NBSIR 73-104

A Non-Contacting Length Comparator

With 10 Nanometer Precision

A. W. Hartman

F. W. Rosberry

J. Arol Simpson

Institute for Basic Standards

National Bureau of Standards

Washington, D. C. 20234

February 9, 1973

Final Report

U. S. DEPARTMENT OF COMMERCE

NATIONAL BUREAU OF STANDARDS

NBSIR 73-104

A NON-CONTACTING LENGTH COMPARATOR

WITH 10 NANOMETER PRECISION

A. W. Hartman

F. W. Rosberry

J. Arol Simpson

Institute for Basic Standards

National Bureau of Standards

Washington, D. C. 20234

February 9, 1973

This report is to be superseded by a future publication which will receive general distribution and should be cited as a reference.

Please consult the NBS Office of Technical Information and Publ ic

•

cations to obtain the proper citation.

CONTENTS

Page

Abstract 1

Introduction 1

Principle of Operation 2

Linear Range 5

Measurements of Displacement and Lengths with the Prototype

Simon Comparator 6

Measurement of Transparent Objects 7

Measurement of Objects with Diffuse Surfaces 8

Sensor Signal Levels 8

Noise Sources 10

Measurement Error Sources . 12

Thermal Errors 12

Optical Errors 13

Transfer Curve Errors 14

Electrical Factors 15

Outlook 16

References 16

Illustrations (Figures 1 - 16) 17-32

ILLUSTRATIONS

Page

Fig. 1 Simon probe radiometry 17

Fig. 2 Simon probe layout 18

Fig. 3 Internal illumination system 19

Fig. 4 Sensor output vs. object displacement (transfer curve ) 20

Fig. 5 Linear range vs. sensor spacing 21

Fig. 6 Improving probe linearity by sensor spacing adjustment 22

Fig. 7 Transfer curve and local slope 23

Fig. 8 Prototype Simon comparator 24

Fig. 9 Response to a transparent object 25

Fig. 10 Response to specular and diffuse reflecting surfaces 26

Fig. 11 Sensor response to specular and diffuse reflecting surfaces 27

Fig. 12 Preamplifier diagram 28

Fig. 13 Probe noise vs. integration time 29

Fig. 14 Probe noise vs. signal strength 30

Fig. 15 Probe offset error 31

Fig. 16 Specimen rotations due to repositioning 32

A Non -Contacting Length Comparator with 10 Nanometer Precision

by

A. W. Hartman, F. W. Rosberry and J. Arol Simpson

National Bureau of Standards

Washington, D.C. 20234

Abstract

A non -contacting length comparator utilizing two specially designed

photo-electric microscopes has been constructed. Performance tests of

this comparator, using lapped and polished steel surfaces demonstrate a

resolution of ~ 1 nanometer, a precision of ~ 10 nanometers, and a linear

range in excess of 50 micrometers.

Introduction

J. Simon^^ has described the use of energy sensing in two planes,

on either side of the microscope image plane, as a detector of position

(2) along the optical axis on the sub -micrometer scale. J. A. Simpson has

shown that this scheme should produce sensitivities below 10 nanometers when

comparing lengths, and using a common research microscope as a basis.

To test these predictions, a prototype length comparator was constructed, and tested against high quality gage blocks. Also, the first

order radiometric theory of reference 2 has been expanded to include the

concept of linear range, applicability of diffuse as well as specular

1
reflecting test surfaces, estimates of signal-to-noise ratios and error

sources

At present, the resolution is better than 1 nanometer. The precision, defined as repeatability of response to the same stimulus repeated after a period of time, is about 10 nanometers. There are indications that the ultimate precision may lie in the 1 nanometer class.

Principle of Operation

The basic Simon probe is shown in figure 1. A microscope with

internal illumination (not shown) illuminates an object which is placed

such that two out -of -focus sensors 1 and 2 produce equal output and hence

zero difference signal. A variation Aq in the object distance q will

bring one sensor toward focus. The sensors are a distance Ap away from

the microscopic image plane, which itself is a distance p away from the

microscope objective. The sensors have an area A

q

, the sensor illuminating beam has a cross section A at the sensor plane. The microscope

transmits radiation with flux F . The sensors intercept flux F which

o

c

is a fraction S of F . This S can be equated with the sensed signal

from each detector.

