the Director,

^ Robert J. Hocken, Chief Automated Production Technology Division Center for Manufacturing Engineering

Test No. 738/S0055A

Date: July 10.1985

Figure 13. Typical scale calibration report (only one example of

a table and a graph is shown)

36
DEV I

m

ION

FROM

NOMINRL

(

10E-4

mm)

h.

•ccuautated during this analysis: seessR / seessB

seesso ^ saessc Meter Bar SIP No. 15480 Lengths at 20 Deg. C

Naan Of Noraal Rnd Rauars* Data

intervrl length CORRECTION RRNDOn SYSTEHRTIC UNCERT. (RlLLlnETERS> (HM) <t1H) <nti) (nn> e.eee TO lee.eee lee.eeeie .eeeie .eeeei .eeeei . eeees e.eee TO 2 ee.eee 2ee.eee25 .eee25 .eeees .eeees . eeee4 e.eee TO see. eee see.eeese .eeese .eeees .eeees . eeeee

e. eee TO 4ee.eee 4ee.eeeE5 .eeees .eeeee .eeee4 .eeeie e.eee TO see. eee see.eeees .eee 62 .eeeee .eeees . eeei

i

e.eee TO eee. eee eee.eee?! .eeen .eeee? .eeeee . eeei

3

e.eee TO ree.eee Tee.eeesE .eeesE .eeeee .eeee? . eeei

3

e.eee TO eee. eee eee.eee?s .eeers .eeeee .eeeee . eeei4

e. eee TO eee. eee eee.eeese .eeese .eeeee .eeeee . eee i

s

e.eee TO leee.eee leee.eeeee .eeeee .eeee? .eeeie .eeei?

i

.

9.0

0.0

-9.0

Figure 13. continued

)

Typical scale calibrtation report

37
graduation in question should be examined for asymmetry, dirt, or

other flaws that could explain the lack of measurement precision.

If it is dirt, or other removable flaw, the scale must be cleaned

and remeasured. If the flaw is permanent, let the uncertainty

stand but describe the flaw and its effect in the calibration

report. This table is used in the calibration report together

with the graph and text.

e. Graph of corrections

Plots of corrections are seldom smooth lines, however, they

should be scanned for points that stand out from the general

pattern. Use the graph in conjunction with table d for detecting

possible dirty or flawed graduations.

4.2 The Scale Calibration report

Each calibration report must contain certain basic information

such as scale identification, measurement method, support method,

graduation segments used, number of measurements, reporting

temperature, thermal expansion coefficient, table of measured

values, explanation of uncertainty and any special information of

importance to the owner.

A typical calibration report is shown in Figure 13. The elements

of the report are identified by letter and each one is discussed

below.

a. Scale identification

Each scale should have a numeric or alpha-numeric identification

imprinted on it to link the report to the scale. If no

identification is present an NBS number should be assigned and

engraved freehand with a diamond tipped pencil or with a

pantograph engraving machine.

b. Name and address of the scale owner

c. Standard introductory paragraph describing the scale and the

method of calibration.

d. Scale measurement results

This is a standard statement describing the derivation of

uncertainty. Modify it by inserting the actual number of

measurements made.

e. Scale support method and line segment used

A description of the method of supporting the scale during

calibration is included here so the scale user can duplicate it.

The graduation segments used during calibration are described for

the same reason.

f. Special information can be added to describe such features as

defects in the scale, special precautions for using the scale, or

recommendations for periodic recalibration in the case of

suspected instability.

38
g. Temperature and scale thermal expansion coefficient

This is a standard statement indicating that all length values

are reported at 20 degrees Celsius. The thermal expansion

coefficient of the scale is also given.

h. Tables of measurement results

The computer print-out of the normal-reversed summary table is

used here.

i. Graph of corrections

The graph of deviations from nominal lengths is used here.

5. MEASUREMENT ASSURANCE

5.1 Definition and principles

Measurement assurance (ref. 16) can be defined as a systematic

program employing controls, redundant measurements and

statistical analysis to determine the uncertainty of a

measurement process on a continuing basis. The concept of

treating regularly performed measurements as a process is the

essence of the program. Any organized measurement procedure that

generates statistically significant amounts of data can be

treated as a process and can be monitored with controls and

analyzed to reveal its characteristics.

A collection of values from repetitive measurements of a stable

control standard can be characterized by the limiting mean value,

process precision, systematic error and process uncertainty. The

values can be plotted against time 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, a normal frequency distribution is formed. This

assumption can be tested by histographic analysis and, if it

meets the test and remains stable, as proven by the control

charts, the process is said to be in a state of statistical

control

.

These are powerful tools for process evaluation because they can

be used to detect errors and malfunctions of all types. Equally

important, the effects of planned process changes are visible on

the control chart and are quantified by the statistics. If

control standard measurement data taken after each process change

are analyzed as a subgroup, the effect on process precision and

the limiting mean will be revealed.

Control standards have been employed in the line scale

calibration process for over 50 years. The ideal control to have

carried forward into the interferometric process would have been

the platinum-iridium meter bar No. 27 that served as the national

length standard from 1890 to 1960. Unfortunately, the graduation

quality is poor by modern criteria and these bars cannot be

measured with adequate precision for present needs.

39
since 1966, the principle control for the interferometric process

has been a modern Invar meter bar, SIP No. 5727 (usually referred

to as M5727) , which has an H-shaped cross section with millimeter

graduations on its neutral axis. It is supported at its Airy

points during use. Other controls of different lengths, materials

and graduation characteristics have recently been introduced.

M5727 is always measured shortly before or after the calibration

of a high precision scale more than 0.25 meter long and it is

occasionally measured at other, less critical, times. Over 70%

of scales calibrated are less than 0.25 meter long. Potential

length-dependent systematic errors are greatly reduced for these

short scales and there is less need for process evaluation with

the control bar.

There are other methods for evaluating process performance at

short lengths. Principal among these is the statistical analysis

produced from each scale calibration. A typical analysis shows

random errors that are proportional to length. Another tabulation

lists differences between mean normal and mean reversed length

values. A third evaluation comes from the graph of length

deviations. If any of these process indicators depart from

expected values, a control bar measurement should be performed.

See Section 4, Measurement Results, for evaluation details.

5 o 2 NBS control standards

Measurement assurance for line scales consists of periodically

measuring three control standards. These controls were selected

for special characteristics important to the program. The most

important characteristic is dimensional stability because a

control that changes length would be useless for determining

consistency of performance in the interferometer. Other

characteristics are covered in the descriptions that follow.

