Optical roughness measurement of ground surfaces by light scattering

Int. J. Mach. Tools Manufact. Printed in Great Britain

Vol. 30, No. 2, pp. 283-289, 1990.

089(I-6955/9053.00 + .00 Pergamon Press plc

O P T I C A L R O U G H N E S S M E A S U R E M E N T OF G R O U N D S U R F A C E S B Y LIGHT S C A T T E R I N G D. Y. YIM* and S. W. KIM*t (Received 16 May 1989)

Ahstraet--An optical method is investigated for the roughness measurement of the ground surfaces in the range of 0.025-1.6 ~m Rq values. The method is based upon the principle of light scattering with an aim to in situ application. Computer simulation and experimental work is conducted in order to establish the scattering behaviours from the ground surfaces. From the results, an optical measuring strategy is suggested and proved by comparing the optical results with those of stylus instrument.

NOMENCLATURE 1, 1(02) 1, Is l~um L Rc R4 T T/Rq cb k 01 02

tr~ o-z

intensity ratio along reflection angle specular intensity ratio for the 0.1 I~m R4 surface intensity ratio in the specular direction partial sum of l(0z) over a collection angle sampling length radius of curvature of roughness elements r.m.s, amplitude roughness correlation distance between roughness elements equivalent radius of curvature of roughness elements collection angle wavelength of light angle of incidence angle of reflection standard deviation of scattered pattern standard deviation of roughness heights slope of roughness elements

1. INTRODUCTION SUITABLE roughness m e a s u r e m e n t sensors are essentially required for successful quality control of w o r k surfaces in most machining processes, especially in precision grinding. F o r this p u r p o s e a considerable a m o u n t of research w o r k has b e e n carried out on characterizing the scattering behaviours of various engineering surfaces [1-16]. As a result two novel models of scattering have b e e n suggested: one is the diffraction m o d e l and the o t h e r is the small mirror facet m o d e l [7-10]. T h e m o d e l s are, h o w e v e r , f o u n d unsuitable for covering the whole roughness ranges of the g r o u n d surfaces which normally lie b e t w e e n 0.025-1.6 ~ m in Rq value. T h e diffraction m o d e l gives g o o d results only for periodic and s m o o t h surfaces such as a d i a m o n d - t u r n e d surface [11-13], but the g r o u n d surfaces present high r a n d o m n e s s . O n the o t h e r hand, the mirror facet m o d e l gives reliable results only for r o u g h surfaces a b o v e 0.5 ixm R a approximately, in which the dispersion of the scattered pattern b e c o m e s significant [9]. In conclusion, neither of the models fits the c o m p l e t e range of g r o u n d surfaces u n d e r consideration on the p r o d u c t i o n line. B a s e d on this fact, in this study, a new scattering m o d e l is suggested based u p o n B e c k m a n n ' s light scattering t h e o r y [17], so that reliable design guidelines of an in-process roughness sensor for the g r o u n d surfaces can be developed. * Department of Production Engineering, Korea Advanced Institute of Science and Technology, P.O. Box 150, Cheongryang, Seoul, Korea. t To whom correspondence should be addressed. 283

284

D.Y. YIM and S. W. KIM 2. BASIC BECKMANN'S THEORY OF LIGHT SCATTERING

In the early 1960s Beckmann [17] suggested a general solution of the light scattering for the Gaussian surfaces. Since the ground surfaces are generally assumed Gaussian with zero mean value, the Beckmann's solution may be usefully adopted. For a given set of the incident angle 01 and the reflection angle 02, the Beckmann's solution gives the intensity ratio 1 as:

1(01 ' 02 ) =

p(2)+ 2 L - -

-

gm

~

,

m=1 m ! \ / m

expl

]j exp ( - g )

(I)

in which

(2) (3)

F = [l+cos(el+e2)]/[cos el(cos el+COS 02)]

Vx = 2~(sin e l - s i n O2)/h

(4)

= 2qv ~ ( c o s el +cos 02)/h

(5)

Po = (sin vxL )/(vxL ).