When the object is displaced by a small amount d(Aq) from the equilibrium position, S varies by a small amount dS, and the system sensitivity to axial displacements can be expressed as

d(Aq)
provided the sensors are able to sense dS in the first place.

The expression for

dS

has been derived in reference 2 for the case of a vanishing small illuminated area of the object surface and a moderately small numerical aperture.

This derivation is included below, to illustrate the relative importance

of the variables involved.

We have the following equations:

FA A

S = - = —a °

a for e«l

F

q

A TT(BAp)

Lens magnification

M =

tan(

$ — % for 9 and 0 small

tan9 9

Therefore , A Ao

and hence

i fAF 1 / o o ^

M0 y nF

For a given operational value of S, its variation with Aq is

3
,2^2 / A s3 = -2M0

5 (Aq) nM^CAq)'

nF3

A F

T

o o

For the two sensors combined, we have then

o(Aq) f A

oF0

= -4M0 W A r i

For the prototype, where

A = 1 x 10"6

m

2

) F i ° \ :. ~ = S = T

-6 , (

F

o 4

A = 4 x 10 iri

0 =0.50 rad

M = 20 x

the resulting values are:

3S = -4 x 20 x 0.50^^0^ = "4000 - 8880111

" 1 d(Aq) ----- — f 1x10"° ^

y( 64

= -0. 0089/micrometer

S itself is 0.25, hence

oS

dg^^ = ~^fp x 1007o /micrometer = -0.0035% per nanometer.

This means that if the sensor system is such that equality of sensor

4
illumination can be sensed to a precision of 1:30,000, axial displacements can be measured with a precision of 1 nanometer. The observed

values are typically:

individual sensor output when at equilibrium: 0.6 volt (after ampl.)

detectable change in sensor output: 0.1 millivolts (after ampl.)

detectable object displacements: 0.2 microinch, or 5 nanometers.

These values therefore support the above analysis.

In order to illuminate both sensors, the arrangement of figure 1 is

actually constructed as in figure 2, using appropriate beam splitters.

The illumination system is of the Kohler type as in figure 3. This provides pencils of parallel light landing on the specimen in all directions,

up to the limit set by the numerical aperture of the microscope objective.

Linear Range

The Simon probe normally operates in a null -mode: the probe is displaced by a measured amount in order to bring the displaced specimen back

in focus. An alternate way is to leave the Simon probe fixed, and use

the unbalanced sensor output to derive the object displacement.

For each sensor, the output vs displacement is a bell -shaped curve

as in figure 4 with a maximum when the sensor is in focus. If the sensors are connected such as to produce output difference, the two focu3

curves combine to an S-like curve. When the sensor distance "a" is

properly selected, the S -shaped "transfer curve" shows a fairly large

5
linear range of appreciable length (of the order 5000 resolution elements) .

If the sensor distance "a" is selected improperly, the range shortens

and non-linearity results, as shown in figures 5 and 6. A transfer curve

which appears on inspection to be linear such as in figure 7, can actually

still contain nonlinear ities of several percent. The graph can not show

these variations in the slope of the transfer curve, but they can be calculated from the sensor data.

Measurements of Displacements and Lengths

with the Prototype Simon Comparator

The measurement of displacement involves one Simon probe, looking

at one face of the object being displaced along the optical axis. For

determination of object length, two Simon probes are needed, on a common

optical axis and looking at opposite faces of the object.

The probes are connected such as to produce the difference between

the two probe outputs, and they have been adjusted such as to have equal

transfer curve slope at zero-output conditions. This feature insures

that small displacements of the object along the optical axis are not

read as changes in object length.

The length measurement is carried out as a comparison of the unknown

with that of a known, nearly equal, length. The comparison can span a

range twice as large as the dynamic range of a single Simon probe, or typically 100 micrometers. The prototype Simon Probe Comparator is constructed

6
such as to allow rapid comparison of gage blocks, and looks much like a

microscope with vertical optical axis (figure 8).

The gage block under test is positioned, against stops, on a horizontal stage. One Simon probe is mounted under this stage, looking at

the bottom surface of the block. Another Simon probe is positioned over

the block, connected to a vertically mounted differential micrometer

-6

slide. This slide has a range of 0.010 inch and resolution 1 x 10

inch.

