Note: Descriptions are shown in the official language in which they were submitted.
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APPARATUS AND METHODS FOR SURFACE CONTOUR MEASUREMENT
Field of the Invention
The invention relates to the field of surface measurement and, more
specifically, to
the field of non-contact surface measurement.
Bacl~~round of the Invention
Dimensional metrology, the measurement of the size and shape of objects, is
very
important in today's manufacturing environment in which machines perform much
of the
fabrication and assembly of complex objects composed of many subassemblies.
The shape
and size of each component in a complex assembly, such as an automobile, must
be held
to close tolerances to ensure that the components fit together properly.
Ideally such measurements of shape and size are accomplished without physical
contact in order to save time in making the measurement. Many non-contact
measurement methods make use of available machine vision systems. The
measurement of
surface contour information is an especially difficult problem in machine
vision systems
since depth information is often Iost or is difficult to interpret. To
compensate for the loss
of depth information and the difficulty in interpreting the information which
is available,
many machine vision systems utilize light to create moire patterns on the
surface of the
object in order to obtain contour information.
Interferometric methods have also been used when detailed measurements of the
surface are needed. Although interferometric systems provide surface contour
information, they axe sensitive to vibrations in both the object being
measured and the
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source of illumination being used. The present invention is less sensitive to
the vibration
problem that has affected previous systems.
Summary of the Invention
The invention relates to an apparatus for determining position information of
a
point on the surface of an object. In one embodiment, the apparatus includes
two sources
of radiation positioned to illuminate the point with the radiation from each
of the sources.
The radiation from each of the sources is coherent with respect to the
radiation from the
other source. In one embodiment, the two sources of radiation are formed by
splitting a
coherent radiation beam, which may be accomplished with the use of a beam
splitter or a
fiber optic sputter.
A control system in communication with one or more of the sources changes the
phase of the radiation from one of the sources relative to the phase of the
radiation from
the other source as measured at the point on the surface of the object. In one
embodiment, in which the radiation source is a frequency tunable laser, the
control system
controls the tunable laser to emit coherent radiation of a changing frequency.
In another
embodiment, in which one or more of the radiation sources is moveable, the
phase of its
radiation with respect to the phase of the radiation from the other source as
measured at
the point on the object, is varied by moving one or more of the sources.
A detector, in communication with a processor, is positioned to receive
incident
radiation scattered from the point on the surface of the object. In one
embodiment, the -
detector is an array of individual photodetector elements. In a further
embodiment, the
array of photodetector elements is a charge coupled device (CCD).
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In a preferred embodiment, a focusing system is positioned between the
detector
and the surface of the object to focus the image of the surface of the object
onto the image
plane of the detector. A polarizing filter may be placed between the focusing
system and
the detector, with the optical axis of the polarizer aligned with the
principal axis of
polarization of the radiation emitted by the two sources, in order to remove
any scattered
light which has been depolarized and thus, which would degrade the signal to
noise ratio
of the system.
The processor, which may also be in communication with the controller,
calculates
position information in response to the relative change in phase of radiation
from two
sources as adjusted by the control system, which adjustment causes changes in
intensity of
the radiation scattered by the point on the surface of the object that is
received by the
detector. In one embodiment, the processor is a single processor operating on
detector
output signals associated with each of the photodetector elements of the
detector array.
In another embodiment, the processor is a multiprocessor, with each
photodetector
1 S element or some subset of elements of the photodetector array in
communication with a
respective processor or some subset of processors of the multiprocessor. In
yet another
embodiment utilizing a CCD array, a plurality of CCD elements is in
communication with
a respective processor of the multiprocessor. Use of the multiprocessor
arrangements
advantageously enhances signal processing speed.
The invention also relates to a method for determining position information of
a
~ point on the surface of an object. The method includes the steps of
providing two or more
sources of radiation illuminating the point to be measured, changing the phase
of the
radiation from at least one of the sources relative to the phase of the
radiation from the
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other source as measured at the point on the surface of the object, detecting
radiation
scattered by the point on the surface of the object, and calculating position
information
from the resulting changes in intensity of the radiation scattered by the
point on the
surface of the object. In one embodiment, the change in phase of radiation
from one of
the sources relative to the phase of radiation from the other source as
measured at the
point on the object is accomplished by using a frequency tunable source of
radiation, such
as a tunable laser. In another embodiment, in which one or more of the sources
is
moveable, the relative phase of radiation from the two sources is changed as
measured at
the point on the object by moving such source or sources.
In another embodiment, the apparatus for determining position information of a
point on the surface of an object includes two sources of radiation positioned
to illuminate
the point on the object to be measured with the radiation from each of the
sources. A
control system, in communication with at least one of the sources of
radiation, changes the
phase of the radiation from one source relative to the phase of radiation from
the other
source as measured at the point on the surface of the object. In one
embodiment, the
phase of radiation from one of the sources is changed relative to the phase of
radiation of
the other source as measured at the point on the object by adjusting a
frequency tunable
laser. In another embodiment, the phase of radiation from one of the sources
is changed
relative to the phase of radiation from the other source as measured at the
point on the
object by moving one or more moveable laser sources. A detector positioned at
the point
on the surface ofthe object to be measured receives the radiation illuminating
the point.
In one embodiment, the detector is positioned on the end of a spring arm which
undergoes
movement in accordance with the surface contour of the object as the spring
arm is moved
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over the surface of the object. A processor, in communication with the
detector, calculates
position information of the point on the surface of the object in response to
the change in phase
of the radiation from the source as adjusted by the control system and the
radiation received at
the point on the surface of the object.
