IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL 41, NO 6, DECEMBER 1992 1057

Surface Roughness Measurement with Optical Fibers Andrzej W . Domanski and Tomasz R. Woliriski

Abstruct-The paper discusses development of a new method of surface roughness measurement utilizing optical fibers. Two general types of fiber-optic roughness measurement are pre- sented: intensity-based and polarization-based which require use of either multimode or single-mode polarization-preserving optical fibers. Some configurations, including different con- structions of a fiber-optic head, and the specific requirements for optical fibers are also discussed. The data obtained from the intensity and polarization measurements are correlated with some roughness parameters.

I. INTRODUCTION VER the past decade, optical methods to characterize 0 surface finish have been increasingly used in indus-

trial applications. Use of optical methods to evaluate the state of surface roughness has many advantages over clas- sical mechanical methods. In addition to high speed of response, great accuracy and reliability, the most impor- tant of these would seem to be: the absence of contact with the measured surface, nondestructiveness, and in- spection of an area instead of a line. The current trend towards much faster and noncontacting techniques of de- scribing the microirregularities of surfaces has led to re- newed interest in the application of optical sensors. How- ever, the classical optical methods [l], such as total integrated scattering (TIS) or angle-resolved scattering (ARS), require complicated optical systems and optical alignment which is an essential drawback, sometimes dif- ficult to overcome.

The aim of this paper is to present a new approach in roughness measurement by optical methods which relies on application of optical fibers to guide optical signals to and from the rough surface. Two types of roughness mea- surement, intensity-based and polarization-based, are dis- cussed, each of them utilizing special types and configu- rations of optical fibers.

11. ROUGHNESS MEASUREMENT Rough surfaces are generally characterized by their av-

erage roughness ( R J , rms or quadratic mean roughness ( R q ) , and rms or quadratic mean slope (Aq), where

Ra = (1/N) Ej lhj I

Manuscript received May 14, 1992; revised August 20, 1992. The authors are with the Institute of Physics, Warsaw University of

IEEE Log Number 9206143. Technology, Koszykowa 75, 00-662 Warszawa, Poland.

where A, = [(h, + - h,)/L] is the j t h slope value in the stylus trace, h, is the j t h value of the trace height, N is the number of sampled points in the stylus trace, L is the sampling length (data-point spacing), and the summation runs over all N values in the trace. Usually, the height profile h(x) is described as a stationary random process with mean value (h (x)) = 0. All the roughness parame- ters described in (1) are not intrinsic properties of the samples, and they are inherently connected with instru- mental parameters.

In this paper we will use the rms roughness R, which is an estimate of the standard deviation of the function h(x), since

L '12

Rq = [ (1/L) So h ( x ) &I [(1/N) Ej$] * (2)

Roughness measurement could be greatly simplified by using optical fibers to guide light to and from the mea- sured surface. Our previous work [2] has shown that con- struction of a fiber-optic head for small roughness mea- surements (Rq in the order of 50 nm) is possible. The head consisted of two detecting optical fibers and one optical source fiber directed at an angle of 45" to the measured surface. The data obtained from the reflected light inten- sity measurements were directly correlated with a number of standard parameters characterizing the surface rough- ness. On the other hand, for rougher surfaces (Rq greater than 150 nm), direct application of optical methods seems to be more complicated. A construction of the fiber-optic head with one source fiber and one detecting fiber [3] gave promising results in differentiating the various surface roughnesses. However, this type of sensor was not stable enough for industrial applications. The next step [4] was to develop a fiber-optic surface roughness sensor incor- porating two different light sources. In this sensor, two different wavelengths of light are guided by bundles of optical fibers with a large numerical aperture, then re- flected from the surface being investigated and detected almost normally. By applying special optimization pro- cedures and using an advanced electronic system we have developed a surface roughness sensor that was immune to small displacements and vibrations, such as those which occur in production control or on-line measurements.

In the past few years, there has been a general interest to exploit the polarization changes in light scattered from a rough surface to roughness measurement. Some ad- vanced classical ellipsometric methods [5] have been suc- cessfully applied indicating that ellipsometry is influ- enced by surface roughness [6], [7]. Following this trend,

0018-9456/92$3.00 0 1992 IEEE

1058 IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT. VOL. 41, NO. 6, DECEMBER 1992

we have recently reported a new fiber-optic method of surface roughness measurement which is based on depo- larization of light reflected from a rough surface [8].