Measurement of Transparent Objects

Displacement and length measurements of transparent objects, such

as gage blocks made from low -expansion glass, are carried out in the

same manner as for opaque objects. In both cases, the surface will be

polished, and exhibit specular reflection. The reflection coefficient

of the transparent object will in general be smaller, with a corresponding loss in signal strength and measurement precision.

A complication arises if the thickness of the transparent object is

comparable to or smaller than the base width of the focus curve of each

Simon probe sensor. The focus curve of each sensor will then exhibit two

peaks instead of one, corresponding to it picking up the reflection of

top and bottom surface. If these peaks are too close together, the transfer curve of the Simon probe becomes distorted, as in figure 9. Thi s can

be avoided by keeping the thickness an order of magnitude larger than the

dynamic range of the Simon probe, or typically larger than 500 micrometers

.
Measurement of Objects with Diffuse Surfaces

If the object has a diffuse surface, with structure details small

relative to the diameter of the illuminated area, the measurement of

displacement and length can be carried out in the same was as for specular surfaces, although a question will arise as to what surface plane

the Simon probe actually measures. The precision with which the diffuse

surface can be located and thereby its displacement measured, is less

than for polished metal surfaces for the following reasons:

(a) the object scatters a large part of the illumination outside

the acceptance angle of the microscope objective.

(b) The illuminated area as sensed by the two Simon probe sensors

is always located right at the object surface, while this plane displaces

at twice the rate when an object with specular surface is displaced. Consequently, the focus curve of each sensor is twice as broad for a diffusing

surface as for a specular surface. This will result in a transfer curve

of the Simon probe which has its slope reduced by one-half.

The above behavior will be somewhat modified by the fact that the surface brightness of the diffusing surface does not remain constant with displacement. The broadening effect of the focus curve is shown in figure 10,

while the reduction in the transfer curve slope and in signal levels is

sh«wn in figure 11.

Sensor Signal Levels

The internal illumination system collects energy from the source

8
-4

within a cone of 3 x 10 steradian; this low value is due to the large

optical demagnif ication. The two-way transmission, including 90% specular reflection from the specimen, is estimated at 1.4%. An additional

diffuser for improved uniformity lowers this value to 0.95%. The light

source is a 45W quartz -iodine lamp with estimated blackbody temperature

3000 K and emissivity 0.5.

When a sensor is in focus, it senses a calculated 2.7 x 10 ^ Watt.

When in balance with the other sensor, the sensed energy is 3 to 4 times

less (see figure 11) or 0.7 x 10 ^W. This estimate can be checked as

follows: observed output under balanced conditions is typically 0.6V

at the meter (figure 8), hence 0.1V at the preamplifier, the detector

-8 -7

current is then 1 x 10 A and its irradiance 1 x 10 W, using a broadband responsivity of 0.1A/W.

The irradiance levels and spectral distribution suggest as sensor

candidate a photovoltaic silicon diode, such as the HP-4207. This

particular diode has been used in the prototype Simon length comparator.

One can introduce thermal protection of the mechanical structure

by long -wavelength blocking of the incoming radiation. This changes the

broad -band responsivity, as shown below. It has not been used as yet.

Spectral Bank Heat Blocked Broad -band Responsivity nm % A/W

400 - inf. zero 0.094

400 - 1100 65 0.27

400 - 900 79 0.21

632.8(he:Ne) near 100% 0.45
Noise Sources

The main noise sources are: shot noise, Johnson noise and circuit

noise. The circuitry consists of: (1) a preamplifier for each sensor

with gain 6.5 x and input impedance 10 Mfi, (2) a signal subtraction

unit, and (3) an integrating voltmeter with integration time 0.1, 1,

and 10 seconds. A diagram of the circuitry is shown in figure 12.

With 0.1 second integration time, the estimated noise figures are

found as follows: The detector current is 14 nA, the shot noise is

~13 -6

1.5 x 10 A rms , or 1.5 x 10 V rms at the preamplifier input or

10 x 10 ^ V at the meter. The Johnson noise for 10 Mf? and 0.1 second

"6

is 1.3 x 10 V rms at the meter. With 1 second integration time, the

rms noise figures go up about 3 times while their relative values (compared to the signal) decrease by a factor 3). The latter change will

show on the voltmeter, because the displayed signal is by internal means

kept independent of the integration time.

