CA1279988C

CA1279988C - Fringe field capacitive sensor

Info

Publication number: CA1279988C
Application number: CA000515648A
Authority: CA
Inventors: Joseph L. Garbini; Laurence J. Albrecht; Jens E. Jorgensen; Georg F. Mauer
Original assignee: Washington Research Foundation
Current assignee: Washington Research Foundation
Priority date: 1985-08-09
Filing date: 1986-08-11
Publication date: 1991-02-12
Anticipated expiration: 2008-02-12
Also published as: EP0221638B1; US4814691A; ATE60436T1; DE3677137D1; EP0221638A1

Abstract

FRINGE FIELD CAPACITIVE SENSOR
Abstract A fringe field, capacitive distance sensor for measuring the distance between a probe and the surface of the conductive body. The sensor comprises a conductive plate element mounted by the probe, the thickness of the plate element being substantially less than the height and width of the plate element. The plate element is positioned adjacent to and normal to the body surface, and the fringe field capacitance between the plate element and the bodyis measured, to thereby determine the distance between the probe and the body surface. The probe may be in contact with and scanned across the body surface, to provide surface profile measurements. A probe including a plurality of plate elements may be positioned inside an opening such as a hole, to measure the geometry of the hole. By maintaining the hole probe adjacent one electrode in contact with the hole wall, both profile and geometry measurements may be made. A noncontacting probe including one or more plate elements may be used to measure surface topography.

Description

9~f~

FRING~ PIELD CAPACITIVE S~NSOR
Field of the Invention The present invention relates to an apparatus and method for measuring the distance between a probe and the surface of a body. Applications 5 of the invention include the measurement of surface profile, hole geometry and surface topography.
~ ~ Background of the Invention Many of the advantages gained through~ automated manufacturing are quickly lost;when~thé speed of ~inspection is inadequate to keep pace with~
10 production. One important~ class of inspection procedures consists of dimensional measurements,~for example measurement of the~ finish or~geometry required in manufacturing of a surface. ~ Finish-refers to the roughness or ~mall scale` height v ariations of ~a surface, where~as geom~etry~efers to~the macroscopic character-istics of the~ surface. ~ ~In-process' inspection~ procedures based~ upon~ the~
15 measurement of such~dimensions~must be~designed~to survive in a comparativelyharsh' environment~ without~sacriflcmg dynamic~range, accuracy, or speed.
The~inspffction ~and~ quality~control~of drilled ~holes is~of a;~special conoern to~oertaln lndustriés, ~such~ as~ the~ aircraft ~in'dustry.~ The~ diameter, finish and shàpe of ~holes~ ~drilled~Ior~fast~ners in ~aircraft manufacturing ~must meet 20 ~exceptionally~high~tolerances,~becQuse~the~fit~of~the~fastener in the~hole~is~
cFiticàl to~the~strength~Rnd fatlgùe life~of~the~Joint.;~This ls partloular1y~true~
where~the components are~high-strength~aluminum ~QlloyS~ which are often~fairly~brittle and~therefore~notch ~sensitivè.~ A~commerclal~jet ~aircraft may contàin~a~
~ millio`n drilled holes, and~ the inspection~ of` all ~such holes ~by conventional 25 techm~ques is~impractical. '~Gurrently,~inspection~procedures~typically`rely;on statistical~inf~rence~bàsed upon~the inspection of a certain fraction of the~holes.
' How~over, even suoh 'pQrtial~inspéobon~;is~time;~consumlne, and depends~to R
cQnsiderable~èxtent~upon~the~skill`and~experience~o~ the inspector, Prior~surface~ finish ;meas'urement~techniques;may be dlvided into~
30 ~two~ classes: ' (l)~those ~which~ measure or~ lnfer ~ or~y average roughness and, ,:
: ~ : ~: ~ :' ; :

.

3&~3 (2) those which record the surface profile, i.e., the local height of the surface as a function of distance along the surface. Although often more difficult to obtain, the surface profile provides substantiaUy more information than average roughness ulone. Higher order statistics, such as skewness, kurtosis, and surface 5 spectra can be computed from the profile record, but not from the v~lue of theaverage roughness. In addition, profile measurements are usually necessary for reliable detection of individual cracks and tool gouges. The average roughness measurement from a surface containing an isolated surface d~fect is often indistinguishable from that of a surface containing uniform roughness of 10 equivalent value.
The stylus-type profilometer is the device most commonly used to measure profile and average roughness. However, there are limitations to the in-process application of stylus profilometers. To measure profile~ the stylus tip must mechanically follow the vertical height variations as the stylus is moved 15 across the surface, and scanning speeds must therefore be relatively slow. Inaddition, the stylus tip suspension is fragile and is easily damaged.
Recently a variety of optical surface measurement techniques have been developed. These are noncontacting systems and have potentially high scanning speeds. Some are capable of profile measurements, as well as average 20 roughness estimates. Disadvantages of these techni~ues are the potential complexity of the optical apparatus tlight source, optics, alignment devices, detectors), and the possibility of errors due to contamination by cutting fluidsand metal particles.
A pneumatic technique has also been used to measure surface 25 finish. In this approach, a close-fitting sensor is placed against a machinedsurface and air is allowed to flOw between the sensor and the surface. The pressure reguired to sustain a fixed flow rate is related to the characteristics of the surface finish. This method is limited to the measurement of average surface roughness, and has comparatively poor time response.
Known capacitive surface finish gauges use a wide, flexible metal electrode located parallel to and in close proximity with a conducting surface to be measured. The capacitance generated between these two conductors is inversely proportional to the average roughness of the surface. The sensor is rugged and~ the method~ is well suited to the manufacturing environment.
35 However, only average~roughness can be measured.
The most common hole geometry measurernent system employed in industry is the air gauge. An air gQuge consists of Q close tolerance rod inserted ` inside the hole to bc measured. Compressed air is then allowed to flow through ~ ~799~

small holes around the rod. By monitoring the airflow, the dia-meter of the hole can be deterrnined. However, the response time of this system is slow, and hence it is not suitable for automated inspection systems.
There are other more exotic ways to measure the geometry of a hole, for example by means of strain gauges or by optical measurement. In both cases, the required apparatus is bulky, and the instrumen~s perform best under laboratory conditions. A
capacitive hole probe system has been developed that consists of a rod of approximately the size of the hole, with smaIl capacitive plates attached along and around the axis of the probe. The hole wall serves as the opposlng side of the capacitor plate. The capacitance created by each plate can then be translated into the distance between the probe and the~hole at various circumferential locations. Unfortunately, such a probe can only~measure the aver-age surface rcughness rathe;r than~the surface profile, and local scratches cannot be detected~by~such a system.
~ ~ ~ Summary of the Invent~ion The~ present invention~provides capacitive distance sensors~that~are capable of distance measurements over a wide range,;e.g. r~ ~0 .~1-2 t O O O microns.~;The~sensors may~be~encased in~
ceramlc~material,~and~are character~lzed by~small~s~ize, fast res-: ~: ~ :,: ~ : , ponse; and rugged~`construction.~ As such, they are well-suited for appllcat~ons in~automated manufac~turing~and~in-process measurementsO
They~can~be~appl~ie~d~individually~or in gxoups to form rnult~i-channel~enzor;~systems.~ Tbe~sensors;~are~based upon measurement of ;~;