The invention also relates to method for determining, on an object having a
surface,
three-dimensional position information of a point on said surface of said
object, said method
comprising the steps of providing two sources of radiation separated by a
distance, said sources
being coherent with respect to one another; illuminating said point on said
surface of said
object with said radiation from each of said sources; moving each of said
sources relative to
each other; detecting radiation scattered by said point on said surface of
said object; and
calculating position information in response to said movement of said sources
and said detected
radiation scattered by said point on said surface of said object.
The invention further relates to an apparatus for determining, on an object
having a
~,urface, position information of a point on said surface of said object, said
apparatus
comprising two sources of radiation separated by a distance, said sources
being coherent with
respect to one another; a control system moving each of said sources relative
to each other; a
detector positioned to receive radiation scattered from said point on said
surface of said object;
and a processor receiving signals from, said detector, said processor
calculating position
information in response to said movement of said sources and said received
radiation scattered
from said point on said surface of said object.
Further, the invention relates to a method for determining, on an object
having a
surface, position information of a point on said surface of said object, said
method comprising
the steps of providing two sources of radiation separated by a distance, said
sources being
coherent with respect to one another; providing a detector at said point on
said surface;
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illuminating said point on said surface of said object with said radiation
from each of said
sources; moving each of said sources relative to each other; detecting said
radiation at said
point on said surface of said object; and calculating position information in
response to said
movement of said sources and said radiation detected at said point on said
surface of said
obj ect.
The invention also relates to an apparatus for determining, on an object
having a
surface, a depth coordinate of a point on said surface of said object, said
apparatus
comprising two sources of radiation separated by a distance, said sources
being coherent with
respect to one another; a control system moving each of said sources relative
to each other; a
detector positioned at said point on said surface of said object to receive
radiation
illuminating said point on said surface of said object; and a processor
receiving signals from
said detector, said processor calculating position information of said point
on said surface of
said object in response to said movement of said sources and said radiation
received at said
point on said surface of said object.
Brief Description of the Drawings
This invention is pointed out with particularity in the appended claims. The
above and
further advantages of this invention may be better understood by referring to
the following
description taken in conjunction with the accompanying drawings, in which:
Fig. 1 is a block diagram of an embodiment of the invention for making surface
contour measurements;
Fig. 2 is a block diagram of an embodiment of the two sources of radiation
shown in
Fig. 1 ;
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Fig. 2a is a block diagram of another embodiment of the two sources of
radiation
~~hown in Fig. l;
Fig. 2b is a block diagram of yet another embodiment of the two sources of
radiation
~,hown in Fig. 1;
Fig. 3 is a block diagram of an embodiment of apparatus for supporting the two
sources
of radiation of Fig. 1 at a fixed distance relative to one another;
Fig. 4 is another embodiment of the imaging system in Fi~_ l .
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Fig. 5 is a block diagram of an alternate embodiment of the invention for
making
surface contour measurements;
Fig. 6 is a flow diagram of an embodiment of the steps utilized by the
processor of ,
Figs. 1 and S in making surface contour measurements;
Fig. ba is one embodiment of a portion of the flow diagram of Fig. 6;
Fig. 6b is another embodiment of a portion of the flow diagram of Fig. 6;
Fig. 6c is yet another embodiment of a portion of the flow diagram of Fig. 6.
Fig. 7 is a block diagram of one embodiment of a detector and processor
arrangement for use with the systems of Figs. 1 and 5;
Fig. 7a is a block diagram of an alternate embodiment of a detector and
processor
arrangement including a multiprocessor for use with the systems of Figs. I and
5;
Fig. 7b is a block diagram of another alternate embodiment of a detector and
processor arrangement for use in the systems of Figs. l and S;
Fig. 8 is a block diagram of another embodiment of the invention for making
surface contour measurements;
Fig. 9 shows one embodiment of photodetector elements positioned on the
surface
of an object in accordance with the embodiment of Fig. 8; and
Fig. 9a shows another embodiment of photodetector elements positioned on
spring
arms for use in the embodiment of Fig. 8.
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Description of the Preferred Embodiment
. While describing the embodiment of the invention, reference will be made to
"sources" and "sources of radiation." These terms are meant to refer to any
source of
radiation, including highly localized sources of radiation.
Referring to Fig. 1, and in brief overview, two sources of radiation P1 and PZ
are
separated by a fixed distance D and have spatial coordinates of {xl,y,,zl) and
(x2xya,zz),
respectively. The radiation from each of the sources P1 and P2 is coherent
with respect to
the radiation from the other one of the sources. Each source, P1 and P2,
directs its
respective divergent beam of radiation 12 and 14 toward a point Po on the
surface of an
object 10. The distance from each respective source of radiation, P, and P2,
to the point
on the surface Po is indicated by Rl and R2, respectively. W is the angle
between the line
extending from the origin to the point Po and the line extending between
sources P, and
Pz, 8$ is the angle between the z axis and the line extending between the
sources PI and P2,
and cc is the half angle subtended by the source points as viewed from Po.
Each beam 12,
' 14 is substantially polarized in the same direction as the other beam 14, 12
and may be
independently scannable to simultaneously illuminate different regions on the
object 10.
Alternatively, the entire object 10 may be illuminated simultaneously.