The total system noise can be estimated by plotting repeated measurements under controlled conditions, from visual inspection one derives

"maximum" fluctuation amplitudes which can be considered 3a fluctuations.

The following variables were used:

Signal: zero, half -value, full -value

int. time: 0.1, 1, 10 seconds

Simon units used: one, two

The results are plotted in figures 13 and 14, from which one can

10
read the following 3a amplitudes

:

Conditions 3q Amplitude of total system noise

0.1 sec int. time 1 sec int. time

Top Unit

-4 -4 zero signal 0.1 x 10 V 0.04 x 10 V

half signal 0.3 0.05

full signal 0.5 0.05

Both Units

zero signal 0.1 0.06

half signal 0.7 0.6

full signal 1.5 1.2

The following tentative conclusions can be drawn:

(1) Dark noise is 1 x 10 "V rms at 0.1 sec and 0.5 x 10 V rms

at 1 second. These values compare with anticipated shot noise and

Johnson noise levels.

(2) For illuminated sensors, a large noise value exists which is

about proportional to signal level. This behavior is not clear under

low-noise conditions (one probe, 1 second int. time). This noise contribution is likely due to circuitry.

(3) Two -unit operation is about 2 to 3 times noisier than one -unit

operation.

(4) At higher noise levels, noise reduction by longer integration

11
time is less effective than at low noise levels.

Measurement Error Sources

The error sources for an operating single or double Simon probe are

of a thermal, optical, mechanical and electrical nature. It is easy to

lose an order of magnitude in accuracy if the design and the operation

of the Simon probes is not very carefully controlled.

At present, the Simon probe has demonstrated in prototype operation

a sensitivity of about 3 nanometers or 0.1 microinch. The precision has

not been fully determined; preliminary estimates are in the 10 nanometer

c lass

In the following sections, an outline is given of potential and

identified error sources.

Thermal Errors

Thermal errors result from dimensional changes in the specimen or

instrument caused by ambient heat sources, such as a lamp, the human

body, etc. The length of the measurement cavity is a function of the

structural assembly temperature, and it is a very sensitive function of

certain temperature gradients within this assembly.

The approximate magnitude of various thermal errors are:

(a) A temperature change of 0.01°C causes in a steel specimen

(gage block) of 25mm length an error of 3nm.

(b) The same temperature change, in a steel structure that keeps

the two probes 25mm apart, causes the same error 3nm. Errors a and b

12
can be made to cancel in the steady state by material selection.

(c) The influence of a temperature gradient can be seen from this

example: let the probe holding structure be equivalent to a "C -clamp"

of radius R, thickness d, linear expansion coefficient X, and radial

temperature difference AT. The measurement cavity, assumed small relative to R, will change by:

v _ 2hXR2£T

d

*

With

R = 5cm

d = 2cm

X = 12 x 10"6

AT = 0.01°C

we find

X = 90nm

which is an amount far larger than the errors a and b. The prototype

design attempted to minimize this effect.

Optical Errors

These errors are primarily alignment errors.

(1) Misalignment within the probe. The object plane, as defined

by balanced sensor output, is not coincident with the object plane n&

defined by the location of the illuminated pinhole image. Such a misalignment causes an offset error: zero sensor output for a speculer

reflecting specimen and for a diffuse specimen occur at different

13
specimen locations, as shown in figure 15. A typical value for this

offset error is 50 microns.

(2) Misalignment between two probes. When the two probes are not

colinear, the measurement of the thickness L of a lisghtly tilted speci

men develops an error. If the probe offset is D and the tilt is <y , the

error in L is approximately qD. In practice, tilt errors of 2 - 5 x 10

rad are common. An indication of this is shown in figure 16, for the

case of a gage block supported on three small and fixed steel balls.

The prototype instrument has a measured offset D = 0.15mm. When

a = 5 x 10 , the error is 7.5nm.

(3) Cosine Errors. This error occurs with a tilted specimen between two well -aligned (D = 0) Simon probes. The error is equal to

/ p -4

l/2o L. When L = 25mm and a = 5 x 10 , the cosine error is 3nm.