:
`:

~ ~'7~t8~

the capacitance resulting from the fringe field between a body surface and an electrode perpendicular to the surface. Unlike prior, parallel-plate capacitive sensors, the sensors of the pre-sent invention are characteriæed by exceptional spatial resolution, and are capable of providing surface profile as well as surface roughness.
In one aspect, the present invention provides an apparatus for determining a measured profile of a body surace of a conductive body along a scanning direction across the body sur-face, the apparatus comprising: a probe having one end shaped to form a skid adapted to move across the body surface in contact therewith; a conductive plate element mounted by the probe and having a fixed positlon relative to the probe, the thickness of the plate element being s~ubstantially :less than the height and width of the plate element, the plate element including an edge parallel to the:width dimension of the plate element; positioning means for positioning the probe such that the skid contacts the body surface, such that~the edge lS posltloned~ln a generally parallel relationship~ to the body~surface and such that the plate element is~normal to the body surface, the positioning means in-~ :
cluding external means for:causing rel:ative movement between the probe and the body~such that the:skid:moves~in:a scanning di~rec-tion across:;the body~surface,;the scanning direckion being normal to::the plate element and~independent to any gulding conformation ~on thé:`body~surface; and~measurement means for measuring the fringe fleld capacitance be~tween~the plate element and the body at a :~

39~38 - 5 - 62839-g36 plurality of probe positions along the scanning direction, to thereby determine the measured profile of the body surface along the scanning direction.
In another aspect, the present invention provides an apparatus for measuring the size and a measured pro~ile of an opening in a conductive body along a measurement direction, the apparatus comprising: a probe having a probe axis and adapted to be inserted in the opening; two plate elements mounted by the probe such that the plate elements are parallel to one another and normal to the probe axis, the plate elements being spaced apart from one another in a direction normal to the probe axis, the thickness of each plate element being substantially less than the height and wldth of the plate element, each plate element including an edge parallel to the width dimension of the plate element;
positioning means for positioning the probe such that the probe is approximately normal to the measurement direction and such that the plate elements are within:the opening and positioned adjacent to and normal~to respective body surfaces thereof such that~each edge is positioned in a generally parallel relati:onship to:its ~0 respective body surfacej and such that adjacent one plate element, the probe contacts the~respective body surface, the body surfaces being spaced apart from one another along the measurement direction, the pos1tioning~mean~s l~ncluding means for causing relatlve movement between the~probe and~the body~suoh that the probe moves within the opening~along a~scanning direction parallel to the probe axis;
and measurement~means for measuring the fringe~field:capacitance : ~

l~t79~8 - 5a - 62839-936 between each plate element and the body at a plurality of probe positions along the scanning direction, to thereby determine the distance between each plate element and its respective body sur-face as a function of probe position along the scanning direction so that the size of the opening along the measurement direction and a measured profile of the body surface associated with said one pl`ate element are measured using a single probe.
In another aspect, the present invention provides an apparatus for determining the geometry and a measured profile of a hole in a conductlve body, the apparatus comprislng: a probe adapted to be inserted in the hole; four conductive plate elements mounted by the probe, the thickness of each plate element being substantially less than the height and width of the plate element, each plate element including an edge parallel to the width dimen-sion of the plate element, and means for moving the probe along a scanning directlon parallel to the probe axis; and positioning means including means~for positioning the probe~such that the plate elements are within the opening, and such that each edge is posi-tioned in a generally;~parallel~relationship to a respective body~
surface and~such that the probe~ad~acent a selected plate~element contacts the~body surface~and~ means for moving~the probe along a scanning~dlrection parallel to the probe axls~ and~measurement means including:Eor~me:asuring the fringe field capacitance between :
each~plate element:~and:the body~at a plurallty of probe positions:- ~:
along~:the~scannlng:dlrection,~to~thereby measure the dlmension of the~hole alony~the~first and second measurement axes and the :: : : :
~: :

.

~ ;~'7~
- 5b - 62839-936 measured profile as a function of probe position along the scan-ning direction.
In another aspect, the present invention provides an apparatus for determining the shape and a measured profile of a surface of a body along a measurement direction, comprising: a probe; a plurality of conductive plate elements mounted by the probe, the thickness of each plate elements being substantially less than the height and width of the plate element, each plate element including an edge extending along the width of the plate element; positioning means for positioning the probe adjacent the surface such that the plate elements are normal to the surface and such that each edge is positioned in a generally parallel relation-ship to the body surface, adjacent at least one plate element, the probe contactln~ the body surface, the plate elements being spaced from one another along the measurement direction; and measurement means for measuring the fringe field capacitance between each plate element and~the body, to thereby~measure the dlstance between each plate element and the body and along sald at least one plate~
element, to determine the~measured profile of the body surface adjacent thereto using a single probe.; ~ ~
The `invention also provides methods corresponding to~the apparatus of the~four aspects~reclted above.-Brief Descrip~ion of th-e Drawings ~ FIGURE 1 is a~schematic view illustrating the principle of~operatlon; of~the present invention;
~ ~ FIGURE 2 is~a~s:chematic view of the electric fringe field :: :

:

, ~1 ~,'7~

- 5c - 62839-936 between an electrode and a surface;
FIGURE 3 illustrates the measurement of surface profile according to the present invention;
FIGURE 4 is a schematic view illustrating the relation-ship between radius of curvature and tilt error;
FIGURE 5 is a schematic view illustrating the relation-ship between radius of curvature and drop-in error;
FIGURE 6 is a graph illustrating selection of the mini-mum total error, FIGURE 7 is a schematic view of an apparatus for measuring the profile of a surface;
FIGURE 8 is a block diagram of the electronic components associated with the apparatus of FIGURE 7;
FIGURE 9 lS an exploded and partially cut-away view of a hole sensor according to the present invention;
FIGURE lO is a cross-sectional view of the hole sensor ::
of FIGURE 9; ~ : :
FIGURE ll is a cross-sectional view taken along line ll-ll of FIGURE lO;
FIGURE:12 is a block diagram of a system for measuring the profile~and~,geometry~of a hole;
~ FIGURE 13~is a block diagram:~of the operation sequence of the~hole sen~sor of FIGURE 12;
~ ~ PIGURE 14 ;Ls;a~cros~s-sectional view of an~apparatus ~ox measuring the~width of a gap ~:and ~ ~
: ~ ~ FIGDRE lS is a cross-sectional view of the apparatus of FIGURE 14:.~

~ : :

~1 ~79~3~3~
.

