Fundamentals and Practices of Sensing Technologies by Dr.
Keiji Taniguchi, Hon. Professor of Xi’ an Dr. Masahiro Ueda, Honorary
Professor, Faculty of Education and Regional Studies Dr. Ningfeng Zeng, an
Engineer of Sysmex Corporation (A Global Medical
Instrument Corporation), Dr. Kazuhiko Ishikawa,
Assistant Professor Faculty of Education and
Regional Studies, [Editor’s
Note: This paper is presented as Part XI of a series from the new book
“Fundamentals and Practices of Sensing Technologies”; subsequent chapters will
be featured in upcoming issues of this Journal.] Chapter Five – Part III 5.9 Surface Displacement Sensor 5.9.1 Introduction In the
manufacturing process of plasma display and liquid-crystal panel, the size of
the original panels become increasingly large to economize time and money; the
size of 1.1m In this section, an optical method for measuring surface displacement in real time has been proposed without any movable components, and some characteristics of the method have been analyzed by means of paraxial optics.27) 5.9.2 Principle and Characteristics A. Principle Figure 5.41 shows the basic optics of this method. This optical system consists basically of Fig. 5.41 Optical arrangement of this
method. a laser, two half-mirrors, two lenses, two photodiodes, and two pin-holes. A collimated laser beam from a semiconductor laser is focused on a measured surface. The scattered light on the surface is collected by means of the first lens, i.e., an objective lens L0, and is focused on a focal point F1 by means of the second lens L1. In the path between second lens L1 and its focal point F1, the light is split into two light beams by means of half-mirror BS2. These two light beams are received onto each photodiode through each pinhole, A1 and A2, located after and before the focal point of the second lens. This is a key point of this method. Figure 5.42 expresses the direction of the reflected light path due to a displacement of the measured surface; a key point of this method can be explained qualitatively as follows. When Fig. 5.42
Reflected light path due to surface displacement. the surface shifts upwards slightly, i.e., B. Characteristics of Paraxial Optics Rough optical characteristics of the method can be obtained by means of an analysis based on the paraxial optics. Figure 5.43 expresses an equivalent optics for the optical arrangement shown in Fig.5.41. An irradiated point near the focal plane of a first lens L0 is imaged in two steps; first, the point is imaged by means of the first lens at a rather far imaging point, and secondly, this point is further imaged at a near focal point F1 of the second lens L1 by this lens. That is, the point on the focal plane of the first lens, F0, is focused on the focal plane of the second lens. Fig. 5.43 Equivalent optics for the
practical optics shown in Fig. 1. From
the imaging formula, 1/(f0 +
This image, which becomes an object for the second lens L1,
is further imaged by the second lens at a point slightly displaced from the
focal point F1 of the second lens,
where d expresses the distance between the first and second
lenses. As thus, Figure
5.44 expresses a change of light intensity on both photodiodes through the
pinhole due to
Fig. 5.44 Light increment through the pinhole
due to under the condition that the light intensity in unit area is
assumed to be constant over the pinhole plane. In Eq. (5.31), IT
expresses the total light intensity through the second lens. Where p is a
pinhole radius, q a distance from pinhole to focal point of the second lens L1,
and r1 a radius of the light beam which focuses to F1. A
small change of
when the pinhole A2 is placed before the focal plane of the second lens, and
when the pinhole A1 is placed after that focal plane. Substituting equation (5.30) into these equations, we obtain,
where h1 is an aperture radius of the second
lens. An increment,
Similarly, an increment,
In a derivation of these Eqs., (5.31), (5.34), and (5.35), a light intensity in unit area is assumed to be constant over the pinhole plane. This assumption is not practically useful and causes discrepancies between analytical and experimental results. However, a rough estimation of the characteristics of this lens system can be obtained as follows. Both the light intensity, IP1 and IP2, are deducted from each other, and the balance, IP1- IP2, is normalized by the sum, IP1+ IP2. Finally this normalized light intensity, (IP1- IP2)/(IP1 + IP2), is used as an output signal. It can then be expressed as:
The sensitivity K of this method defined by K = I/
As is expected from Eq. (5.36), the output signal I is not
basically affected by the light fluctuation of the laser and the reflectivity
of the irradiated surface, since the output I is normalized by the same light
intensities, IP1 + IP2. This is another merit of this
method. Further, a linear relation between the normalized light intensity I and
the surface displacement Figure