5.2.1 Invar Meter bar M5727

This is the primary control for line scales. It is an Invar, H

cross section bar manufactured c. 19 60 by SIP. It is graduated

every millimeter for the one meter length and has two subdivided

millimeters (with 0.1 mm intervals), one at each end of the bar

outside the one meter area. Measurements of M5727 started in

1964. This bar sags enough in the center to degrade focus

somewhat in the area from 300 to 700 mm and this leads to

slightly lower precision in that area. The long measurement

history, the stability and the high quality graduations (for

metal bars) make this an invaluable control standard.

Specifications

Material: Invar (43% nickel steel)

Coefficient of thermal expansion: 1.23 ppm/degree C

Graduation location: on the neutral axis of the bar

Graduation width: 10 pm

Cross section: H

Alignment and graduation segment marks: two

longitudinal parallel lines, 0.2 mm apart,

40
running the full length of the scale.

Support method: support at the two points indicated

on the front face of the bar.

Microscope objective: 32 mm (5x)

5.2.2 Twenty inch steel bar No. 6495

This is also an H cross section bar made by SIP c. 194 0 for the

twenty foot waybed now located in Room A 15. It is graduated at

0.05 inch intervals for 20 inches. Measurements of this bar

started in 1982. It is flat (no focusing problems from sag), has

high quality graduations, and has a high coefficient of

expansion. The high expansion coefficient is an advantage for

detecting temperature measurement problems.

Specifications

Material: steel

Coefficient of thermal expansion: 11.5 ppm/degree C

Cross section: H

Graduation location: neutral axis

Width of graduations: 5 ;iim

Alignment marks: two short lines bracket the tips of

the 0 and 20 inch graduations. Use the tips of

these for alignment and for identifying the

terminal graduations.

Line segment for measurement: use a 0.2 mm segment

just below the bracketing lines described above.

Support method: support at the points marked on the

outer face of the bar.

Microscope objective: 32 mm (5x)

5.2.3 Twelve centimeter quartz scale No. 5541

This quartz scale with chromium graduations is the only

representative of modern transparent-substrate scales in the

measurement assurance program. The scale was made c. 1960 but

its manufacturer is unknown. It is graduated at each millimeter

for its full length of 120 millimeters. Measurements of this

scale started in 1982.

Specifications

Material: fused quartz

Coefficient of thermal expansion: 0.4 ppm/degree C

Graduation location: upper surface

Graduation width: 12 ;tim

Alignment and line segment marks: two parallel lines

0.2 mm apart running the length of the scale.

Support method: Airy points

Microscope objective: 32 mm (5x)

5 . 3 Monitoring the process with the control standards

5.3.1 Measurement of Invar meter bar M5727

At least three measurements per year must be made of the

decimeters on M5727 to provide the data base needed for

measurement assurance. In addition it should be measured

41
whenever any of the following conditions arise: (1) If a

precision scale longer than 0.25 meter is calibrated, M5727

should be measured before or after (or both in special cases)

(2) If any significant change is made in the measurement process

such as modifying the comparator structure, changing any units of

the laser system, or recalibrating the temperature measurement

system. (3) If causes of suspicious data cannot be otherwise run

down.

After any of these kinds of changes, a series of measurements of

the decimeters on M5727 should be made, analyzed, and entered on

the control charts to determine if there is a change in the

measurement parameters. Only one process change should be made

at a time so the cause of any performance change can be

identified by measurement of the appropriate control standards.

Measurement assurance data should be maintained on the subdivided

millimeter, the first 10 millimeters, the first 10 centimeters

and the decimeters.

5.3.2 Measurement of 20 inch steel bar No. 6495

No. 6495 can be used in place of M5727 whenever its

characteristics will be useful. For example, this scale has a

thermal expansion coefficient ten times larger than M5727 so it

is ideal for detecting temperature measurement errors. This

scale must be measured at least twice a year to maintain an

adequate measurement assurance data base. Measure two groups of

graduations: (1) all the 0.05 inch intervals in the first inch

and (2) each inch from 0 to 20.

5.3.3 Measurement of 12 centimeter quartz scale No. 5541

This quartz scale should be measured at least twice a year to

build its data base. Measure the millimeters in the first

centimeter and each centimeter from 0 to 12

5 . 4 Measurement assurance data and its evaluation

5.4.1 Evaluation scope

This discussion will be concentrated on the principal control

standard M5727 because it has a long history and a comprehensive

data base. Measurements have been made since 1964 on the

decimeter intervals. In 1984, repeat measurements were started

on a group of centimeter, millimeter, and tenth millimeter

intervals but there are insufficient data accumulted on these

shorter intervals to be significant at this time. Results of

measurements on the 20 inch and 12 centimeter control standards,

which have relatively short histories, will also be discussed as

well as two special intervals, 3 and 29 micrometers long. The

latter two intervals give clues to the lowest uncertainties

achievable.

By monitoring all these intervals, it is possible to detect (1)

42
the effect of process changes at any length, (2) out-of-control

conditions of the process at any length, (3) the effect of

graduation type or quality on measurement precision, (4)

temperature effects, and (5) the secular stability of the control

standards. No other method of measurement error analysis can

provide comparable breadth of information.

5.4.2 M5727 data evaluation

Figures 14 through 23 are control charts for some of the

intervals on M5727. The principal interval, 0 to 1 meter, is

shown in figure 14. Vertical dividing lines between groups of

values indicate the dates of major measurement process changes.

Group mean values, indicated by solid lines, and group random

error limits (process precision) , indicated by dashed lines, are

process parameters.

Each time the measurement process is changed, the subsequent

measurement values are treated as a sub-group. New process

parameters are computed starting with the fourth value (a minimum

for statistical significance) and are then updated periodically

as data accumulates.

Process precision is taken to be ±3s where s is the standard

deviation of a single value. The significance of the random

error limits is that they predict future process performance

based on past performance. There is a 99.7% probability that the

next value will fall within these limits. If a new data point

falls outside these limits the measurement process is

statistically out of control and the cause of this condition must

be sought and corrected. Once the cause is corrected, it is

statistically acceptable practice to delete the outlying point

from the record.

There are four mean values on each of the M5727 control charts.

In table 5 the symbols for these means and the process changes

they represent are shown.

Table 6 is a summary of mean values for most of the intervals

being monitored on M5727. Table 7 is a pro-rata adjustment of

table 6 to a condition of equality of the 0 to 1 meter lengths,

that is, zero correction. This removes all the length dependent

differences to reveal the relative lengths of the intervals as

measured by the four different processes.

