3D optical profilometer for wide range topographical measurement

197

Wear, 165 (1993) 197-203

A fast 2D/3D optical profilometer measurement

for wide range topographical

M. Zahidi, M. Assoul and J. Mignot Laboratoke de ~~t~~o~.e des Interfaces Techn~ues, Insritut Unive~ita~re de Tec~o~~~,

25009 Besangon Cedex (France)

B. Bellaton Digital Surf SARL, Valparc Valentin, 29 route d’Epina1, 25048 Besangxm Cedev (France) (Received

Juiy 20, 1992; accepted

December

17, 1992)

Abstract profilometer, based on a triangulation principle, has been designed to measure the topography of surfaces. It uses a laser diode source (h=0.788 pm) and position sensing detectors. Response is obtained with a minimum of error due to a double detection system. Sensitivity is about f3 grn for a vertical range of 1 mm. Vertical range can attain 5 mm, and more than 10 mm with a wide range numerical arrangement. Non-contact with the surface means a scanning speed of about 4 mm s-l, and a 512~512 matrix (with a 12 bit definition) can be created in 9 min.

An optical

1. Introduction

The measurement of the surface topography of most functional surfaces has now become necessary. Usually, this measurement is made by means of a mechanical profilometer; the measurement system is based on the vertical displacement of the tip of a diamond pyramid in contact with the surface, in movement in a given direction, with a constant speed. This type of measurement has two disadvantages: There is true contact between the surface and the profilometer; even when the contact pressure is very light, a plastic deformation of the surface can occur [I-41* Mechanical contact requires the use of a stylus speed of less than 0.5-0.8 mm s-“, engendering a long measurement time, especially when 3D measurements are required. Numerous optical detectors have been developed over the last few years. All of them are based on a focusing technique and show a relative slowness in measuring speeds because of the necessity of the displacement, at each step of measurement, of a mechanical part (the focusing system). To respond to the demands of non-contact and more rapid acquisition of data, we are proposing a new optical system.

2. The principle of the optical system This system is based on a triangulation method, already in use in apparatuses other than those used for topography measurements. This method uses three reference points (Fig. 1): the fixed source (a laser diode); the point of the surface to be analysed (the height of which varies depending upon the local relief); and the image of this point formed on the detector plane. Manufacturers such as SITEK [5} use such a system for distance and proximity measurement and for analysis of structure vibrations. STS Relais Ltd [6] uses the same principle for position measurement. Lee [7] aimed at extracting the shape and waviness of solids, since only an approximate value laser

diode

s*mph

Fig. 1. The principle

of the triangulation

method.

0 1993 - Eisevier Sequoia. All rights resewed

M. Zahidi et 01. I Fust 2Dl3D optical profilornctc~r

1%

of the roughness is deduced from the light distribution according to the Beckmann theory [8]. The principle proposed by Lee is shownin Fig. 2, in which the incident laser beam is parallel and the detectors are composed of a set of photo diodes. The use of a system where the detector is not perpendicular to the surface gives a response which distorts the initial signal. In the system we propose, two detectors are used, placed symmetrically in relation to the perpendicular surface. Figure 3 shows the distortion of the two output signals given by each detector from the same surface profile. The use of two symmetrical detectors yields a mean value showing a minimum of distortion and noise. The principle is demonstrated in Fig. 4: from the source, a first optical system Ll focuses a beam on a point of the surface of the sample. The size of this spot is about 6 pm. The divergence of this incident beam depends on the choice of the Ll system. A lens with a focal length of 80 mm or more can be used to decrease the beam divergence. The spot created in this way is used as a new source for the

ifier

Fig. 4. The

principle

of the measurement

incide

t

system.

light

P

d’.‘erN

Fig. 5. The

principle

of the PSD

system.

measurement optical system L2, which forms an image on the focal plane of L2 from this spot. On this plane the detector measures the lateral position of the image and thus determines the height z of the analysed point of the surface. The last lens used in this optical receiving system has a focal length of 48 mm.

3. Source and incident

J Fig. 2. Optical

measurement

of waviness

and form

by Lee et al

beam

The source is a laser diode (06 DLL type by MELLES GRIOT) with the following general characteristics: power, 3 mW; wavelength, 0.788 pm; diameter, 7.5 mm; divergence, 0.2 mrad. The inherent astigmatism of the diode is less than 5 pm and is corrected by a weak cylindrical positive lens. The circularity of the output diode laser beam, measured by the beam size ratio in two orthogonal directions, is better than 1.1.

171.