Detailed Description of the Invention The principle of operation of the present inventian is illustrated schematically in EIGU~ES I and 2. FIGURE 1 illustrates body 12 having surface 14, and electrode 20 positioned Q height h above the surface. Body 12, or 5 at least the portion of body 12 adjacent surface 14, is composed of an electrically conductive material such as metal, graphite composite or the like.
Electrode 20 comprises a thin metallic plate perpendicular to surface 14, the electrode having height H, width W, and thickness T. A voltageV is applied between electrode 20 and body 12, resulting in an electric field that is sche-10 matically illustrated in FI(~URE 2. The electric field lines 24 are perpendicularto surface 14 and to the surfaces of electrode 20, and the equipotential lines 26 are perpendicular to the electric field lines.
The electric field between the two plates of a capacitor is often described in terms of the direct field and the fringe field. The term "direct 15 field~ refers to that portion of the electric field directly between the two plates or conductors. In FIGURES 1 and 2, the direct field corresponds to the field between the lowermost edge of electrode 20 and area 16 of surface 14 directly below the electrode. For conductors oriented as in FIGURE 1, the term "edge field" may be used to denote the direct field. The "fringe field" is the field that 20 occupies the space not directly between the two conductors. As indicated in FIGURE 2, as long~ as electrode 20 is perpendicular to surface 14 and the thicknessT of the electrode is sufficiently smàll, the electric field between electrode 20 and surface 14 is essentially a fringe field. As a result, the total capacitance between the electrode ànd the surface is essentially Q result of the25 fringe field, and the~contribution of the edge~field to the totaI capacitance is negligible.
The behaYior of the sensor illustrated in FIGURES 1 and 2 may be derived from an analysis of the electric~ field. For an infinitely thin electrode of width W and height H displaced a distance h above an infinite plane, the fringe 30 field capacitance C is: ~

~= 47,W In~l ~ (1) ; ~ h~
where it is assumed that the material surrounding the electrode has a uniform dielectric constant e ~and that electrode height H is substantially greater thandistance h. The capacitQnce is directly proportional ~to the width W and inversely proportionàl to~the logarithm of the instantaneous SepQratiOn distance h. The ~, .~distance between electrode 20~and sur~qce 14 oan therefore be inferred from the ; ~:

;'9~3~

magnitude of the fringe field capacitance C. Equation (1) illustrates that as the distance between the electrode and the surface becomes small, the capacitance increases rapidly. The sensitivity K of the measured capacitance with respect tothe average height above the surface ho is:

K = dC ¦ = 4eW
dh Ih = ho trho ( ) Thus the sensitivity is proportional to the electrode width W, inversely proportional to the average height ho~ and is independent of the electrode 10 height H. Equation (2) further demonstrates that when ho is small, i.e., when the electrode is nearly touching surface 14, the sensitivity of the probe is high and small variations in the surface profile can be measured. The fringe field capacitive sensor of the present invention is therefore adapted for measuring the profile of a surface. Conversely, when electrode 20 i5 relatively far away from 15 surface 14, the sensivity decreases and variations in surface profile no longer cause a detectable variation in capacitance. In this mode, the sensor becomes Q
macroscopic distance measuring device that can be used to detect the spacing between the electrode and the average surface. As described below, sensors comprising a plurality of electrodes can be used to measure both the geometry 20 and surface profile oi a hole, as well as the topography of a surface.
An ideal sensor for measuring surface profile would be sensitive or~y to the height of the surface directly beneath the electrode. However the shape of the electric field and the measured value of the capacitance are also influenced by the shape of the surrounding surface. The spatial resolution of the 25 sensor is determined by the~ extent to which the shape of the surrounding surface affects a measurement at any single point. In particular, it may be shown that if electrode 20 is~ moved across surface 14 in a direction perpendicul~r to the plane of the electrode, i.e., in the X direction in FIGUR~3 1, the measured height hm(x) above the surface at position x along the X axis iS given by:

hm(x) = ho + ~Q h~(x) = ho ~ ~ s (x - x') ~ h (x') dx' (3) where ~ àhm(x) is the measured or inferred height variation with respect to average height ho~ ~ih(x) is the actual height with respect to ho~ and where s(x) 3 is the sp }tial unit impulse response ~unction:
s(x)~= _ (X2 + h 2)-1~

79~

Thus the measured change in surface height hm(x) is equal to the spatial convolution of the actual surface height h(x) with the spatial unit impulse response of the capaciti~e electrode. The measurement of the surface profile using a fringe field capacitive sensor can therefore be considered to be 5 equivalent to a spatial filter. In the frequency domain this filter is represented by:

~Hm(k) = S(k) '4~(k) (5) 10 where :~Hm(k), ~(k) and ~H(k) are the Fourier tran5forms of the corresponding functions ahm~x), s(x), and ah(x), and where k = 2 7rl A is the spatial frequency of the sinusoidal component oE wavelength A . From equation (4) above:

S(k)=J~ e i Xdx=exp(-hO¦k¦) (6) The value of S(k) decreases monotonic~lly as the absolute value of k increases.
The sensor therefore acts as a low-pasS spatial filter, attenuating high frequency components (short wavelengths), while allowing low frequencies (long 20 wavelengths) to pass with little change.
For some applications, the loss of high frequency components due to spatial filtering maY be unacceptable. In such cases,; a dynamic compensationtechnique may be adopted based upon equation (5) above. A single parameter, the average height ho~ describes the theoretical impulse response of the sensor.25 For any surface, ho can be~estimated from a simple static calibration of the sensor. It is therefore possible to recover an improved estimate of the surface profile based upon knowiedge of the dynamio characteristics of the sensor. The dynàmic compensation takes the form of an inverse filter. Equations (5) and (6) above can be combined to produce:
~ ~
4h(x)=F lLexp(-hOlkl)p~(~hm~(x))l ~ (7) where F( )~and~F 1( j represent the Fourier transform and inverse Fourier transform~`respectively.~ ~Determination of ~h(x) by this dynamic compensation 35 ~technique~ there-ore begins with ~ ineasurement o f ~hm(x) from ~ actual capacitance measurements, using, for example, an empirical itqtic calibration curve~of capacitance versus distance. The Fourier transform of ~h (x) is then computed, and~the~ inierse filter~lunctlon is estimated using a value of ho .
~ ~ :

~ ~'i'9~
g computed from the average value of ~ hm(x). The ~ourier transform of ~ hm(x) is multiplied by the inverse filter function, and the estimated actual profile ~ h(x) may then be computed from the inverse Fourier transform. The inverse Fourier transform should be taken over a frequency range limited by the signal-S to-noise ratio of the measured signal, i.e., the dynamic compenSQtion must not be applied below the noise floor of the measurements.
Average surface roughness sensors are known that comprise a relatively wide electrode located parallel to, and in close proximity with, the conducting surface whose roughness is to be measured. The capacitance 10 generated between these two conductors is inversely related to the average roughness of the surface. Although these sensors are well suited to manu-facturing environments, only average roughness can be measured. The high spatial resolution of the fringe field sensor of the present invention allows the surface profile to be obtained. Knowledge of the actual profile permits the 15 determination of high order statistics, such QS skewness, kurtosis, and surface spectra. In addition, in many cases, profile measurements are required for reliable detection of individual cracks and tool gouges.
Use of the sensor of the present invention to measure surface profile is illustrated schematically in FIGURE 3. The sensor for measuring the 20 profile of surface 14 includes probe 18 an~ electrode 20. Probe 18 is composed of a ceramic or o~her insulating mate~ial, and rests directly on surface 14.
Electrode 20 is embedded in probe ~0 with the lower edge of the electrode flush with the lower surface of the probe. As in FIGURES 1-2, the electrode has a height H, a width W, and the thickness of the electrode (aIong the X axis) is 25 much less than the height and width. The width of the electrode must be comparatively large, preferably 2 mm or more, to ensure adequate sensitivity.
This consideration tends to limit tbe technique to surfaces witb predominantly one-dimensional roughness variations. However, the~majority of manufacturing operations, such as milling, turning, drilling, and ~shaping, produce surfaces 30 h~ving a parallel lay, and the p,rofile of such ~ surfaces may therefore be determined by the sensor of the present invention. ~ ~
In FIGURE 3, surface ~l4 extends in the X and Y directions, and has a lay parallel to the;Y d;reGtion. The;electrode is positioned perpendlcular to the surface and ~parallel to the lay, and is moved relative to thq surface~ in the 35 X direction, I.e. in a~ direction normal to the lay and perpendicular to the plane of the~electrode. The lower surface of probe 18 contacts surface 14, forming a slcid that maintains a~constant average distance between the lawer tip of the .A electrode and the surface. As the ~probe moves across the sur~ace, a suitable .

