A novel technique to determine difference

8/7/2019 A novel technique to determine difference

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Optics and Lasers in Engineering 44 (2006) 2540

A novel technique to determine difference

contours between digital and physical objects for

projection moire interferometry

Mark Kimber, Jonathan Blotter

Department of Mechanical Engineering, Brigham Young University, Provo, UT 84602, USA

Received 27 October 2004; accepted 15 February 2005

Available online 26 April 2005

Abstract

Projection moire interferometry (PMI) is an out-of-plane displacement measurement

technique, and consists of capturing reference and deformed images of a grid pattern projectedon the test object. By differencing the reference and deformed images of the projected grid

pattern, a fringe pattern is generated from which the displacement field can be extracted. Due

to the projection-oriented nature of this technique, measuring displacements in applications

with non-viewable, hidden, or inaccessible reference surfaces excludes the use of PMI. This

paper presents a technique for computing the difference contours between a digital and

physical object. A CAD model of the inaccessible surface is converted to a point cloud and a

surface interpolation function is implemented to generate a digital displacement field, which

can be correlated and differenced from the displacement field of the physical object determined

through traditional PMI methods. These techniques are validated by comparing results from

an airfoil with other measurement methods.

r 2005 Elsevier Ltd. All rights reserved.

Keywords: Moire; Inaccessible surface; Difference contours; CAD

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0143-8166/$ - see front matter r 2005 Elsevier Ltd. All rights reserved.

doi:10.1016/j.optlaseng.2005.02.004

Corresponding author.

E-mail address: [email protected] (J. Blotter).


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1. Introduction

Optical-based measuring techniques are currently used for many types of

measurements including flow field [1,2], displacement [3,4], surface roughness [5,6],and temperature [7,8] as well as others. In most instances, optical techniques are

preferred over traditional methods because they are typically non-invasive and

provide whole-field measurement data. Projection moire interferometry (PMI) is a

low-cost, non-intrusive, whole-field displacement measuring technique. PMI has

proved a useful tool in numerous applications such as wind tunnel tests of large-scale

structures [9,10] and surface contour measurements [11]. A typical PMI configura-

tion is shown in Fig. 1, where a light source is projected through a grid pattern and

focusing lens on to the structure of interest. When the structure is in a reference state,

the grid lines have a spatially uniform distribution. Under load conditions, the object

deforms and changes the distribution of the grid lines. When the deformed grid lines

are subtracted from the reference grid lines, a fringe pattern is generated. This fringe

pattern is an interferogram which contains information (moire fringes) from which

the magnitude of the structural displacements can be extracted. The magnitude of

the displacements is computed using the fringe sensitivity coefficient (FSC) [12]. The

FSC values are computed through a calibration procedure which consists of

analyzing fringe patterns generated from known displacement fields.

As is common with most measurement techniques, PMI has inherent character-

istics that allow or limit its use in certain types of applications. The limitation

addressed in this work is the inability to perform a PMI analysis in applicationsinvolving inaccessible surfaces. Current PMI techniques require at least two images

to be captured. One of these corresponds to a reference image of the grid pattern.

Obtaining this image becomes difficult when the reference object is inaccessible for

the camera and cannot be acquired through traditional PMI methods. One example

of this occurs when a part is produced using a mold or die. The mold and the actual

workpiece represent the reference and deformed surfaces, respectively, but the

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Fig. 1. Typical PMI setup.

M. Kimber, J. Blotter / Optics and Lasers in Engineering 44 (2006) 254026


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3. Inaccessible surface measurement procedures

Once the FSC values are extracted, a difference or displacement field can be

generated for any surface with respect to the reference plane. In many instances, itwould be extremely advantageous to directly compare a surface contour to that of an

inaccessible surface. These surfaces could be inverted, hidden, or simply only exist as

a CAD model.

