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Location and shape measurement using a portable fringe projection system


In this paper we present a portable fringe projection system developed for the measurement of the three-dimensional shape and position of complex aircraft parts. We describe the prototype instrument and processing algorithms designed, implemented, and tested during this study, and we discuss several applications throughout the lifecycle of the aircraft.

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angle between projection and observation axes, rad


modulated phase, rad

Φ* :

phase estimator, rad

α, β:

angles of laser beam, rad

A :

background illumination

b :

distance between camera focal point and laser source, mm

f :

effective focal distance of the camera lens, mm

f 0 :

carrier frequency

I :

image intensity

i, j :

image pixel coordinates

K :

calibration constant

O :

object image

O :

camera focal point

P :

pitch of the reference image

P(X p ,Y p ,Z p ):

point in object

p(x p ,y p ):

projection of pointP onto the image plane


quality value of the phase differences

R :

reference image

S :

laser source

s :

camera magnification, mm pixel−1

x, y :

CCD physical coordinates, mm

X, Y, Z :

real world coordinates, mm


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Ortiz, M.H., Patterson, E.A. Location and shape measurement using a portable fringe projection system. Experimental Mechanics 45, 197–204 (2005).

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Key Words

  • fringe projection
  • shape
  • position
  • location
  • aircraft component