NATL INST OF STAND & TECH

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AlllDb T7flflll IBS

REFERENCE Pub,i

cations

NBSIR 73-219

Eight Techniques for the Optical

Measurement of Surface Roughness

Russell D. Young

Institute for Basic Standards

National Bureau of Standards

Washington, D.C. 20234

May 25, 1973

Interim Report

it

QC100

U56

73-213

ID 73

U. S. DEPARTMENT OF COMMERCE

NATIONAL BUREAU OF STANDARDS

NBSIR 73-219

EIGHT TECHNIQUES FOR THE OPTICAL

MEASUREMENT OF SURFACE ROUGHNESS

use?

Russell D. Young

Institute for Basic Standards

National Bureau of Standards

Washington, D.C. 20234

May 25, 1973

Interim Report

U. S. DEPARTMENT OF COMMERCE. Frederick B. Dam. Secretary

NATIONAL BUREAU OF STANDARDS. Richard W. Rotorts. Director

Eight Techniques for the Optical Measurement

of Surface Roughness

by

Russell D. Young

Abstract

The need for a fast, on line, non -destructive technique for

measuring surface roughness has recently accelerated the decade

long development of optical methods. It is anticipated that these

new techniques will add a new dimension to the surface roughness

measurement system which may require an appropriate NBS response.

In order to formulate this response, the eight optical techniques

which have been identified are briefly described and are summarized

and compared in Table 1.

It is concluded that model deficiencies, questionable theoretical bases, as well as physical and analytical limitations cast serious doubt on the present accuracy of these techniques for absolute

measurements. Optical techniques seem more suitable for comparison

measurements, i.e. measurement after appropriate calibration using

surfaces which have been measured using other techniques. Thus, it

is concluded that the most appropriate NBS response to the Increased

use of optical techniques is to concentrate our limited resources

on developing much improved instruments such as the Topograf iner

and traditional stylus instruments so that highly refined optical

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surfaces can be measured and their surface parameters determined

accurately.

Introduction

The need for a fast on line, non -destructive technique for

measuring surface roughness has recently accelerated the decade

long development of optical methods. It is of particular concern

to NBS that certain high technology industries are rapidly developing proprietary and perhaps patentable optical instruments for

measuring roughness. Our concern is that we may soon be called

upon to mediate calibration disagreements arising from model

dependent measurements which result from pairs or groups of instruments which have different theoretical bases. Of still greater

concern is the immediate need for accurate measurements of the

extremely smooth surfaces which are typically investigated by

optical techniques. The following brief evaluation is an attempt

to predict the impact of these optical techniques on the surface

roughness measurement system.

The eight distinct optical techniques which have been evaluated to date are briefly described in the following pages, together

with a table comparing their performance, cost, operation skill, and

other parameters. The techniques are then evaluated, the potential

impacts on NBS identified and a response proposed.

- 3

-

I . Speculai ar. il Diffuse Light Scattering .

During the last decade a number of investigators, particularly

Bennett et al,' ^ have studied the relationship between light reflection and surface roughness in order to measure the surface finish

of optical components. Experimentally, the specular and/or diffuse

reflectance of the specimen surface is measured as a function of

another parameter, for example angle of incidence, angle of reflection, acceptance angle of detector, wavelength, reflectance per

unit solid angle, etc. Assuming that the surface roughness height

and roughness periodicity along the surface are Gaussian, one or more

of the above measurements can be related to the rms surface roughness

height and the autocovar iance length of the surface roughness.

Theory: Scalar and Vector Theories of Specular and Scattered

Reflectance .

6 -8

In the scalar theory, the incident radiation is assumed to

be modulated in phase by the height variations along the surface

so that, at a certain point above the surface, the resultant intensity is derived from a complex diffraction pattern. It is further

assumed that (1) the roughness height is Gaussian with an rms

roughness of 6, (2) the autocovariance function is Gaussian with

a standard deviation a, (3) the surface is perfectly conducting and

would have a specular reflectance of unity if perfectly smooth.