~ 9~

detection circuit, described below, measures the fringe field capacitance between the electrode and the surface. As indicated in equation (1), the capacitance varies as a function of the distance between the bottom of the electrode and the portion of surface 14 beneath the electrode. The surface 5 profile is inferred from a record of the capaCitQnce variation as a function of electrode position along the X axis. As shown by equation (2) above, wear of theprobe and electrode caused by rubbing against the surface does not alter the sensitivity of the sensor, and is of minor importance in calibration.
As indicated above, the fringe field capacitive sensor acts as a low 10 pass filter, attenuating high spatial frequency components while allowing lowspatial frequencies to pass with little change. The width of the spatial frequency response characteristic is inversely proportional to the average height ho of the electrode above the surfaee. This characteristic of the fringe field capacitive sensor is an advantage, since for most machined surfaces, the average 15 wavelength tends to decrease as the average roughness decreases. Thus, since ho also decreases as roughness decreasesj the fringe field capacitive sensor provides a wider frequency response when measuring higher frequency components.
Probe 18 has two basic functions. The probe encases all but the lower edge of electrode 20, protecting the electrode from contamination and 20 mechanical damage. The electrode and the~ accuracy of the profile measurementare therefore not affected by severe environmental conditions. In addition, as the probe is moved across the surface, the base of the probe broadly ContQctS the surface, forming a skid that maintains a~ constant average distance between the lower edge of the electrode and the surface. Unlike mechanical stylus devices, 25 the profile measuring sensor of the present invention need not mechanically track~ fine surface;variat~ons, and the scannlng speed of the probe across the surface is therefore not limited by inertial effects. Excellent results have been achievèd at scanning speeds as high as 100 mm/sec.
A~ suitable material for ~probe l8 is a machinable glass ceramic 30 material, such as the ceramic material available from Corning Glass WorIcs under the trademark~MACOR.~ MACOR ceramic material has good thermal stability and~ can be~ shaped by ordinary machining operations. Probe 1~ is preferably constru~ted~from two blocks of ceramic material by forming the electrode on one of the ceramic blocks using an evaporative deposition technique, and then 35 bonding the~blocks together~so as to enclose the electrode. The thickness of electrode 20 should be small in comparison with the smallest surface wavelength to be~ meRsured.~ A ~ suitable ~electrode ~materlal is~ ailver, ~which has a high conductivityj good resistance to corrosion, and adheres well to ceramic material.

9~
-For determining the profile of a typical machined metallic surface, a suitable electrode thickness is 0.1 micron, and suitable widths for electrode 20 are in the range of 2-5 mm. These dimensions result in a nominal sensor capacitance on the order of 0.5 picofarads.
Since probe 18 is in contact with surface 14, the shape and alignment of the bottom surface of the probe are significant design considera-tions. The effectiveness of the skid formed by the probe is improved by curving the bottom surface of the probe in a plane parallel to the direction of travel, i.e., in a plane perpendicular to surface 14 and parallel to the X direction. Asillustrated in FIGURES 4 and 5, two types of measurement error are determined by the radius of curvature of the skid. FIGURE 4 illustrates a tilt error that occurs when there is angular misalignment between the electrode and the direction normal to surface 14, such misalignment causing the electrode to be lifted above the surface. This tilt error Et in the height of the electrode is equal to Rsin ~ where ~ is the angle of deviation of the electrode from the normal and R is the radius of curvature of the lower surface of the probe. The tilt error is therefore minimized by decreasing the radius R. A second source of error is the "dro~in" error illustrated in FI~URE 5, and is a result of the skid riding over the surface peaks and dropping into the troughs of the surface. The drop-in error is given by: ~
Ed=R-~ (8) wbere A is the surface wavelength. Increasing radius R ther~fore reduces the dro~in error. A compromise value ~of the radius can be selécted by minimizing the combination; of both errors. Since the errors are statistically independent,t~ie expected value of the total error Es, is glven by:
:: :
ES = lEd2 + Et2 ~ ~ (9) By way of example,~ FIGURE 6 shows the normalized (with respect to A ) drop in error, tiIt~ ~error and expected ~error, assuming a tilt misalignment of 0.25 degrees. The optimum value for radius of curvature R in this example is 75~ microns. ~ ~
~ ~ An~apparatus~ for ~carrying out the surface profile measurements according to the present~ invention is illustrated in FIGURES 7 and 8. Referringinitially to ~IGURE 7,~conductive body 12 is mounted by horizontal translator~
suoh that suiface l4 whose profile is to be measured faces upward and is :
: ~ :
`

