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BACKGROUND OF THE INVENTION
1. Field of the Invention
This invention relates to a method of deformation measurement using speckle
interferometry which enables nondestructive measurement of the deformation
of a machine tool, industrial product or other such object using speckle
interferometry.
2. Prior Art Statement
Since speckle interferometry can be used for contactless, highly accurate
measurement of the vibration and deformation distribution of even rough
surfaced objects such as machine components, it is an important
measurement technology. Particularly significant one among the different
types of speckle interferometry is electronic speckle pattern
interferometry (ESPI). With ESPI it is possible to obtain interference
fringes by taking a speckle pattern images with a TV camera and processing
the video signals with electronic circuits or storing the images in a
frame memory and processing them with a computer. Since ESPI is simpler to
conduct than conventional real-time holography interferometry using
photographic plates, it can be expected to find applications in
nondestructive inspection etc. at the point of production.
On the other hand, even though such methods of measurement using
interferometry are highly accurate, they have the disadvantage of being
limited to a narrow measurement range. Speckle interferometry has a
particularly severe limitation in that speckle noise on the interference
fringes may, at large deformation or vibration, cause the density of the
interference fringes to become so high as to make it impossible to read
the interference fringes and thus impossible to carry out the measurement.
This invention was accomplished in light of the foregoing circumstances and
has as its object to provide a method of deformation measurement using
speckle interferometry which is able to maintain high measurement accuracy
and achieve measurement over a wide range, specifically to enable
measurement even when the deformation of the object being measured is on
the millimeter order.
SUMMARY OF THE INVENTION
For achieving the aforesaid object, this invention provides a method of
deformation measurement using speckle interferometry comprising the steps
of forming a series of speckle images at specified time intervals by using
an interferometer to superpose a laser beam reflected from an object whose
deformation is to be measured and a laser beam not passing via the object,
storing the series of speckle images in a memory as they are formed, using
the difference between an appropriate two of the plurality of speckle
images to measure the deformation of the object during the time interval
between the formation times of the two speckle images, repeating the
preceding step to obtain a plurality of deformation measurements, and
summing the plurality of deformation measurements to obtain a measurement
of a large deformation not measurable by ordinary speckle interferometry.
A laser beam reflected from the deforming object and a laser beam not
passing via (i.e. unaffected by) the object are superposed to obtain a
continuous series of speckle images. A stopped down TV camera successively
records the speckle images at regular time intervals (64 speckle images at
1/30 intervals, for example). Later, two of the speckle images are
retrieved and the difference between them is calculated by a computer.
This makes it possible to observe the deformation that occurred in the
object between the recording times of the two images as interference
fringes. The interference fringe pattern represents the deformation
distribution in the form of contour lines and each interference fringe
corresponds to a distance equal to half the wavelength of the laser beam
used. The foregoing procedure is then repeated and the deformation
measurements obtained are added together. As a result, it is possible to
measure the distribution of large or rapid deformation not measurable with
ordinary speckle interferometry and to do so contactlessly and with high
resolution (on the submicron order).
The above and other features of the present invention will become apparent
from the following description made with reference to the drawings.
BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1 is a schematic view of a deformation measurement apparatus using
electronic speckle pattern interferometry.
FIG. 2 is an equivalent optical system of the apparatus shown in FIG. 1.
FIG. 3(a) is a graph showing the analytical results for the deformation
(S.sub.0,3) of a beam between time 0 and time 3.
FIG. 3(b) is a graph showing the analytical results for the deformation
(S.sub.3,6) of a beam between time 3 and time 6.
FIG. 3(c) is a graph showing the analytical results for the deformation
(S.sub.6,9) of a beam between time 6 and time 9.
FIG. 4 is a graph showing the distribution of a large deformation S.sub.0,9
obtained by summing deformation S.sub.0,3, S.sub.3,6 and S.sub.6,9.
FIG. 5(a) is a graph showing an analysis of deformation between time 0 and
time 1.
FIG. 5(b) is a graph showing an analysis of deformation between time 1 and
time 2.
FIG. 5(c) is a graph showing an analysis of deformation between time 2 and
time 3.
FIG. 6 is a graph showing the distribution of deformation S.sub.0,3
obtained by summing the analytical results of FIGS. 5(a), 5(b) and 5(c).
FIG. 7 is a graph showing the difference obtained by subtracting the
analytical results of FIG. 3(a) from the analytical results of FIG. 6.