With these assumptions, the relative reflectance of the surface

- 4 -

1

when light is normally incident is

4

(1)

where R is the reflectance into a cone of half angle iy about the specular direction, R

Q

is the total reflectance of the sample, and X is the

wavelength of the incident light. The first term is the well-known

specular reflectance of the surface. The second term gives the fraction of scattered light which falls within a half angle cr of the

specular direction. It is assumed in the derivation that 6 < < X.

The scalar scattering theory is energy conserving in the sense

that all incident light lost from the specular beam should appear

in the scattered beam. The reflectance of the material can be taken

into account in equation 1 by calculating the reflectance relative

to the reflectance of an ideally smooth surface of the same material.

However, this does not account for losses or extra emission due to

surface currents (called plasmons). It was also assumed in deriving

equation 1 that the autocovariance length a is of the order of or

greater than X.

7 9-18

In the vec tor theory, ' the polarization and the wave

vector components are used both to match boundary conditions at

the surface and to determine the intensity of the radiation after

reflection. For example, a plane wave incident upon a flat surface

- 5

-

sets up curr< nts having the same component of wave vector In the

surface as the Incident wave in order to match the boundary conditions on the electric and magnetic fields. Thus, radiation is

only found in the specular direction. Rough surfaces cause currents with normal as well as tangential wave vectors which are

modulated by the roughness height.

In the case where plasmon excitation does not make an important contribution, the reflectance distribution per solid angle

i

• a • 2 , 10

for normal incidence is given by

8TI3

6a a

s Cos

2

cr dve) / e-Sln2 ^

v/e-Sina a4Co8 a /c-Sina a+Co8 a

na

a Sina

iy (2)

-where a is the angle between the specular direction and the scattering

direction and e is the dielectric constant of the reflecting surface.

The first term in curly brackets represents p polarized light (light

polarized in the plane of incidence), the second is a polarized

scattered light (light polarized perpendicular to the plane of incidence).

Near the specular direction where <y is small, the reflectance

2 distribution is simply:

(3)

which does not result in strong forward scattering near the specular

direction. In addition to a thorough textbook treatment of the

- 6 -

of the subject, there are several recent theoretical treatments of

9-18

scattering.

In general, the scalar theory of scattering is used when theory

is compared with experiment because the complicated vector theory

makes the determination of the roughness very difficult. Typically,

a measurement is made of the specular reflectance and the rms roughness is determined by using the first term of equation 1. Then the

reflectance is measured for the case where <y is appreciable and

both terms of equation 1 are used to obtain the autocovariance length.

Experiment .

In order to test equation 1 Bennett and Porteus first measured

the wavelength dependence of the relative reflectance of a finely

ground glass surface (see fig. 1).

70 -

u »0 -

;

- /

pm

Fig. 1. Relative reflectance of a finely ground

glass surface. Circles Indicate experimental

points - the solid curve is from eq. 1 and the

dotted curve includes a correction for near specular scattering.

- 7 .

At the lower end of the curve in figure 1, the requirement that 6 < < \

is violated. It is noted that at wavelengths greater than 8 micrometers

the agreement is very good without correction for scattering near the

specular angle. Experimental results indicated that accurate measurements would be expected below 6 100 - 200 A for X 1 micrometer.

19 Birkebak compared the results obtained by a number of invest i - 20-25

gators using long wavelength specular reflection measurements

interpreted according to the first term in equation 1 as shown in

figure 2.

0 i 0 « 0 «. 5*6 . 0 i 2 ti f* I 6

' 19

Fig. 2. Optical vs Mechanical Roughness. Birkebak,

Torrance^ amd Bennett* used a stylus of 12.5ujn radius.

Depew and Weir**** used a 2.54um stylus and Torrance » used a 1.25 um stylus. The figure suggests that smaller

styli result in much improved agreement between stylus

and light scattering measurements.

- 8 -

In another approach, the acceptance angle of the optical system

is varied and the relationship between relative intensity and accept'

ance angle is used to determine both 6 and mean slope of the surface

26 1 roughness m. (Note: It can be shown that m, 6 and a are related

by the expression a fl 6/m) . Table 2 shows the rras roughness and

slopes of polished fused silica samples measured interferometrically

je.^ A i 27-29,49

26

(in brackets) and with the acceptance angle technique. A number

of other scattering measurements have been reported.