99~

horizontal. Probe 18 having embedded electrode 20 is mounted by one end of arm ~4, the opposite end of arm 44 being pivotally mounted to vertical translator 46 at pivot 48. The end of arm 44 to which the probe is mounted includes electronics compartment 50, described below. During measurement of 5 the profile of surfac0 14, ~rm 44 is free to pivot about pivot 48, such that probe 18 rests against surface 14. Horizontal translator 40 moves body 12 in a horizontal direction past the probe and electrode, to produce variations in the capacitance between the electrode and the body, as described previously. The apparatus is calibrated by locking arm 44 against rotation about pivot 48, and by 10 then causing vertical translator 46 to lift the electrode vertically away from surface 14 while capacitance measurements are made.
Referring now to FI~URE 8, variable capacitor C represents the fringe field capacitance between electrode 20 and surface 14. Capacitor C is connected as an element of a multivibrator circuit comprising inverters 52 15 and 54 and resistors 56 and 58. As is well known, the frequency of oscillation of such a multivibrator will be proportional to capacitance C. The output of the multivibrator passes through buffer/inverter 60 and is input to phase lock loop 62. Inverters 52, 54 and 60 and resistors 56 and 58 may conveniently be mounted in electronic compartment 50 on arm 44. Phas~lock loop 62 produces 20 an output signal on line 64 having a magnitude corresponding to the frequency of oscillation of the multivibrator, and therefore to the value of fringe field capacitance C and to the height of the electrode above the surface. The signal on line 64 is digitized by A/D converter 66, and input to microcomputer 68.
Microcomputer 68 controls horizontal translator 40 by means of start/stop 25 commands on line 70. The stHrt/stop commands are received by horizontal control and measurement circuit 72, and result in the production of appropriate sync signals on line 74 that control movement of the horizontal translator. The horizontal translator includes an optical encoder that produces a series of pulses, each pulse corresponding to a preselected horizontal distance through which the 30 horizontal translator has movedO Such pulses are transmitted to horizontal control and measurement circuit 72 over line 76, and result in Q position signalon line 78 that is received by microcomputer 68. In a similar manner, vertical translator 46 is controlled through vertical control and measurement circuit 80 that is coupled to the vertical translator by lines 82 and 84. The vertical control 35 and measurement circuit receive~ start/stop Rnd lock/unlock commands from themicrocomputer via line 86, and returns position information to the micro-computer via line 88.~ The lock/untook signals on line 86 correspond to locking ' and unlocking of arm 44, to switch between calibration and measurement modes, respectively.
The apparatus of FIC;URES 7 or 8 illustr~te one example of a surface profile meusuring apparatus according to the present invention. It is tobe understood, however, that the particular apparatus used for a giYen applica-tion will depend upon the nature, size and shape of the surfaces whose profiles are to be measured, RS well as upon the over~ll manufacturing process in which the profile measuring technique is incorporated. For example in many situations,it will be more convenient to maintain the surface stationary and move the probeacross the surface during a measurement. As a further exa1llple, numerous electronic techniques are available for measuring variations in fringe field capacitance C, and the multivibrator based detection circuit shown in FIGURE 8 is but one example of such techniques. The frequency response of the detection circuit must be sufficient to track variations in capacitance as the sensor moves across the surface. The nature of the spectrum of the surface profile and the desired probe velocity will fix the bandwidth requirement. The nature of microcomputer 68 will also depend upon the overall environment in which the profile measuring technigue is used. For demonstration and testing applications, Q Fluke 2450 measurement and control system has been found suitable.
One important application of the sensor of the prèsent invention is the inspection of drilled holes. In the aircraft and other industries, highly automated facilities have been increasingly used to locate and drill holes, and to insert and seat the fastener, e.g., the rivet or bolt, in the hole. A rapid and reliable technique for inspecting a hole between the~ drilling step and fastenerinsertion step is therefore highly desirable. The inspection technique is preferably capable of measuring the diameter of the hole in at least two perpendicular directions at closely~spaced intervals along the hole axis, as well QS of distinguishing between individual tool scratches and continuous finish variations. The identification of tool scratches requires measurement of surfaoe3û profile rather than average roughness, and prior parallel plate capacitive techniques have therefore been found to be inadequate. As a result, prior hoIe inspection methods have generally required a stylus profilometer technique for surface profile and an additional, separate technique for hole geometry.
~ A ~fringe field~capQcitance sensor oapable of measuring both hole geometry~ and~ surface profile is illustrated in FI(~URES 9-11. The sensor 100 comprises~ ~ a n elongated~ structure that includes probe 102 having electrodes 104-107; embedded therein. As described below, each electrode is connected to a suitable capacitance measuring circuit. Electrodes 104 and 106 ' 9~

are positioned along axis ll0 and electrodes 105 and 107 are positioned along axis 112, axes 110 f3nd 112 being perpendicular to one another and both being perpendicular to longitudinal axis 114 of sensor 100. The plane OI each electrode is also perpendicular to axis 11~. Probe 102 is adapted for positioning in 5 hole 116, the diameter of probe 102 being selected such that it is somewhat less (e.g., 0.5 millimeters less) than the diametet- of the hole. In ~IG(JRE~S 10 and 11, the diameter of hole 116 relative to probe 102 has been somewhat exaggerated for ease of illustration. Probe 102 is positioned in hole 116 such that the probe adjacent one electrode, such as electrode 106 in FIGIJRE 11, rests directly on 10 (i.e., is tangent to) the hole wall to make surface profile measurements, while the other electrodes are spaced from the hole wall to make distance measure-ments. The diameter of the hole along axis 110 CQn be determined by adding the spacing detected by electrode 10d~ to the probe diameter, while the diameter along axis 112 can be obtained by adding the distances measured by 15 electrodes 105 and 107 to the probe diameter. Both the surface profile and geometry of hole 116 can therefore both be determined by sensor 100 by passing the probe axially through the hole, with the probe adjacent electrode 106 in contact with the hole wQll. More detailed measurements can readily be obtained by providing additional electrodes, by rotating the sensor about QXiS 114 as the20 probe is moved along such axis, and/or by making multiple passes of the probe into and out of the hole.
Sensor 100 comprises probe 102, stem 118, plate 120 and sleeve 122. Probe 102 comprises disks 124 and 126, disk 126 including mounting stem 128. The disks are preferably fabricated from a ceramic m~aterial, such as 25 MACOR. Electrodes 104-107 are deposited on face 130 of disk 126, preferably by evaporative metal deposition. In one suitable technique, chromium is first deposited to establish a good bond with the MACOR, then a layer of silver is deposited to produce a total electrode thickness of approximately 0.1 microns.
Four electrodes are deposited, each 1.6 millimeters wide and oriented at an 30 angle of 90 with respect to one another. Before the deposition process, foursmall wires 132 Qre secured using epoxy glue inside four drilled holes 125 leading to surface 130 of disk 126. As the metal is deposited, the electrodes and the wire are galvanically connected. After the deposition process, disk 124 is gluedto disk 126 with epoxy, sandwichin~ the electrodes between the disks. The entire35 probe 102 can then be turned down to the deslred shape on a lathe. The diameter of probe l02 is preferably approximately l.0 millimeters or less below the nominal diameter of the hole to be measured. The relief space created by the - probe diameter being less than the hole dlameter provides for ease of insertion 3~3~

and prevents the probe from jamming inside the hole due to misalignment. The appropriate relief space is a significant parameter, because the sensitivity quickly decreases as the electrodes get farther away from the hole wall. Por a given application, optimal spacing can be determined from static calibration curves.
Stem 118 comprises a stainless steel tube, the purpose of the stem being to support the probe and to serve as a shield for wires 132. Plate 120 is mounted within stem 118, and wires 132 ar0 embedded in thin grooves along each side of the plate. A suitable material for plate 130 is Plexiglass sheet material.
The wires are preferably spaced with respect to one another and with respect to stem 118 to minimize the total capacitance created by the stem and wires.
Sleeve 122 provides a mounting for stem 118 and may have any suitable construction.
FIGURE 12 illustrates a system for measuring the geometry and surface profile of a hole by means of sensor 100. The system comprises four detector circuits 14O-143J multiplexer 144 and reference circuit 146. Detector circuit 140 includes comparator lg8, NAND gate 149, resistor 150, diode 151 and variable capacitance Cl, capacitor Cl corresponding to the fringe field capaci-tance between electrode 104 and the body in which hole 116 has been drilled.
Detector circuits 141-143 are identical to detector circuit 140, except that detector circuits l41-143 comprise variRble capacitors Ca-C4 (not shown) that correspond to the fringe field capacitance between electrodes ~105-107 and the body in which hole il6 has been drilled. The body is assumed to be at ground potential. ~ ~
Reference circuit~ 146~ comprises comparator 152, NAND gate 153, diode 154, resistor 155~ and variaMe~ reference capacitor CR. The reference circuit is connected to multiplexer 144~ through line~ pair 160, and detector circuits 140-143 are connected to multiplexer 144 by line pairs 161-164, respectively. I n response to an Qddreas~ o n address lines l56, /multiplexer connects line pair 160 to one of line pairs~l61-164. When;each detector circuit,for example detector circuit 140, is connected ~to reference circuit 146 by the multiplexer,~the~detector and reference~circuits comprise a differential pulse width~ ~ modulation sensor that ~ produces a square wQve output iignal on line pair 158 that has a duty cycle rela~ed to the relRtive magnitudes of cQpacitors Cl ~ and ~CR. ~ W~hen the~ output~ of ~ NAND ~gate 149 is high, capQoitor Cl charges through~resistor :150 until the voltQge ~cross the capQcitor is equal to VREF, Rt which time comparator 14û forces the output of NAND gate 149 low, whereupon A cap~oieoi cl~ rapidly~ d(soharges through diode 151. In a similar manner, a high :