Light scattered 20 by the point Po is detected by a photodetector 22. In one
embodiment, the photodetector 22 comprises an array of photodetector elements
providing a two dimensional image of the object 10 to be measured. In a
further
embodiment, the array of photodetector elements is a charge coupled device
(CCD). The
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detector 22 provides an output signal 26 comprising one or more individual
signals, each
one associated with a corresponding one of the photodetector elements of the
detector 22.
In a preferred embodiment, a focusing element 24 is positioned between the
point
Po on the surface of the object 10, and the photodetector 22, so as to image
the
illuminated portion of the object including point Po onto the detector 22.
Because of the
roughness of the surface of the object, and because the illuminating radiation
is coherent,
the focused image will be speckled. The output signal 26 from the
photodetector 22 is the
input signal to a processor unit 28.
A polarizer 30, in one embodiment, is placed between the focusing element 24
and
I O the detector 22. Polarizer 30 is oriented in a direction to maximize its
coincidence with
the principal polarization component of the scattered light 20, so as to
improve the
speckle contrast. With this arrangement, the signal-to-noise ratio associated
with light
scattered from the surface of the object 10 is maximized.
In one embodiment, the processor 28 is a single processor which operates on
15 detector output signals 26 associated with each of the photodetector
elements of the
detector array 22. In another embodiment, the processor 28 is a multiprocessor
having a
plurality of individual processors and each photodetector element provides an
input signal
to a respective one of the processors. In yet another embodiment, in which the
detector
22 is a CCD array, a plurality of the CCD elements provide an input signal to
a respective
20 processor of a multiprocessor. With the multiprocessor arrangements,
computations on
signals from a plurality of individual photoelements occur substantially
simultaneously,
thereby enhancing the signal processing speed.
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A control unit 32 controls the operation of the sources of radiation, PI and
P2, so
as to change the phase of the radiation of one of the sources relative to the
phase of the
radiation from the other source as measured at the point Pa on the surface of
the object 10.
The processor 28 may be in communication with control unit 32 via signal line,
or bus 34.
For example, in certain applications it may be desirable for the processor 28
to process
signals from the detector 22 at specific times relative to the scanning of the
sources P1 and
P2 over the surface of the object 10 or relative to the rate at which the
frequency of the
radiation from the sources is swept. Since such scanning and frequency
sweeping
operations are controlled by control unit 32, communication between the
control unit 32
and the processor 28 is desirable in these circumstances. It will be
appreciated that the
control unit 32 and the processor 28 may be physically separate units or,
alternatively, may
be implemented by a single processing system.
Referring now to Fig. 2, in one embodiment the sources of radiation P, and Pz
are
formed from the radiation emitted from a tunable laser 40. The radiation beam
44 emitted
I5 by the tunable laser 40 is split by a beam splitter 48. The radiation beam
50 reflected by
the beam sputter 48 is caused to diverge by a lens 52. The divergent beam is
then
reflected by a moveable aiming mirror 54. The radiation beam reflected by the
aiming
mirror 54 provides one of the sources of coherent radiation, P I . Similarly,
the radiation
beam 46 passing through the beam splitter 48 is caused to diverge by a lens 58
which
directs the divergent beam to a second moveable aiming mirror 60. The
radiation beam
reflected by mirror 60 provides the second source of radiation, P2. Aiming
mirrors 54 and
62 may be pivotable to selectively illuminate the surface of object 10. They
may also be
moveable to vary the positions of sources P, and P2.
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Referring to Fig. 2a, another embodiment of the sources of radiation P 1 and
P2 is
shown to include a tunable Iaser source 40 providing a beam of radiation 44.
The
radiation beam 44 passes through a lens 62 which causes the beam to diverge,
providing
divergent beam 64. Divergent beam 64 is then reflected by beam sputter 48 to
provide a
first beam 66. A second beam 68 passes through the beam sputter 48, as shown.
Moveable aiming mirrors 54 and 60 reflect beams 66 and 68 to provide sources
P1 and P2,
respectively.
Referring to Fig. 2b, in another embodiment the sources of radiation P, and P2
are
split from the radiation emitted from a tunable laser 40 using a fiber optic
sputter 56.
Fibers may have beam-forming elements at their end to control or set the
divergence angle
of the two beams, and in one embodiment the beam-forming elements may be
lenses.
Sources P ~ and P2 may alternatively be formed from a pair of tunable lasers
which are
frequency locked together. Other suitable embodiments of radiation sources
include any
sources which generate a wave having a controllable phase, such as microwaves
and sonic
waves.
In one embodiment, the sources of radiation P1 and P2 are maintained at a
fixed
distance D from one another by attaching each source to one end of a bar
comprised of a
material having a small coefficient of expansion. In another embodiment, the
sources of
radiation Pl and Pa are not held at a fixed distance but instead the distance
between them,
D, is known to a high degree of accuracy.
One illustrative bar 70 for supporting radiation sources Pi and P2 at a fixed
distance D relative to one another is shown in Fig. 3. A bar 70 is provided
with sockets
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74 at opposite ends thereof. A ball joint 76 is pivotally positioned within
each of the
sockets 74, as shown. Each of the ball joints 76 has an end of a fiber from a
fiber optic
sputter 56 (shown in Fig. 2b) positioned therein and an aperture 80 through
which
divergent radiation passes. Fibers may have beam-forming elements at their end
to control
or set the divergence angle of the two beams and in one embodiment the beam
forming
elements are lenses. In operation, the ball joints 76 are pivotable as shown
by arrows 78
within the respective socket 74 and may be under the control of control unit
32 (shown in
Fig. I). With this arrangement, the divergent beams 12 and 14 provided by the
sources PI
and P~ at the ends of the fibers can be directed as desired to illuminate all,
or a portion, of
the object 10 including the point Po to be processed, while maintaining a
fixed separation
distance D.