FIGS. 8(a)-(e) are schematic views of the measurement method of the present
invention, wherein FIG. 8(a) shows a series of recorded speckle pattern
images, FIG. 8(b) shows an image representing the deformation between time
0 and time 6 obtained by taking the difference between the first and sixth
images shown in FIG. 8(a), FIG. 8(c) shows an image representing the
deformation between time 6 and time 10 obtained by taking the difference
between the sixth and tenth images shown in FIG. 8(a), FIG. 8(d) shows an
image representing the deformation between time 10 and time 12 obtained by
taking the difference between the tenth and twelfth images shown in FIG.
8(a), and FIG. 8(e) shows the image obtained by summing the deformations
shown in FIGS. 8(b) to 8(e).
FIG. 9 shows an image representing the deformation between time 0 and time
12 obtained by taking the difference between the first and twelfth images
of FIG. 8(a).
DESCRIPTION OF THE PREFERRED EMBODIMENT
An embodiment of the method of deformation measurement using speckle
interferometry according to the invention will now be explained with
reference to the drawings. FIG. 1 shows the configuration of a deformation
measurement apparatus using electronic speckle pattern interferometry,
which is used to conduct the deformation measurement method of the present
invention. The measurement apparatus, indicated by reference numeral 1, is
equipped with a He-Ne laser or other such laser beam source 2, a mirror 3,
a microscope object lens 4, a pinhole 5 and a half mirror 6. A reference
object is placed on the transmission side of the half mirror 6 and an
object to be measured 8 is placed on the reflection side thereof. A TV
camera or other such image pickup device 11 is disposed on the opposite
side of the half mirror 6 from the object to be measured 8. The image
pickup device 11 is connected with a frame memory 12, a monitor 13 and a
personal computer 14.
When the deformation measurement apparatus 1 is operated for measuring the
deformation of the object 8, the laser beam l emitted by the laser beam
source 2 is reflected by the mirror 3 through the microscope object lens 4
and pinhole 5 so as to become a divergent beam which is then amplitude
divided by the half mirror 6. One of the divided laser beams (the
reflected laser beam l.sub.1 in the illustrated example) is directed onto
the object to be measured 8 and the light scattered by reflection from the
object 8 (the object light) transmits through the half mirror 6 and enters
the image pickup device 11. The other divided laser beam (the transmitted
laser beam l.sub.2 in the illustrated example) is directed onto the
reference object 7 and the light scattered by reflection from the
reference object 7 (the reference light) is reflected by the half mirror 6
and enters the image pickup device 11 where it is superposed on the object
light. As the reference object 7 there can be used a concave mirror.
Insofar as the luminous energy is sufficient, the lens aperture of the
image pickup device 11 (ordinarily a TV camera) is stopped down so as to
increase the speckle size. In this specification, the superposed image
produced by the object light and the reference light reaching the pickup
element of the image pickup device 11 is referred to as a speckle pattern
image.
The explanation of the present invention will be better understood if
preceded by an explanation of ordinary speckle interferometry. In ordinary
speckle interferometry, before starting the measurement a speckle pattern
image of the object 8 before deformation is stored in the frame memory 12.
Next a speckle pattern image of the object 8 after deformation is stored
in the frame memory 12. Then by taking the difference between the speckle
images before and after deformation it is possible to observe a speckle
interference fringe pattern. The interference pattern appears as dark and
light showing the deformation distribution. When the deformation is large,
however, the measurement by this method produces interference fringes of
such high density that they may not be possible to read. In conventional
real-time holographic interferometry, holograms have to be remade many
times in the course of the deformation. Therefore, the measurement is not
only discontinuous but highly troublesome to conduct.
In contrast, in the present invention, which uses electronic speckle
pattern interferometry, only speckle pattern images of the continuously
deforming object to be measured are stored in real time (at the frame rate
of the TV camera) one after another in the large capacity frame memory 12.
Then, at a later time, the difference is taken between an appropriate two
of the speckle images and a calculation is made to determine the
deformation of the object during the interval between the times that the
two speckle patterns were formed. The same procedure is then repeated for
other speckle image pairs and the deformation measurements are summed to
obtain a large deformation measurement not possible by ordinary speckle
interferometry without loss of continuity.
An example of the present invention will now be described.