Table 2 RMS roughness anti slope of polished fiucd mIwj

(IntciTcromeiric values in brackets)

Fmul o(nm) mxlO'rad

polishing

time (min)

15 0 97 (0-76) 1-25 (0-32) 45 0 73 I 12 75 068 078

120 <>5<> 0 59 330 0 23 (0 24) 0 .38 (0 21)

Despite the success of the scattering technique, there are several studies which suggest that a healthy skepticism should be exercised.

Bennett et. al. found that in the case of a silver surface, there was

no difference between the Infrared reflectance of rough and smooth

• 30 samples up to 45 A rms , in disagreement with the theory. This observation is attributed to the anomalous skin effect. It is also

- 9

-

important to avoid wavelengths where plasma resonances are likely

to occur, as those may cause greatly enhanced scattering in the

10 31 32

presence of surface roughness. ' ' Furthermore, it must be

noted that scattering experiments are typically carried out with

surfaces produced through random abrasion of many particles, and

that machined surfaces with deterministic roughness are avoided.

The most telling criticism of the light scattering technique

33

is due to R. P. Edwin of NPL. He performed a careful measurement

of angular dependence of scattering from highly polished surfaces

using the apparatus shown in figure 3.

//

Fig. 3. Special apparatus for measuring the

angular dependence of light scattering.

- 10 -

The results of the measurement are shown in figure 4.

lOOCf

Fig. 4. The variation with angle of the scattered

light intensity for Lapmaster polished Spectrosil B

(dots). The straight lines were obtained form theory

assuming values for a and a indicated.

The author attributes the rather gross discrepancy to either the

rather small ratio of roughness to wavelength (6/\ 0.002) or more

probably to the fact that the surface structure is not well described

by Gaussian statistics. The presence of pits in the surface, even

though small in number, may well dominate over roughness scattering.

It is important to note that freshly cleaved mica which should not

be pitted, gave a similar curve. The author then points out that

fringe contrast and speckle contrast techniques have been proposed

but no experimental results have been obtained. The Topografiner*

1. Instrument developed at NBS for high resolution topographic mapping.

See article in RSI Vol. 43, No. 7, July '72 by Young, Ward, and Scire.

\ is particularly mentioned as having superior resolution.

Sprague also reported that his specular reflectance measurements only applied to certain types of finishes and that correlation

for a more general category of surfaces was not sufficient to ensure

38

accurate measurement.

II. Laser Speckle Method of Measuring Surface Roughness .

It has been proposed that laser speckle may be used to measure

3 3 *36

the roughness of surfaces although this has not been experimentally verified. Speckle patterns result when spatially coherent

light waves are reflected from a rough surface. The average size

of the speckles is determined by the aperture function of the illuminating source, while the fine structural details of the speckle is due

to the roughness of the reflecting surface. By determining the autocorrelation and spectral density information from film records of

the speckle pattern, it should be possible to extract surface rough37

ness information. Goldf ischer carried out the first detailed solu35 tion of speckle patterns and Crane then calculated the characteristics of speckle resulting from random (Gaussian) surface roughness.

The complex formulas resulting from the theoretical solutions of

this problem limit the potential usefulness of the technique. While

it might well be used as a quality control technique by comparing

the speckle from similar surfaces, it is doubtful that values for

roughness height and autocovar lance length can be extracted from

12 -

speckle photographs without considerable difficulty. The usefulness

of the technique will be determined by future developments.

Ill . Surface Roughness Measurement with White Light Speckle (see

Sprague, ref. 38 )

.

We noted above that when a rough surface is illuminated with

coherent light using an optical system with a finite aperture, speckle

is produced. Light at each image point originates from a small area

on the object because of resolution limitations. If the height on

the object surface varies appreciably across the width of the point

spread function, speckle will result from interference effects. The

size of the speckle depends on the system aperture; the contrast of

the speckle depends on the surface roughness. Two conditions are

necessary for high contrast speckle: (1) the interfering waves must

have phase difference of at least \/2 to give complete destructive

interference at points in the pattern, (2) the interfering waves must

be temporally coherent. For the first reason, the speckle contrast

is low for smooth surfaces. The second condition presents an opportunity to measure surface roughness since speckle contrast is related

38

to the relative values of the roughness and the coherence length.