The coordinates of point Po on the surface of object I O are (xxy,z). Although
the x
and y coordinates of Pa are generally directly determinable from the geometry
of the
detector 22 and the object 10, taking into account any magnification by
intervening
focusing element 24, the depth coordinate z, where the z axis is defined as
being parallel to
the optical axis of the imaging system, is not directly obtainable. The depth
coordinate, z,
however can be measured by first considering the difference in path length
s-R2-Rl~ S~ (1)
from the radiation sources P1 and P2 to the point Po on the surface of the
object I0. The
quantity Sa is included to account for any path length difference in the beams
that may
occur before they reach points P1 and P2.
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If s is non-zero, then changing the frequency of the radiation emitted from
sources
Pt and P2 will result in the phase of the radiation from one source, as
measured at point Po,
changing with respect to the other source. This phase change results in a
modulation of
intensity of the radiation at point Po. The change in frequency, Ov, required
to complete
one cycle of a change in intensity is given by the expression:
dv = -
c (2)
S
where c is the speed of light. Thus, by measuring the change in laser
frequency, w,
needed to cause one oscillation of intensity, the path difference s may be
determined. The
measurement of z is then based on determining the value of s for each value of
x and y, as
discussed below.
Improved accuracy in the determination of s is obtained by measuring dv over
many oscillation cycles. In practice it is convenient to work in terms of the
number of
oscillation cycles N (not necessarily a whole number) induced by a total
change in
frequency B.
I 5 N is given in terms of w and B as
N _ Q~
_ _B (3 )
Elimination of w from Eq. (3) using Eq. (2) yields the following expression
for s in terms
of N: '
s __ c N {4)
B
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An uncertainty 01V in the measurement of N, corresponds to an uncertainty 0s
in s
of
- s~
Equation (5) indicates that if the uncertainty ~1V to which a single
oscillation cycle
can be determined remains constant, the uncertainty ds in s is reduced by a
factor equal to
the number of cycles N that are measured. There are numerous methods for
determining
N to various levels of resolution ~N that are known to those skilled in the
art. Examples
of methods yielding a resolution of roughly one oscillation-cycle count (~N=1)
are to
perform a fast Fourier transform (F'FT) on the data sequence or to count zero
crossings of
the high-pass filtered signal. Improved resolution of a fraction of an
oscillation-cycle
count (dN< 1 ) can be achieved, for example, by finding the argument of the
discrete
Fourier transform (DFT) where the magnitude of the DFT is maximized or by
inspecting
the phase of the oscillation cycle at the ends of the frequency scan. One
technique known
to those skilled in the art for accurate inspection of the phase is to insert
a phase
modulator in one leg of the beam path, i.e., between the beam sputter or fiber-
optic
splitter and one of the sources PI or P2 in Figures 2, 2(a), and 2(b).
If h, I2, and I3 are signal intensities corresponding to phase shifts induced
by the
phase modulator of -90°, 0°, and 90°, respectively, then
the phase ~ of the oscillation
cycle is given by:
= tan 2~~ - I1 - ~' 6
()
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For a typical frequency scan of B=lSTHz for a tunable diode laser, and for an
uncertainty of ~N = 1 cycle, an uncertainty of ~l.r = 20 ~,m is provided. An
uncertainty of
ON = 0.1 cycle would improve the uncertainty in s to ~.s = 2.0 ~,m, provided
that the
spread in s over the lateral resolution is smaller than this quantity. If the
spread in s over
the lateral resolution on the surface of the object is larger than ds, then
the improved
resolution in the measurement of s may still result in an improved estimate of
an average
or representative value of s over that lateral resolution.
In terms of the coordinate system:
s= ~x-x2)2 +(Y-Y2)2 +(z-z2) - (x-x~)2 +~Y-Y~)2 +(z-zy2
To make the calculation simpler, assume that the two sources PI and PZ are
located
symmetrically about the origin at {xlzyi,zi) and (-xl, yt,-zi). Then Eq. (7)
becomes, in
terms of (xl,yl,zl):
s-'V1x+x1)2 +(y+Y~)z +tz+zl)2 -.~~x-xi)2 +~y-Yi)2 +(z-ziJ . {8)
Solving for z, Eq. {8) becomes:
4{W +YYi )z~ ~ 2 16(W ~' YYi )2 + (s2 - 4zi )(s2 - D2 - 4x2 - 4y2 )
IS z = (9)
s2 - 4zi
where D is the distance between the two sources Pi and Pa. Thus z is
determined to
within an ambiguity due to the existence of the positive and negative roots of
Eq. (9).
Qne way to avoid this ambiguity is by illuminating the object 10 so that the
s=0 Iine
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(labeled 16 in Fig. 1 for the case so=0) does not bisect the region of the
object to be
imaged. One way of moving the s=0 Iine is to vary so in Eq. (1).
y The sensitivity of the system to changes in s is shown by the ratio of
dsldz, where
dz is the uncertainty in z introduced by an uncertainty Ds in the value of s.