Figure 14, the 0 to 1 meter control chart, shows that each of the

two interferometric process changes make the interval appear

longer. If all the mean lines and error limit lines are removed

from the chart one might conclude from visual inspection that the

meter bar is growing. However, the other charts must be examined

and other possibilities considered before concluding that the bar

is unstable.

Figures 15 and 16 (0 to 500 mm and 500 to 1000 mm intervals) also

show the growth pattern, as expected, since their sum is equal to

i

I

1 43
Symbol

Ml

Table 5. Process changes for M5727

Process Change

Mean of data from classical meter bar

intercomparisons (individual points not shown)

M2 Mean of data from first interferometric

measurements

M3 Mean of data taken after the microscope, beam

splitter, and reference mirror were rigidly

coupled and kinematically mounted.

M4 Mean of data taken after substitution of an

HP interferometer system for the original

Michelson type, plane mirror, interferometer.

No carriage pitch and yaw correction after

this change.

the one meter interval. But when one examines figures 17, 18,

19 and 20, the evidence for instability is less convincing.

Comparing the first two groups of interferometric measurements

(M2 and M3) in figure 14 gives credence to the instability

hypothesis but fails to do so in figures 17, 18, 19 and 20. This

is because the mechanical distortions of the interferometer and

microscope were not uniform over the length of the scale and the

measured values were, therefore, not consistent as can be seen in

table 6. Kinematic mounting of the optical elements freed the

system from practically all of the mechanical distortions present

in the original structure.

At the time of the first group of interferometric measurements

(M2) the microscope, beam splitter and reference mirror were

bolted to the waybed. Although rigidity was given to the

structure with an "I" beam, coupling the microscope body to the

top of the beam splitter assembly, this mounting system caused

changes to occur in the distance between these optical components

when the carriage, weighing over 90 kg, moved on the waybed. Any

change in the relative positions of these components during a

measurement resulted in an error. For this reason the M2 values

are the least reliable of the interferometric measurements.

However, when they were made in the 1960s, the agreement with the

results of the classical meter bar intercomparisons was

considered very good. The usual uncertainty for intercomparison

measurements at that time was 0.5 jam. In table 6, agreement

between Ml and M2 is 0.20 jum or better in all cases. The same

can be said for the agreement of Ml with M3 and M4 . In table 7,

with relative lengths, the agreement is 0.12 or better. It is

quite remarkable that such continuity was achieved in view of the

major changes in techniques. Special importance was given to

designing the photoelectric microscope to agree with human

observers in graduation position interpretation.

44
Table 6. M5727, summary of mean values

Mean Corrections

( in Aim

)

Interval

(mm

)

Ml M2 (3s) M3 (3s) M4 (3s)

0 to 1000 1.33 1.13 ( .23) 1.34 ( .20) 1.42 ( .11)

100 to 900 .88 .78 ( .29) .83 ( .16) .90 ( .10)

100 to 800 .58 .54 ( .34) .54 ( .14) .63 ( .11)

200 to 900 1.08 1.05 ( .42) 1.05 ( .11) 1.11 ( .11)

200 to 800 .76 .81 ( .51) .76 ( .07) .84 ( .12)

0 to 500 -.01 .02 ( .11) .11 ( .21) .12 ( .10)

100 to 600 .14 .15 ( .23) .11 ( .14) .19 ( .09)

200 to 700 .31 .42 ( .47) .34 ( .10) .44 ( .13)

300 to 800 .78 .86 ( .43) .77 ( .12) .86 ( .10)

400 to 900 .80 .81 ( .24) .75 ( .18) .80 ( .09)

500 to 1000 1.34 1.16 ( .14) 1.20 ( .31) 1.29 ( .10)

0 to 200 -.16 -.18 ( .35) -.05 ( .19) -.06 ( .05)

200 to 400 .28 .24 ( .18) .30 ( .07) .31 ( .05)

400 to 600 .06 .18 ( .24) .03 ( .10) .09 ( .05)

600 to 800 .44 .40 ( .13) .43 ( .06) .44 ( .05)

800 to 1000 .71 .54 ( .23) .64 ( .12) .62 ( .06)

0 to 100 .04 .10 ( .22) .16 ( .07) .15 ( .04)

100 to 200 -.20 -.27 ( .19) -.22 ( .14) -.22 ( .05)

200 to 300 .00 -.04 ( .08) -.01 ( .06) -.01 ( .04)

300 to 400 .28 .28 ( .10) .31 ( .05) .32 ( .04)

400 to 500 -.13 -.04 ( .17) -.13 ( .06) -.12 ( .06)

500 to 600 .19 .22 ( .08) .16 ( .12) .22 ( .06)

600 to 700 -.03 .00 ( .07) .01 ( .07) .04 ( .09)

700 to 800 .47 .39 ( .11) .41 ( .07) .40 ( .06)

800 to 900 .30 .23 ( .20) .30 ( .08) .27 ( .06)

900 to 1000 .41 .31 ( .08) .35 ( .10) .37 ( .05)

45
- 2 -

Table 7. M5727, summary of mean adjusted values

Mean Calibration Corrections

(in ;am)

Interval Ml M2 M3 M4

(mm)

0 to 1000 0 o o 0 o o 1

• o o • o o 100 to 900 -.19 -.13 -.25 -.24

100 to 800 -.35 -.25 -.40 -.36

200 to 900 .15 .26 .11 .12

200 to 800 -.01 .13 -.04 -.01

0 to 500 -.67 -.54 -.55 -.59

100 to 600 -.53 -.42 -.56 -.52

200 to 700 -.35 -.14 -.33 -.27

300 to 800 .12 .30 .10 .15

400 to 900 .13 .24 .08 .09

500 to 1000 .67 .54 .55 .59

0 to 200 -.43 -.41 -.32 -.34

200 to 400 .02 .02 .03 .02

400 to 600 -.21 -.05 -.23 -.19

600 to 800 .18 .18 .16 .15

800 to 1000 .44 .26 .36 .36

0 to 100 -.09 -.02 .04 .01

100 to 200 -.31 -.39 -.36 -.35

200 to 300 -.16 -.15 -.14 -.17

300 to 400 .15 .17 .17 .19

400 to 500 -.27 -.15 -.26 -.27

500 to 600 .06 .10 .03 .08

600 to 700 -.16 -.10 -.13 -.10

700 to 800 .34 .28 .29 .25

800 to 900 .16 .11 .15 .13

900 to 1000 .28 .15 .21 .23

46
CORR.

IN

MICROMETERS

CORR.