4. Detection

w-

“I

Fig. 3. Shape

‘s of the

16 signals

15 given

20 by each

mm

detector.

and treatment

of the signal

In order to reach sufficient sensitivity, the detectors used are of the PSD (position sensing detector) type, chosen because of their capacity to measure the position of scattered light emitted by a source whatever the light intensity. The model is the lL10, manufactured by SYTEK [5]. The charge emitted by the semiconductor migrates through the resistive coating P (Fig. 5) and is then collected by the electrode located at each side of the PSD. Since the resistive coating is uniform, the photocurrent collected by one electrode is inversely

M. Zahidi et al. / Fast 20130

proportional to the distance separating the impact point from this electrode. The position of the spot is then deduced from the difference i, -iz between the photo currents received by each of the two electrodes. The characteristics of the detectors are summarized as follows: sensitive area: 10X2 mm rise time: 2 ps resolution: 1 pm bandwidth: 2 MHz detector resistance: 50 kR position non-linearity: * 0.1%

make the treatment easier, a summing amplifier adds a voltage P,,, equal to the amplitude of the measured signal S(t). The modulated signal is thus: P,(t) “P,

+s(t) cos CLJt

x= (il - i,)/(i, + i,)

(2)

If, for example, the measured sine law: Pm(t) =P,[l+

(S,/P,)

signal S(t) obeys a

sin wt] cos f&t

Pm(t) “P,

cos QcJ + (mPJ2)

cos&

- o)t

cos(r(2, + w)t

(4)

The modulated spectrum is composed of three components with frequencies Q, - o, Q, and Q, + w. For a real signal s(t), with the frequency limits w, and %,, the modulated spectrum is composed of two frequency bands (Fig. 8):

(1)

At each point of measurement, the system must be able to read the four elementary currents (il, i,, irl, i’J and to calculate the sums and differences previously defined. All these measurements and calculations must be performed during displacement between two neighbouring points of the surface. The synoptic scheme of the treatment is given in Fig. 6, where all the electrical signals necessary for the measurement are indicated. With these capabilities, such a system must be able to function independently of external residual lighting. In fact, the detector is sensitive to all the light energy on its surface and in particular to the surrounding light. In order to avoid this problem, a modulation of the laser beam is used. The incident laser beam is modulated by a sine wave at a frequency J&,of 10 kHz. A multiplier circuit is used as indicated in Fig. 7, and in order to

and [a,+

wh,

%

+

;wh}]

To increase the sensitivity of the measurement, there are four possible values of magnification, based on the multiplication of the initial values of the differences (V, - Vz) and (V’, -V’,) by given constant coefficients. The choice of the magnification coefficient, i.e. the choice of the vertical range of the system, is made by software. A 4052 analogue multiplexer selects (Fig. 9)

Fig. 7. Adder

and

multiplier

circuit.

Pm

( /yy (,Fh IO-oh RO -cob n0 Fig. 8. Modulated

Ditfl

Fig.

DlffP

6. Synoptic

(3)

and for the modulating ratio rn =&,/Pm, then

+ (mPJ2) In order to take into account the variation of light intensity due to local reflectivity [9, lo], the (iz-il) difference is normalized by the sum i, +i,, which is proportional to the light intensity. The final signal which is used for each detector is

199

optical projilometer

s1

scheme

52

of the

53

54

treatment

11

of signals.

aO+ob RO+oh

spectrum

of a real

signal.

12

Fig. 9. Selection

of the vertical

magnification.

200

M. Zahidi et al. J Fast 2Dl3D optical profilometer

one of the resistors on the muItiplexer_ After the range coefficient is determined, the anafogue signal is sent to a 12 bit analog/digital converter.

5. Antomatic approach to the surface: auto focus A focal length is chosen between the optical device and the surface to be measured. A stepping motor vertically displaces the optical profilometer. The displacement is deduced from the measurement of the VI, V, and Vi, v’, values. A VI - V, #O and/or a v’,v’,#O value measured before the beginning of the procedure controls the displacement of the optical system until these differences reach a minimum value. The signals given by the detectors are in the middle of the range and a 2D or 3D measurement can begin.

6. Increase of the range

Fig. 11. Vertical

Table 1 shows the width of the vertical range of the system and its ~ncomitant required sensitivity. In special cases, a greater width might be desired for this range, without any sensitivity loss. To deal with such a problem, particularly for the measurement of surfaces showing a large defect of form and a low roughness, the vertical position of the optical profilometer adapts to the shape of the analysed surface. This vertical displacement, obtained by using a stepping motor, is independent of the mechanical precision of this device because of the following numerical treatment, already utilized in a mechanical profilometer [ll]. The digital signal given by the profilometer is converted into a numerical value between 0 and 4095. This range is divided into five zones (Fig. 10). (1) From zero to satmin (satmin is a numerical value which varies with magnification). In this zone, every point of measurement leads to the saturation of the electrical signal. When a point reaches this value, the measurement process must be stopped. This zone constitutes the limit of measurement of the lowest height. (2) From satmin to (Y.This zone forms the disconnected lower part of the vertical range, in which every TABLE