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output from NAN~ ga~e 153 charges capRcitor CR through resistor 155 until the voltage across the capacitor is equal to VREF, at which time comparator 152 forces the output of N~ND gate 153 low, whereupon the capacitor rapidly discharges the diode 154. Voltage VREF may be set to any convenient value, such as one-half of the supply voltage. The square wave output on line pair 158 will therefore be in one state (e.g. high) for a time determined by the size of capacitor Cl, and will be in the opposite state (e.g. low) for a time corresponding to the magnitude of capacitor CR. The frequency of the square wave signal on line pair 158 is typically on the order of 200-300 kilohertz.
Lowpass filter 170 averages the signal on line pair 158 to produce a slowly varying differential signal on lines 172 that is converted by differential amplifier 174 into a single ended analog signal on line 176. The signal is againfiltered by lowpass filter 177 to produce an analog signal 178 that is converted to a digitHl capacitance signal by A/D converter 179. The resulting capacitance signal on line 182 is input to measurement and control system 1~0.
Measurement and control system 180 may comprise a Fluke 2450 measurement and control system or its equivalent. The measurement and control system controls the movement of sensor 100 into and out of hole 116 via position sense/control circuit 186, movement commands being transmitted to the position sense/control circuit via line 188, and signals indicative of sensor movement being transmitted to measurement and control system 180 ViQ
line 190. The measurement and control system ~also controls multiplexer 144 ViQ
address lines 156 to cause the multiplexer to selectively activate the detector circuits. During the time that a~ particular detector circuit is activated, the measurement and control system determines and stores the distal capacitance signal on line 182, and the corresponding probe position. The capacitance and position data may be processed directly by the measurement and control system, and/or transferred to a process control computer ViQ Q serial data link.
The capacitQnce signal produced by each deteotor circuit 1~0-143, for example detector circuit 140, is an essentially linear function of the capQcitance Cl as long QS CR, is selected to be of approximatley the same magnitude as Cl. The amplitude V of the capacitance signal on line 182 may therefore be written:

V = A + B In(h) (10) The constants~A and B may be obtained by routine calibration techniques. For example, the probe 102 and electrode 106 CQn be positioned above the polished ~`~

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surface of a straight hole, and the signal on line 182 can then be recorded every 0.~ microns as ~ function of vertical displacement. The coefficients A and B canthen be determined by a suitable least squares curve fit technique.
Equation (1) is Q good approximation of the capacitance C for comparatively small values of h. However when h is on the order of or greater than the electrode height H, the capacitance is given by:

C = 4eW ln H +J;~ (11) h The signal amplitude V is then V = A' + B' [ln (H + ~;~ )- ln(hJ (12) The three variables A', B' and H in equation (12j are adjusted iteratively until the least squares error is a minimum. The electrode height H is treated as an unknown because of the complex geometry of the ground surfaces around the electrode.
FIGURE 13 sets forth a suitable sequence of operations for measurement and control system 180. The system commences inspection of a new hole at block 200 by moving the probe to a starting position at the hole entrance. The starting position is adjusted such that one of the four electrodes, e.g.~ electrode 106j is positioned~ tangent to the hole surfsce. In blocks 202 and 204, detector circuit 140 corresponding to tangential electrode 10~ is firstactivated by means of an appropriate command on address lines 156, and the probe is then maved into the hole. During` movement of the probe into the hole (forward motion phase), raw surface profile data is acquired at equal distance increments, for example every 5 micrometers, ~long the axis of the hole.
When the probe~ has reached the réquired depth in the hole, probe motion is~reversed at Mock ~206, and the probe begins to ~move back out of the hole. During this reverse motion phase, detector circuits 140-143 are activated sequentially~by multiplexer 144 in response to addresses supplied by the measure-ment and control~system. ~ Each time a detector circuit is activated, the measurèment~and~control system acquires and stores the raw distance data, such data acquisition occu~ring, for example, every 50 microns along the hole axis.
At the~end of the reverse motion phase, the probe is retracted from the hole at block 208. ~ The~ sequential ~aetlvation of the detector circuits, such that only one such circuit is activated at any one timej prevents crosstalk and interference ~",~ : :

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7~3 between the measurements made through the several electrodes, and is a preferred aspect of the present invention.
In block 210, the measurement and control sgstem converts the raw geometry data acquired during the reverse motion phase into diameters along 5 axes 110 and 112 by means of equation (12), such diameters being tabulated as a function of distance along the hole axis. At block 212, the refined geometry data is compared with preestablished criteria, and a decision is made whether toaccept or reject the hole. The actions (if any) taken at this point upon hole rejection depend upon the particular process in whicn the probe is employed. In 10 any case if the hole is accepted, the measurement and control system proceedsat block 214 to convert the raw profile data acquired during forward motion phase into a surface proile by converting the frequency measurements into heights by means of equation (10). The surface profile data may then be refined in block 216 by means of a dynamic compensation technique exemplified by 15 equation (7). In block 218, the refined surface profile data is examined to identify isolated surface defects. Profile parameters, such as skewness, kurtosis and surface spectra may also be determined at block 218. The results of the analysis in block 218 are compared with preestablished criteria in block 220, and a decision is made to accept or reject the hole. In block 222, the geometry and 20 profile results are reported to a process control computer, and inspection of the hole is complete.
The sensor of the present invention is suitable~ in many circum-stances for measuring surface topography, i.e., the macroscopic shape and contour of a surface. For example, many composite structures are formsd from 25 layers of graphite fiber "tape" impregnated with epoxy resin. The tape is typically 100 microns thick and 150 ~millimeters or more wide. The width of the gap between adjacent tapes is an important parameter in determining the overall quality of the composite structure. The tapes are layed down by high-speed automated equipment. Since each layer of tape is eventually~covered by Qnother 30 layer, the task of measuring the gap between adjacent tapes must be accomplished during the tape lay-down process. The continuous measurement of the gap width is useful both for process monitaring and for control of the lay-down operaiion. The width of the gap may v~ry from less than~ 0 (i.e., overlap) to 7 millimeters or more. The required ~ccuracy of the gap measurement Is on the 35 order of 100 microns. Surface contamination, low contrast, and mechanical vibrations have heretofore limited the~application of optical methods of imagingand measuring the gQp~ width. ~
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The measurement of a gap width amounts to an assessment of the surface topography on a line across the gap. A suitable gap measuring system using fringe field capacitance sensors is illustrated in FIGURES 14 and 15.
FIGURE 14 illustrates gap 230 formed between graphite tapes 232 and 234 that 5 have been layed down on underlying tape 236. The gap width is measured by a sensor comprising ceramic probe 240 in which a plurality of electrodes 242 are embedded. The electrodes are aligned parallel to one another in three rows, as indicated in FIGURE 15, each electrode being perpendicular to lower surface 244 of probe 240 and to the top surfaces of tapes 232, 234 and 236. The staggered 10 arrangement allows wider electrodes for increased sensitivity, and diminishes cross-coupling between the electrodes.
Each electrode extends to and is flush with lower surface 244. The probe is inclined with respect to the boundaries 246, 248 of gap 230 such that the electrodes are spaced from one another in a direction normal to such boundaries.15 In particular, the inclination of the probe and the spacing of the electrodeswithin the probe are such that the electrodes are evenly spaced from one anotheralong a measurement direction perpendicular to boundaries 246 and 248, as indicated in FIGURE 14. Electrodes 242 are each connected in a suitable capacitance measuring circuit, such as the detector circuits shown in 20 FIGURE 12. The detector circuits are sequentially activated, and the distancefrom each electrode to the underlying surface is determined as~probe 240 moves along the gap in the scanning direction indicated by arrow 250. For example, probe 240 may be positioned and moved directly behind the apparatus for laying down the tapes. An image Is thereby produced of the height of the surface along 25 the measurement direction as a function of position along the gap. ~s predicted by equation (4) above, this image becomes sharper as the probe is moved closer to the underlying surface. The image may be processed by appropriate techniques to determine the positions of boundaries 246 and 248, from which the width of gap 230 as a function of position along the gap may~be determined A
30 suitable technique for locating the positions of boundaries 246 and 248 is tolocate the poi~nt at which ;the beight changes most rapidly with respect to distance along the measurement direction.
~ ~ FIGURES 14 and~ 15 illustrate one specific application of the present invention to; ~the~ measurement of surface topography. It will be 35 appreciated, however, that numerous variations will be appropriate for different applications.;~ For example, a;iingle~electrode could be scanned along a surface~e.g. baek and forth acioss~a gap) to measure the width of a gap or other features .. :
i 1;~799~38 of a surface. Stationary or moving arrays of electrodes can readily be constructed to optimize the measurement of any required surface shape.
While the preferred embodiments of the invention have been illustrated and described, it should be undergtood that the variations will be 5 apparent to those skilled in the art. Accordingly, the invention is not to be limited to the specific embodiments illustrated and described, and the true scope and spirit of the invention ought to be determined by reference to the followingclaims.