The inaccessible surface measurement procedure presented in this paper consists

of three steps as outlined in Fig. 3. The first step is to extract a point cloud from the

CAD model, which is first converted into a common format known as stereo

lithography, or STL. This point cloud represents discrete surface points of the CAD

model. The second step requires changing the orientation of the point cloud in order

to measure displacements along the same direction as the displacements in the PMI

analysis. However, methods must first be employed to determine this direction and a

plane from which the magnitudes will be measured. For the present study, these

parameters are described by the reference plane established during the PMI analysis

from which the displacement direction is perpendicular. The third step is to create a

displacement field by applying a surface interpolation function [14] to the point

cloud to create a continuous surface of points. A prerequisite to this step is

determining the geometric points on the reference plane represented by each pixel of

the camera. In this research, results from camera calibration are used in this step,

thereby generating a displacement field obtained directly from the CAD data, which

can then be compared to the displacement field found through a PMI analysis of theobject. Each of these three steps will now be discussed in more detail.

3.1. 1Point cloud extraction

The first step in creating a displacement field from a CAD model is to convert it to

a point cloud. For this research, the CAD model is first converted into stereo

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Fig. 3. Inaccessible surface measurement procedures.



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matrix (HT) is shown in Eq. (1), and consists of a 3 3 rotational submatrix (R) and

a 3 1 translational vector (T). The rotational submatrix is composed of three

separate 3 3 rotational matrices as shown by Eq. (2), where (yx, yy, yz) represent

the rotations about each of the three original coordinate axes. This describes therelative orientation from the original to the new coordinate system. The translational

vector is shown in Eq. (3), and is composed of three translations (tx, ty, tz) along each

of the original axes to describe the relative position from the original to the new

coordinate system. This 4 4 matrix describes transformation from any one

coordinate system to another. When post multiplied by a vector of the form

w2 x2 y2 z2 1T, yields a solution of the form w1 x1 y1 z1 1

T, where w1 and w2represent vectors in the original and new coordinate systems, respectively. The

homogeneous transformation is determined from the actual setup to the point cloud

and multiplied by all point cloud data to convert it to a coordinate system identical

to that of the actual setup.

HT R33 T31

013 1

" #, (1)

R

1 0 0

0 cos yx sin yx

0 sin yx cos yx

264

375

cos yy 0 sin yy

0 1 0

sin yy 0 cos yy

264

375 cos yz sin yz 0sin yz cos yz 0

0 0 1

264

375,

(2)

T tx ty tzT. (3)

3.3. 3Displacement generation

To generate displacements, first the geometric location on the actual object

represented with each camera pixel must be determined. Since camera perspective is

removed from all images during the PMI analysis, only the pixels per unit length andheight ratios need to be determined, which can be done with a variety of techniques.

For the present work, this is accomplished by placing a planar checkerboard in the

reference plane established in the PMI analysis. An image is then captured and

dewarped. A corner extracting algorithm [16] accurate to roughly 0.1 pixels is then

used to determine the pixel locations for each checker corner in the image, and used

in conjunction with the geometric size of the checkers to determine the pixel. This

creates a mesh of data points where displacements may be generated corresponding

to camera pixels. Since the pixels do not necessarily lie on top of the point cloud

data, a surface approximation can be applied to the point cloud to create a surface of

points with identical spacing on the point cloud as the pixel array has on the actualobject. This is performed using interpolation functions [14]. This surface of points is

then directly compared to the displacement field generated from a physical object

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using conventional PMI methods and the differences can be determined between an

inaccessible surface and an actual object.