As seen in equation (1), the Rq(=O-z) value of a surface can be obtained if the intensity ratio is measured optically for a certain set of 01 and 02, provided the correlation distance T is known. The wavelength h should be selected so as to satisfy the basic assumption implied in the solution: the radius of curvature Rc of the roughness elements should be large compared with h. For real engineering surfaces, T/Rq may be assumed equivalent to Re. Figure 1 shows the T/Rq values of the ground surfaces obtained by using Talysurf 6 in this study. It can be decided that the correlation distance T can be the average value of the spacing of adjacent crests as shown in Fig. 1. Although T/Rq tends to decrease against Rq, its minimum value is 20 when Rq reaches 1.6 I~m approximately. Thus, if a H e N e laser of 0.633 ~m wavelength is used, T/Rq turns out to be at least 30 times larger than h and the basic assumption becomes generally feasible. 3. SPECULAR INTENSITY RATIO FOR FINE SURFACES When a roughness measurement sensor is designed, various combinations of 0~ and 0z are possible. The most desirable configuration may be decided to be the specular T/R q ,

mean

T (prn)

Iin e

Air / / / / / / / ~ / / / A / / / /

Metal

140 : correlation distance

T

120

T / R q :equivalent radius of curvature 100 -

0 : T/Rq

8O 6O 4-0 2O I

I

I

I

I

0.1

0.2

0.4

0.8

1.6

Rq

(#m)

FIG. l. Average correlation distances of ground surfaces.

Optical Roughness Measurement

285

Is

:specularintensityratio at the normal i n c i d e n c e consideredcorrelatione f f e c t s --- Is neglectedcorrelatione f f e c t s Is

1.0 t

I

0.8

s

narmal ~0incidence specula~ d i f f u s e

0.6 0.4

collectlon~ \ i L.,.,.o,oo / ~ an le angle ~ ////x~/////" g e= surface

0.2 ,

J

L0125 0.025 0.05 0.1 0.2 0.4 Roughness Rq (/~rrL)

i

0.8

I

1.6

FIG. 2. Variation of specular intensity ratio at normal incidence.

reflection with the normal incidence, i.e. 01=02=0 ° as shown in Fig. 2. This combination can maximize adaptability of the sensor to complicated shaped workpieces. In this case, the intensity ratio in the specular direction, Is, can be computed by using equation (1). As for the correlation distance T, the values obtained in Fig. 1 can be used. Figure 2 shows how Is varies according to the Rq values of the ground surfaces. It can be noted that, when Rq is less than 0.1 rLm, an apparent variation in Is is noted. On the other hand, when Rq becomes larger than 0.1 p~m, no distinguishable variation is noticeable. It can then be concluded that the specular intensity Is is a good measuring parameter only for the fine ground surfaces whose roughnesses are below 0.1 ~ m Rq. In addition, for the fine surfaces, the correlation effects may be ignored (as shown in Fig. 2). Thus, the specular intensity ratio can be approximated from equation (1) as:

,,expE Let ,to be the specular intensity ratio from the 0.1 p,m Rq surface, i.e.

Ioexp[ -

-

]

.

(7)

Then, from equations (6) and (7), the roughness gq for a surface whose specular intensity ratio measured by Is can be determined, by using Io as a reference, as:

Rq ~ [0.12

In (IJlo) ],/2 (4~rcos 0,/h)2J '

(8)

4. SCATTERED PATTERN RECOGNITION FOR ROUGH SURFACES

For the rough surfaces whose roughnesses are over 0.1 I~m Rq values, the scattered pattern over a certain collection angle has to be considered. The scattered pattern is mainly characterized by the slope distribution of the surface profile. Since the height distribution of the ground surfaces has been assumed Gaussian with zero mean, their slope distribution may also be assumed Gaussian. The standard deviation of the slope distribution is then determined as tan- l (2Rq/T)/X/~. From the viewpoints of geometric optics, when the slope of a small facet of the roughness element is ~, the scattered

286

D . Y . YIM and S. W. KIM

Ib=) ....