This ratio
ranges between zero, for a system lacking any practical range sensitivity and
two, for a
theoretically maximal system. A value of two is impractical to achieve because
the surface
of the object 10 would have to Iie between the two point sources P1 and P~ and
only one
side of the surface could be illuminated from each beam. The ratio ~s/dz is
calculated by
taking the partial derivative of s with respect to z, from which the following
expression for
the range resolution is obtained:
4z=ds z+zi z-zl 1 10
DZ f Da
Ro+RoDcosyr+ 4 Ro-RoDcosyr+
In equation (10), Ro is the distance from the origin to Po and ~ is the angle
between the
Line extending from the origin to the point Po and the line extending from
point PI to point
Pi as shown in Fig. 1. A useful configuration that provides good range
resolution is to set
~=~90° for which the expression for ~z simplifies to
__ 4s
~ 2sinacos8s _(11)
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where 8$ and a. are as shown in Fig. 1. In terms of Ro and D, tanoc=D/(2Ro).
Equation
(I 1) shows that the range resolution improves as the angle a. increases and
the angle 8t
decreases. For values of ~S~ixn, a=IO°, and 6s=45°, the range
resolution is ~z=20p,m.
Uncertainties (~lx, ~y) in the lateral position {x, y) of the observation
point P also
affect the range resolution ~z. If the two source points lie in the x-z plane,
then the
measurement of z is insensitive to uncertainties ~y. For ~=90°,
uncertainties L1x in x cause
an uncertainty
4z = dx tan 8s ( 12)
in the measurement of z. Therefore, angles near 6s 0° offer the best
immunity to
uncertainty in the lateral position of point Po.
Because the depth of focus decreases as the lateral resolution of the optical
system
improves, there is a tradeoffbetween lateral resolution and maximum object
depth. One
method for reducing this limitation in object depth is to sequentially focus
on different
range planes and use only those pixels that are within the depth of focus. For
example, a
100p.m lateral resolution would limit the depth of field to the order of 1 cm,
and an object
with a 10 cm range could be imaged at full resolution by focusing sequentially
at ten
different ranges. To minimize the effects of depth of field, the z axis can be
defined in a
direction that minimizes the range extent, i.e., normal to the average plane
of the surface
of the object. To increase the lateral area that can be imaged without losing
lateral
resolution, multiple cameras {i.e., detector arrays 22) can be used to cover
the entire area
of interest of the object 10 or individual cameras can be used for inspecting
regions of
interest. Alternatively, the focal plane of single lenses can be populated
with a plurality of
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detector arrays. These arrays can be translated independently to inspect
various regions of
the object at high resolution. Translation of individual detector arrays along
the z axis or
tilting of the detector arrays can achieve simultaneous focusing for regions
of the object at
different depths to increase the allowable object depth.
A potential di~cuIty with the optical imaging system in Fig. 1 is that the
bistatic
angle between the sources and the detector may introduce shadowing effects.
These
effects can be reduced by placing the Iens closer to the sources as in Fig. 4
and using the
lens in an off axis configuration where the detector is offset laterally in
the image plane. If
the lens is designed for this purpose or has a sufficiently large field of
view, then
aberrations resulting from ofd axis imaging can be minimized.
Refernng to Fig. 5, an alternate embodiment of the present invention includes
a
moveable radiation source P1 and a stationary radiation source Pa, each
providing a
divergent beam 150 and 154 and having a path length labeled R~ and R2 between
such
radiation source and a point Pa on the surface of an object 10, respectively.
The sources
P1 and PZ may be generated by any suitable source of coherent radiation, such
as a
monochromatic laser, which is split to provide the two point sources P1 and
P2.
Moreover, various techniques are suitable for splitting the radiation from the
coherent
radiation source, such as the beam splitter embodiments of Figs. 2 and 2a and
the fiber
optic splitter embodiment of Fig. 2b.
The divergent beams 150 and I54 are directed toward a surface of an object 10
on
which a point Pe is located having position information which is to be
measured.
Illumination scattered by the surface of the object 10 is focused by a
focusing element, or
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lens 158 to impinge on a detector array 22. The lens can be used in an off-
axis
configuration as illustrated in Fig. 4 to reduce shadowing effects due to the
bistatic angle.
An optional poIarizer (not shown) of the type described above in conjunction
with Fig. 1
may be positioned between the focusing element 158 and the detector array 22
in order to
improve the contrast of the speckle image incident on the detector array 22.
The detector array 22 is in communication with a processor unit 28 for
processing
the image incident on the detector, as will be described. A control unit 32 is
in
communication with at least the moveable source P 1 for moving the source P,
along an
axis 160. As noted above, the control unit 32 and the processor unit 28 may be
implemented by separate devices or alternatively, may be part of a single
system.
Additionally, the control unit 32 and the processor unit 28 may communicate
with each
other, as may be desirable in certain applications.
As described above in conjunction with Fig. 1, the depth coordinate z
associated
with a point Po on the surface of the object 10 can be determined as a
function of the
difference, RZ-R~, between the path lengths Rl and Ra of beams 150 and 154,
from sources
P1 and PZ respectively, to point Po. In the embodiment of Fig. 5, the phase of
the radiation
from moveable source PI is changed by moving the source P, along the axis 160
under the
control of the control unit 32. With this arrangement, oscillations in the
intensity at point
Po are produced.