An ESPI system was configured in accordance with FIG. 1. As the large
capacity frame memory 12 there was used an Image PC1181 produced by EDEC
Co. The memory had the capacity to store four pictures each consisting of
256.times.240 pixels at a density of 8 bits (256 shades). As the personal
computer 14 there was used a PC9801VM produced by NEC. The computer had a
clock speed of 10 MHz and was equipped with a 40 MB external hard disk. As
the image pickup device 11 there was used a Sony XC-57 CCD camera having
510.times.492 available pixels and equipped with a TV camera zoom lens.
The lens aperture was set to F8. The monitor 13 was a 9-inch monochrome
display. As the laser beam source 2 there was used an NEC 632.8 nm
wavelength He-Ne laser with an output of about 15 mW. The object to be
measured 8 was cantilevered beam consisting of a 157 mm (h).times.40 mm
(w).times.2 mm (t) rectangular plate of transparent vinyl chloride painted
white and fixed in a vice up to 32 mm from its bottom edge. The measured
region of the cantilevered beam was up to 34.5 mm above its bottom edge
(the fixed edge). The reference object 7 was a 100 mm (h).times.85 mm (w)
rectangular plate whose surface was painted white to obtain a light
scattering surface.
Deformation was produced by bringing a micrometer head into contact with
the rear side of the cantilevered beam a point about 15 mm from its upper
edge (free edge) and manually imparting deformation in approximately one
graduation (10 .mu.m) increments. First, the cantilevered beam was
imparted with an appropriate deformation to bend it forward and the
speckle image S.sub.0 at this time was stored in the frame memory. The
image date was then immediately stored in the hard disk. This was defined
as the state before deformation (the undeformed state). The micrometer
head was then turned one graduation to bend the cantilevered beam further
forward and the speckle image S.sub.1 at this time was stored in the
frame memory and the image data was immediately stored in the hard disk.
The micrometer head was then turned one graduation to bend the
cantilevered beam further forward than at S.sub.1 and the speckle image
S.sub.2 at this time was stored in the frame memory and the image data was
again immediately stored in the hard disk. In this same way a total of 10
speckle images (S.sub.0 -S.sub.9) were recorded. The computer was then
used to calculate the difference between the undeformed state and each of
the deformed states (S.sub.0,i =S.sub.i -S.sub.0,i =1, 2, . . . , 9).
The experiment was conducted using the optical system of FIG. 1. The
equivalent interference system obtained by bending this relative to the
half mirror is as shown in FIG. 2. The CCD camera and the object to be
measured are directly opposed. The focal point of the microscope object
lens coincides with the center 0 of the thoroughly stopped down aperture.
In FIG. 2, define the width of the object as W and the distance between
the object and the diaphragm 9 of the TV camera as L. Then the view angle
.theta. satisfies the relationship tan .theta.=W/(2L). Assume that a point
P located approximately at the center of the object moves distance D (the
amount of deformation) along the optical axis. Since .theta..apprxeq.0,
the phase .phi. of the light emitted from point P onto the CCD element Q
changes by
.phi.=2D (2.pi./.lambda.) (1)
where .lambda. is the wavelength of the laser beam. The measurement is
conducted by using Eq. 1 to calculate the deformation amount D from the
observed interference fringe phase .phi.. The deformation amount D in Eq.
1 is deemed to be the component in the direction of the view angle
.theta.. In the test under discussion, the value of W was 40 mm (34.5 mm
in the height direction) and the value of L was 500 mm. The view angle
.theta. was therefore approximately 0.04. The relative error of the
deformation amount D is 1-cos (0.04)=0.8.times.10.sup.-3, or less than
0.1%. It must be noted, however, that deformation D involves a
three-dimensional spectrum and when a fixed point of zero deformation
cannot be identified, it is ordinarily determined by finding the phase
change .phi.i from four directions (i=1-4). In the experiment under
discussion, the direction of deformation and the fixed edge of the object
were known and the object view angle was small. The analysis at any point
on the object could therefore be conducted using Eq. 1. Since the purpose
of this explanation is to demonstrate that the proposed method is able to
measure large deformations, the analysis was not conducted over the entire
area. Instead the analysis was limited to manually determining the peak
positions of the dark fringes along the center line in the height
direction of the object. In this case, the deformation D.sub.N at the Nth
dark fringe from the fixed edge can be obtained as
D.sub.N =(.lambda./2)N (N=0, 1, 2 . . . ) (2)
FIGS. 3(a), 3(b) and 3(c) show the results of the analysis for deformations
S.sub.0,3, S.sub.3,6 and S.sub.6,9. The deformation amounts at the center
position 33 mm from the bottom (referred to as the "observation" point)
were 5.71 .mu.m, 5.36 .mu.m and 5.38 .mu.m. Combining these gives a
deformation amount of 16.45 .mu.m. This is the deformation amount that
could not be measured with S.sub.0,9. FIG. 4 is a graph showing the
distribution of the object deformation S.sub.0,9 obtained by summing
deformations S.sub.0,3, S.sub.3,6 and S.sub.6,9.