5.45 shows this relation. Thus, the sensitivity K is expressed as an inclination
of the straight line, which is twice that of the usual method utilizing only
one light beam. A measured value usually has an error normalized by IP1
+ IP2, SN, and this determines a spatial resolution of
the measurement, i.e., the measurable smallest displacement
Thus, a high sensitivity and a small error are required for
high resolution, i.e., for a small Fig. 5.45 Expected relation between normalized light intensity I and
surface displacement
5.9.3 Result and Discussion A. Experimental Results A
preliminary experiment has been carried out to verify the above theoretical
analysis based on paraxial optics. Fig. 5.46 shows some normalized light
intensities I in relation to the surface displacement Fig. 5.46 Normalized light
intensity I to a small shift of object surface shape in radial direction practically, even if the light
intensity is constant at the exit of the laser, mainly due to the directivity
of the scattered light on measured surface and the spherical aberration of both
lenses L0 and L1. Thus, the light intensity near the axis
has greater effect on the sensitivity than that far from the axis. The others
will be discussed in detail in a next section 5.9.3B. However, the effects of
both parameters, f1 and q, on sensitivity are roughly in conformity
with the analytical sensitivity. B. Effect of Error Regarding Received Light Intensity
on Sensitivity The theoretical analysis in section 5.9.2.B. was obtained based on the assumption that the light intensity in unit area is constant over the pinhole plane. However, the assumption can't be realized practically due to two main factors: one is the noise due to the speckles of laser light28), while another factor is the noise due to a surface having a mirror-like smoothness. A rather small portion of irradiation is not a perfect rough surface but a mirror-like smooth surface when this method is used for measuring bearing wear or cuts. This causes the scattered light to have directivity. Fig. 5.47 shows the prospected light intensity on the pinhole plane due to the speckles of the laser light (a) and directivity of the scattered light (b). Fig. 5.47 Prospected light
intensity on the pinhole plane due to laser speckle (a) and mirror-like surface
(b). The practical light intensity will have such non-uniform distribution
in radial direction because the scattered light on the surface will be speckled
and show a different directivity at every measurement. In this case, the light
increments on both the photodiodes,
where, SN1 and SN2 expresses normalized
errors in IP1 and IP2, SN an error due to SN1
and SN2. In this equation, the maximum error is considered,
and the relation, (
Thus, an error rate SN/I becomes large as C. Reduction of Error by Means of Smoothing One of
the useful methods for reducing a measured error is a smoothing of the data
obtained at slightly different surface positions, in other words, a spatial
smoothing. One of the purposes of this method is the application to the
measurement of wear. In this case, the measured data have usually random noise
in the signal, and spatial smoothing can be effectively used. As is well known,
the noise power SN can be reduced to SN/ D. Merits of Proposed Method First, this method has a high measuring frequency compared with other method such as the one presently marketed26), as discussed above. That method is based on focusing of an object, i.e., an irradiated surface, by shifting the objective lens up and down manually or by vibrating it with an electro-magnetic force electronically. This vibration limits the measuring frequency within this frequency and the range of displacement within this amplitude. In contrast, our method has unlimited measuring frequency and range of measurable displacement because this method has no movable component in the optical arrangement. This enables the real-time measurement of surface displacement, in other words, surface roughness. Secondly, this method utilizing two light beams achieves a high spatial resolution twice that of the usual method which employs only one light beam, as expressed by equation (5.36) and (5.37). Lastly, this optical system is simple and easy to construct, and thus is economical. E. Adaptability of This Method This optical system can also be used for measuring wear and cuts in real time in many machine industries; it could predict the reciprocation of expendable supplies such as shafts, bearings, brake discs, etc., making over-exchange needless and thus preventing serious safety accidents. It could also further enhance the accuracy of parts manufacture by means of feedback control. All of these characteristics could economize time and money. In the past, wear and cutting were measured by stopping an operation, i.e., an off-line method. Recently, Honda et. al proposed an optical method for observing wear in real time by flashing a stroboscope synchronously with a shaft rotation.31) The method cannot, however, measure wear quantitatively. In conclusions, the following results were obtained. (1) This method is based on the split of the scattered light into two laser beams. The sensor head consists of a laser, two half-mirrors, two focusing lens, two photo-receivers, and two pinholes. (2) The system is simple and easy to construct, and is economical. (3) The analytical sensitivity K defined by normalized light intensity to surface displacement can be expressed by K = -2(f1/f0)2(1/q), where f0 and f1 are the focal lengths of the first and second focusing lenses, and q a distance between the focal plane of the second lens and a pinhole. (4) The smallest measurable surface displacement of this