I(e2)no,m :normalized I(oz) with with that of 0.1um Rq surface

1.0

0.05 - - I /

0.8-

2 =0.6528um, L =550um

Rq =O'lMm ~

0.2-X X /

0.60.40.20 -

I

I

I

1

I

-5-4-3-2 -1 0 1 2 3 4 5 r e f l e c t i o n angle ( 02 deg.) FIG. 3. Normalized scattered patterns at normal incidence.

Standard deviation :

L

fT(o2)d2]e

1(e,) I=um=f,I(e2) d 02 - ~

[ C&=Lj i.."

1(02) :inte, qsity ratio along g2

02 :reflection angle

-~)'2

0

~//2

L 02

~

:collectian angle

FIG. 4. Standard deviation of scattered pattern.

light reflects with a reflection angle of 0 2 = 2 0 . Therefore, the standard deviation of the scattered pattern, ors, can be determined as I--

(rs = V2 tan -1 (2gq/T).

(9)

Then, Rq is obtained as:

Rq = T tan((rJ,~F2)/2.

(10)

Figure 3 shows some scattered patterns over a collection angle d#. The patterns are normalized with respect to the response from the 0.1 Ixm Rq surface. The range of £b was taken -+5 ° . As illustrated in Fig. 4, the standard deviation of the scattered pattern, cry, can be determined as:

O's =

Is~m

in which

Isum= f, I(02)d02.

(12)

Then, by substituting equation (11) into equation (10) gives

T

R q = ~ tan

[[~1 j(1(02) d0211/2. ~ , / s u m 022

(13)

Optical Roughness Measurement O-s

IO.O

287

: s t a n d a r d deviation of scattered pattern normallsed with that of O.lum Rq surface

:0.6328 Win, L :350 wm

8.0 6.0 4.0 2.0 1.0 0

1

I

I

0.1 0.2

I

0.4

I

I

0.8

I

1.2

I

I

1.6

Rq (lJm) Flo. 5. Variation of standard deviation of scattered pattern.

Figure 5 shows how ~s varies along with R q , o"s increases at a consistent rate for all the range of roughnesses under considerations. 5.

EXPERIMENTAL RESULTS

A prototype sensor has been built to verify equations (8) and (13) suggested in the previous chapter. The sensor is composed of three main parts as shown in Fig. 6; a HeNe laser generator, an image sensing unit, and a digital data processor. The wavelength of laser is 0.633 ~m and the diameter of the parallel beam projected onto the target surface is 0.8 mm. The image sensing unit is composed of two beam splitters, a condensing lens, a photodetector and a CCD linear array. The laser beam is projected onto the target surface through a beam splitter at the normal incidence. The scattered light is collected through the condensing lens and then divided into two parts by a beam splitter: one part is directed onto the photodetector through a field stop to measure the specular intensity ratio. The other part is imaged on the CCD sensor for measurement of the scattered pattern. The CCD array is made of a line array of 4096 photodiode elements with 7 I~m spatial resolution. The digital data processor compares the specular intensity ratio Is with the reference specular intensity ratio Io prepared carefully from a reference ground specimen of 0.1 ~m Rq value. If Is is larger than Io, it is taken to evaluate the Rq value by using equation (8). Otherwise, the scattered pattern measured through the CCD array is taken and its standard deviation ~s is computed by using equation (13). A test was carried out on a series of ground surfaces and the results are summarized in Fig. 7. Performance of the sensor was verified by comparing the optical readings with those measured by using Talysurf. As seen in the figure, the results are in good agreements with less than 5% errors. 6.

