NBSIR 73-106 (/?)

A System for Computerized Surface

Roughness Measurement

Dennis A. Swyt

Institute for Basic Standards

National Bureau of Standards

Washington. D. C. 20234

February 20. 1973

Final Report

U. S. DEPARTMENT OF COMMERCE

NATIONAL BUREAU OF STANDARDS

NBSIR 73-106

A SYSTEM FOR COMPUTERIZED SURFACE

ROUGHNESS MEASUREMENT

Dennis A. Swyt

Institute for Basic Standards

National Bureau of Standards

Washington, D. C. 20234

February 20, 1973

Final Report

U. S. DEPARTMENT OF COMMERCE, Frederick B. Dent, Secretary

NATIONAL BUREAU OF STANDARDS, Richard w. Roberts. Director

CONTENTS

Page

Introduction 1

Data Acquisition 2

Data Analysis of Step Heights 2

Data Analysis of Surface Roughnesses . . , 3

Calibration of Step Heights and AA Values 3

Program Operations 4

The AA Calculation and the ANSI Standard f 5

Noise Effect in AA Measurements 9

Partial Estimate of Accuracy 10

Preliminary Results , 12

Appendix A. The Linear Least Squares Curve Fit 18

Appendix B. Step Location 20

Appendix C. The Mean Distance Between Two Non-Parallel Lines ... 22

Appendix D. Slope Scale Factor . , 25

Appendix E. Filter Characteristics 27

Appendix F. Program Operation 28

Appendix G. Operator's Instructions: Interdata 3/Talysurf 4 System 34

Appendix H. Checklist for Proper Electrical Operation , 38

ILLUSTRATIONS

Page

Figure 1. Function Diagram of Talysur f/lnterdata System 2a

Figure 2. Step Height Calculation 2b

Figure 3. Teletype Output of Step/Surface Roughness Calibration . 4a

Figure 4. Noise Effect Measurement 9a

Figure 5. Noise Effects in AA Readings 10a

Figure 6. Uncertainties in AA Readings 12a

Figure 7. Chart Paper/Memory Location Map 20a

Figure 8. Proper Location of Step Relative to Event Marker . . . 20b

Figure 9. Selection of A^ and A^ Locations 20c

Figure 10. Proper and Improper Selection of A^ and 21a

Figure 11. Vector Analysis of Step 24a

Figure 12. Filter -Amplifier Gain -Bandpass Characteristics .... 27a

Figure 13. Observed Amplifier -Filter Phase Delay 27b

Figure 14. Internal Computer Lead Connections 34a

Figure 15. Interface AC Power Connection . 34b

Figure 16. System Lead Connections 34c

TABLES

Page

Table 1. Time Study of Measurement Procedure: Step 6

Time Study of Measurement Procedure: Roughness .... 7

Table 2. Contributions to Uncertainties in AA Readings 13

Table 3. Uncertainties in AA readings for Different Magnifications . 14

Table 4. Comparison of Results for NBS Master Roughness Block . 15

Table 5. Preliminary Measurements on NBS-1 Caliblock 16

Table 6. Summary of Preliminary Results 17

Table 7. Master Program Outline 29

Table 8. Numerical Values in Sample Program Operation 31

Table 9. Characteristic Parameters of Entire System 32

A SYSTEM FOR COMPUTERIZED SURFACE ROUGHNESS MEASUREMENT

Dennis A. Swyt

Introduction

Prior to the development of the system to be described, the

available basis for calibrations by NBS of roughness specimens for

industrial consumers was by means of comparisons with a roughness

master. The values assigned to the master involved single displacement calibrations of stylus instruments and hand calculations from

planimeter measurements of surface profiles. The overall method

has several limitations. Individual calibrations are referred to

the historical values of roughness assigned to a unique artifact

which is subject to loss , damage and deterioration with ordinary

use. AA values, indicated on an integrating meter, are only accurate

to 37o of full scale, cannot be displayed digitally, and must be subjectively interpolated between scale divisions. To eliminate these

difficulties, a new system has been developed. At present, an Interdata 3 Minicomputer has been fully interfaced with a Talysurf 4

Stylus instrument. The completely operational system offers:

(1) instrument calibration at each use by means of interferometrically measured gage block steps;

(2) considerably more accurate AA values, computer -calculated

for arbitrary specimens;

(3) computer -calculated thin film thicknesses;

(4) precise, digital print-out of measurement results in permanent record format;

(5) access to punched tape surface profile data which may be

analyzed by a larger, faster computer to yield further information,

e.g. peak height and roughness wavelength distributions.

Scheduled to be completed before the end o f FY 1973 are:

(1) a complete determination of the dynamic operating characteristics of the entire system;

(2) the development of a range of interferometrically measured

thin-film and gage-block steps;

(3) a changeover of surface roughness calibration services from

those based on a roughness artifact to the new system;

(4) the introduction of thin-film thicknesses measurement services based in part on the computerized stylus instrument system.

1
Data Acquisition*

The means by which topographical profiles are converted to surface

roughness data is represented by the functional schematic in figure 1. When the stylus is traversed across a surface, the profile is indicated

on the strip chart recorder; the signal driving the recorder, amplified

and filtered, appears at the analog -to -digital converter (A/D).