system was about 3 The system is now under construction for measuring bearing wear. 5.10 Hybrid
Sensor for Surface Displacement 5.10.1 Introduction Surface defects and surface profile including surface undulation, surface roughness and surface contour have become increasingly important issues in fields such as the precision machinery industry and the semiconductor industry, which includes the manufacture of silicone wafer discs, liquid crystal panels, and plasma display panels. Although defects in silicone wafers and flat panels are of great scientific and technological interest32), the present paper focuses on the more important problem of establishing a method for measuring a wide range of longitudinal surface displacement since such techniques are of great interest in production processes. The
surfaces of silicone wafers and display panels currently being manufactured are
extremely flat, with a surface roughness of a few nm. However, surface
undulation will become very large: up to a few hundred In
contrast, the ground surfaces of precision machinery are not mirror-like and
are somewhat rough, with a roughness of approximately The
above two methods developed by the present authors for the measurement of
surface undulation at a nm accuracy and displacement at a 5.10.2 Both Methods and Hybrid Sensor The
methods for both nm measurement and A. Method and a Sensor for nm Measurement Based on Laser
Reflection This method aims at measuring the surface undulation, i.e., the extremely slowly changing height displacement, of a flat panel at a nm level of accuracy and does not attempt to measure surface roughness since the lateral resolution is not important in these flat panels. Thus, the irradiation spot size can be relatively as large as 0.5~1.0. mm, which results in a lateral resolution of the same order. However, the surface undulation at the center of an irradiated area can be measured at a lateral resolution of the laser's smallest scanning amount or sample size since the undulation can be determined by means of the inclination of the irradiated area's smoothed surface. Surface undulation and surface displacement always have a local inclination. This inclination is very small when the surface is almost flat, as in the case of a silicone wafer, plasma display panel or liquid crystal panel. The method described here can successfully measure a very small undulation on such surfaces. The basic principle of this method can be outlined in three steps as is shown in the following. Figure 5.48 expresses the principal optics utilized for this method. A laser light irradiates a mirror-like surface and the reflected light is directed to a photo receiver S through a mirror M and half-mirror HM. Fig. 5.48 Optical arrangement for nm
measurement based on laser reflection. The reflected light deviates to a point Q(X,Y) from the
origin Os (0,0) due to the small inclination,
or in two components,
where
Here, D expresses an optical path length, which is the distance from an irradiated point to a photoreceiver (i.e., in this case a CCD camera); DZ is the distance from an irradiated point to the mirror, DL is the distance from the mirror to the half-mirror and DS is the distance from the half-mirror to the photo receiver. The
height increment in a small region i.e., displacement, can be obtained as
follows. Figure 5.49 shows a diagram of this process. The inclination at the
irradiated position,
where
This is expressed as follows using two components, x and y:
where
Fig. 5.49 Surface Inclination and Displacement. Here,
where
This is expressed in practical form by means of the sum
total of
or, in two components,
where
Thus, the surface undulation at any position p(x,y) can be calculated in terms of the sum total. This method thus consists of three steps. The first step obtains the surface inclination at each surface position. The second step calculates the surface displacement in each small region. The third step sums these small displacements over the required region. Figure
5.50 shows a block diagram of the practical application of these three steps.
Two signals were produced on a personal computer: one is a driving signal to
move the surface or the laser head, while the other is a timing signal to
measure the position of the reflected light on the CCD camera synchronously.