111. OPTICAL FIBER SENSORS

Optical fibers can be divided into two classes: single- mode (SM) fibers and multimode (MM) fibers, depending on the number of modes which can be propagated along a fiber. The main difference between SM and MM fibers is core size. Typical core radius is -25-50 pm for MM fibers, but SM fibers require - 2-5 pm. Typical cladding radius is 125 pm for both SM and MM fibers. For en- hancing intensity of the light transmitted, bundles of MM fibers are used in which every single fiber has core radius 40 pm and cladding 60 pm.

A well-defined and controlled state of polarization of the light along the fiber path is preserved only in a polar- ization-maintaining fiber (PMF). There are generally two kinds of PMFs: high-birefringence (HB) fibers and low- birefringence (LB) fibers. HB optical fibers eliminate the influence of external parameters in unstable environments and simultaneously preserve the linear polarization state of light injected into a fiber in a plane parallel to one of its two principal axes. For any other input polarization direction, the two orthogonal quasi-linear polarized field components HE, and HE, of the propagation dominant mode HEll (or LPol) are excited. Since the two orthogo- nal mode components have different propagation con- stants &, by, they run into and out of phase at a rate de- termined by the birefringence of an HB fiber, thus producing a periodic variation in the transmitted polar- ization state from linear to circular and back again. The radial scattered intensity, which is dependent on the po- larization of the transmitted light, fluctuates with the same periodicity, beat length LB, defined by LB = 27r/(& - p,). LB fibers are characterized by negligible internal birefringence (high beat length values) and are made by rotating the preform of a conventional fiber about its lon- gitudinal axis during fiber drawing so as to impart a per- manent twist to the fiber.

Over the last decade, there has been extensive research and development activity to design and realize fiber-optic sensors for the measurement of physical and chemical variables. Examples of typical measured parameters in- clude pressure, temperature, flow, vibration, electric, magnetic and acoustic fields, linear and rotatory displace- ment, velocity, chemical concentration, pH, and the par- tial pressure of gases. Today and in the near future fiber- optic sensors are supposed to be used increasingly in a number of areas, including industrial process control; the electric power industry; the military sector; the biomedi- cal and chemical sector; aerospace; robotics; nondestruc- tive testing and evaluation and in many other fields. These newly emerging fiber-optic devices offer important advan- tages in comparison to conventional sensors. Since they are fabricated from dielectric materials (silica or plastic) they are suitable for use in electrically dangerous, hazard-

ous, noisy, or explosive environments; they are com- pletely immune to the effects of electromagnetic interfer- ence, and they have far greater sensitivity. Adding to their effectiveness is the fact that they are directly compatible with fiber-optic telemetry, optical data transmission sys- tems over long distances, and optical multiplexing/de- multiplexing technology.

There are two general categories of optical fiber sen- sors: extrinsic and intrinsic sensors. In extrinsic sensors, the optical fiber is simply used to guide light to and from a place in which a fiber-optic head is located. The sensor head is designed to modulate the properties of light in response to changes in the measured parameter of inter- est. In this way, optical fibers transmit optical energy to the sensor head, where the light exits from the fiber, then is appropriately modulated and coupled back via a sec- ond, receiving fiber, which guides it to the optical detec- tor. Intrinsic sensors operate through the direct modula- tion by the measured parameter of the light guided in the fiber. Optical fiber sensors, either extrinsic or intrinsic, may be classified into one of the four general categories: amplitude (intensity) sensors , wavelength or frequency sensors, interferometric sensors, and polarimetric sen- sors.

Surface roughness optical fiber sensors belong to ex- trinsic, either intensity-modulated or polarization-modu- lated sensors. The intensity-modulated sensors utilize either bundles or single MM fibers to guide optical signals to and from the rough surface, whereas the polarimetric sensors are based on polarization-maintaining fibers. In particular, an HB PMF can be suitable for delivering op- tical signals to a rough surface, whereas LB fibers with birefringence reduced by fabrication processes can be used to guide light for short distances from the rough surface while maintaining its state of polarization.