At a particular point in the stroke, the stylus arm activates a relay, which in turn generates two pulses. The first pulse, one second long, appears at the common input of the recorder and interface

amplifier. (The source of the event pulse is in the information channel only for the duration of the pulse). Coincident with the leading

edge of the event pulse is a fifty -microsecond interrupt pulse to the

A/D converter. On receipt of the interrupt at the A/D, a programmed

one-second delay is executed, and the analog signal at the filter output is converted to binary data points and stored sequentially in computer memory. (Thus the event mark, recorded on the strip chart, does

not appear in the digital data). The results of the computer analysis

of the stored data are output to the Teletype, Model 33.

Data Analysis of Step Heights

In order to efficiently handle the discontinuity in the trace

which comprises the step height and to eliminate restrictions on

the alignment of the step artifact, a mathematical model of the step

data in the computer memory has been devised. Figure 2a represents

a general step profile in which the traces on opposite sides of the

discontinuity are wavy and parallel neither to each other nor to the

sides of the strip chart.

Linear least -squares curves are fitted to the segments designated

by LI and L2 in figure 2b (appendix A) ; the segments are located at

"Certain commercial equipment, instruments, or materials are identified in this paper in order to adequately specify the experimental

procedure. In no case does such identification imply recommendation

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

that the material or equipment identified is necessarily the best

available for the purpose.

2
2a
FIGURE 2 . STEP HEIGHT CALCULATION

a) Step Profile Input

b) Linear Least Squares Line Segments

c) Perpendicular Distances at X between the Two Lines

d) Mean Distance of Step Height

2b
the operator's discretion relative to the event mark (appendix B), are

of equal lengths and constitute one-half of the total trace. From the

slopes and intercepts of the two computed lines, Si and S2 in figure 2c,

are calculated the distances Hi and H2 (appendices C and D) ; the two

heights are the perpendicular distances from the points on each line,

having the coordinate xm, to the opposite lines. The distance HM in

figure 2d is the arithmetic mean of Hi and H2.

Data Analysis of Surface Roughnesses

The AA roughness for a surface profile is computed from the data

in memory in a manner analogous to the operation of an integrating

meter. Since the profile signal has wavelength cut-off restrictions

imposed by analog filtering (appendix E) , no digital filtering or

signal conditioning is involved. The value corresponding to the center line of the profile is the arithmetic average of all points in the

record. The AA value is the arithmetic average of the magnitudes of

the deviations of each point from the mean.

Calibration of Step Heights and AA Values

When the binary HM value of the calibration step profile has been

computed and the decimal Ho value of the inter ferometr ically measured

calibration step entered at the Teletype, a conversion constant, KCAL,

is computed:

KCAL = Ho (decimal)/HM (binary).

The calibrated values of unknown steps and surface roughnesses are then

of the form:

3
HM (decimal) = HM (binary) x KCAL

and

AA (decimal) = AA (binary) x KCAL.

Program Operations

An example of a calibration, wherein an unknown step and roughness are measured, may be illustrative. A sample Teletype output is

given in figure 3. Further details appear in appendix F.

After an appropriate magnification has been selected, the corresponding gage block step is aligned on the Talysurf and program

execution begun. At the proper point in the program, the operator is

informed at the teletype to begin the stylus stroke in order to enter

the calibration step profile. In this case, a 50 microinch step at

20,000 mangi f ication produces a one-inch displacement on the chart

and a one -volt output to the amplifier. The signal is amplified by

10, filtered (appendix E) , converted to 512 twelve-bit data points

over a 25 second record length and stored in memory. The operator

is then instructed to enter HO, the measured value of the gage block

step, at the teletype; this four decimal -digit number is converted to

binary and stored. The operator now enters the information at the

teletype which locates the step discontinuity in the stored data;

the information is derived from the chart trace and the step locator

chart (appendix B).

The step height is computed, converted to decimal and printed;

the printed calibration step height HM should conform within tolerances

4
OEOOG

STEP /SURFACE ROUGHNESS C AL I BR AT I OM

ENTEh DATA/ IN ENTER HO 901 A EN I" ER UNITS TU ENTER Al 1 1 HA ENTER AS 1 ?. \ A

HI H2 HO UNITS

00009014 00009014 00009014 TU MORE? Y H OR R? H

ENTER DATA/ IN ENTER HO ENTER UNITS TU ENTER Al U8A ENTER A2 1214

HI H2 HO UNITS

00008993 00008993 00008993 TU MORE? Y H OR R? H

ENTER DATA/ IN ENTER HO ENTER UNITS TU ENTER Al 1 1 8A ENTER A2 1214

HI H2 HO UNITS

00008998 00008998 00008998 TU MORE? Y H OR R? H

ENTER DATA/ IN ENTER HO ENTER UNITS TU ENTER Al 1 1 8A ENTER A2 1214

HI H2 HO UNITS

00009015 00009015 00009015 TU MORE? Y H OR R? H

ENTER DATA/ IN ENTER HO ENTER UNITS TU ENTER Al 1 1 8A ENTER A2 1214

HI H2 HO UNITS

00009009 00009009 00009009 TU MORE? Y H OR R? H

ENTER DATA/ IN ENTER HO ENTER UNITS TU ENTER Al 1 1 8A ENTER A2 1214

HI H2 HO UNITS

00009013 00009013 00009013 TU MORE? Y H OR R? R ENTER DATA/ IN

AA UNITS

00001214 TU

00001217

00001213

00001205

0000121

1

00001202

MORE? Y H OR R? R ENTER DATA/ IN

AA UNITS

00001204 TU

00001208

00001210

00001213

00001206

00001208

MORE? Y H OR R? R ENTER DATA/ IN

AA UNITS

00001202 TU

00001205

00001 199

00001201

00001204

00001209

MORE? Y H OR R? R ENTER DATA/ IN

AA UNITS

00001212 TU

00001201

00001210

00001208

00001207

00001204

MORE? N FINI

FIGURE 3

4a

the HO previously entered.