IN

MICROMETERS

CORR.

IN

MICROMETERS

1.7

1.6

1.5

1 . 4 1.3

1.2

1 . 1 1.0

.3

.0

I I I . I I . I . I 65 66 67 60 63 70 71 72 73 74 75 76 77 70 73 00 01

YERR - 02 03 04 85

Figure 14. M5727 control bar (0 to 1000 mm)

.4

.3

.2

. 1

0

-. 1 -.2

-.3

65 66 67 60 63 70 71 72 73 74 75 76 77 70 73 00 01 02 03 04 05

YERR

Figure 15. M5727 control bar (0 to 500 mm)

YERR

Figure 16. M5727 control bar (500 to 1000 mm)

47
CORR.

IN

MICROMETERS

CORR.

IN

MICROMETERS

CORR.

IN

MICROMETERS

1 .2 -

1 . 1 1.0

.9

.0

.7

.6

.5

.4

85 66 67 68 69 70 71 72 73 74 75 76 77 78 79 00 01 82 03 04 85

YERR

Figure 17. M5727 control bar (100 to 900 mm)

1.0

.9

.8

.7

.6

.5

.4

.3

.2

. 1

Figure 18. M5727 control bar (100 to 800 mm)

Ml

-*-*M4

1 .1, J t 1 1 1 1 1 » I I I 1 I » I I .j L_i I I

I 1 » I 1 « 1 » I

' 1 L_i_

65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85

YERR

Ml M4

I . I

1 . 1.1 . I . 1 . 1 i I . 1 .^,1

1.6

1.5

1.4

1.3

1.2

1 . 1 1.0

.9

.8

.7

.6

.5

Figure 19. M5727 control bar (200 to 900 mm)

I . I . I . I . I . I . I . I I .’*1

. I . I . I . I . 1 L 1 1 _1 . I . 1 . 1 . 1 1. 65 66 67 60 69 70 71 72 73 74 75 76 77 70 79 80 01 02 83 04 85

YERR

48
in

q:u

u

z:o

Oi. u»—

t

ZLZ

q:z

o

u

65 66 67 68 69 70 71 72 73 74 75 76 77 70 79 80 81 02 83 84 85

YEAR

Figure 21. M5727 control bar (0 to 100 mm)

. 1 in

QC 0

Ulz

• u

T* — O

• H ) •

! ,1

* »*-• M4

2: M2 1- » . » -.3 • •

oi. o • ^ - u . . -.5 -

-.6 —

1 1 1 1 i

1 1 1 1 1 1 j 1 1

1—\—1—1

I—1

1—1

^—1

1—I

1—

—1

'

65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 01 82 83 04 05

YEAR

Figure 22. M5727 control bar (100 t0 200 mm)

49
tn

Q£U

h“U

x:o

KU

• Q£KO

u

YEAR

Figure 23. M5727 control chart, 200 to 300 mm

MILLIMETERS Figure 24. M5727, corrections to the dm intervals

Figure 25. M5727, adjusted corrections to the dm intervals

Figure 26. Interferometer carraige pitch and yaw

50
CORRECTION

IN

micrometers

CORRECTION

IN

MICROMETERS

30

30

10

0 TO 20 INCH INTERVAL (508 MH)

0.00 a2" 83 04

YEAR

. 10

as

u 0.00

10

-.20

YEAR Figure 27. No. 6495, 20 inch scale, control charts

0 TO 100 HH interval

30

-.40

-.50

02 03

YEAR 84

20

85

0.00

-.10

Figure 28. No. 5541, 12 cm scale, control charts

28.84

- 28.83

28 . 82

NLAN length « 20.830 MICHOME lERS, 3S - .009

28 8 1 , i 1 1 I I i i I I I 1 J 1 1 t 1 I 1 I I 1 I 1 1 1 I I I 1 I 16 20 24

TIME IN MONTHS

2.91

2 . 90

ro

CK« 2.89

2.82,

MEAN length » 2.990 MICROMETE.RS, 3S - .012

• »

I I I I I ‘ ‘ I ‘ ‘ I ‘ ‘ I 1 1 i ‘ I ‘ ‘ ‘ I I IG 20 24

TIME IN MONTHS Figure 29. 3 urn and 29 urn intervals, control charts

51
On the subject of stability of M5727, there is also the distinct

possibility that the increase in length values between M3 and M4

on all these charts is caused by an error in the assumed

wavelength of the HP laser. The manufacturer's value is being

used because the wavelength has not been measured at NBS . On the

other hand, during the period represented by M3 there are two

benchmark measurements made with an iodine stabilized laser (ref.

9) whose wavelength is known to a few parts in 10^ . Data points

from these measurements are represented by asterisks on the

charts

Another possible contributing factor to the M4 - M3 difference is

the loss of automatic correction for carriage pitch and yaw with

the demise of the Michelson interferometer. Lack of carriage

correction is compensated by careful alignment of the scale

graduation axis with the interferometer axis to minimize Abbe'

offset and its consequent length measurement error. This error

is proportional to the sine of the pitch angle, and it is a

random error if the scale axis is high and low by an equal amount

an equal number of times. The bias, if any, is likely to be

small. Figure 26 is a graph of carriage pitch and yaw.

In December 1981, an experiment was performed to determine the

effect of off-axis measurements. On three consecutive days, with

no change in interferometer alignment, M5727 was measured at

three elevations relative to the interferometer axis: 3 mm below,

3 mm above, and on-axis. Results are shown in table 8 together

with the M4 values which are the mean values for that period.

For a 5 second carriage pitch and a 3 mm off-axis mounting, the

error in the 0 to 1 m length should be 0.07 Mm. In table 8 the

measured error averages 0.13 which suggests that the actual

Table 8. Effect of off-axis mounting of M5727

Corrections in Micrometers

Interval

3 mm 3 mm On-axis Mean of M4 High - Low - (mm) High Low High & Low On-axis On-axis

0 to 100 .15 . 14 . 14 .14 .15 .01 .00

200 -.05 -.10 -.08 -.08 -.07 .03 -.02

300 -.04 -.13 -.07 -.08 -.08 . 03 -.06

400 .29 . 19 .25 .24 .24 .04 -.06

500 .23 .07 . 16 . 15 .12 .07 -.09

600 .43 .27 .37 .35 .34 .06 -.10

700 .48 .31 .42 .40 .38 .06 -.11

800 .90 .70 .82 .80 .78 . 08 -.12

900 1.16 .93 1.08 1,04 1.05 .08 -.15

1000 1.56 1.29 1.45 1.42 1.42 . 11 -.16

pitch value may be about 8 seconds. It is unlikely that the bar

has been off axis by more than 1 mm in practice, and this would

result in an error, probably random, of 0.04 at most.