IV. REFLECTION OF POLARIZED LIGHT FROM ROUGH SURFACE

Ellipsometry (measurement of the ellipse of polariza- tion) is an optical technique for the characterization and observation of events at an interface or film between two media and is based on the polarization transformation that occurs as a beam of polarized light is reflected from or transmitted through the interface or film. Ellipsometry re- lying on the measurement of the state of polarization of the wave vector of the polarized light reflected from a sample with a thin optical film has traditionally been used to characterize the optical properties of a reflecting spec- imen in terms of two parameters, % and A [ 5 ] . % is an angle whose tangent gives the ratio of the amplitude at- tenuation (or magnification) upon reflection for two ei- genpolarizations (parallel and perpendicular to the plane of incidence), whereas A gives the difference between the phase shifts experienced upon reflection by the two po- larizations. When a specimen under investigation is suf- ficiently flat, the changes in the polarization state of light reflected from the surface are completely determined by

DOMA~ISKI AND WOLINSKI: SURFACE ROUGHNESS MEASUREMENT 1059

these two ellipsometric parameters, and the thickness of the optical film together with its refraction coefficient can be easily calculated. The same approach can be applied directly for smooth surfaces without an optical film being deposited.

However, for rough surfaces, it is not adequate to de- scribe the effect of reflection only in terms of * and A [7]. Apart from changes in the state of polarization of the reflected light, there may be significant amounts of de- polarization and cross-polarization resulting in a change in the degree of polarization, which cannot be character- ized without the introduction of additional parameters. One of the approaches describing not only the state of polarization but also the degree of polarization of a quasi- monochromatic (or monochromatic) light wave is the Stokes method, in which a plane wave of light can be represented by a set of four real quantities called the Stokes parameters, So, SI, S,, S3, each of which has the dimension of light intensity. With the aid of the Stokes parameters, we can describe first the degree of polariza- tion of partially polarized light:

(3) 2 1/2 P = &,/4ot = [(S: + G + S3)l /So

where Zpol is the intensity of polarized light and I,,, is the total light intensity, and second, the state of polarization by calculating ellipticity angle E (arctg E = b / a , where a and b are elliptical axes as seen in Fig. 1 (C), of the ellipse of polarization:

E = $ arcsin is3/[($ + S: + ~ 3 1 ' / ~ ) (4)

e = arctg s2/sI (5 )

and third, the azimuth 8:

defining the position of the elliptical axis towards a given coordinate system (Fig. l(C)).

The Stokes method can be very useful in the analysis of polarization properties of light reflected from a rough surface since all the elements of the Stokes vector can be calculated from experimental data obtained with the help of a quarter-wave plate and an analyzer to measure the following intensities: So = Z(0, 0) + Z(90°, 0), SI = Z(0,

90') - Z(135", 90"), where the first value in the brackets defines the position of the fast axis of the analyzer and the second one signifies the presence (90) or absence (0) of the quarter-wave plate [8].

0) - Z(90°, 0), S2 = Z(45", 0) - Z(135", 0), S3 = Z(45",

V. EXPERIMENTAL Depending on the measurement principle (intensity-

based or polarization-based) , two generally different ex- perimental setups for roughness measurement have been used. Intensity-based measurement was performed in the setup whose diagram was described in details elsewhere [4]. In this measurement, a three-branch optical fiber ca- ble with MM fibers was used in which two branches were coupled to two different sources (light-emitting diodes) and the third was coupled to a photodetector. A special

(b) hY1 BIREFRINGENCE

I ....................... ///////////////////m - 0 2

ROUGH $URFACE

(a)

Fig. 1 . A general configuration (a) of the polarization-based surface roughness sensor with an orientation of birefringence axis of an HB source fiber (b) and parameters of the polarization ellipse of an LB detect fiber

L ?J2 P CHOPPER

SINGLE-MODE\ "--"/ SINGLE-MODE LOW- BIREFRINGENT FIBER POLARIZATION-

MAINTAINING FIBER - - - /;- j l 0 .6 ,,,,,, (SMLBF) (SMPMF) 7///,//N/N//~///////~/////// ,

<-.....---*

Fig. 2. Experimental setup for polarization measurements of light scat- tered from a rough surface.

optimization procedure was performed which relied on a proper choice of light sources, distribution of optical fi- bers in fiber-optic head, and distance characteristics.