Transfer Curve Errors

The main features of the transfer curve are:

(1) The zero -crossing point.

(2) The overall slope.

(3) The slope linearity.

The main uses of this curve are:

(1) As a null -indicator (use zero-crossing point only).

(2) As a measurement tool for displacements that are too small to

be implemented by standard mechanical means.

The curve features can be altered by the following causes:

14
(1) Misalignment within the probe: the zero-point for reflective

and for diffusive specimens are not coincident.

(2) Changes in light output of the illuminating system. This changes

the curve slope accordingly. The slopes are typically 1000 Volt per inch

or 4 x 10 "V/nm, while the total span of the linear part of the curve is

typically 2 mils = 50 microns or 2 Volts. If the lamp voltage changes

-4 -3

by a factor 10 , the output changes by 10 and the sensor signal changes

by +lmV at the ends of the linear range. Thus, an error can be introduced

to an amount +25nm maximum. The power supply for the lamp has therefore

to be well -isolated from line and load fluctuations. Likewise, the optical properties (reflection, transmission) of all optical surfaces should

be sufficiently stable during the measurement.

Electrical Factors

The prototype instrument output exhibits short-term fluctuations

(5 - 20nm) and long-term drift (3 - 15nm/minute) . The fluctuations are

considerably larger than would be expected from shot noise and Johnson

noise. Their source should be sought in the sensor electronics and in

the illumination system; this process is in progress at the present time.

There are several ways open to improve the noise figure. One way

is to improve the electronics (using lower-noise operational amplifiers,

etc.). Another way is to use photomultipliers for the sensors instead

of photodiodes. When photomultipliers are used, the shot noise levels

will go up somewhat, because the quantum efficiency is 3 to 5 times

15
lower. However, the signal levels go up several orders of magnitude,

and the relative influence of circuit noise (the main noise factor at

present) becomes small. Both approaches are investigated.

Outlook

The process of comparing lengths using Simon probes is essentially

a determination of radiometric balance between two sensors. The obtained

precision of this balancing process is not very large at present, as

can be seen from this example:

Sensor output: 0.5 Volt

Sensor pair sensitivity: 2 Volts/mil, or 0.08mV/nm

Measurement precision: 0.8mV = lOnm.

The precision of the radiometric balance determination is 0.8mV in

0. 5.olt, or 1 in 600, while the sensitivity is 1 in 6000.

This result does not represent the state-of-the-art; half -shadow

techniques using polarization angles can do at least 10 times better;

therefore a precision of lnm in Simon probe measurements should be a

realizable goal.

References

1. J. Simon, Applied Optics 10, 2337 (1970).

2. J. A. Simpson, Rev. Sci. Instr. 42_, 1378 (1971).

16
SENSOR

SENSOR 2

// // // // // >*

OBJECT

DISPLACED OBJECT

SIMON PROBE RADIOMETRY

FIGURE 1

17
r

S8 C3

I <rjr> l

i

o, J— ~!

4>L

!

L

"i i i V

rrrrrm

i

SIMON PROBE LAYOUT

FIGURE 2

18

I

SENSOR OUTPUT vs. OBJECT DISPLACEMENT

("TRANSFER CURVE")

FIGURE 4

20
LINEAR RANGE vs. SENSOR SPACING

FIGURE 5

21
IMPROVING PROBE LINEARITY BY

SENSOR SPACING ADJUSTMENT

FIGURE 6

22
TRANSFER CURVE AND LOCAL SLOPE

FIGURE 7

23
— Top

Light Source

Top

Simon Unit

Gage Block

Being Measured — Bottom

Simon Unit

(Bottom Light

Source Behind

Instrument)

PROTOTYPE SIMON COMPARATOR

FIGURE 8

24
RESPONSE TO A TRANSPARENT OBJECT

(COVE'R- SLIDE

5

FIGURE 9

25
V

£ 0.3

QL

O 0.2

o

co o.l

z

</>

0

^q. SENSOR B

Dlrr Uot bUKrALL — (MgO)

^^SENSOR A

1

S

1 1 1 1 DU f 0 IUU I<lD /tin

SPECIMEN DISPLACEMENT

V

1.6

Q- 1.2

O

K 0.8

O

uj 0.4

CO

0

SENSOR B

SPECULAR SURFACE

(Polished Steel)

SENSOR A

0 25 50 75 100 125 /tm

SPECIMEN DISPLACEMENT

RESPONSE TO SPECULAR AND DIFFUSE

REFLECTING SURFACES.