The operator now aligns the specimen to be measured on the stylus

instrument. On being queried at the Teletype, the operator indicates

the type of artifact. If it is a step, an H is entered and the procedure for entering a step profile repeated. If a roughness is to be

measured, the proper filter cut-off and stroke speeds are selected, an

R entered at the teletype and the stroke begun. The computer calculates either a step height or roughness AA, prints the result, and

asks if more measurements are to be made from the same calibration.

If more are to be made, a Y is entered at the teletype and the measurement of the unknown as described in this paragraph repeated. If

no more measurements or those at a different magnification are to be

made, an N is entered and the program is terminated.

A rough timetable for the program operation is given in table 1.

The AA Calculation and the ANSI Standard

The AA roughness value of a surface profile is defined as the

arithmetic average deviation from the center line; the center line

in turn is defined by the ANSI B46.1 standard as "the line parallel

to the general direction of the profile within the limits of the

roughness width cut-off, such that the sums of the areas contained

between it and those parts which lie on either side of it are equal".

The specific details involved in the implementation of these

definitions in the operation of analog or digital devices are not

delineated in the standard. While band-pass characteristics in

5
Time Study of Measurement Procedure

Step

Operator Function; Machine Function:

Align Calibration Artifact; Begin

Program (5 min.)

Select Al and A2 from Chart &

Scale, enter (1 min.)

Align Unknown Step

(5 mi n .

Select Al & A2 from Chart &

Scale, enter (1 mine)

—— Input Step Data (0.5 min.)

Compute Step Height

(0.25) min.)

Input Step Data

(0.5 min.)

Compute Unknown; Exit

(0.25 min.)

Operator Function Time

(12 min.)

Total Time

13.5 min.

Machine Function Time

(1.5 min.)

Table 1

6
Time Study of Measurement Procedure: Roughness

Operator Function Machine Function

Align Calibration Artifact; Begin

Program (5 min.)

Select Al and A2 from Chart &

Scale; Enter (1 min.)

Align Unknown Roughness

(5 min.)

Operator Function Time

0.1 min J

Input Step Data

(0.5 min.)

Compute Step Height

(0.25 min)

Input Roughness Data

(0.05 min.)

Compute AA; Exit (0.25 min.)

Machine Function Time

( 1 min. )

Total Time

12 min.

7
terms of half -power points and roll -off rates are specified, the exact

nature of center-line, to which a profile is instantaneously referenced, is not clearly specified (again see appendix E for filter characteristics) .

In the operation of an integrating -meter stylus instrument, the

filtered signal represents the surface profile with wavelength cut-off

restrictions imposed. The continuous analog computations of the center

line and average deviation from the center line are made by integrating

circuitry. Specifically, the stylus instrument stroke is begun and

the resulting signal integrated to establish a center-line; at a particular point in the stroke, the instantaneous signal is compared to the

established center line and the magnitude of the difference integrated

for the remaining length of the stroke. Mathematically, the operation

corresponds to the integral:

This equation reflects the necessity in an analog device of comparing

the instantaneous signal to a center line which does not bracket the

signal, but rather represents a segment of the profile of which the

signal is the trailing edge.

In the operation of the present digital system, the filtered

signal is digitized and stored in the computer memory; the conversion rate (1.64 kHZ) is sufficiently high to reproduce the analog

(f(t)

8
information in the filter bandpass (f = 300 HZ) with no loss of fiI ,c delity. The record length of the data corresponds to five wavelength

cut-off widths. Since wavelength cut-off restrictions have been

imposed on the signal by filtering, the center line is computed over

the record length. Mathematically, the operation corresponds to the

integral

Although the mathematical descriptions of the analog and digital

computations differ, it is believed that the digital computations are

in accord with the present ANSI B46.1 surface texture standard, in

terms of the fundamental definitions of AA and the center line. Since

the effective center line is computed as the mean over the record

length and the record width is five times the cut-off width, the effect

of a fractional roughness wavelength in the record length is greatly

diminished

It is known that measurements of ultrafine finishes are limited

in accuracy by the inherent noise level of the stylus instrument itself. The specific effect of this noise has been established by a

study of the computer measured AA values as a function of the signalto-noise ratio. The experimental set-up is shown in figure 4. An

operational amplifier was employed as an inverting adder without

(f(t)

Noise Effect in AA Measurements

9

TRUE AA i/i )

.25 .50 .75

T

<

<

+

<

<

.75 •<

<

Q

LU

50 >

tr

LU

if)

CD

o

.25

/

/ x ULTRAFINE SURFACE

o ELECTRONIC (ALSO, ELECTRONIC

8 MECHANICAL) NOISE

0*-

I 2

AA(S) / AA(N)