The block diagram in Fig. 2 shows the experimental setup for polarization-based measurements of light scat- tered from a rough surface. Linearly polarized monochro- matic light from a He-Ne laser (A = 633 nm) chopped at 130 Hz was launched along a birefringence axis into an HB 600 York bow-tie fiber. The HB fiber preserved the input polarization state of the light, which was guided to a rough surface. The orientation of the birefringence axes is shown in Fig. l(B). The signal scattered by the rough sample was transmitted through a short length of LB fiber (with no bending) and after passing through a quarter- wave plate (optionally) and an analyzer, was detected se- lectively by a photodiode. The distance between the op- tical fibers and the sample was optimized to 0.6 mm.

Fig. 3 presents constructions of the fiber-optic head for intensity-based (A) and polarization-based (B) roughness

1060

SOURCE FIBERS

&- 20" 4

(b) Fig. 3 . Design of the fiber-optic head for the intensity-based (a) and po-

larization-based (b) roughness sensor.

measurement. In the polarimetric sensor, a bending of the input HB fiber was assumed. All the experiments were conducted on rough samples obtained from the electro- spark machining with an isotropical distribution of rough- ness. The finest specimen had a value of rms surface roughness R, = 0.47 pm while the roughest had the value R, = 30.0 pm.

VI. RESULTS AND CONCLUSIONS The intensity-based roughness measurement was

strongly dependent on distance characteristics which is the essential problem of the method. However, for every sin- gle configuration of MM optical fibers [4], there is an op- timized insensitive region of the displacement character- istics (fiber-optic head - rough surface) for which resolution of roughness measurement is high enough to differentiate various rough surfaces. Fig. 4(a) presents the insensitive (d = 20 mm) and the steep (d = 34 mm) re- gions of the displacement characteristics in the intensity- based measurement.

In the polarization measurement (experimental setup presented in Fig. 3) we measured six light intensities: Z(0, 0), Z(90", 0), 1(45", 0), Z(135", 0), Z(45", 90"), and 1(135", 90"), for the six rough samples and for different positions of the input polarization plane defined by the angle CY (Fig. 1). Based on the data obtained, we calcu- lated the degree of polarization P, the azimuth 8, and el- lipticity E. The results indicate that there is no correlation between rms R, roughness and the state of polarization of the light scattered from the sample, for various angles CY

and different configurations presented in Fig. 2. How-

L J 20 30 0 10

HB-6W INPUT FIBER I I

I

6 11 16 21 26 31 36

RMS ROUGHNESS, lOOnm CO)

Fig. 4. (a) Intensity-based fiber-optic roughness measurement in a steep (d = 34 mm) and insensitive (d = 20 mm) region of displacement char- acteristics. (b) Dependence between the R, roughness parameter and the degree of polarization for the incident polarization defined by the angle a = 45" from Fig. 1, in polarization-based fiber-optic roughness measure- ment (incidence angle also is equal to 45").

ever, the degree of polarization P , for angles which are not equal to 0" and 90", depends on the roughness param- eter R, which is shown in Fig. 4(b), for the angle CY = 45". The results were obtained for several values of in- cident angles and finally, the angle C#J = 45" was chosen along with five selected positions of the plane of polari- zation of the light incident on the rough surface. Since in polarization measurement single-mode PMF's are used (core diameters about one order of magnitude lower than for MM fibers) the best coupling conditions are achieved for small optical fiber head - rough surface distances (less than 1 mm).

Our work allows us to conclude that our cost-effective (specially in the case of intensity-based measurement) and uncomplicated fiber-optic method with its compact, flex- ible, remote-controllable setup, allows differentiating sur- face roughnesses in the range of 0.5-30.0 pm (R,) based

DOMANSKI AND WOLINSKI: SURFACE ROUGHNESS MEASUREMENT

on measurement either of light intensity (intensity mea- surement) or of the degree of polarization (polarization measurement) of light scattered from the rough surface.

We believe this represents an interesting approach in fiber-optic metrology of a new generation, particularly promising for production control or industrial on-line measurement.

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