52
still another contributing factor could be interferometer

alignment. Misalignment always results in shorter values for the

measured length, an error proportional to the length and the

cosine of the misalignment angle. Alignment of the Michelson was

more difficult than alignment of the HP system. It required

careful tracking of the laser beam as the plane mirror was moved

through the full range of carriage travel and, after the beam was

expanded and collimated at a 2 inch diameter, another centering

procedure was performed. Alignment of both the Michelson and the

HP require very careful visual judgments. The fact that the 3s

limits are larger for M3 than for M4 in all but three cases in

table 6 probably indicates that the Michelson alignment procedure

is more error prone and can result, on average, in shorter length

values

.

Figure 24 shows the complete calibration plots for M3 and M4 and

the difference, M4 -M3. The length proportional component of

the difference has been removed in table 7 and figure 25. This

latter plot of adjusted differences shows a systematic difference

with an 0.04 /im maximum. Its cause has not been proven, but it

could be the result of the change from control to no control on

carriage travel geometry.

A final comment about meter bar M5727: the graduated surface is

not flat when the bar is mounted for measurement. Like most

scales of this length and design it sags somewhat in the center

area resulting in some degradation of graduation image sharpness.

Careful focusing of the 0 and 1 meter graduations is always done

in the preparation procedure and an objective lens is selected

which is a compromise between high magnification and depth of

focus. The 0 through 200 mm and the 800 through 1000 mm

graduations are in good focus but the 300 through 700 mm

graduations are, to varying degrees, slightly out of focus. The

lowering of measurement precision caused by this condition occurs

in individual runs where the normal and reversed passes are made

but does not occur in the long term as demonstrated by the

precision indicators in figures 21, 22 and 23 and in table 6.

5.4.3 No. 6495 data evaluation

Only limited data are available for twenty inch control standard

No. 6495, but figure 27 shows that measurement precision on it

may prove to be better than that for comparable lengths (500 mm

and 100 mm) on M5727. This is a good sign that the temperature

measurement system is working well because the thermal expansion

coefficient for No. 6495 is nearly ten times that of M5727.

5.4.4 No. 5541 data evaluation

Data available from measurements on twelve centimeter quartz

control standard NBS No. 5541 are also limited. The control

chart in figure 28 shows a measurement precision somewhat worse

than comparable intervals on M5727. This finding is unexpected

because the graduations on the quartz scale are judged to be of

53
excellent quality and superior to those on M5727. Further

measurements should provide interesting information on this type

of graduation.

5.4.5 Data from very short intervals

Measuring very short intervals minimizes all length dependent

errors. Sufficient data are not yet available from the short

intervals on the control standards, but figure 29 shows results

on two very short intervals, 29 pm and 3 pm long, from a special

scale measured over a 32 month period from 1976 to 1979. These

data afford an assessment of the measurement process at a level

where length dependent errors are at the vanishing point. The 3s

limit of 0.01 pm represents the best precision attainable at that

time. Ten millimeter and 4 inch intervals are shown in figures

27 and 28 for comparison and they show 0.03 pm and 0.02 pm limits

respectively

5.4.6 Summary and conclusions

This review of measurement assurance data reveals three areas

where potential improvements in the measurement process can be

made. First, the wavelength of the HP laser must be measured to

remove its uncertainty. Second, the procedure for interferometer

alignment should be improved, if possible. Third, the

uncertainty about the effect of carriage travel geometry on the

measurements must be eliminated. This review also reveals the

power of measurement assurance to pinpoint problems.

A summary of long term precision for various lengths and control

standards is given in table 9.

Table 9. Summary of long term precision

Nominal Control Long Term

Length Standard Precision,

(mm) (Mm)

1000 M5727 0.11

700 M5727 0.11

500 M5727 0.10

200 M5727 0.05

100 M5727 0.06

508 (20 in.) SIP No. 6495 0.08*

101. 6 (4 in.

)

SIP No. 6495 0.03*

100 NBS No. 5541 0.12*

10 NBS No. 5541 0.03*

0.029 Special 0.01*

0.003 Special 0.01*

* Based on limited data.

54
5.5 Error sources and error analysis

Measurement uncertainty has two components: that resulting from

random error and that resulting from systematic error. These two

components are added to give the stated uncertainty. Random

error is taken as three times the standard deviation of the mean

value as shown in section 2.5.2.

Random errors are easily observed and quantified from redundant

measurement data. Systematic errors come from a number of

sources and result in incorrect length values. They are not

readily observed, but must be searched out and corrected by

painstaking experiment and analysis.

The following is a list of potential systematic error sources;

-Wavelength

a. Vacuum wavelength of the laser

b. Refractive index of air determination

(1) Refractive index equation

(2) Air temperature measurement

(3) Atmospheric pressure measurement

( 4 ) Humidity measurement

-Interferometer

a. Alignment of interferometer axis with carriage path axis

b. Structural characteristics

(1) Constancy of distance between reference mirror and

microscope

(2) Constancy of distance between beam splitter and

microscope

(3) Constancy of distance between measuring

retroreflector and scale

-Scale

a. Scale temperature measurement

b. Thermal expansion coefficient

c. Graduation quality

Most of the above parameters are also sources of random error.

With the exception of structural characteristics of the

interferometer and scale graduation quality, these parameters

cause length-dependent errors. Their relative effects are

illustrated in table 10 where it is shown, for example, that an

error of 0.01 degree C in the temperature measurement of a one

meter steel scale will result in a 0.1 ;um error in the

measurement of its length.

The structural characteristics of an interferometer can be

significant contributors to error but in this case their

contributions have been greatly reduced by rigid construction,

kinematic mounting of critical components, and precise

temperature control.

55
No controlled experiments have been completed to evaluate the

influence of graduation quality on systematic and random errors.

It is reasonable to assume, however, that ideal graduations

should be between 2 and 10 urn wide, have smooth sharply defined

edges, be symmetrical, be uniform and free from imperfections,

and have high contrast with a flawless background. Equally

important is the flatness of the graduated face because a poorly

focused graduation is even more deleterious to precision than a

poor quality graduation. See 3.1.1, Evaluation of the scale, for

further discussion of this subject.