4. Experimental setup and validation

The test object was a section of an airfoil (approximately 27 cm long and 12 cm

wide). The images used for testing represented a small portion of the airfoil

(approximately 10 cm 9 cm). During the assembly process, the airfoil is pressed

into a fixture and riveted to an elastic frame. When it is removed from the fixture, the

airfoil experiences some springback and does not maintain the exact shape of the

fixture. Therefore, discrepancies exist between the internal surface of the fixture and

the external surface of the assembled airfoil. The goal of this test was to determine

the shape differences between the airfoil fixture and the assembled airfoil. These

differences were measured by comparing the displacement fields of the assembled

airfoil and a CAD model representing the internal surface of the fixture. This

experimental displacement field was then compared to displacements obtained using

a coordinate measuring machine (CMM) with an accuracy of75mm. Scans were

performed with the CMM on both the assembled airfoil and internal surface of the

fixture, and then differenced to acquire the displacement field under investigation.

This section continues by presenting and discussing the results of this test.

The experimental PMI setup is represented in Fig. 1 and consisted of a digital

projector (Epson model 7700p) with a native display format of 1024 768 pixels forthe light source and focusing lens. The grid pattern used was a bitmap image

(640 480 pixels) with 0.25 lines/pixel. The CCD camera (Hitachi, model KP-M1U)

with 640 480 pixel resolution was controlled by a computer, which had a frame

grabber to digitize the pixel-sensed voltage to an 8-bit intensity pattern. A flat

aluminum plate (15 cm 15 cm) was used as the PMI reference plane to measure

displacements and was mounted on a rotary turntable with 1/601 resolution.

The airfoil was positioned as shown in Fig. 5, where parallelism was forced

between the flat bottom edge of the airfoil and the reference plane. The center of

rotation was used as the origin with displacements measured along the z-axis as

shown in the illustration. FSC values were determined within the PMI setup andapplied to a fringe pattern generated by differencing the projected grid patterns of

the airfoil and reference plane in order to create a displacement field. The offset

shown in Fig. 5 was then added to each displacement value resulting in a surface

topology of the assembled airfoil. The images used for testing represented a small

portion of the airfoil (approximately 10 cm 9 cm). The experimental displacement

field from the PMI analysis is shown in Fig. 6.

4.1. 1Point cloud extraction

After generating displacements through the PMI analysis of the assembled airfoil,a similar displacement field for the CAD model of the internal surface of the

assembly fixture was created. The solid CAD model and the extracted point cloud

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M. Kimber, J. Blotter / Optics and Lasers in Engineering 44 (2006) 2540 31


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are shown in Figs. 7 and 8. The extracted point cloud was generated by converting

the solid CAD model into STL format, which represents the surface as triangle

shaped facets. The vertices were read from the file and plotted in space. For this

object, 46 triangles were needed to describe the surface using 138 vertices. The

vertices are shared between triangles, and therefore not all are unique geometriclocations. The total number of unique points in the point cloud data is 48. However,

since the form of the fixture (and airfoil for that matter) allows two different z-values

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Fig. 6. PMI displacement field.

Fig. 5. Position for airfoil insertion in PMI setup.



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for any xy coordinate, the point cloud must be trimmed to prevent problems during

surface fitting. The CAD model was trimmed to slightly larger than the viewing

window in the PMI analysis. This is seen in Figs. 9 and 10, where the surface is

trimmed at 15.00 and 11.15 cm along the two directions shown.

4.2. 2Point cloud registration

The coordinate system of the point cloud was transformed to match that of the

assembled airfoil. Visualization of the needed transformation is shown in Fig. 11,which suggests that a simple rotation about the z-axis describes this transformation.

The homogeneous transformation matrix from object to point cloud consisted of a

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Fig. 7. Solid model of internal surface of fixture.

Fig. 8. Extracted point cloud from solid model.



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single rotation about the z-axis (yz 901) with no other rotations or translationsneeded. This was then used to transform every coordinate of the point cloud

according to Eq. (4), where (X; Y; Z) represent point cloud data and HT is the

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Fig. 9. Trimmed solid model of internal surface of fixture.

Fig. 10. Trimmed extracted point cloud from solid model.

Fig. 11. Coordinate system registration.