Thus, if roughness and coherence length are comparable, speckle contrast

will be reduced. Coherence length can be defined as the pathlength

difference in a Michelson interferometer where the fringe contrast goes

essentially to zero, and, for a square spectral distribution, is equal

to the velocity of light divided by the frequency bandwidth.

- 13 -

Sprague points out that there is an opportunity in speckle

measurements to introduce a parameter which if similar to the roughness width cutoff--the greatest spacing of surface structure to be

included in the measurement . An exact equivalent cannot be attained

because the optical image is the Fourier transform of the object.

However, a similar effect can be created by moving the detector somewhat ahead of the image plane, causing the point spread function to increase in width. When projected back in object space onto the rough

surface, this width can be set to the roughness width cutoff.

V

Surface

\

,' AjM rlunI'i.tilM.l' T~Z" .'l>..ii<i.\.vt..r

Sn.-i.ti'.' i in., ,

l!.IIH

Fig. 5. Apparatus used to measure speckle contrast by scanning speckle pattern pest a point

detector.

The experimental apparatus is shown in figure 5. The rough surface is translated perpendicular to its axes so that the speckle pattern is scanned across the pinhole. The aperture must be small enough

- 14 -

so the speckle size is larger than the pinhole. The maximum separation of surface points contributing light to the same spot in the

image plane is set equal to the roughness width cutoff by moving the

pinhole ahead of the image plane. The light source is a tungsten

zirconium arc, yielding a coherence length of 1.5 urn with no filters.

This coherence length can be increased to 30 \m by Inserting a filter

in the beam.

The instrument shown in figure 5 was tested by measuring the

arithmetic average absolute deviation of the speckle intensity from

its mean value for a series of metal roughness standards. The re"

suits are shown in figure 6. As expected the contrast drops close

0.1 0.2 0.4 O.o l.C 3.2

Fig. 6. Speckle contrast vs surface roughness as measured with a Prof Home ter. The contrast is seen

to become small when the roughness is comparable in

magnitude with the coherence length of illumination

(1.5 urn) and when the roughness is less than a quarter of the mean wavelength of illumination (X"0.5mp»).

- 15

to zero when tv/ice the roughness Is about equal to the coherence length

of the il luminal ion , and also drops when the sample Is so smooth that

the surface roughness is smaller than the mean wavelength. It is particularly significant that the relationship between contrast and roughness is independent of the surface finishing technique.

The above technique has certain limitations. The necessarily

small pinhole results in very low signal levels. Image points are

measured serially; only a small part of the signal is used at a time,

requiring long measurement times. Furthermore* only a small part of

the surface is sampled. These limitations can be avoided by measuring

the whole image with nonlinear photoconduc tors as detectors. Nonlinear photoconductive cells are used for detecting maximum image contrast in automatic focus detectors. By splitting the beam in front

of the detector and adding a diffuser (to eliminate speckle) and a

second detector, it is possible to measure the ratio of the resistances of the two photoconductors and thus measure the contrast in the

speckle pattern. In practice a variable neutral density filter is

adjusted for each sample to give a standard reading on the reference

detector, and the resistance difference is used to determine the

speckle contrast. The results of measurements with the modified

apparatus is shown in figure 7. Unfortunately* the nonlinear detectors have a high temperature sensitivity which limits the accuracy

of measurements.

- 16 -

G • ground

BL • OUnchard ground

T turned

Surf-co Rouchnesa. micrometers

Fig. 7. Photocell difference reading vs surface

roughness as measured with a profilometer. The

coherence length of illumination was approximately

8.5 urn. with a mean wavelength of 0.75 tun. The

apparent linearity of response is due to the com- bination of nonlinear photocell response with a nonlinear contrast curve.

The white light speckle technique, after instrument calibration,

is particularly useful for measuring rough surfaces and as a quality

control device. Its usefulness would be enhanced by a firmer theoretical base.