FIGURE 5

10a
weighting. The apparatus allowed the stylus instrument output to be

measured separately and combined with a measured signal. Measurements were made of the inherent electronic noise in the system (with

the stylus stationary), the mechanical and electronic noise (stylus

resting on a plane which traversed with the stylus), and the stylus

output while traversing an ultrafine surface (a float-formed glass

substrate). The results for each case, normalized to the zero signal input level, are indicated in figure 5. The smooth curve represents the equation:

2 2 1/2. Signal Output = [(Signal Input) + (Noise) ]

The actual "noise" levels associated with the three cases above

indicated: (1) an electronic noise of .13m.", (2) a mechanical and

electronic noise of .16m," and (3) a probable minimum AA reading of

. 25u.". It has not been determined what portion of the minimum AA

reading is due to the highly polished surface. Therefore, it is

assumed that the full minimum reading is due to the instrument; thus,

the total inherent noise is taken to be .25|jl" and its effect on AA

readings is also shown in figure 5.

Partial Estimate of Accuracy

The elements which contribute to the overall accuracy of the

roughness measurements are manifold; they include the accuracy of

the inter ferometry measurement of the calibration step, the transfer

characteristics of the stylus instrument and interface hardware, the

computational precision of the software, the suitability of the

10
mathematical models, and the noise levels in the system.

In table 2, the contributions of the operating characteristics

of the interface hardware (amplifier, filter and A/D converter) are

itemized; the total error in the signal due to the interface is estimated to be .15%. The uncertainty in the computation of the AA values

due to the intermediate calculations of the calibration step height,

calibration constant and AA values, is considered to be .0757o . The

sum of the effects of the interface and computation is, therefore,

about .25%, as indicated by a(comp) in table 2.

The uncertainty in the inter ferometric measurements of the gage

block steps is + 1 microinch. The corresponding percentage uncertainties, a (cal), range from 57o to .025% for the different magnifications involved.

Finally, a constant noise level of about .25 microinches contributes uncertainties at different magnifications ranging from 170

to 0%.

The effect on the observed AA values of incremental changes in

the calibration, computation and noise levels appears as:

which leads to the first order uncertainty in the AA values given by:

AA(obs) = (1 + A (cal))(l + A (comp))

AAA = AA [|a (cal) I + | A (comp) | + | A (N) ]

where

AN = (1 +

The uncertainty of the AA measurements (exclusive of stylus

11
preamplifier response) as indicated in table 3 is shown in the graph

of figure 6. The curve indicates accuracies for the standard 20 and

120 microinch patches of + .2 and + .4 microinches, respectively.

These partial estimates of accuracy correspond to uncertainties of

+ 1.2 and + 12.0 for integrating meter readings of the stylus instrument and +2.04 and + 0.93 for the round -robin determinations of the

NBS master artifact; a comparison summary of these results appears

in table 4.

Preliminary Results

Trial measurements of the round -robin calibrated artifact, designated NBS-1, have been made on the nominal 20 and 125 microinch patches.

The roughnesses were measured at least four times at each of five different locations on each of the two masked regions of the patches. The

results, including 3a values , are given in table 5. A general summary,

including the estimate of accuracies of individual readings based on

figure 6 and including the results of the round-robin calibration, appear

in table 6.

Some interesting effects are indicated in tables 5 and 6. First,

the reproducibility of readings at individual scan locations is not

significantly different than the reproducibility of readings for the

masked regions of the patch; i.e.,

3a (scan) ^ 3a (patch)

This result may indicate an important contribution of stylus response

to overall accuracy. Second, the results of the computer AA values and

12
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Table 5. Preliminary measurements on NBS-1 Caliblock,

Nominal 20 microinch patch

Scan Location AA(y")* 3a(y")

1 20,74 0.24

2 20.69 0 21

3 20.87 0.24

4 20.77 0.10

5 20.90 0.15

*Average of four readings with an estimated accuracy in each reading

of 0.2y" based on Figure 6.

Nominal 125 microinch patch

Scan Location AA(u") 3o~(y")

1 121.0 1.4

2 121.1 1.2

3 121.3 1.5

4 121 6 1.2

5 121.6 1.2

Average of five readings with an estimated accuracy in each reading

of 0.4 u" based on Figure 6.

16
the round -robin values agree almost within the one a of either measurement ; i.e.,

(AA + a) computer (AA + a) round -robin.

Further studies into the overall precision and accuracies of the computer calculated surface roughnesses are to be made and may reveal

the bases for these results.

Table 6. Summary of Preliminary Results

Nominal Calibration Calibration Average Round

AA Step Check AA 3a Robin 3ct

(m-"> (h") (h") (p.") (n

M

) (u") (^")

125 901.4+1.0 901.5 121.3 1.5 120.76 2.04

20 75.0+1.0 74.4 20.79 0.3 20.34 0.93

17
Appendix A

The Linear Least Squares Curve Fit

For the general case of a linear least squares (LSQ) curve fit

of the form:

y = a x + b,

where y is the dependent variable, x the independent, a the slope, and

b the intercept, the following formulae apply:

(1 > b = !

s

*i -t**i

N S x y - (Ex.) (E y ) (2) a = § 2~

N E xf - (E x.)

i i

where E indicates the summation over the n index from 1 to N.