There are two ways of estimating the systematic component of

uncertainty. First, a complete error analysis can be made where

each error source is evaluated and assigned an uncertainty and

the overall uncertainty is taken as a combination of the

individual uncertainties. Second, where completely independent

and equally valid measurements of the same scale are available,

the difference between these measurements is an estimate of

systematic error. It is best to use both methods and that is

done here.

Estimated systematic error contribution of each source is listed

in the last column of table 10. The combined value is 0.15 jam/m.

Two interchanges were made to evaluate the systematic error by

the second method. The first interchange was with the National

Table 10

Relationships Between Length-Dependent Errors and Errors

in Measurement Parameters

and

Estimated Process Systematic Error (S.E.)

Error in a One--Meter Length Process S.E.

Parameter

1 part in 10^

or 0.1 um/m

1 part in 10®

or 0.01 um/m

parts in 10®

Wavelength

Vacuum wavelength 1 part in 10 1 part in 10® 2

Refract, index eq. 1 part in 10^ 1 part in 10® 5

Air temp. 0 . 1 deg . C 0.01 deg. C 0

Pressure 0 . 3 mm 0 . 03 mm 4

Rel. Hum. 12% rh 1.2% rh 1

Interferometer

Alignment 0.45 mm/m 0 . 14 mm/m 1

Scale

Steel temp. 0.009 deg. C 0.001 deg. C 2

Glass temp. 0.012 deg. C 0.001 deg. C

Invar temp. 0.067 deg. C 0.007 deg. C

Quartz temp

0.25 deg. C 0.025 deg. C

56
Research Council of Canada in 1973-74, and it resulted in a

difference of 0.10 >im/m on a one meter invar scale. This

exercise took place when Lamb dip stabilized lasers were in use

with their uncertainties of several parts in 10^

.

The second interchange, sponsored by the International Bureau of

Weights and Measures (BIPM) , and involving fourteen of the

national laboratories of the industrialized countries ran from

1977 to 1984. The NBS value on the one meter SIP steel scale

agreed with the mean of twelve values (two values were not used

because they were identified as outliers by statistical test) to

the nearest 0.01 jum/m. An iodine stabilized, helium-neon laser

with a wavelength stability of a few parts in lo'^ and an

uncertainty of only 2 or 3 parts in 10*^ was used in the NBS

measurements

.

This evidence shows that systematic error in NBS measurements is

no greater than 0.15 yum/m and is probably 0.10 jui^/m or better

when the iodine stabilized laser is used and all subsystems are

calibrated and adjusted. This must be verified by close

surveillance of the two principle control standards, M5727 and

No. 6495. The value on the one meter length of M5727 obtained

during the period when measurements of the BIPM bar were made

provides an especially strong benchmark.

5.6 Minimizing errors

In the short term, every scale measurement should be done with

care by following established procedures. The following

precautions and procedures are recommended:

-Review the operational check list (Appendix A) before starting a

measurement

.

-Update the measurement assurance data frequently by measuring

one or more of the control standards. This is indespensable for

detecting measurement errors and instrument malfunctions.

-In the long term, improvements in the measurement process should

be made. Scientific methods should be scrupulously followed in

designing the experiments used to examine the effectiveness of

changes made in the instrumentation or procedures. Make only one

change at a time and then test its effect by measuring the

appropriate control.

57
6.

APPENDICES - DETAILED PROCEDURES

Appendix A - Temperature measurement system calibration (see

2.4.1)

Four components of the system require calibration or

verification: the Mueller bridge, the standard platinum

resistance thermometer (sprt), the thermocouples and the

nanovoltmeter. Calibration procedures and frequency are given

below.

- Mueller bridge

Recommended procedures are in NBS Monograph 126, appendix H (ref.

11) . All the necessary auxiliary equipment and supplies are

available in the line scale laboratory.

Auxiliary Equipment and Supplies

10 ohm standard resistor, NBS No. 77613

adjustable decade resistance box

precision slide wire resistor

supply of clean mercury

heavy gauge solid copper wire

Because it changes with time, the 10 ohm standard resistor should

be calibrated every two or three years by the NBS Electricity

Division. The most probable value for the resistor at any given

time is best arrived at by fitting a curve to the data. Five

data points have been taken on this resistor since 1968.

Proceed with preparation and calibration in the following

sequence:

1. Clean and grease the bridge decade switches.

2. Clean and renew the mercury on the R & N switch and the 10 ohm

decade switch.

3. Replace the batteries if necessary.

4. Clean the peg in the ” Zero-Meas-Rat io” switch and fit it

tightly (contact resistance here will introduce errors)

5. Adjust the ratio arms to equality.

6. Determine the bridge zero.

7. Measure the 10 ohm standard at least 2 times.

8. Connect the decade resistance box and the slidewire resistor

to the bridge.

9. Calibrate the 10 ohm decade of the bridge at 10 , 20 and 30

ohms only (no need to go farther)

10. Calibrate the 1 ohm decade at 1 through 10 (X)

11. II » . 1

" II " .1 II 1(X)

12. II " .01 " II " .01 II .1(X)

13 . II ” .001 " II " .001 II .01(X)

14. II " .0001" II " .0001 II .OOl(X)

15. Remeasure the 10 ohm standard resistor at least 2 times

16. Compute the bridge corrections and write the calibration

report.

58
- standard platinum resistance thermometer

Initial calibration of any SPRT must be done by the NBS

Temperature Group where several thermometer constants are

determined and a table is prepared for the calibration report.

Ro, the resistance at 0 degrees C, is the only constant that will

change as long as the International Practical Temperature Scale

of 1968 is in effect. Rq must be periodically remeasured in the

laboratory with a triple point of water cell, following

procedures given in NBS Monograph 126, section 7. Mechanical

shock to the SPRT is the usual cause of change in Rq , therefore,

an SPRT that remains undisturbed such as in the line scale system

is more likely to be stable than a system that is moved about.

- Thermocouples

Copper-constantan thermocouples have an average value of 40

microvolts per degree C, the value found in handbooks. This

equals 0.025 degree per microvolt. Experience at NBS has shown

variations from 0.0248 to 0.0252 degree per microvolt in

calibrations. When the line scale interferometer is in use the

temperatures of the scale and in the air path do not deviate from

the 20.000 degree reference by as much as 0.025 degree. Under

this condition it is not necessary to do a full calibration of

the individual thermocouples. Instead, a verification of

thermocouple equality is made by placing all the measuring

junctions in a common heat sink such as the cavity in a copper

block. After equilibrium is reached, the readings of the

individual thermocouples should not deviate from each other by

more than a millidegree for a temperature differential of 0.1

degree. Since thermocouples are very stable, one test for

equality will suffice. If, at any time, a full calibration is

deemed necessary, the procedure is described in NBS Monograph

152, section 4.1 (ref. 17).