The instantaneous coordinates of moveable point source P1 are
x~ = a ~ s~ Yt = ~2g~ and z! = ans ( 13)
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where a represents the magnitude of translation of point source P1, and 2 8,
nzS, and nB are
direction cosines representing the direction of translation with respect to
the x, y and z
axes, respectively. The phase difference of the radiation from the sources P1
and P2 as
measured after propagation to point Po is given by:
~ _ ~ (RZ - R~) + ~ o
( 14)
where ~o represents a constant phase offset that may exist between the two
coherent
sources P, and P2. As P1 translates along axis 160, the value of Ri changes,
causing ~ to
vary as a function of a.
The number ofintensity oscillations that occur at point Po as point source P1
I O moves away from the origin is given by:
__ ~{a) - ~(Q) __ Ro. - Ri __ _1 a z z 2 - z z
IV 2~ ~ ~~ x +y +z - (x-a2s) +(y-ams) +(z-an~.) ~ (15)
where Ro is the distance between point Pa and the origin of the coordinate
system, ~ (a) is
the angle of translation measured at a, and ~(0) is the angle of translation
measured at 0.
Consideration of Eq. (I S) reveals that the number of intensity oscillations,
N, resulting
from movement from source P1 is independent of the location of the stationary
source P2.
This independence permits the sources P, and PZ to be positioned in close
proximity to
one another. With this arrangement, the divergent beams 150 and 154 from
respective
sources Py and P2 experience common disturbances, such as air turbulence and
vibrations.
In this way, the effects of such disturbances are minimized. Additionally,
beams 150 and
154 reach the surface of the object 10 with substantially identical
polarization.
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Since the magnitude of translation a of point source Pi is relatively small as
compared to the values ofx, y and z, Eq. (15) can be approximated to second
order in
alRo as follows:
2
N = ~ Ccos yr - ~ sin2 yr ~ _ ~ cos yr sin2 r~ ~2 ( 16)
where W is the angle between the line extending from the origin to the point
Po and the line
defined by the direction of translation of P1.
Eq. (16) indicates that to lowest order in a/R-0, knowledge ofN allows the
angle ~r
to be determined. Given knowledge of yr from three or more locations, the
(x,y,z)
coordinates of Po could be determined through triangulation. We now describe
an
embodiment similar to the one corresponding to Fig. 1, where the x and y
coordinates are
determined from location of the image point in the detector array.
The measurement of z for a given (xy) location can be made either by counting
the
number of intensity oscillation cycles N that occur as P1 moves over a
distance a or by
measuring the rate at which such intensity oscillations occur. Consider first
a
1 S measurement of z based on counting the number of cycles N. With N known,
all of the
variables in Eq. (15} are known except for z. Solving Eq. (1 S) for z yields
the following
expression:
fl~t.q t p A'' =(PZ Zrzs )(x2 +y2) I7
( )
P _ ns
where
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A=x.~s+ynzs+~(pz-1) (l g)
and
p = a (19)
Equation (I9) defines a dimensionless parameter having a magnitude ranging
between
S zero and unity that represents the average modulation rate of the speckle
intensity in terms
of oscillation cycles N per wavelength unit traveled by PI. For values of a
approaching
zero, Eq. (I7) can be approximated as:
z - (x~s + yms)ns ~ p (x2s + ym,.)z -(pz -ns ~~xz +yzl (20)
Pz -nz
s
The expressions for z in Eqs. 17 and 20 can be simplified by setting ns = 0,
so that
I0 the translation of source P1 is confined to the x y plane. This arrangement
represents a
good practical choice for translation of source P1, as described below. The
resulting
expression for z can be written as follows:
~z -xz -yz (21)
where the distance Ro from the scattering point Po to the origin of the x, y
coordinate
- 15 system is given by the exact expression:
x~s+yms+~tp'--1)
(22)
P
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When a is small, RQ can be approximated as:
~ y x2s + yms 23
( )
Consider now the measurement of z based on knowledge of the instantaneous rate
at which the intensity oscillations occur. The instantaneous oscillation rate
p can be
S expressed in a manner similar to the average oscillation rate in Eq. (19},
as follows:
(24)
Substituting the expression for the number of intensity oscillations, N, from
Eq. (15) into
Eq. (24) yields:
p - xPs + ynZs + zn,. - cr - 25
{x-cr~s~2 +(y-ams}a +~z-ans?z
where the relation:
~a + msa = ;isa = 1 (26)
has been used to simplify the numerator. For small values of a, p can be
approximated as:
p ~ cos qr - sine ~r ~ - ~ cos yr sin Z yr ~2 (27)
Solving, Eq. (25) for z yields:
z= ~t
Pa -~a (2g)
s
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where
O = ~x~s + yms +a(pz -1)I~S (29)
and
~ =P a(Pz -1)~2{x~s + yms)-a(2s +ms )~+{x~s +yms)2 -(p2 -ns )(x2 +y2) (30)
When ras = 0, Eq. (29) can be written in the form of Eq. (21 ), with:
a{p2 1)~2{x~s +yms}-a-+~x2~r +ymSJ2 31
Ipl ( )
For small values ofa, Eqs. {28) and (31) can be approximated by Eqs. (20) and
(23),
respectively, with p replaced by p.
in order to estimate range resolution, consider the uncertainty dz in the
measurement ofz that would be introduced by an uncertainty (ON or ~.p) in the
quantity
being measured. For simplicity, this calculation is based on the approximate
expression
for N given by Eq. (16}. To find ~z, we take the partial derivative of N {or
p) with
respect to z and equate this derivative to the ratio ONl~lz (or dp/dz), to
yield:
~z = G R° ~,dN = GR°OP (32)
a
where
G = - 1 (33}
ns. -{k'~s. +~xms. +nns)n sinBcosBs~sinB-cosBcos~~-~5~~
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is a geometrical factor that accounts for the direction of translation and the
direction to
the scattering point. In the first form for G,
.~ °xlRa, m y/Ra, and zz z/Ro (34) .
are direction cosines for the Point Po. In the second form for G, 8 and c~ are
the polar and
azimuthal angles, respectively, representing the direction from the origin to
P° in a
spherical-polar coordinate system. Likewise, the direction of translation of
the source
point is given by 8$ and ~8.