IV. Surface Roughness Measurement by Holographic Inter ferometry (Ribbens) .

Holographic techniques are particularly attractive for roughness

measurements since they permit an optical comparison of a given surface

- 17 -

with a slightly displaced version of itself while maintaining the

phase associated with the reflection from each element of the surfac

This process is most easily understood by reference to figure 8. Th

light from the laser is split into two beams. Beam u illuminates

Fig. 8. Instrumentation for holographic inter - ferometric surface roughness measurement.

the object and u

f serves as a reference beam for holograph ically recording the light amplitude reflected from the test specimen.

is a partially reflecting mirror, and are totally reflecting

ultraflat mirrors, LP^ and LP^ are lens -pinhole spatial filters and

is a collimating lens. If the hologram formed at is photographically recorded, and the holographic plate placed at P^ , when

the hologram is illuminated by the reference beam u^ a portion of u^

is diffracted, this being denoted u_. If, in addition, the plate

- 18 -

is Illuminated by beam u^ from the test surface, an interference

pattern is formed between and u^* The interference pattern is

a consequence of the imperfect registration of the hologram plate

when it is returned to P^. The misalignment is controlled by means

of micropositioning screws which position the plate.

The contrast ratio of these fringes is a measure of the cross

correlation between the light amplitude components u^ and u^, which

in turn depends on the spatial and temporal coherence of the incident

light beam and by the roughness of the test specimen. If the beam

is sufficiently coherent and if the specimen is flat compared to

the light wavelength, then the contrast ratio is uniquely determined

by the surface roughness of the test specimen. The interference contrast is measured in plane P^.

Theory -- While the vector theory (see scattering theory) is

necessary to interpret the interference contrast properly, the scalar

theory offers valuable insight and agrees well with experiment. Assuming a Gaussian distribution of roughness with an rms value of a, the

contrast ratio R is given by:

R

( P + exp [(-tfgZ/Z]

\? - exp [-kV/2]

where k 2tt/X, P is the ratio of the amplitude of u^ and as determined by the reference beam and hologram efficiency.

An experimental investigation of the technique was conducted by

- 19 -

measuring the contrast ratio of a number of finished ateel specimens

e using a wavelength of 6328 A. The fringe intensity distribution was

measured with a scanning photocell whose aperture was small compared

to the fringe spacing. The contrast ratio is obtained from the maxima

and minima of the photocell output. The results of these measurements

are shown in Figure 9.

——Th.-jfy -AW

oo-f c<i o.:o 040 o.eo

Fig. 9. Comparison of theory and experiment.

The correlation between theory and experiment is quite good

between roughness values of 0.050 yja and 0.40 |im (2-16 u"). The

poor agreement below 0.05 um is a consequence of finite laser coherence. A contrast ratio of about 9 is the maximum that can be

obtained for this configuration.

V. Inter ferometric Fringe Contrast Method of Measuring Surface Rough -

ness (Ribbens) .^ 0

In addition to the holographic technique discussed above, Ribbens

- 20 -

has also proposed that fringe contrast inter ferometry be applied to

40

roughness measurement. The accuracy of this technique improves

with the smoothness of the surface. A schematic drawing of the instrument is shown in figure 10. The instrument is an interferometer whose

(...- a*e J*csr\ lion tout

:

i _ • t __ (Mllll. V>>t'-C

A3*'*** / ± ! l.lm

• ~~7\ —

n

I tn< wkxi

//.//...//

Fig. 10. Schematic drawing of instrumentation used In roughness measurement.

reflecting surfaces are under study. The fringe contrast of the instrument is determined by the mutual coherence of the wavefronts from the

two reflecting surfaces which in turn is determined by the roughness

of the two reflecting surfaces. If the reference mirror is sufficiently

smooth and flat, fringe contrast will be determined by the test flat

only. It is then necessary to determine the relationship between fringe

contrast and surface roughness in order to determine the roughness of

the test surface.

Theory It is assumed that light is normally incident on the

test surface, that the Fraunhofer approximation applies and that the

surface is smooth enough so that shadowing does not occur. Under these

- 21 -

circumstances, tt can be shown that the rms surface roughness Is

given by:

o =

where R is the contrast ratio and P is the ratio of the reflectivities

of the reference and test surfaces. The lower roughness limit is

determined by the roughness of the reference mirror, which may be as

e low as 10 A, and the coherence of the laser, which may provide con -

5 6

' • trast ratios as great as 10 or 10 , again implying a 10 A roughness

limit. The validity of the maximum roughness limit rests on the

assumptions used in the theory and is best determined experimentally.