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Claims

1. An apparatus for determining a measured profile of a body surface of a conductive body along a scanning direction across the body surface, the apparatus comprising:
a probe having one end shaped to form a skid adapted to move across the body surface in contact therewith;
a conductive plate element mounted by the probe and having a fixed position relative to the probe, the thickness of the plate element being substantially less than the height and width of the plate element, the plate element, the plate element including an edge parallel to the width dimension of the plate element;
positioning means for positioning the probe such that the skid contacts the body surface, such that the edge is posi-tioned in a generally parallel relationship to the body surface, and such that the plate element is normal to the body surface, the positioning means including-external means for causing relative movement between the probe and the body such that the skid moves in a scanning direction across the body surface, the scanning direction being normal to the plate element and independent of any guiding conformation on the body surface; and measurement means for measuring the fringe field capacitance between the plate element and the body at a plurality of probe positions along the scanning direction, to thereby determine the measured profile of the body surface along the scan-ning direction.

2. The apparatus of claim 1, wherein the measurement means comprises dynamic compensation means for processing the measured profile to produce an estimate of the actual profile.

3. The apparatus of claim 1, wherein the skid is curved along a direction parallel to the scanning direction, and wherein the radius of curvature of the skid is selected so as to minimize the combination of the misalignment error and the drop-in error.

4. The apparatus of claim 1, wherein the body surface has a lay having a characteristic wavelength, and wherein the position-ing means includes means for causing the scanning direction to be perpendicular to the lay, such that the width of the plate element is parallel to the lay.

5. The apparatus of claim 4, wherein the width of the plate element along said edge is in the range of 2-5 mm.

6. The apparatus of claim 4, wherein the thickness of the plate element is substantially smaller than the characteristic wavelength.

7. The apparatus of claim 1 wherein the plate element is embedded in and encased by the probe except where the skid con-tacts the body.

8. The apparatus of claim 7, wherein the probe comprises two blocks of ceramic material having respective joining surfaces, the plate element being deposited on one of the joining surfaces, the blocks being bonded to one another at their respective joining surfaces.

9. A method for determining a measured profile of a body surface of a conductive body along a scanning direction across the body surface, the method comprising:
providing a probe having one end shaped to form a skid adapted to move across the body surface in contact therewith, and a conductive plate element mounted by the probe and having a fixed position relative to the probe, the thickness of the plate element being substantially less than the height and width of the plate element, the plate element including an edge parallel to the width dimension of the plate element;
positioning the probe such that the skid contacts the body surface with the plate element normal to the body surface and normal to the scanning direction, and such that the edge is positioned in a generally parallel relationship to the body sur-face, and causing relative movement between the probe and the body such that the skid moves in the scanning direction across the body surface independent of any guiding conformation on the body surface; and measuring the fringe field capacitance between the plate element and the body at a plurality of probe positions along the scanning direction:, to thereby determine the measured profile of the body surface along the scanning direction.

10. The method of claim 9, comprising the further step of :

dynamically compensating the measured profile to produce an esti-mate of the actual profile.

11. The method of claim 9, wherein the body surface has a lay having a characteristic wavelength, and wherein the scanning direction is perpendicular to the lay, such that the width of the plate element is parallel to the lay.

12. An apparatus for measuring the size and a measured pro-file of an opening in a conductive body along a measurement direction, the apparatus comprising:
a probe having a probe axis and adapted to be inserted in the opening;
two plate elements mounted by the probe such that the plate elements are parallel to one another and normal to the probe axis the plate elements being spaced apart from one another in a direction normal to the probe axis, the thickness of each plate element being substantially less than the height and width of the plate element, each plate element including an edge parallel to the width dimension of the plate element;
positioning means for positioning the probe such that the probe is approximately normal to the measurement direction and such that the plate elements are within the opening and positioned adjacent to and normal to respective body surfaces thereof such that each edge is positioned in a generally parallel relationship to its respective body surface, and such that adjacent one plate element, the probe contacts the respective body surface, the body surfaces being spaced apart from one another along the measurement direction, the positioning means including means for causing relative movement between the probe and the body such that the probe moves within the opening along a scanning direction parallel to the probe axis; and measurement means for measuring the fringe field capa-citance between each plate element and the body at a plurality of probe positions along the scanning direction, to thereby deter-mine the distance between each plate element and its respective body surface as a function of probe position along the scanning direction so that the size of the opening along the measurement direction and a measured profile of the body surface associated with said one plate element are measured using a single probe.

13. The apparatus of claim 12, wherein the measurement means comprises a detection circuit associated with each plate ele-ment, each detection circuit being adapted to measure the capacit-ance between the body and the plate element associated with the detection circuit, and means for selectively activating the detection circuits for making capacitance measurements such that no more than one detection circuit is activated at any given time.

14. The apparatus of claim 12, wherein the measurement means comprises dynamic compensation means for processing the measured profile of the body surface to produce an estimate of the actual profile of the body surface.