That is, the position Q(X,Y), in other words, tan( Fig. 5.50 Block
diagram of surface inclination measurement and displacement calculation. The longitudinal resolution of this method is thus of nm order. On the other hand, the lateral resolution is determined generally by the spot size of the irradiation area. However, the lateral resolution depends only on the smallest amount of lateral scanning shift when the surface has a slow undulation with very small inclination as in the case of flat panels. In the present experiment, the spot size was 0.5~1.0 mm in diameter. B. Method and a Sensor for In contrast to the reflection method described above, an imaging method,26) a laser interferometry method,34),35) and a two-laser light method27),38) can all be successfully used for almost all the samples, since a rough surface can be examined by means of the scattered light on the surface. Figure 5.51 shows the basic optics of this method. A laser light is focused on the surface to be measured. The scattered light on the surface is collected by means of the first lens, L0, and is focused on a focal point by means of the second lens, L1. The light after the second lens is split into two by means of a half-mirror BS2. These two lights are received onto the two photodiodes through the two pinholes, A1 and A2, located after and before the focal point F1. This is a key point of this method. When the surface shifts upwards slightly, Fig. 5.51 Optical arrangement for i.e., The rough optical characteristics of this method can be obtained by means of an analysis based on paraxial optics. The normalized light intensity defined by both the light intensities is expressed as follows: 27),38)
where f0 and f1 are the focal lengths
of the first and second lenses, respectively, q is the distance between the
pinhole and the focal point of the second lens for both laser lights, and
The longitudinal resolution of this method was approximately
a few C. Hybrid Sensor As is shown in Figures 5.48 and 5.51, the above two methods are very similar, and the two optical sensors can be united in one body; we call this a "hybrid sensor." Figure 5.52 shows the optical configuration of this hybrid sensor, and figure 5.53 shows a photograph of it. The sub-sensor for nm measurement is shown in the upper parts of
the figure and that for
Fig. 5.52 Optical arrangement of the hybrid
sensor system. Fig. 5.53 Photograph of the hybrid system. measurement is shown in the lower parts, and both sensors
are mounted on a scanning system by means of a stepping motor. A laser beam is
collimated by an aperture, A, with a proper diameter to limit the irradiation
area for nm measurement. In this arrangement, the scattered light used for This hybrid sensor has the following distinguishing characteristics: (1) It can measure surface displacement such as undulation at nm accuracy when the surface is sufficiently flat, as in the case of an optical mirror. (2) It can measure surface displacement in height such as
roughness at (3) As a result of (1) and (2), it can most effectively be
used for measuring the surface undulation over the very wide range from nm to a
few hundreds (4) This hybrid sensor is relatively compact, and the cost/performance ratio of this system allows its practical use. (5) The measuring frequency for nm measurement is 24 Hz, and
approximately a few hundred Hz for The only disadvantage of this hybrid sensor is that the measuring points of both sensors are slightly different as is shown in Figures 5.52 and 5.53, which limits it use. However, both points can be focused on the same position by means of a liquid-crystal lens with on-off focusing at high frequencies for an objective lens L0. 5.10.3 Experimental Results by Means of This Hybrid Sensor A preliminary experiment was carried out using the experimental setup shown in Fig. 5.53. A. Experimental Results Based on Laser Reflection The
reflected light is detected on a CCD camera which has a pixel size 6.45 Figure
5.54 shows a change of the CCD camera's position caused by a small change of
surface inclination due to a laser scan on the concave mirror with a curvature
radius of 2000mm and a diameter of 30mm. The mirror was placed on the table and
the table was moved by a stepping motor at a smallest step of 10
for D=290mm, Fig. 5.54 Position change on the CCD camera caused by a small change of
surface inclination due to a laser scan on the concave mirror. directions due to the
laser scans in the x and y directions, respectively.