Thermocouples must be electrically insulated from each other.

Each thermocouple in this system is insulated by a layer of

transparent tape, and if this insulation slips off, or wears

through, a short circuit can occur. If any two or more become

shorted the whole system will give erratic readings that make it

obvious that something is wrong.

- Nanovoltmeter

Accuracy of temperature measurements depends upon the accuracy of

the thermocouple voltage readings. Periodic comparison of the

nanovoltmeter with a standard source is necessary to ensure

validity. Use a precision voltage divider together with a

reasonably accurate voltage input to obtain accurate

nanovolt-level voltages for the comparison. Be sure to follow

the manufacturers instructions for eliminating the effects of

thermal emfs and offset currents.

Appendix B - Barometer calibration (see 2.4.2)

The barometer described in section 2.4.3 is a Rosemount Model

1201F. It was originally calibrated by the NBS Pressure Group.

Over a period of three years it has been regularly compared with

59
a standard aneroid barometer maintained by the Pressure Group to

ensure that its original calibration is still valid. This

periodic verification should continue at monthly intervals.

The comparison must be made with a transfer standard since it is

not convenient to move the Rosemount to the standard barometer.

A Wallace & Tiernan Model FA 139 aneroid barometer in the line

scale laboratory is the transfer standard and it is calibrated by

comparison with the standard barometer. It is then carried back

to the laboratory and immediately compared with the Rosemount.

Be sure, when comparing two barometers, that they are at the same

elevation (that is, on the same table) . Keep a record of the

comparisons and have the Rosemount recalibrated by the Pressure

Group if there is any evidence of a change.

Appendix C - Hygrometer calibration (see 2.4.3)

Calibration instructions for the hygrometer are in the manual but

periodic checks against a chilled mirror standard hygrometer or

other accurate reference should be made approximately every three

months as a quick method of verification.

Appendix D - Interferometer alignment (see 3.1.6)

The following procedure is for aligning the interferometer when

no carriage pitch and yaw correcting devices are operating. If

such devices are operating, omit step 3. It is also assumed that

the interferometer is badly out of alignment. If alignment

verification or trimming adjustments is all that is needed start

with step 8, but read step 5 to learn how adjustments are made.

1. Mount scale at selected elevation and bring it into focus.

2. Remove the remote interferometer.

3. Set the center of the retro coincident with the scale

graduation axis. Make this adjustment both vertically and

laterally (see 3.1.6).

4. Place the two hole magnetic target on the face of the retro

and center it. Also turn the face plate on the laser so its

target is at bottom center. Use the large face plate aperture in

the laser beam.

5. Adjust laser elevation and azimuth until the beam tracks the

target holes as the carriage is moved back and forth over its

full range. Make elevation adjustments by turning all three

knurled nuts equally on the large threaded vertical studs, but

start with the laser head approximately horizontal as indicated

by a spirit level. Make azimuth adjustments by moving the beam

bender along the laser head axis. Loosen the set screw holding

the beam bender and make adjustments with the screw provided.

Tighten the beam bender set screw after each adjustment and

re-aim the beam with the knurled knobs in the base of the beam

bender. Make the elevation and azimuth adjustments when the

carriage is farthest from the laser and check the adjustment when

the carriage is closest to the laser. The coarse alignment is

now complete.

6. Remove the target from the retro and switch to the small

60
aperture on the laser face plate. Track the reflected beam on

the face plate target as the carriage is moved back and forth,

and make elevation and azimuth adjustments as before when the

retro is farthest from the laser. Check the spot position when

the carriage is close. If it is off, adjust the beam bender to

center the spot on the target cross mark, then move the carriage

to the far end and make further adjustments. Make this alignment

precisely.

7. Mount the remote interferometer and attach the two hole

magnetic target to its face. Using the large aperture on the

laser face plate, adjust the remote interferometer vertically and

laterally until the beam enters and exits through the holes.

This completes coarse adjustment of the remote interferometer.

8. Make the final fine adjustment using the small aperture.

Start with the carriage close and adjust the remote

interferometer by rotating it around the horizontal and vertical

axes until coincidence is achieved at the target cross mark.

Move the carriage to the far end and adjust laser elevation and

beam bender axial position until coincidence is achieved.

Continue back and forth until alignment is achieved. When making

these fine adjustments, sensitivity can be enhanced by holding a

piece of paper between the remote and the retro and alternately

blocking and letting through the beam reflected from the retro as

the target is being watched. If step 6 was done carefully and

the angle of the remote interferometer was adjusted carefully in

step 8, then only small adjustments in the laser elevation and

azimuth should be necessary.

Appendix E - Operational check list

The following is a list of important adjustments, calibrations,

maintenance items, and precautions that must be observed to

ensure the integrity of line scale measurements. Each item has a

section number at the end for reference to more details.

1. Kinematic support balls centered and unlocked (3.1.5)

2. Interferometer aligned (3.1.6 and Appendix B)

3. Scale cleaned, mounted, aligned, focused and set on the zero

line p.1.4 and 3.1.5)

4. Uniform illumination in microscope field (3.1.5)

5. Microscope masks adjusted to the proper line segment and

microscope slit aligned with graduation (3.1.5)

6. Housing covers not touching microscope (3.1.3)

7. Oscilloscope controls set correctly (3.2.2)

8. Micrcpscope photomultiplier voltage, gain and time constant set

for optimum line signal (3.2.2)

9. Line signal on scope adjusted for width and height (3.2.2)

10. Bright/dark switch set for type of line (3.2.2)

11. "Line present" control adjusted (3.2.2)

12. Threshold level adjusted to 50% of line signal height (3.2.2)

13. Error signal adjusted for damping rate (3.2.2)

14. Laser and electronics sufficiently warmed up (3.2.1)

15. Reference temperature at 20.000 degrees C (3.1.7)

16. Temperature uniform and stable, fan running (3.1.7)

17. Atmospheric pressure sufficiently stable (3.2.6)

61
18. Water level in reservoir sufficient (3.1.3)

19. Hydraulic lines bled of air and filled with fluid (3.1.3)

20. Water pump motor oiled every 3 months (3.1.3)

21. Waybed and lead screw cleaned and oiled every 3 months

(3.1.3)

22. Environmental measurement systems calibrated at appropriate

intervals (Appendices A, B, and C)

Appendix F - Microscope angle adjustment (see 4.1 c)

The purpose of microscope angle adjustment is to make the gptical

axis normal to the scale axis. When this condition is met there

will be minimum differences between the normal and reversed

measurement values on a scale that is out of focus in the center

because of sag. The reason for these measurement differences is

that the apparent position of a graduation differs from its true

position as shown in figure 30. Graduation displacement, x,

microscope angle, ©, and the distance, d, of the graduation below

the focal plane are related by

X = d tan *©•.