For the special case of equally spaced x increments, x^ may be

replaced by an integer n corresponding to the value of i and the sum2 mations over x. and x. evaluated as standard series.

x 1

(3) S x. = S n = | (N + 1)

(4) E x

2 = S n

2 = | (N + 1) (2 N + 1)

Substitution of equations (3) and (4) into equations (1) and (2),

with some simplification, leads to:

(5) b = I S y. - |(N + 1)

18
12 S n y - 6 (N + 1) S y

(6) 3 = N(N + 1)(N -1)

3 Where N is large, the denominator may be approximated by N . (In the

case of 128 data points, the subsequent error in the calculated slope

is about .0057o .) Thus,

(7) a = ±r- [12 £ n y - 6 (N + 1) S y ].

N

19
Appendix B

Step Location

At the interrupt signal generated at the appropriate position in

the stylus stroke, a one second delay is executed by the computer and

data is read into memory for twenty-five seconds at the rate of approximately twenty points per second. Since the event marker is in the

information channel, the delay is necessary to avoid reading the event

marker as data. The signal which is recorded in those twenty-five

seconds is thus entered as 512 data points in memory locations 1000^

to 1400^. The memory locations of selected points and the corresponding positions on the strip chart (measured in mm relative to the trailing edge of the event marker as in figure 7) are indicated in figure 8.

Figure 8a represents a properly positioned step, approximately

centered within the 40 mm - 110 mm region. A representation of the

data recorded im memory is given in figure 8b.

The length of the segment on the chart, corresponding to the 128

points over which a leas t -squares straight line is computed, is 37.5 mm.

The address A^ (input during program execution) must correspond to a

location in the region 40 mm to the step edge; similarly, A2 must

correspond to a location in the region between the step edge and the

110 mm position (see figure 9a). The line segments corresponding to

the A^ and selected are indicated in figure 9b. Choices for A^ and

A? are limited to pairs of points situated equally distant to the left

20
MM ADDRESS MM ADDRESS

0040 1116 0075 1206

0041 11 IE 0076 120E

0042 1124 0077 1214

0043 112A 0078 121A

0044 1132 0079 1222

0045 1138 0080 1228

0046 1140 0081 1230

0047 1146 0082 1236

0048 114E 0083 123E

0049 1154 0084 1244

0050 115A 0085 124A

0051 1162 0086 1252

0052 1168 0087 1258

0053 1170 0088 1260

0054 1176 0089 1266

0055 117E 0090 126E

0056 1184 0091 1274

0057 118A 0092 12 7A

0058 1192 0093 1282

0059 1198 0094 1288

0060 11A0 0095 1290

0061 11A6 0096 1296

0062 11AE 0097 129E

0063 11B4 0098 12A4

0064 11BA 0099 12AA

0065 11C2 0100 12B2

0066 11C8 0101 12B8

0067 11D0 0102 12C0

0068 11D6 0103 12C6

0069 11DE 0104 12CE

0070 11E4 0105 12D4

0071 11EA 0106 12DA

0072 11F2 0107 12E2

0073 11F8 0108 12E8

0074 1200 0109 12F0

FIGURE 7

20a
FIGURE 8 . PROPER LOCATION OF STEP RELATIVE TO EVENT MARKER

20b
FIGURE 9 . SELECTION OF A

1 AND A

2

LOCATIONS

20c

and right of the step location, S, such that:

S (mm) - (mm) = (mm) - S (mm)

.

A^ and A^ determine individually over which segment lines are to be

computed; the mean of A^ and A^ determines the location at which a

step is to be computed from the two lines. The effect on the calculation of the step height of proper (figure 10a) and improper (figure 10b) selection of A, and A0 may be significant.

21
21a
Appendix C

The Mean Distance Between Two Non-Parallel Lines

The following vector analysis is employed to define the "mean

perpendicular distance" between two non -parallel lines at some x

coordinate xm. Line L^ is defined by its slope, a^, and the point

with x and y coordinates (0,b^); line is similarly defined by a^

and point A^ at (x , b^) as in figure 11. The general approach is to

define vectors, and , coincident with lines L^ and L^ , respectively, and to find the perpendicular distances: h^ from the point on

V, , with coordinate x , to V„; and h„ from the point on V , with

i ml Z 2 coordinate xmi, to V.. The mean distance, h , is then defined as the

m

arithmetic average of h^ and h^.

The vector is defined as the difference between the vector

to the general point and that to A^

(1) V

i = P

!

" A

i

(2) = [i (x.) + j (a, X1 + b.)] - [i (0) + j GO]

(3) = (i + a

1 j) x^

Similarly

(4) V

2 = P

2

" A

2

22

(5) V

2 = (i + a

2 j) x

2

.

The general vector between points T?^ and P^ is:

(6) H = P

x

- P

2

(7) = i (x

l

- x

2

) + j (a

1 xL - a

2 x2

+ b

x

- b

2

)

To find the perpendicular distance from point P^ to the line V

2

,

the product H • is evaluated, set equal to zero, and the coordinate

x

2

determined as a function of x^.

Thus ,

(8) H • V1 = x

l (x^ - x

2

) + a

][ x

1 (a^ " + bx

" = 0

and

2 f x (1 + a ) + a (b - b')

(9) x0 =

(1 + a

x a

2

)

The magnitude of the perpendicular distance, , is

2 / 2 1 1

2

(10) H

x = [(X]L - x

2

r + (a^ - a

2 x2

+ \> x

- b^] *

,

Substitution of equation 9 into equation 10 yields:

(11) H

x = [(3l

- a

2

) X;l + (b

1

- b'2

)](l + a

x

2

) 1/2

(l + a^)"1

23
To find the perpendicular distance, H,, > from point to the line

V-^, the product H « V£ is evaluated similarly, with the result.