Figure 11 shows the relative error for stylus Instrument and

fringe contrast measurements between 0.1 and 10 uln. measured with

Fig. 11. Relative error vs rms roughness,

a number of steel surfaces. It is evident that the theory Is not

applicable beyond a few microinches although a calibrated fringe contrast instrument might extend to much higher roughness values. The

upper limit can be extended by employing longer wavelength light.

- 22 -

O o Thus , the range of validity is nominally 10 A to X/5 A.

41

Munnerlyn and Latta have proposed the use of a Twyman Green

interferometer, CO^ laser and a liquid crystal detector in a similar

experiment. They derive a somewhat different relationship between

fringe contrast and roughness.

VI. Multiple Beam Interference (Tolansky) Measurement of Surface

Roughness . 43 While interference microscopes have long been used to estimate

surface quality, the low cost, elegance and sensitivity of the multi44 pie beam interference microscope, mostly due to Tolansky, has

brought it to the forefront in surface roughness measurement in the

range where the peak to valley distance is less than X/2 (10 micro

inches). The optical components of such an instrument are shown in

44 figure 12.

In the multiple beam interferometer, the lower surface of the

flat glass plate (Fizeau plated is coated with a layer of silver which

may be up to 977. reflecting. The light reflects between the Fizeau

plate and the test specimen (usually coated with an opaque layer of

silver) many times, perhaps 50 - 100 times, before passing through

the Fizeau plate again and into the eyepiece. Since there is a

very small wedge between the Fizeau and the test specimen, the light

tends to move laterally after many reflections ("walk off"), typically

as much as 5 wavelengths. This tends to limit the lateral resolution

to 2.5 urn. While commercial instrument makers quote a vertical

- 23 -

\ /

V /

\ / Opt. ci tU

Spec iincn •

Ftg. 12. Mul tiple -beam interference microscope. Monochromatic light from the source illuminates a slit focused

at the back focal point of the objective. Parallel light

is transmitted through the silver film on the lower surface of the optical flat to the specimen surface. After

repeated reflection a fraction of this light returns

through the objective to the eyepiece. The resulting

fringes can be pictured as arising from the intersection

of the surface and a set of parallel lines spaced a half

wavelength apart. (From reference 44).

e resolution of about 25 A, Tolansky claims that, by careful work, the

vertical resolution may be extended to 5 k.

Surface roughness is determined by drawing a straight mean line

through an interference fringe and plotting the line profile. The

amplitude is determined by the knowledge of the fringe spacing (of

- 24 -

known half wavelength) and the ratio of the fringe deviation to this

distance. As coramer ical instruments become more readily available,

this technique is gaining in popularity where roughness is less than

10 microinches. A more sophisticated data acquisition system, similar

to the FECO instrument, is equally applicable to the multiple beam

instrument.

VII. Surface Roughness Measurement with FECO (Fringes of Equal Chromatic

Order) .

Bennett and co-workers have exploited the unusual properties

associated with fringes of equal chromatic order in measuring sur2 42

face roughness. ' Figure 13 shows the most recent version of their

measurement system. A white light source Z illuminates the interferometer I through beam splitter B. One element of the interferometer

is the highly reflecting (coated) specimen surface to be measured.

Slit S serves to define a narrow (1 mm x 3 \m) region on the specimen

surface. The light then passes through spectrometer p and an image

is formed in front of the slow scan TV as shown in the inset. The

resulting fringes (see fig. 14) all come from the same region on the

specimen. The fringes to the right in figure 14 come from the red

part of the spectrum with order of interference 7, while the fringes

to the left have order 8 and are in the blue green spectral region.

The image of the fringes and reference spectral lines is detected

by a slow scan TV camera employing an image dissector tube with 500

scan lines. A single line is scanned repetitively with the output

- 25 -

. .CO I.Vli lit 1 r.UVlkHUC f.UftfACt SCANNC.lt

Fig. 13. Schematic diagram of FECO Interferons trie Surface Scanner used to measure surface roughness of plana

samples. The image detected by the alow scan TV la shown

at right center and a single acan line is shown above it.

going to a signal averager until the signal to noise level is adequate

and the contour appears as in the upper part of figure 13. Then the

information on the scan line is digitized and fed to a minicomputer

which calculates and stores the wavelength of the segment of the

interference fringe contained in the scan line. The camera now

shifts to the next scan and repeats the process until a 500 point

wavelength (spacing) profile is obtained. These data can then be

used to obtain the usual surface parameters (rms roughness, height

distribution, autocovarlance fen, etc.). The system, when fully

- 26 -

FUSED QUARTZ

6-7A

GLASS

6-25A

\ .