1. Vertical

Fig. 10. Zones of the numerical

range and sensitivity

Amplification

Sensitivity (brn per digit)

Vertical km)

1 2 3 4

0.41 0.19 0.06 0.03

2500 1150 370 210

range

(3) (4)

(51

displacements

signal.

in function

of the signal.

point of measurement must be moved to the central zone by a displacement of the measurement system. The first zone is thus avoided by mechanical vertical displacement of the measurement system, so that a signal with a value near the middle of the vertical range can be obtained. During this vertical displacement, the horizontal displacement of the sample is stopped to bring the reading into the useful range again (Fig. 11). From a to j?: this zone is the useful range, in which the signal obeys the linear law i = LYZ. From, p to satmax: this zone has the same characteristics as that of [satmin, CX].It constitutes the disconnected high part in which every point of measurement should be moved by displacement into the [(Y,p] zone. From satmax to p: when a point reaches this value, the measurement process is stopped.

The maximum travel Iength that can be described using the same optical apparatus without this wide range arrangement depends on the local slope of the measured surface. With our system, the vertical range given in Tabie 1 can be greatly increased. The only l~itation is that of the range of the stepping motor. When the signal given by the detectors reaches zone 2 or 4, the vertical displacement is linked to the measurement of the numerical signal as follows. If j is the point corresponding to the jth vertical displacement, this point has a zj measured height. The real height relative to a fixed origin is

M. Zahidi et al. I Fast 2Di3D optical projilometer

201

where c&e& is the sum of all the previous vertical displacements, from the first measuring point on. At each new translation, the new value of offset, is given by f-$LW =

+ I

offseti + (2.I+ 1 measured

-Z. J + 1 measured

before

displacement

after displacement >

(6)

Using this principle, the mechanical errors due to vertical displacements of the optical system do not affect the accuracy of the measurement, since only the numerical values of the signal before and after each displacement are taken into account, whatever the real displacement. An example of the wide range measurement of surface topography is given in Fig. 12, where a triangular standard is used, showing 12 000 pm of vertical range (Fig. 12(a)), and a real difference in height of 4000 pm after elimination of the artificial slope (Fig. 12(b)).

Fig. 13. Defect of flatness of the reference by measurement of a perfect plane.

(2)

7. Accuracy and reproducibility of the measurements The purpose of our apparatus is to measure surface topography showing the significant differences in height, at a fast rate of measurement. The accuracy of this system depends on a number of factors. (1) The defect offza tnes.r of the reference plane generated by thex andy slides. The mechanical device which is chosen can radically affect accuracy. We have found that the Schneberger@’ system, which displaces a plane over balls as shown in Fig. 13, gives the best results: residual waviness is insignificant inside the analysed area (7.5 ~7.5 mm) and roughness is about 1 pm. This figure is obtained by the measurement of a perfect standard plane

ismm

(0)

(4)

(b) Fig. 12. (a) Initial surface;

(3)

(b) after levelling of the surface.

plane used (obtained

with surface defects of less than 5/1000 pm over a 70 mm diameter. The variations of the spot size can be a significant source of error when surfaces with great defects are measured. The PSD is sensitive to the position of the centre of gravity of the spot and not to the shape of the whole lit area. Therefore, if a small error is made in the determination of the spot position, then the lateral resolution will change with the real size of the spot and will induce a more serious error. For example, with a focusing lens with a focal length of about 48 mm, the size of the spot becomes 150 pm after a vertical displacement of about 1 mm when no special system of increasing the vertical range is used. The variations in spot size induce errors in the determination of roughness or shape. In the measurement of a periodic grating (with P, = 3370 pm), the maximum difference in the results is P, = 3350f 137 pm when the focusing point is displaced between the lowest and highest points of the profile. The no&e of all the electronic parts of the system can be measured by means of the fluctuations of the output digital signal when the surface is perfectly flat or when the measuring point remains the same. The mean fluctuation is about + 4 digits over a vertical range of 12 bits (4096 values), i.e. an error of about &-l/1000 of the full range. The reproducibility of the measurement is given in Table 2 for two extreme cases: either for low amplitude defects (R, = 19.6 pm; R, = 3.17 pm) or for wide amplitude defects (Pt =3336 pm; P, =867 pm). In both cases, 10 measurements were made on the same profile, each of them obtained after a new focusing on the surface. The results show a low dispersion expressed by the standard deviation.