(12) H

2 = [(a

x

- a

2

)x

2

+ (t^ - b

2

>](l + a

2

2

) 1/2

(l + a^) _1

Since b

' = b„ - a.x and x. and x_ are chosen to be x , the distances

I I I Y I m

h^ and h

2 as indicated in figure 11 are given by:

(13) h

x = [(a

x - a

2 )x

m

+ (b

x - b

2

+ a

2

x)](l + a^) 1 (1 + a^)

and

(14) h

2 = [(ax

- a

2

)x

m

+ (b

x

- b

2

+ a

2

x)](l + a

2 V/2

(l + a^)"1.

The mean perpendicular distance is then:

(15) h = 1/2 (h. + h_). m 1 z

24
FIGURE 11

24a

Appendix D

Slope Scale Factor

Since the linear least squares curve fit utilizes single precision hexadecimal numbers as y coordinates and hexadecimal memory

addresses as x coordinates, it is necessary to scale this coordinate

system to that of the chart recorder.

The following transformation applies:

(1) y (chart) = k y(hex)

(2) x (chart) = x(hex)

The slopes are then related by:

(3) a(chart) = dy <chart > = k dyjhexl U; a^cftart;

dx(chart) * dx(hex)

(4) a (chart) = k a (hex).

Substitution of equations 1, 2 and 4 into equation 11 of appendix C

produces

(5) H

x = [(kax

- ka

2

)x

1 + (kbl

- kb

2 + ka^) ] x

[1 + (kai ) 2

] 1/2

[l + (ka

1 )(ka

2

)]' 1

= k [(a

x

- a

2

) Xl + (b

x

- b

2

+ alX)][l + (kai ) 2

]

1/2 [l + k2 a

x

Since similar equations apply to and H

2

, the relationship between

25
the two is independent of the leading multiplier and it may be omitted

to give heights of the form:

(6) H

L = [(a

1

- a

2 )x

1 + (bx

- b

2

+ a lX)][l + kai ) 2

][l + (ka^ (ka

2

) ]~ 1

Equation 3 may be evaluated using the full scale parameters of

the chart and hexadecimal coordinate systems:

(5) 25.4 mm/37.5 mm = k (07f

f

16/°1°°16)

which yields in hexadecimal and decimal values:

(6) k

1Q = 0.08466

(7) k

16 = 0.15ACD.

26
Appendix E

Filter Characteristics

The gain -bandpass characteristics of the filter circuits have

been designed to conform with ANSI Standards when the device is used

in conjunction with a Talysurf 4. The filter 3 db down points are

related to the conventional wavelength cut-offs through the stylus

speed

f(Hz) = .06 in/sec -r \ (in).

c The filters are active Butterworths with selectable high-pass cut-off

frequencies as indicated by figure 12. Roughness measurements are

made with one of three high-pass filters in series with the single

low-pass filter. Step height measurements are made with only the

low-pass filter in the circuit.

The conformity of the filters to specified operation is indicated

by the band pass curves in figure 12 and the observed phase delay in

the low pass filter in figure 13.

27
2 7a

Appendix F

Program Operation

A flow-chart indicating the points in the program operation at

which information is input at the A/D converter and Teletype and at

which results are output at the eletype is shown in table 7. In

table 8 are shown numerical values of parameters involved in a sample

program operation in which a fifty microinch calibration step is used

in the measurement of an unknown step height and an unknown roughness

specimen. A compilation of characteristic parameters of the entire

system is given in table 9.

28
TABLE 7

MASTER PUOCKAM LEVEL 0

Program Input Output at TTY

Level 0 ADC TTY Format Data

Clear Flag

Print

Print

•Set Step Parameter

Wait for Interrupt

Read Step Step Data

Reset AA Parameters

Print

Print

Read 4 (Ho) Ho

Pr int

Read Units Units

Print

Read 4 (Al) Al

Print

Read 4 (A2) A2

Print

Calculate Step

• Y - Test Flag - N

Compute KCAL 1 •Convert/Print-Steps

Print

Branch Uncond

.

Interrogate

• H - Branch-R 1 H;R

Set Flag

Branch Uncond.

Print

Wait

Read AA AA Data

Print

Heading

Fnter Data

In

Enter Ho

Enter Al

Enter A2

HI. . . .Units

Steps

Units

H or R?

Enter Data

In

29
Table 7 cont.

Program Input Output at TTY

Level 0 ADC TTY Format Data

Print AA Units

Compute/Print AA AA

Print Units

-Interrogate More?