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homogeneous transformation matrix. With this registration complete, the point

cloud data are ready to be used in generating displacements.

cosyz sinyz 0 0

sinyz cosyz 0 0

0 0 1 0

0 0 0 1

26664

37775

zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl}|fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{HTX

Y

Z

1

26664

37775. (4)

4.3. 3Displacement generation

In order to generate displacements, the pixel representation on the object was firstdetermined. A 25 17 checkerboard pattern of 1 cm square checkers was placed in

the reference plane, and an image was captured and dewarped. This image was

analyzed to determine the pixel per length and height ratios by using a corner

extracting algorithm to find the pixel locations of each checker corner in the image.

The average calculated ratios were 0.2413 and 0.2416 mm/pixel in the horizontal and

vertical directions, respectively. These values were then used as inputs in the surface

interpolation program, specifying points in two directions (along the x- and y-axis)

in which to create displacements in the third direction (along the z-axis). The

resulting displacement field is shown in Fig. 12, where each data point represents a

single pixel. Since the CAD model was perfectly flat along the vertical direction, the

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Fig. 12. Displacement field from surface interpolation of point cloud data.



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resulting flatness of the interpolated data was analyzed to gage the accuracy of the

algorithms. The standard deviation of the displacements along each column is shown

in Fig. 13 with an average for all columns of 0.35 103 cm. This suggests that

displacements have been generated within reasonable limits and the interpolation

functions employed yield acceptable results.

5. Results

The variations between the assembled airfoil and CAD model of the fixture were

then determined by differencing the displacement fields. The results are shown in Fig.

14. This was then compared to the displacements found using the CMM. The CMM

displacement field is shown in Fig. 15, and for this work was used as a benchmark to

judge the accuracy of the developed methods. Differences between the CMM and

developed methods are considered to be the introduced errors in the overall process.

Percent error was computed for each pixel and the results are shown in Fig. 16. This

varies throughout the entire measurement domain from 14.39% to 14.31%. To

better illustrate the overall results, a cross-sectional slice of data was examined, andis shown in Fig. 17. The error bars shown approximate the 95% confidence interval

of measurement capability.

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Fig. 13. Standard deviation of columns for interpolated surface.



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6. Discussion and summary

A method has been developed for determining out-of-plane deformations with

inaccessible reference surfaces. The test case performed has shown errors within

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Fig. 14. Experimental springback measurements.

Fig. 15. CMM springback measurements.



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Fig. 16. Percent difference (experimental vs. CMM springback measurements).

Fig. 17. Cross-sectional slice of displacement data.



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714.4%. For the present study, there are two recognized sources of error. One

source of error is attributed to the camera resolution. A higher resolution camera

will assist in this effort, but it is also worthwhile to investigate any image analysis

algorithms that might enhance image quality without requiring a higher resolution.A second source of error is introduced by the PMI measuring techniques. Projection-

oriented measuring systems typically are not as precise as other methods, but for

some applications, the relatively uncomplicated layout and cost-effectiveness

outweigh the negative effects of accuracy. For this reason, they are ideal for large-

scale applications. Typically, the PMI errors lessen as the FSC values increase,

producing a more sensitive setup. However, as this is done, more fringes will appear

for a given displacement. Too many fringes with respect to the camera resolution

produce an unrecognizable fringe pattern. In a way, the PMI errors are limited to the

FSC values, which are dependent on the camera resolution. In addition, the

displacements measured during the PMI analysis of the assembled airfoil (difference

between reference plane and assembly) were roughly 20 times as large as those

measured during the combined process (difference between assembly and fixture).

This creates somewhat of a dilemma in choosing suitable FSC values. For an

application where both sets of displacements are nearly equal, results will produce

less error. In conclusion, applications where PMI techniques have not traditionally

been used due to inaccessible reference surfaces could now benefit from a whole-field

projection measuring system. This would greatly increase inspection efficiency of

large production parts and final assemblies.

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A novel technique to determine difference