The analytical results for deformations S.sub.0,1, S.sub.1,2 and S.sub.2,3
are shown in FIGS. 5(a), 5(b) and 5(c). FIG. 6 shows the composite
deformation amount obtained from these analytical results. Since the
composite deformation amount of FIG. 6 should coincide with the
deformation amount of S.sub.0,3 of FIG. 3(a), the error e between the two
deformation amounts calculated as e=(S.sub.0,1 +S.sub.1,2 +S.sub.2,3)-
S.sub.0,3 becomes as shown in FIG. 7. The largest error is 0.4 .mu.m.
Defining the offset as -0.2 .mu.m, this amounts to an error of .+-.0.2
.mu.m. The small magnitude of the error, which is thought to occur during
reading of the interference fringes, demonstrates that by summing the
speckle interference fringe patterns it is possible to measure large
deformations with high accuracy.
On the basis of the foregoing results, the following method was developed
for determining large deformation using ESPI.
First, a series of speckle pattern images starting from that before the
deformation (S.sub.0), continuing through those in the course of the
deformation (S.sub.1, S.sub.2, S.sub.3 . . . , S.sub.n-1) and ending with
that after completion of the deformation (S.sub.n) are stored in a frame
memory. This completes the measurement. The analysis processing is then
started. The difference S.sub.0,1 between the first speckle pattern image
S.sub.0 and the first speckle pattern image after the start of deformation
S.sub.1 is found. If the number of interference fringes is small, the
difference S.sub.0,2 with respect to the second speckle pattern image is
found. In this way, the differences with respect to progressively later
speckle pattern images are determined until the speckle interference
fringe image S.sub.0,1 enabling determination of the largest possible
deformation is found. In a similar manner, the differences S.sub.i,i+1,
S.sub.i,i+2, . . . , are found until the speckle interference fringe image
S.sub.i,j enabling determination of the largest possible deformation is
found. This process is repeated to find differences S.sub.j,k, . . . ,
S.sub.l,m and the final difference S.sub.m,n. The symbols i, j, k, l, m, n
represent positive integers satisfying the relationship i<j<k<l<m<n. By
adding together S.sub.0,i to S.sub.m,n it is possible to measure the
distribution S.sub.0,n of any deformation no matter how large.
Thus the method of deformation measurement using electronic speckle pattern
interferometry according to this invention extends the range of
deformation measurement by storing speckle pattern images one after
another and then at a later time successively finding the differences
between appropriately selected pairs of the stored speckle pattern images.
When an attempt is made to use the prior art method of deformation
measurement using electronic speckle interferometry for measuring large
deformation, the density of the interference fringes may become so high as
to make them unreadable. In real-time holographic interferometry,
holograms have to be remade many times in the course of the deformation.
Therefore, the measurement is not only discontinuous but highly
troublesome to conduct. In contrast, in the present invention, which uses
electronic speckle pattern interferometry, since the speckle interference
fringes first appear as a result of taking the difference between speckle
images before and after deformation, only speckle pattern images of the
continuously deforming object to be measured are recorded in real time (at
the frame rate of the TV camera). For example, 12 images S.sub.0 -S.sub.11
are recorded, as shown in FIG. 8(a). Then, as shown in FIGS. 8(b), 8(c),
8(d), for determining the deformation between images S.sub.0 and image
S.sub.11, the images are divided into groups S.sub.5 -S.sub.0, S.sub.9
-S.sub.5 and S.sub.11 -S.sub.9, the difference between the first and last
member of each group is taken, and the differences in deformation are
summed. The result is shown as an image in FIG. 8(e). In the image of FIG.
8(e), the object to be measured shows the greatest deformation at the
point at the upper right and an analysis can be conducted on the basis of
the manner in which the deformation occurred. For comparison, FIG. 9 shows
the deformation image obtained when the difference between images S.sub.0
and S.sub.11 is obtained without dividing the images into groups. It will
be noted that the image of FIG. 9 contains no interference fringes and
consists solely of speckle noise (the dots in the image), making
measurement of the deformation impossible. This is because the large
deformation produced so many interference fringes that they cannot be
individually distinguished.
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