202

M. Zahidi et al. I Fast 20130

TABLE

2. Reproducibility

of measurements

Profile

R,

R,

p,

P,

1 2 3 4 5 6 7 8 9 10

3.19 3.22 3.16 3.16 3.16 3.14 3.17 3.15 3.19 3.5 x=3.17 a=0.023

19.68 18.75 19.92 20.04 20.62 18.8 19.33 20.27 19.57 18.98 x= 19.61 o= 0.58

3336.4 3336.4 3338.1 3334.7 3338.1 3336.4 3336.4 3334.7 3334.7 3336.4 x = 3336.25 o= 1.19

866.8 867.1 867.1 867 867.3 867.1 867 867.3 867.1 867 x= 867.0 v= 0.12

Fig.

14. Practical

realization

of the optical

optical profilometcr

15. Two personal computers are used: a PC/AT for the acquisition of the data, the control of the displacements and the elementary operations between the signals; and a Macintosha personal computer, which, upon receiving the profile or the 3D image of the surface via a local connection, produces all the numerical treatments and displays.

9. Examples

of practical

applications

The purpose of the following examples is to show the potential for this system, and its limitations in measuring small defects and a wide range defects of form. For all these cases, the sensitivity of the system will be given. In order to show the applications of this apparatus, two examples follow. The first example is related to a surface which presents a periodical shape with little amplitude. This surface has a maximum variation of amplitude of about 12 pm only. Figure 16 gives the three-dimensional representation of this surface and shows an uncertainty of about t-2 pm, thus indicating the lower limits of the system. The same precision, however, can be obtained inside a vertical range of 1.2 mm. The second example is related to the study of the topography of a plastic material used in the car industry. Such surfaces present a relief (Fig. 17) whose horizontal

system.

Fig. 16. Sample area after form filtering. is about 6 pm (area 0.57X0.72 mm).

Fig.

15. The

8. Practical

principle

entire

amplitude

of the system.

realization

of the measurement

system

The practical realization of the optical system is shown in Fig. 14. The laser diode and the focusing lens make up the central part; the two optical detecting systems and the preamplifiers are located on each side, with a 45” angle from the perpendicular to the surface. The

The maximum

measurement

system

is described

in Fig.

Fig. 17. Example (R, = 120 pm).

of surface

with

a relief

of mean

amplitude

M. Zahidi et al. / Fast 20130 optical projiiometer

203

distribution plays a major role in the visual aspect. A good knowledge of the topography is therefore needed by car manufacturers in order to ensure good product quality. The vertical amplitude of such defects reaches 120 pm, with a horizontal mean wavelength of about 800 pm. For defects of this range of amplitude, our detector is well adapted, even for a real time control.

large defects of form. A vertical range of up to 1.2 mm can be analysed with a sensitivity of 3 pm: a scale of 8 mm is available with the same characteristics of measurement speed. For greater vertical differences in height, a wide range algorithm controls the vertical displacement of the optical system, thus yielding an important increase of the range with no loss of sensitivity.

10. Conclusions

References

This new optical profilometer is based on a triangulation principle. In order to minimize the response distortion, a double symmetrical detection system has been used. Because of the absence of contact, data acquisition can be obtained very quickly. Measurement time depends on the choice of the displacement system (continuous or stepping motors). With our apparatus, a speed of measurement of up to 4 mm s-’ can be reached. Using this speed value, 3D data acquisition of a 256~256 matrix of points takes less than 6 min. When this decrease in measurement time is compared with the value obtained using a mechanical system, it is clear that the extent of the vertical range of our system allows the measurement of surfaces with even

1 A. W. Bush, R. 0. Gibson and G. P. Keogh, Mech. Res. Commun., 3 (1976) 169-174. J. Dyson and W. Hirst, Proc. Phys. Sot., 67 B (1954) 309-312. W. B. Estill and J. C. Moody, ISA Trans., 5 (1966) 373-378. V. Radakrishnan, Wear, 16 (1970) 325-335. SITEK”, Electra optics, Position Sensing Detector, Ogardeswagen 13A 43330, Partille, Sweden. STS Relais Ltd, Photoelectric cell, Zac Nord, 10 Rue des petits ruisseaw, 91370 Verrieres le Buisson, France. C. S. Lee, S. W. Kim and D. Y. Yim,Annals CIRP, 36 (1987) 332-339. P. Beckmann and A. Spizzichino, The scattering of electromagnetic waves from roughness surfaces, Artech House Inc., Norwood, MA, 1987, p. 14. 9 H. E. Bennett and J. 0. Porteus, .I. Opt. Sot. Am., 51 (1961) 123-129. 10 C. A. Depen and R. D. Weir, Appl. Opt., 10 (1971) 969-970. 11 M. Chuard, J. Mignot, Ph. Nardin and D. Rondot, J. Manufi System., 6(3) (1987) 223-231.