CONCLUSIONS

The theory of light scattering given by Beckmann has been adopted to develop an in-process optical roughness measurement method for the ground surfaces. For the fine surfaces whose roughness values are below 0.1 ~m Rq, the intensity ratio only in the specular direction can be a good measuring parameter. On the other hand, for the rough surfaces in the range of 0.1-1.6 ~m Rq, the standard deviation of the scattered pattern yields a good measuring parameter. A prototype sensor was built and tested. Experimental results obtained by using the prototype sensor proved that the optical

288

D.Y. YIM and S. W. KIM

photodiode element 7 -4,4I-- pitch (P) /

Main software

Digital Data P'rocesso'r

8088 CPU &

memory

CCD image sensor I L _~ I

A/D

~ scattered pattern

converter L

1

CCD image sensor

photodetector

Image Sensing Unit

beam splitter

Lase'r Generator

I el nsC°ndspltierbeam

ground surface

FIG. 6. Schematic diagram of prototype roughness sensor.

1.6

o :optical roughness Rq

0.8

o ~

0.4 o

a~ 0.2 8- 0.1 0.05

o

°

°o//

0.025 I

I

I

I 1.6

Tolysurf Rq(urn) FIG. 7. Verification of optical results using Talysurf 6. m e t h o d established in this study is capable of real-time monitoring of the roughnesses ranging 0.025-1.6 txm Rq with less than 5% errors c o m p a r e d with stylus m e t h o d . REFERENCES [1] D. J~ WHITEHOUSE,'Comparison between stylus and optical method for measuring surfaces', Ann. CIRP 37, 649-653 (1988).

Optical Roughness Measurement

289

[2] L. H. TANNERand M. FAHOUM,'A study of the surface parameters of ground and lapped metal surfaces, using specular and diffuse reflection of laser light', Wear 36, 299-316 (1976). [3] E. L. CHURCH, 'The measurement of surface texture and topography by differential light scattering', Wear 57, 93-105 (1979). [4] E. G. THWAITE, 'Power spectra of rough surfaces obtained by optical Fourier transformation', Ann. CIRP 29, 419-422 (1980). [5] E. G. THWAITE,'The extension of optical angular scattering techniques to the measurement of intermediate scale roughness', Ann. CIRP 31, 1 463-465 (1982). [6] I. INASAKI,'Development of In-process Sensor for Surface Roughness Measurement', 23rd Proc. Much. Tool Des. Res. 109-113 (1983). [7] R. BRODMANNand G. THURN, 'An optical instrument for measuring the surface roughness in production control', Ann. CIRP 33, 1 403-406 (1984). [8] R. BRODMANN, O. GERSTORFERand G. THURN, 'Optical roughness measuring instrument for finemachined surfaces', Opt. Engng 24, 3 408-413 (1985). [9] R. BRODMANNand G. THURN, 'Roughness measurement of ground, turned and shot-peened surfaces by the light scattering method', Wear 109, 1-13 (1986). [10] R. BRODMANN,'Roughness form and waviness measurement by means of light scattering', Precis. Engng 8, 4 221-226 (1986). [11] H. T. HINGLE and J. H. RAKELS, 'The practical application of diffraction technique to assess surface finish of diamond turned parts', Ann. CIRP 32, 1 499-501 (1983). [12] J. H. RAKELS, 'The use of Bessel functions to extend the range of optical diffraction techniques for inprocess surface finish measurements of high precision turned parts ~, J. Phys. E: Sci. Instrum. 19, 76-79 (1986). [13] J. H. RAKELS, 'In-process surface finish measurement of high quality components', Proc. Int. Congr. for Ultraprecision Technology, pp. 303-316, Springer (1988). [14] F. SWEENEYand T. A. SPEDDING,'A simulation technique to investigate rough surface scatter', Wear 109, 43-56 (1986). [15] C. S. LEE, S. W. KIM and D. Y. YIM, 'An in-process measurement technique using laser for non-contact monitoring of surface roughness and form accuracy of ground surfaces', Ann. CIRP 36, 425-428 (1987). [16] M. SHIRAISHI,'A consideration of surface roughness measurement by optical method', A S M E J. Engng Ind. 1119, 100-105 (May 1987). [17] P. BECKMANNand A. SPIZZICHINO, The Scattering o f Electromagnetic Waves from Rough Surfaces. Pergamon Press, Oxford (1963).