-Y - Branch - N Y;N

Print ' Exit

Table 7

30
X > > 4 • O o o c > ' 1 o • < o • I 1 a o c In Th m 1 o 1—

m o —

1 I o

C- o CM cm CM o O 1 1 o u* •H o o O 1 1 1 o

0) • • • • X rH 1 fa o u

O 1 •

4-1 rs o o o o o o O fe ! 1 • • • ONm i 1 1 m

CO CM + 1 + r-l

w

H ! 1 y-' o C o CM 1 1 1 CM

X • • O

—s c o r*""N o > t> *—

O • < o • CM I i o o V—

m a UJ S ' 1 1 o c In m in o o CO o fa r-l o o CO O 1 1 1 o 2 a * • • • • X rH o CO fa / V o —

CO

O 1 • o o o o o o 8 o CO • CO • • CO • cn O 1 1 1 o

co

m CM 1 + i + rH en

m r-l

O

V

v—

o \—

m i l 1 m

>-» 0) iH

rH

co s X > c4—s

/-—s • • o > > S—

'—

oc o o c o o o m • • •' • X rH fa o rH rH o O fa CM + 1 + rH CO • • a 1 s o o <t o c o V o o m m

CM c CM CM

00

CO u co

•H

4-1 COo

•r-i U-l •HC

oo

CO

CO H

COOce

9)U

tO iH

fa

J300 ou

fa

<4-< M3

C/3

CO H

CO 3

fa

4J3oa

to

•H

HH

4-1 CO3

faC

00

<u rH

JC

CO H > o .i0 •H •H rJ a» JS < to u "O CO

4) ^; 0) 4-1 fa CO 4-1 rH O a O

rH >

</) 4-1 r-* fa

X

"Mi

0) 4-1 •H 4J rJ u £ QJ 5 <J "tj c0 O 'ob "to U 41 4J •H a) 4J cr CJ QJ a< 1) 60 w

cn CO • 0) CO •H 0» fa </> & 4J 4-1 M 3

4-1 0) fa PS co fa rH

a fa rH

(0 fa 01 CO 1)O c0 • rH o 4J -a 4J > -o > X 3 CO rH CO O cu CO 01 ^

0) rHO co PS 4J 3 4J 4J XI CO 0) CO rH o CO rH CJ

)-l T3 CO

u CO 4_» CO CO c CO 0) <D CO XI e 3 JO e H-l •H 0) a. rH 4J rJ •r-t •H fa •H •H •H C o CO <H < rH O f= rH CJ 4J o •H rH CJ o rO 0) 0 CO <U w

us

J to CO > Ui CJ o CJ CJ <
Table 9

Characteristic Parameters

Talysurf A

Profile Output (nominal) + IV

Relay Output (nominal) -AV

Magnification (vertical, max.) 1U

Stylus Speed (AX) 3.6"/min.

O 79 M u • / i- 1/m-ln nun

.

(100X) 0.1A"/min.

Scan Distance (.030" cutoff, AX) .150"

Chart Speed lA.A"/min.

Filter-Amplif ie r

Input (limited) + IV

Input Impedance ioo m

Gain (nominal) 10X

High Frequency cut-off 300HZ

Low Frequency cut-off 6HZ

2HZ

. on/., Filter Roll-Off -12 db /octave

Flatness +.02 db

Overall Linearity .02%

Output (nominal) +10V

Noise Output <5 mv.

Interface Circuitry

Inverter Output +AV

hvent Marker Output +1.35V (1 sec Interrupt Signal Output 3V (50 usee)

32
Data Input; Step Mode

Record length (time) 25 sec. (chart) 5.9" (150 min)

.

(surface, 100X) .060

(surface, 20X) .300"

Number of data points 512

Time per data point 50 msec Horizontal Resolution (100X) 120u"

(20X) 600u"

Vertical Resolution (A/D resolution .02y"

at highest Talysurf gain)

.

Data Input: AA Mode

Record length (time) 2.5 sec

(chart) .6"

(surface, 4X) .150"

Number of data points 4096

Time per data point 600 usee

Horizontal resolution (4X) 37u"

Vertical resolution (at 10 5 X) .005u

" Short Wavelength cut-off 200 u"

Long wavelength cut-off .010"

.030"

.100"

A/D Converter

Input Voltage + 10V

Input Impedance ioo m

Output (including sign) 12 bit

Resolution (voltage) 5 mv

(relative) .025% FS

Linearity .010% FS

33
Appendix G

Operator's Instructions: Interdata 3/Talvsurf 4 System

I . Preliminary Set-up

A. Instrumentation : the following connections are necessary:

1. those on the Talysurf for normal operation as indicated

by the Talysurf Operating Instructions manual;

2. those internal to the A/D converter as shown in figure 14;

3. the power cord of the interface electronics as in figure 15 (N.B. Disconnect main power line to computer when connecting

this line).

4. The external leads between the Talysurf, interface electronics and A/D converter as in figure 16.

B. Software : the following programs must reside in memory:

1. the hexadecimal monitor (3A80-3FFF)

;

2. the arithmetic subroutines (3010-35FF)

;

3. the master program (0080-1000).

II. General System Operation

A. Calibration of Stylus Instrument

1 . Magnification Selection

(a) Align unknown specimen on Talysurf;

(b) traverse stylus with chart recorder on and select

magnification on Talysurf electronic unit to obtain approximately

three-quarters of maximum on-scale deflection of recorder pen;

(c) turn off recorder and select calibration step

34
B

M

fa

34a
34b
v£5

34c

artifact of appropriate size.

2. Input of Calibration Step: Set-up

(a) Set switches

(1) Talysurf Electronic Control Unit

(1) Magnification: as determined in

(2) Cut-off: K

(3) Operation: N

(2) Talysurf Gear Box

(1) Stroke knob: L

(2) Speed knob: X20

(3) Interface Electronics

(1) Mode Select: 10X

(2) Cut-off: Step

(b) Align artifact and traverse stylus to obtain trace

with step edge in proper position relative to the event mark (see

appendix B)

.