1 '

i -1

ELECTROLCSS NICKEL ; 6-25A > -j

lJ.

Fig. 14. FECO fringes obtained from (a) a super polighed

fused quartz optical flat, (b) a good quality polished glass

surface, and (c) a very smooth polished metal surface. The

reference surface in all cases was a superpolished fused

quartz optical flat.

e completed, should be able to detect irregularities under 10 A peak -to*

valley provided that the lateral scale of roughness is greater than

the three micron lateral resolution limit of the optical system.

The FECO system requires critical adjustment of the interferometer as well as extremely costly electronics, computer and spectrometer. For this reason, it is unlikely that more than one or two

- 27 -

such instruments will be constructed.

VIII. Womarski Differential Interference Contrast Technique for

Measuring Roughness . 46 47

The Nomarski technique ' is an excellent qualitative method

for observing the fine detail of surface roughness at high resolution.

In effect, two images of the surface, displaced by less than the resol

ution of the microscope, are made to Interfere destructively (interference contrast). Only where there is a difference in altitude of

adjacent regions is the image illuminated. However, the system is

sufficiently sensitive so that, when properly adjusted, the full

microdetail of the surface is seen in high contrast. The essential

elements of the instrument are shown in figure 15. The polarised

Polarizer

Analyzer

Beam splitter

Wotlaston

prism

Objective

Reflecting

object

Fig. 15. Schematic diagram of a reflected -light system for differential inter ference -contrast microscopy. (Separation between

the two wave fronts is exaggerated.)

- 28 -

light source from the left Is reflected along the optical axis of

the instrument by the beam splitter. The polarized beam is angularly

split by the Wollaston prism into two mutually coherent beams which

arrive at the specimen displaced by about 1 urn, the approximate resolution of the microscope objective. After reflection, the beams are

recombined at the Wollaston prism and then pass through second polarizer which is crossed with the first. If the path difference for

adjacent rays of the two beams is zero, a dark field results. Any

displacement of the rays at tilted areas of the specimen leads to

their return through a non -symmetrical path in the optical system.

The field therefore has a dark appearance , with tilted features appearing

bright on the dark background. Since white light is used, the contrast

in the image is also seen as color variations which exploit the high

sensitivity of the human eye to color.

The differential interference contrast technique suffers mainly

from the limitation that it is not quantitative. Bennett suggests

that autocovariance function can be obtained by scanning superimposed

Nomarski micrographs.

Conclusions

An examination of the eight techniques, which are intercompared

in Table 1, reveals some common limitations for certain subgroups of

the eight. The light scattering, white light speckle, laser speckle,

holographic inter ferorae try and interference contrast techniques presume

a Gaussian model for surface roughness which is probably characteristic

- 29 -

of only a limited number of surface finishes. The concept of the cut

off length, used to separate roughness from vaviness , is very difficult

to implement optically. All of these techniques involve a trade off

in that their inherent averaging property precludes examining a single

defect, say a pit or scratch, in isolation. Some of these techniques

require the use of infrared (invisible) radiation.

One clear advantage of using a light scattering technique in

evaluating optical surfaces is that it often measures precisely the

needed parameter, the light scattering properties of the optical element, without introducing the intervening parameter, surface roughness. However, when used to obtain a quantitative measurement of

surface roughness, the strong model dependence together with the

questionable theoretical base, limit severely the reliability of these

measurements.

The second group of optical techniques includes multiple beam

interference, FECO, and Nomarski. The first two techniques employ

a rather simple model and yield surface profiles of rather limited

horizontal resolution. The user is immediately faced with the task

of extracting roughness parameters from an optical representation of

a profile. The necessity of coating the surface renders this a

destructive test in cases where the metallic coating cannot be safely

removed. In addition, there is risk of damage when the Fireau plate

contacts the specimen surface. The Normarski technique is not quantitative. Thus, this last group of techniques has model integrity but

- 30 -

suffers front physical and analytical limitations. The multiple beam

technique seems to have the least severe limitations, particularly

cost and ease of Interpretation, and Is finding Increased use, par tic

larly In conjunction with replicating techniques.