Consideration of Eq. (32) reveals that range resolution degrades with
increasing
object distance Ro and improves with increasing magnitude of translation a of
source P I.
Consideration of Eq. (33} reveals that the geometrical factor G ranges between
unity and
infinity, where unity corresponds to the best range resolution achievable.
The optimal direction of translation of source P~ for a given scattering-point
direction is obtained from Eq. (33} by choosing 2 s, m8, and n8 such that G is
minimized for
the given values of.2 , m and n. Application of this constraint yields:
~~'s,nl~.,rzs~ ~~ , zzm ~ 1-~z (35)
1-Yt2 1-f22
which implies that the optimal translation direction is orthogonal to the line
extending
from the origin to the scattering point Po (fir=90°) and lies in the
plane of incidence formed
by said line and the z axis (~s c~). Substitution of the values in Eq. (35)
into Eq. (33) ,
results in:
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G - I _ 1 __ 1 - (36)
1-n2 f2 +m2 sing
From Eq. (3 6), it is observed that the best achievable G value of unity
occurs when n = 0
(6 = 90°), which implies that the scattering point lies in the x y
plane. It is also observed
that the resolution degrades such that G approaches infinity for scattering
points lying on
the z axis. For example, G = 2 for 8 = 30° and G = 5.76 for 8 =
10°. Although it is not
possible to satisfy Eq. (35) for every point in the image without changing the
translation
direction fox each point, the condition for optimal resolution can be
approximated by
satisfying Eq. (35) for a representative image point.
By Eqs. (25) and (27), the instantaneous modulation rate p vanes as a function
of
the offset magnitude q of the translating point. For techniques based on
measuring p, it is
desirable for p to vary as little as possible during the scan so that there is
nearly a one-to-
one correspondence between values of p and z. Then standard spectral-analysis
techniques can be applied to estimate the value of p and determine z. To
quantify the
degree of nonuniformity in p that occurs during a scan, we define:
x - P(g) - P(~) - P(a> - cos yr (37)
p(0) cos yr
Substitution of the approximate form for p from Eq. (27) into Eq. (37) and
keeping only
the lowest order term containing a, yields:
sine yr a
x ~ cosqr Ro _ (38)
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Equation {38) states that the modulation nonuniformity increases linearly in
the ratio a/Ro
of scan length to object distance. Furthermore, the nonuniformity vanishes
when yf=0°
and increases without bound when ~r=90°. We observe, however, that
there is no range
resolution when 4r=0° because all points on the yr=0° Iine have
the same modulation rate,
regardless of range, i.e., Goo in Eq. (33). Therefore, there is a
tradeof~between
minimizing the nonuniformity and obtaining optimal range resolution.
A reasonable measurement configuration that simultaneously provides good range
resolution and reduced modulation nonuniformity is to set fis 0 and to use an
off-axis
optical system with the offset in the ~$ direction, i.e., ~=~8. Then Eq. (33)
for G reduces
to:
-2 { )
G = 39
sin(28)
As an illustrative example of the measurement technique, suppose it is desired
to
image an object that is 200 mm by 200 mm in the x y plane from a distance of
Ro=lm
using a laser of wavelength ~.=0.7~m. If ns 0 and the center of the object is
located at
6=30° and c~=~S, then, by Eq. (39), the geometric factor G wilt vary
between 2.1 and 2.6
over the field of view. By Eq. (32), a translation of cr=Smm will produce a
range
uncertainty of ~80~n (in the middle of the image) for an uncertainty in the
number of
oscillations of one-quarter count, i.e., ~N=0.25. The total number of
oscillation counts _
for the entire scan is N=3600 by Eq. (16). To estimate the modulation
nonuniformity at
the center of the image, we set ~=60° in Eq. {38) and obtain x=0.0075
so that there is less
than a 1% nonuniformity over the scan. This nonuniformity could be reduced
further by
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introducing slight variations in the scan rate during the scan to compensate
for any change
in frequency during the measurement.
Figure 6 depicts an illustrative series of steps to be executed by the
processor 28 of
Figs. I and 5 to determine the depth coordinate z at each point {x, y) on the
object. The
processor begins (step I00) by measuring a parameter of the intensity of the
radiation
scattered by a plurality of illuminated points on the object surface (step
108). From this
information, the z coordinate for each measured point is calculated (step I
12).
An optional filtering process may be performed in step 1 I6. Suitable filters
known
to those skilled in the art include, but are not limited to, smoothing
filters, median filters
and curve-fitting filters. Thereafter, the mapped points can be displayed or
output in
anyway known to one of ordinary skill in the art, following which the process
is
terminated in step 124, as shown. In one embodiment, the mapped points are
plotted as a
function of the computed z information on a mesh plot in step I20.