(c) Rotate the Talysurf Setting Lever at the left (CCN)

position (see p. 4 of Talysurf Manual and Note 1 below).

3. Input of Calibration Step: Program Execution

(a) Begin program executive from TTY Control (OEOOG)

(b) At "enter data": turn on the chart recorder and

gently move the Setting Lever to the right (OW) ; data will be read

for twenty-five seconds.

(c) At In: shut off the chart recorder and tear off

the recorded trace;

35
(d) Al and A2 selection:

(1) with the "Step Locator Scale", determine the

position in mm of the step edge relative to the trailing edge of the

event mark (see appendix B)

;

(2) select Al and A2 symmetrically about the step edge

(3) Decord on the strip chart the mm and address locations of Al and A2

;

(e) At "Enter HO": type in the step height value as four

digits and depress the space bar on the TTY;

(f) At "Enter Units": type in a two character unit symbol

(do not press the space bar)

;

(g) At "Enter Al"; type in the four -digit address Al and

depress the space bar;

(h) at "Enter A2"; either A2 as above; the computer will

now print out the computed step heights Hi, H2 and HM with units.

(i) At "More?":

(1) If the computed step heights are unsatisfactory,

type N and repeat the procedure from step 3a;

(2) If the heights are satisfactory, type Y.

B . Calibration of Unknown Specimen

1. Align the specimen on the Talysurf and traverse the stylus

to obtain a properly centered trace.

2. Calibration of a Step

(a) Repeat procedure in IIA2 , b and c

;

36
(b) At "H or R? M

: type in H;

(c) At "Enter Data", follow procedure from IIA3, b thru h;

3. Calibration of a Roughness

(a) Select filter cut-off on interface; select X4 stroke

speed on Talysurf; type R.

(b) At "Enter Data", rotate the Setting Lever to right

position (CW) ; data will be read for 3.5 seconds.

(c) The computed AA and units will now be printed.

4. At "More?":

(a) If a step is to be calibrated, type Y; then at

"H or R?", type H.

(b) If a roughness is to be calibrated, type Y, then

at "H or R?", type R.

(c) If no more measurements are to be made, exit from

program by typing N.

Note 1. The Event Marker appears on the chart recorder at the "Start

of cut-off average" position in the stroke. With the stroke knob on

the gear box at position L, the event mark appears when the marks on

the gear box window are aligned as indicated below. Therefore, in

returning the Setting Lever to the left (CCW) position, it is necessary

only for L mark to be to the left of the rightmost mark on the upper

scale

.

37
Appendix H

Checklist for Proper Electrical Operation

Talysurf Outputs

(1) The profile Output should produce a voltage of nominally

+1 volt when the pen is at the 2 inch mark on the strip chart and

-1 volt at the zero inch mark.

(2) The relay output should be a negative - going step of four

volts at the "Start of cut-off average" position of the stylus stroke

(see Talysurf Manual).

A/D Outputs

(1) With the Talysurf relay output connected to the Interrupt

Input terminal on the A/D converter front panel, the A/D output at

the Pulse Output terminal should be a zero to volts pulse of about

one second duration; (simultaneously the computer interrupt should

trigger internally).

Interface Electronics Outputs

(1) With the system fully wired (figure 16), the output at the

X10 OUT should be the amplified, filtered Profile Out Signal;

(2) A one -second pulse of nominally one volt should be present

at the "PROFILE IN" terminal (and a similar one recorded on the chart

recorder) at the "Start of cut-off average" stroke position.

Internal A/D Signals (A/D Multiplex or Board).

With the Talysurf relay signal at the Interrupt Input:

38
(1) the output of the signal inverter (daughter board 44)

should be a pos it ive -going step of four volts;

(2) the output of the A/D Interrupt pulse (daughter board 40)

should be a 50 microsecond positive -going pulse of about four volts.

39

form NB5-I I4A (1-71) •r AT ION OR REPORT NO.

J "sheet ' NBSIR 73-106

2. Gov't Accession No.

3. Recipient's Accession No.

4. TITLE AND SUBTITLE

A SYSTEM. FOR COMPUTERIZED SURFACE ROUGHNESS MEASUREMENT

5. Publication Date

6. Performing Organization Code

7. AUTHOR(S)

Dennis A. Swyt

8. Performing Organization

NBSIR 73-106

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

Covered

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.)

An overall system for computerized surface roughness measurements, involving a commercial stylus profile instrument and a minicomputer, is described. The

method allows: direct displacement calibration of the stylus instrument by means of interferometrically measured gage block steps; the elimination of

roughness artifacts as calibration standards; and access to punched-tape surface profile data which may be given detailed analysis on a larger, faster

computer. Details of system operation and precision are included.

17. KEY WORDS (Alphabetical order, separated by semicolons) . Surface profile instrumentation; surface roughness calibrations; surface roughness

measurement

.

18. AVAILABILITY STATEMENT

I | UNLIMITED.

fx~1 FOR OFFICIAL DISTRIBUTION. DO NOT RELEASE

TO NTIS.

19. SECURITY CLASS

(THIS REPORT)

UNCLASSIFIED

20. SECURITY CLASS

(THIS PAGE)

UNCLASSIFIED

21. NO. OF PAGES

22. Price

USCOMM-DC 66244-P71