FIGURE 10

26
CL

hZ>

O

QC

O

CO

Z

LU

CO

-5 L

^25

«—«—° SPECULAR SURFACE

(Polished Steel) - —- DIFFUSE SURFACE

(MgO)

SENSOR RESPONSE TO SPECULAR

AND DIFFUSE REFLECTING SURFACES

FIGURE 11

27

0,\ MV (2 Owdfyw"]

1 i : !'

. 1 ;1 "

i

:

•J-,-! .-4-

/«? j^^as.

j

FIG. 13 PROBE NOISE VS INTEGRATION TIME

PIN HOLE IMAGE

SIMON PROBE

(MICROSCOPE OBJECTIVE)

^-2a -—J

i

'

P, P2 «

P, PLANE OF FIELD STOP IMAGE

P2

* PLANE, SENSED BY BALANCED SENSOR PAIR

THE SENSOR PAIR WILL BE IN BALANCE, WHEN

A DIFFUSE SURFACE IS LOCATED AT PLANE P2 , OR

A SPECULAR SURFACE LOCATED MIDWAY BETWEEN

P, AND P 2

.

PROBE OFFSET ERROR

FIGURE 15

31
BALLS 1,2,3 ARE ATTACHED TO PART A

BALLS 4,5,6 ARE ATTACHED TO PART B

REPEATED POSITIONING OF THE GAGE BLOCK

AGAINST ITS STOPS (BALL I 6) PRODUCES

LIGHT DIRECTION VARIATIONS «x AND ct

x (mm) 21.0 21.0 21.0 21.2 20.4 21.0 21.0 20.9

y (mm) 8.8 8.8 8.8 8.7 8.7 8.7 8.8 8.7

ctx < I X IO" 4 rad, a

y

Six I0" fl rad

SPECIMEN ROTATIONS DUE TO REPOSITIONING

FIGURE 16

32
FORM NBS-114A (1-71) u.s. dept. of comm. 1 . PUBLIC ATION OR RE PORT NO. 2. Gov't Accession

BIBLIOGRAPHIC DATA mgIR 73.^4 *H fc fc 1 fasU4k:^,..*.„., «.^...,_

3 • R.t c i pi cnt s Acccssi on No*

*»• ill i -p. AIn IJ oU oil! Lx,

A Non -Con tac tine Lencth. Comoaratoir with 10 Nanometer Precision

J • r UUllLd U 1 Ul J L/a IC

6. Performing Organization Code

7. AUTHOR(S)

A. W. Hartman, F. W. Rosberry and J. Arol Simpson

S. Performing Organization

NBSIR 73-104

9. PERFORMING ORGANIZATION NAME AND ADDRESS

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

10. Project/Task/Work Unit No.

11. Contract/Grant No.

12. Sponsoring Organization Name and Address

Same

13. Type of Report & Period

Covere d

14. Sponsoring Agency Code

15. SUPPLEMENTARY NOTES

16. ABSTRACT (A 200-word or less factual summary of most significant information. If document includes a significant

bibliography or literature survey, mention it here.) A non -contacting length comparator utilizing two specially designed photo-electric

microscopes has been constructed. Performance tests of this comparator, using

lapped and polished steel surfaces demonstrate a resolution of ~ 1 nanometer, a precision of ~ 10 nanometers, and a linear range in excess of 50 micrometers.

17. KEY WORDS (Alphabetical order, separated by semicolons)

Dimensional metrology; displacement measurement; microscope; noncontact sensing;

optical surface probe; surface detection.

18. AVAILABILITY STATEMENT

I I UNLIMITED.

tX~l FOR OFFICIAL DISTRIBUTION. DO NOT RELEASE

TO NTIS.

19. SECURITY CLASS

(THIS REPORT)

UNCL ASSIFIED

20. SECURITY CLASS

(THIS PAGE)

UNCLASSIFIED

21. NO. OF PAGES

22. Price

USCOMM-DC 86244- P71