Figure 30. Effect of scale sag and microscope canting on

apparent position of graduations

62
Table 11 shows graduation displacements for various values of

microscope angle and scale sag.

Table 11. Graduation Displacement (in micrometers)

Microscope Angle (degrees)

Sag

itm) 0.1

1

• 1 1

O

1

•1

(ji 111

1

1 1 2

1 .00 .01 .02 .04

5 .01 .04 .09 .18

10 .02 .09 .18 .35

50 .09 .44 .87 1.75

Angle adjustment of this microscope is a difficult procedure and

the adjustment is frequently lost when the objective lens is

changed or refocusing is done by moving the microscope in its

collar. Furthermore, after the initial careful adjustment, the

procedure has questionable value for two reasons: (1) Averaging

normal and reverse values results in an accurate measurement even

though the microscope is not precisely normal to the scale

because the displacement of the out of focus graduations is

symmetrical. (2) The effect of a small angular deviation is to

increase the random error and thus the uncertainty in the out of

focus area. This increased uncertainty reflects reality since a

scale that sags is not of ideal quality and cannot be used to the

degree . of accuracy implied by measurements made with a perfectly

oriented microscope.

Two methods are described below for orienting the microscope

normal to the carriage travel: (1) autocollimation and (2) trial

and error. The first is of marginal value because the special

autocollimating lens does not produce good results and the second

is tedious because it entails repeated measurements of a meter

bar in normal and reversed positions. Only the angle of the

microscope with the line of the carriage travel is critical. In

the other direction, crosswise of the carriage, the angle is

important only to the extent that it might effect scale

illumination.

- Autocollimation procedure

(1) Mount the mirror on the carriage while the 32 mm objective

lens is in place. Bring the mirror edges at both ends into sharp

focus so the mirror lies in the plane of the carriage travel as a

scale would when being measured.

(2) Replace the objective lens with the 8-inch collimating lens

and raise the microscope so the end of the lens housing is about

one inch above the mirror surface.

(3) Remove the masking assembly from the side of the microscope

housing and insert in its place the red filter assembly (point A

in the diagram)

.

(4) Center the red filter disc in the field of view while the

normal illuminating lamp is in place.

(5) Remove the microscope illuminator lamp assembly and the

63
photomultiplier tube assembly to expose the microscope slit.

Illuminate the slit with a high intensity lamp pointed down the

microscope tube. This projects an image of the slit onto the red

filter.

(6) The slit should be imaged at B (approximately on the center

of the red filter) as a bright line. Adjust the illumination and

the filter position as needed. The part of the image that goes

through the slit in the filter is reflected from the mirror and

returns to appear at C (somewhere along the slit)

(7) Rotate the collimating lens 180 degrees and observe that the

reflected part of the slit image moves. This is because the lens

is off axis. Make a mental note of the mean of the two slit

image locations.

(8) Change the angle of the microscope until B coincides with the

mean location of C. Change the angle by raising or lowering the

right end of the meter long, 4-inch diameter, support tube at the

support ball. When B and C coincide, the microscope optical axis

is normal to the mirror.

-Trial and error procedure

(1) Measure M5727 in both normal and reversed positions and

examine the N-R difference. If N-R is negative by 0.15 /im or

more between the 300 and 700 mm lines then lower the right end as

in step 8 above. If N-R is positive then the right end should be

raised. Remeasure M5727 and again examine the N-R difference.

Adjust the microscope tilt as necessary to bring the difference

down to 0.15 pm or less.

64
7.

REFERENCES

1. Beers J. S. and Lee K. Interferometric Measurements of Length

Scales at the National Bureau of Standards. Precision

Engineering, Oct. 1982, Vol. 4, No. 4

2. Judson L. V. and Page B. L. Calibration of the Line Standards

of Length of the National Bureau of Standards, Journal of

Research of the National Bureau of Standards, Dec. 1934, 13

3. Page B. L. Calibration of Meter Line Standards of Length at

the National Bureau of Standards. Journal of Research of the

National Bureau of Standards, January 1955, 54(1)

4. Judson L. V. Calibration of a Divided Scale. Circular of the

National Bureau of Standards, No. 329, May 13, 1927

5. Cook H. D. and Marzetta L. A. An Automatic Fringe Counting

Interferometer for use in the Calibration of Line Scales. Journal

of Research of the National Bureau of Standards, April- June 1961,

65C(2)

6. McNish A. G. Lasers for Length Measurement. Science, 9 Oct.

1964, 146(3641)

7. Gilliland K. E. , Cook H. D. and Mielenz K. D. Use of a Laser

for Length Measurement by Fringe Counting. Metrologia, July 1966,

2, 95-98

8. Line Standard Interferometer. National Bureau of Standards

Technical News Bulletin, March 1967

9. Layer H. P. A Portable Iodine Stabilized Helium-Neon Laser.

IEEE Transactions on Instrumentation and Measurement, December

1980, IM-29(4)

10. Hocken R. J. and Layer H. P. Lasers for Dimensional

Measurement. CIRP Annals, 1979, 28(1), 305

11. Riddle J. L., Furukawa G. T. and Plumb H. H. Platinum

Resistance Thermometry. National Bureau of Standards, Monograph

126, 1973

12. Handegord G. 0. et al Humidity and Moisture. Vol. I. Reinhold

Publ. Corp., N. Y., 1963, 265

13. Hedlin C. P. Humidity and Moisture. Vol. I. Reinhold Publ.

Corp., N. Y., 1963, 273

14. Documents Concerning the New Definition of the Meter.

Metrologia, 19, 1984

15. Edlen B. Metrologia, 1966, 2(2), 71

16. Cameron J. M. Measurement Assurance. Journal of Quality

65
Technology, January 1976, 8(1)

17. Beers J. S. A Gage Block Measurement Process Using Single

Wavelength Interferometry. National Bureau of Standards,

Monograph 152, 1975

66

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