3D SHAPE MEASUREMENT AT DIFFERENT LENGTH SCALES USING
SPECKLE AND GAP EFFECT
1
Fu-pen Chiang1, Gunes Uzer2,
SUNY Distinguished Professor& Chair,
2
SUNY Graduate Student
Dept. of Mechanical Engineering
Stony Brook University
Stony Brook, NY 11794-2300
[email protected]
ABSTRACT:
There is a need to measure the height of an object at the micro/nanoscales. The electron speckle method [1] can
measure in-plane distance and strain of an object but it cannot be applied to measuring height. In this paper we
propose a method of height measurement using speckle and the gap effect [2-4] to measure height, thus the 3D
shape of an object. This technique can be applied to objects of various sizes ranging from meters to microns
depending on whether the recording system used is an ordinary macro camera, an optical microscope or a scanning
electron microscope.
INTRODUCTION:
Stress analysis techniques based on 2 dimensional imaging that assume plane specimens are well known, including
classical moiré and moiré interferometry [5], speckle interferometry [6], digital image correlation techniques [7], etc. If
the specimen is deformed along the optical axis or the specimen have curved surfaces (i.e. sphere), most of these
techniques will suffer from errors caused by the out-of plane displacements due to the perspective effect. This
perspective effect is present in in-plane moiré [2] and speckle photography methods [8]. Sciammarella and Chiang
derived an equation to take into account of this effect in the in-plane moiré method [2]. Chiang and Asundi [8] showed
that the same phenomenon prevails in speckle photography. They later used the effect to map the 3D displacement
of the object. [4].The gap effect is the result of optical perspective. That is: an object appears to be larger when it is
closer to the recording camera. This effect gives rise to fictitious strain ε as shown in Fig.1.
Figure 1. Optical perspective effect caused by movement along optical axis.
EXPERIMENT:
The experimental set-up consists of a CCD camera with 2048x2048 pixel resolution and divergent white light
illumination. A speckle pattern of average speckle size of 0.2mm covers the specimen surface.To test the validity of
gap effect we first applied the technique to flat plates of 45mmx45mm in size. Fig. 2 shows the schematic of
experimental setup together with a typical set of displacement vector field and u and v displacement contours.
Figure 2. (a) Test setup for flat plate specimen with dimensions 45mmx45mm, (b) the displacement vector field as a
result of the perspective effect, (c) displacement contours u and v along the x and y directions respectively.
The gap equation [2] ε = ∆ Z / Z where Z is the original distance from the object to camera lens predicts such a
phenomenon as shown in Fig.3 as solid lines. Thus by obtaing the fictitious strain using the speckle photography
technique and knowing Z, the 3D shape , i.e. the variations of Z can be calculated.Displacement contours obtained in
Fig.2 are used to calculate the fictitious strain and compared with the predictions of ε = ∆ Z / Z . As can be seen
from the Fig. 3 experimental results are in good agreement with the theoretical predictions.
Figure 3. Comparison of experimental results and theoretical prediction using the gap equation
ε = ∆Z/Z
.
We then used an hollow spherical ball to perform a similar experiment. Fig 4 shows the experimental setup and the
resulting fictitious strain field in terms of u and v displacement contours.
(a)
Camera
Z
dZ
(b)
(c)
Figure 4. (a) Test setup for sperical ball specimen, (b) and (c) as a result of the perspective effect displacement
contours u and v along the x and y directions respectively.
Then 3rd polynomial fitted to displacement data from u and v fields, Fig. 5(a) shows the fitted polynomial from v field
of the ball . Thus strain along the v direction represents the shape of the object since ε = ∆ Z / Z is the only strain.
Fig 5(b) shows the shape of the ball.
(b)
15
Displacement
10
5
0
0
500
1000
1500
Strain
y = 1E-09x3 - 3E-06x2 - 0.0175x + 12.894
-5
-10
Pixel
-15
Pixel
(a)
REFERENCES:
1.
Chiang, F., Raymond D. Mindlin 100th Anniversary Symposium 15th U.S. National Congress on Theoretical
and Applied Mechanics Jun 25 - 30,Boulder, CO, 2006
2.
Cesar A. Sciammarella, Chiang FP., ZAMP, vol.19, 326, 1968
3.
Chiang FP, A. Asundi, Applied Optics vol. 21(13), 2167-2169, 1982
4.
Chiang FP, A. Asundi, Applied Optics, vol. 21, 1887-1888, 1982
5.
Albert S. Kobayashi, Society of Experimental Mechanics, 1993.
6.
Chen DJ, Chiang FP., Applied Optics, vol. 32, 225 – 236, 1993
7.
Chu TC, Chu, Ranson WF, Sutton MA, Peters WH., Experimental Mechanics, vol. 25(4), 232 -244, 1985
8.
Chiang FP, A. Asundi, Applied Optics, vol. 20(13), 2167-2169, 1981