Figure
5.55 shows the theoretical and experimental values of the surface displacement
on a concave mirror. The theoretical values shown by the solid curve were
calculated by means of a circular equation. The experimental values shown by
for X=5 Fig. 5.55 Surface displacement on a concave mirror. The solid curve
shows the theoretical value calculated by a circular equation
with center at O(x=0, y=0, z=2000 mm) and a radius of R=2000 mm. Experimental values
shown by by means of equation (5.42)
with each scan interval of ( inclinations at each
position, tan( and directions, respectively. undulation, i.e., a resolution of B. Experimental Result Based on Laser Scattering A few optical values for this set-up are f0=16 mm, f1=50 mm, and q=10 mm. Thus, the theoretical absolute sensitivity, KT, of this subsystem can be calculated by means of Eq. (5.46):
Figure 5.56 shows the experimental results obtained by means of this set-up. Each value is the mean of ten measurements. The straight line in this figure is obtained by means of the method of least squares, which is used as the calibration curve for the surface roughness. The experimental absolute sensitivity is KE=1.55 mm-1, which is slightly lower than the theoretical value of 1.95. Fig. 5.56 Relation
between the normalized light intensity and the surface displacement obtained by means of the experimental setup
shown in Figure 5.53. The first and main reason for this difference is the pinhole size, which was assumed to be infinitely small in the theoretical analysis but in practice was 0.2 mm. The second reason is that this theoretical value was obtained based on the paraxial optics as was shown in a previous paper.38) The final reason is a slight shift of both optical axes on the pinholes A1 and A2, which is another main reason for this difference. The
resolution can be determined with a normalized noise power
Thus, high sensitivity and low noise power are required for
a small value of In conclusions, the following results were obtained. (1) The hybrid sensor consists of two sensors: one is based on laser reflection and is used for measuring surface undulation, while another is based on laser scattering and is used for measuring surface roughness. (2) The sensor for measuring surface undulation has a spatial resolution of 1nm with a measurement frequency of 24Hz. (3) The sensor for measuring surface roughness has a spatial
resolution of about 2 (4) Thus, the hybrid sensor can measure surface displacement
in height over a wide range from a few nm to a few hundreds of References 26) Keyence: Displacement detection using movable lenses, All-aroud Cat. (2004) p. 694. 27) T. Kozuki, l. Zhu, T. Honda, M. Ueda: Discussion on a real-time measurement of surface roughness by means of two laser beams (for tribo- viewer) Rep. 320th Topical Meeting, Laser Soc. Jpn. No. RTM-04-07 (2004) p. 7. 28) Laser Soc. Jpn (ed): Laser Handbook, (Ohmsha, 1982) p. 92. 29) M. Ueda, K. Ishikawa, C. Jie, S. Mizuno, and M. Tsukamoto: Thickness measurement of polyethylene foam by light attenuation, Rev. laser Eng. 21(1993) p. 1266. 30) B. P. Lathi: Communication System (Wiley, New York, 1968) p. 130. 31) T. Honda, S. Otsubo, and Y. Iwai: Optical visualization of wear precess and in-situ monitoring of the volume loss using live observation system(LOS), J. Jpn Soc. Tribolo. 48 (2003) 990. 32) Ganesha Udupa, B. K. A. Ngoi, H. C. Freddy, & M. N. Yusoff: Defect detection in unpolished Si wafers by digital shearography, Meas. Sci. Technol. 15(2004) p. 35. 33) T. Yoshimura, S. Nishi, and M. Itoh: Techniques for fine measurements, Hitachi Metals Technical Reports, 17(2001) p. 129. 34) T. Yokoyama, S. Yokoyama, K. Yoshimori, & T. Araki: Sub-nanometre double shearing heterodyne interferometry for profiling large scale planar surface, Meas. Sci. Technol. 15(2004) p. 2435. 35) S. H. Wang & C. J. Tay: Application of an optical interferometer for measuring the surface contour of micro-conponents, Meas. Sci. Technol. 17(2006) p. 617. 36) T. Kozuki, M. Kawabata, T. Sakurai, & M. Ueda, Rep. 332th Topical Meet: A high resolution method for a surface measurement by means of laser reflection and integration methods, Laser Soc. Jpn. Laser Meas. RTM-05-05(2005) p. 1. 37) Shimadzu Corp.: Lead the market on semiconductors・FPD/liquid displays using the detection devices, Boomerang (Special Feature)8(2004) p. 19. 38) T. Kozuki, T. Honda, T. Sakurai, & M. Ueda: Real time measurement of a surface displacement with two laser beams, Rev. Laser Engr. 32-10(2004) 648. 39) Liang-Chia Chen, & Chu-Chin Liao: Miniaturized 3D surface profilometer using digital fringe projection, Meas. Sci. Technol. 16(2005) p.1061. 40) Liang-Chia Chen, & Chu-Chin Liao: Caribration of 3D surface profilometry using digital fringe projection, Meas. Sci. Technol. 16(2005) p.1554. 41) K. Meiners-Hagen, V. Burgarth, & A. Abou-Zeid: Profilometry with a multi-wavelength diode laser interferometer, Meas. Sci. Technol. 15(2004) 741. 42) F. Zhu, K. Ishikawa, T. Ibe, K. Asada, & M. Ueda: A practical system for measuring film thickness by means of laser interface with laminar-like laser, Rev. Laser Engr. 32-7(2004) 475. [The fourth
and final segment of Chapter 5 will be presented in the upcoming
January-February 2011 issue of this Journal.] [ BWW Society Home Page ] © 2010 The Bibliotheque: World Wide Society |