There Is little doubt that the surge In popularity of optical

techniques will disturb the surface roughness measurement system,

perhaps severely. The above review suggests that optical techniques

will become more popular because of their Inherent attractiveness

for on line, non contacting measurements rather than because of

Increased accuracy In measuring surface roughness parameters. In

other words optical techniques seem more suitable for comparative

measurements, i.e. measurements after appropriate calibration using

surfaces which have been measured by other techniques.

Thus, it Is concluded that the most appropriate NBS response to

the Increasing use of optical techniques is to concentrate our limited

resources on developing much improved Instruments, such as the Topografiner^ and traditional stylus Instruments, so that extremely smooth

optical surfaces can be measured and parameterized accurately. These

measurements could then be utilized, through appropriate transfer

artifacts, to characterize and calibrate optical instruments used in

surface roughness measurement.

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Reference!

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.

Amer. 51 123 Feb 1961.

Bennett, H. E. , Bennett, J. M. , Stanford, J. L. , "Surface Irregularities and Scattering," Proc. of The Infrared Information Symposium, Huntsville, Ala. Jan 16, 1973.

Bennett, H. E. , Porteus, J. 0., Bennett, J. M. , and Stanford, J. L.

"Surface Evaluation for High Energy Laser Windows" High Energy

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Bennett, H. E. , Bennett, J. M. , and Ashley, E. J., "Infrared

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Davis, H. , "The Reflection of Electromagnetic Waves from a Rough

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Surfaces by Light Scattering" App. Optics 9 2470, Nov 1970.

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- 33 -

[20] Birkebak, R. C. , '•Monchromatic Directional Distribution of

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[24] Depew, C. A., and Weir, R. D. , "Surface Roughness Determination

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[25] Torrance, K. E. , "Monochromatic Directional Distribution of

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M. S. Thesis, U. of Minn. 1964.

[26] Hodgkinson, I. J., "A Simple Scatter Method for Optical Surface

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[27] Greenwood and Edward Powers, "Determination of Surface Height

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[28] Corey, H. S. , "Optical Surface Finish Measurement" Oak Ridge

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[29] Hasunuma H. , and Nara, J., "On the Sheen Gloss" J. Phys. Soc.

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[30] Bennett, H. , Bennett, J., Ashley, E. , and Motyks, R. , "Verification of the Anomalous - Skin - Effect Theory for Silver

- 34 -

in The Infrared", Physical Review 1_63 755 , 15. Jan. 1968.

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[ 32 J Kretschmann, E. , "The Angular Dependence and the Polarization

of Light Emitted by Surface Plasmons on Metals Due to Roughness," Optics Communications 5_ 331 August 1972.

[ 3 3 J Edwin, R. P., "Light Scattering as a Technique for Measuring

the Roughness of Optical Surfaces," J of Phys. E 60 1973.

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Scattered Light (Theory) Proc. of IEEE 60 339, March 1972.

[35] Crane, R. "Use of Laser -Produced Speckle Pattern to Determine

Surface Roughness," J. Opt. Soc . Amer. 60 1658, Dec. 1970.

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Inter ferome try" , Applied Optics U_ 807 April 1972.

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2 Laser Source" Applied Optics (Letter) 1_ 1858 Sept 1968.

- 35 -

[42] Bennett, H. and Bennett, J., "Precision Measurement In Thin Film

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N. Y. 1970 .

[48] Young, Russell, Ward, John and Scire, Fredrlc, "The Topograflner

:

An Instrument for Measuring Surface Micro topography" , The Rev.

of Sci. Instr. Vol 43 No 7 July 1972.

[49] Westberg, John, "Assessing the Quality of Very Fine Surfaces - A

Coming Breakthrough for Lightref lection Photoelectrical Methods?"

Proceedings of the International Conference on Surface Technology,

May 1 - 3, 1973.

USCOMM-NBS-OC - 36 -