Referring also to Fig. 6a, one embodiment of steps 108 and I 12, suitable for
use
with the embodiment of Fig. 1 is shown. In step 108', the intensity of the
scattered
illumination is measured as a function of laser frequency ofl'set and N is
measured using
one of the methods known to those skilled in the art. Thereafter, s is
calculated for each
location (xy) in step 110' using Eq. (4) and z is calculated for each location
(xy) in step
112' using Eq. (9).
An alternate embodiment of process steps 108 and 112 for use in conjunction
with
the embodiment of Fig. 5 is shown in Fig. 6b. In this case, the parameter of
the intensity
measured in step 108" is the number of times, N (not necessarily a whole
number), that the
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intensity cycles as the moveable source Pi (Fig. 5) translates. Once N has
been
determined in step 108" through one of the methods known to be skilled in the
art it is
converted to p by Eq. (19) in step I IO". z is then calculated in step 112"
with the use
Eqs. (17) and (18). Another embodiment of process steps 108 and 1 I2 for use
in
conjunction with the embodiment of Fig. S is shown in Fig. 6C. Here, the
parameter of
the intensity measured in step I08" is the instantaneous oscillation rate p at
which
oscillations occur as the source point P1 translates. p is converted to z in
step 112"'
through Eqs. (28)-(30).
Various arrangements of detector 22 and processor 28 are possible. In one
embodiment, shown in Fig. 7, the photodetector elements 221,1 to 22~,m of the
detector
array 22 are read out serially. The serial output 36 of detector array 22
provides an input
to a processor 28. Processor 28 may comprise a single processor or
alternatively, may be
a multiprocessor comprising a plurality of processors.
Referring also to Fig. 7a, an alternate detector and processor arrangement is
shown. In this embodiment, the processor 28 is a multiprocessor comprising a
plurality of
processors 281,, to 28~m. Each of the photodetector elements 221,1 to 22~,,m
of the detector
array 22 provides a respective output signal 38 to a corresponding one of the
processors
281,1 to 281,,",. With this arrangement, each of the processors 281,1 to
28~,,m is able to
operate substantially simultaneously, in order to provide substantial
performance
advantages. More particularly, each processor 28,,1 to 28~,m in the
multiprocessor unit 28
is responsible for making the z coordinate calculation based upon the data
received from
the corresponding element 221,1 to 22~m of the photodetector array 22. Thus,
the z
coordinate for each location of the surface of the object 10 may be determined
rapidly.
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Fig. 7b shows a further alternate embodiment of the detector and processor
components for use in the systems of Figs. l and 5 in the form of a unitary
detector and
processor array 25. The array 25 is fabricated on, and supported by, a common
substrate
or is fabricated as a Multi-Chip Module (MCM) or with Surface Mount Technology
(SMT). The detector portion ofthe array 25 includes photodetector elements
221,1 to
22~,~ and the multiprocessor portion of the array includes processors 281,,
'to 28",m. More
particularly, each of the detectors 221,1 to 22",m is associated with, and
positioned adjacent
to, a respective one of the processors 281,1 to 28",~, and provides an input
signal to the
respective processor, as shown. The processors 281,1 to 28",m process the
information
from the respective detectors 221,1 to 22",m substantially simultaneously to
provide the
determined depth coordinates.
Referring to Fig. 8, another embodiment of the invention includes an array of
detectors 22' placed against the surface of the object 10 whose surface
contour is to be
measured. With this arrangement, rather than observing the Light scattered
from the point
Po on the surface of the object 10 to determine z, the measurement of the
phase shifting of
the light is performed directly at the surface of the object. Although not
shown, the
system of Fig. 8 includes a control unit 28 for controlling sources P, and P2
and a
processor 28 for processing radiation incident on detector 22' as shown and
described
above in conjunction with Figs. 1, 5 and 6.
The arrangement and mechanism for locating the photodetector elements 23 on
the
surface of the object 10 may vary. In one embodiment shown in Fig. 9, a
plurality of
individual photodetector elements 23 of array 22' are positioned on the
surface of the
object 10 in the area of interest.
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In another embodiment, shown in Fig. 9a, individual photodetector elements 23
of
the array 22' are mounted on spring arms 84 cantilevered from a support and
control
unit 88. The spring arms 84 are moved over the surface of the object 10 by the
control
unit 88 in order to contact specific points, or regions of interest. The
cantilevered support
of spring arms 84 causes each individual detector 23 to remain in contact with
a location
on the surface of the object 10 as the arms 84 are moved thereover. That is,
as the
contour of the object surface varies, the spring arms 84 move up and down
accordingly.
It will be appreciated that three or more additional radiation sources may be
used
in apparatus and methods of the present invention. For example, an additional
source or
sources can be used to determine xy coordinate information regarding the
object or a
portion thereof. Additionally, extra radiation sources may be used to reduce
any
processing inaccuracies or ambiguities attributable to shadowing of a region
of interest.
It will also be appreciated that other variations to the embodiment involving
moving source points may be used. For example, the two points may both move
with
opposing motion, they may both move in the same direction with constant
separation, they
may rotate about a common center point, or motion may be simulated by using an
array of
source points that can be switched on and offby the control system.
Having described and shown the preferred embodiments of the invention, it will
now become apparent to one of skill in the art that other embodiments
incorporating the
concepts may be used and that many variations are possible which will still be
within the
scope and spirit of the claimed invention. It is felt, therefore, that these
embodiments
should not be limited to disclosed embodiments but rather should be limited
only by the
spirit and scope of the following claims.