15. The apparatus of claim 12, wherein the body surfaces have a common lay having a characteristic wavelength, and wherein the positioning means includes means for causing the scanning direction to be normal to the lay, such that the width of the plate element is parallel to the lay.

16. The apparatus of claim 15, wherein the width of each plate element along its edge is in the range of 2-5 mm.

17. An apparatus for determining the geometry and a measured profile of a hole in a conductive body, the apparatus comprising:
a probe adapted to be inserted in the hole;
four conductive plate elements mounted by the probe, the thickness of each plate element being substantially less than the height and width of the plate element, each plate element including an edge parallel to the width dimension of the plate element, and means for moving the probe along a scanning direction parallel to the probe axis; and positioning means including means for positioning the probe such that the plate elements are within the opening, and such that each edge is positioned in a generally parallel relation-ship to a respective body surface and such that the probe adjacent a selected plate element contacts the body surface and means for moving the probe along a scanning direction parallel to the probe axis; and measurement means including for measuring the fringe field capacitance between each plate element and the body at a plurality of probe positions along the scanning direction, to thereby measure the dimension of the hole along the first and:

second measurement axes and the measured profile as a function of probe position along the scanning direction.

18. The apparatus of claim 17, wherein the measurement means comprises a detection circuit associated with each plate element, each detection circuit being adapted to measure the capacitance between the body and the plate element associated with the detec-tion circuit, and means for selectively activating the detection circuits for making capacitance measurements such that no more than one direction circuit is activated at any given time.

19. The apparatus of claim 17, wherein the width of each plate element along its edge is in the range of 2-5mm.

20. The apparatus of claim 19, wherein the thickness of each plate element is approximately 0.1 microns.

21. A method for measuring the size and measured profile of an opening in a conductive body along a measurement direction, comprising:
providing a probe having a probe axis and adapted to be inserted in the opening, the probe including two plate elements parallel to one another and normal to the probe axis, and spaced apart from one another in a direction normal to the probe axis, the thickness of each plate element being substantially less than the height and width of the plate element, each plate element includ-ing an edge parallel to the width dimension of the plate element;
positioning the probe such that the probe axis is ap-proximately normal to the measurement direction, such that the plate elements are within the opening and positioned adjacent to and normal to respective body surfaces thereof and such that adjacent one plate element, the probe contacts the respective body surface, such that edge is positioned in a generally parallel relationship to its respective body surface, the body surfaces being spaced apart from one another along the measurement direction;
causing relative movement between the probe and body such that the probe moves within the opening along a scanning direction parallel to the probe axis; and measuring the fringe field capacitance between each plate element and the body at a plurality of probe positions along the scanning direction, to thereby determine the distance between each plate element and its respective body surface along the mea-surement direction as a function of probe position along the scanning direction and the size of the opening along the measure-ment direction and a measured profile of the body surface asso-ciated with said one plate element using a single probe.

22. The method of claim 21, wherein the fringe field capa-citance is measured by a detection circuit associated with each plate element, and wherein the detection circuits are selectively activated for making capacitance measurements such that no more than one detection circuit is activated at any given time.

23. The method of claim 21 comprising the further step of dynamically compensating the measured profile to produce an estim-ate of the actual profile.

24. The method of claim 23, wherein the body surfaces have a common lay having a characteristic wavelength, and wherein the scanning direction is perpendicular to the lay, such that the width of each plate element is parallel to the lay.

25. The method of claim 24, wherein the width of each plate element along its edge is in the range of 2-5 mm.

26. A method for determining the geometry and a measured profile of a hole in a conductive body, the method comprising:
providing a probe adapted to be inserted in the hole, the probe including four conductive plate elements, the thickness of each plate element being substantially less than the height and width of the plate element, each plate element including an edge parallel to the width dimension of the plate element, the plate elements being parallel to one another, the direction normal to the plate elements defining a probe axis, a first pair of plate elements being spaced apart along a first measurement axis normal to the probe axis, and a second pair of plate elements being spaced apart along a second measurement axis normal to the probe axis and to the first measurement axis;
positioning and moving the probe such that the plate elements are within the opening such that each edge is positioned in a generally parallel relationship to a respective body surface, and such that the probe adjacent a selected plate element contacts the body surface, and such that the probe moves along a scanning direction parallel to the probe axis; and measuring the fringe field capacitance between each plate element and the body at a plurality of probe positions along the scanning direction, to thereby measure the dimensions of the hole along the first and second measurement axes and the measured pro-file as a function of probe position along the scanning direction.

27. The method of claim 26, wherein the fringe field capacitance is measured to a detection circuit associated with each element, each detection circuit being adapted to measure the capacitance between the body and the plate element associated with the detection circuit, and wherein the detection circuits are selectively activated for making capacitance measurement such that no more than one detection circuit is activated at any one time.

28. An apparatus for determining the shape and a measured profile of a surface of a body along a measurement direction, comprising:
a probe;
a plurality of conductive plate elements mounted by the probe, the thickness of each plate element being substantially less than the height and width of the plate element, each plate element including an edge extending along the width of the plate element;

positioning means for positioning the probe adjacent the surface such that the plate elements are normal to the surface and such that each edge is positioned in a generally parallel relationship to the body surface, adjacent at least one plate ele-ment, the probe contacting the body surface, the plate elements being spaced from one another along the measurement direction; and measurement means for measuring the fringe field capacitance between each plate element and the body, to thereby measure the distance between each plate element and the body and along said at least one plate element, to determine the measured profile of the body surface adjacent thereto using a single probe.

29. The apparatus of claim 28, further comprising means for moving the probe parallel to the surface in a scanning direction normal to the measurement direction, to thereby measure the shape of the surface at a plurality of positions along the scanning direction.

30. The apparatus of claim 29, wherein the measurement means comprises a detection circuit associated with each plate element, each detection circuit being adapted to measure the capacitance between the body and the plate element associated with the detection circuit and means for selectively activating the detec-tion circuits for making capacitance measurements such that no more than one detection circuit is activated at any one time.

31. The apparatus of claim 29, wherein the plate elements are parallel to one another.

32. The apparatus of claim 31, wherein the plate elements are aligned with one another in a plurality of parallel rows, the rows being inlined with respect to the direction normal to the measurement direction such that the plate elements of each row are spaced from one another along the measurement direction.

33. A method for measuring the shape of a surface of a body and determining a measured profile of the body surface along a measurement direction, the method comprising:
providing a probe having a plurality of conductive plate elements mounted by the probe, the thickness of each plate element being substantially less than the height and width of the plate element, each plate element including an edge extending along the width of the plate element;
positioning the probe adjacent the surface such that the plate elements are normal to the surface and such that each edge is positioned in a generally parallel relationship to the body surface, the probe adjacent at least one plate element contacting the body surface, the plate elements being spaced from one another along the measurement direction; and measuring the fringe field capacitance between each plate element and the body, to thereby measure the distance between each plate element and the body and to determine the measured profile of the body surface adjacent said at least one plate ele-ment using a single probe.

34. The method of claim 33, comprising the further step of moving the probe parallel to the surface in a scanning direction normal to the measurement direction, to thereby measure the shape of the surface at a plurality of positions along the scanning direction.

35. The method of claim 34, wherein the plate elements are parallel to one another.