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Theory

Electronic Speckle Pattern Interferometry (ESPI)

ESPI on the other hand, records the surface displacement of an object in response to the applied force. ESPI can be used in arrangements where fringes will represent lines of either in-plane or out-of-plane displacement.  The out-of-plane set-up can be briefly described as follows: A laser light beam is split into two. One of the beams, the object beam, is used to illuminate the object. A video camera is then used to view the illuminated object. The other beam, which is called the reference beam, is directed in such a way that it intersects the line of view between the object and video camera. At that point, a partial mirror is used to deflect the reference beam into the video camera causing it to combine with the light reflected off the object. Due to the monochromatic properties of the laser light, the object and reference beam interfere to produces a unique speckle pattern. The speckle pattern is recorded by the video camera and digitised in a computer in a similar manner to the shearography system. The figure below schematically details the layout. 

The in-plane set-up differs from the out-of-plane set-up in that there is no defined reference beam.  The laser beam is as before split into two seperate beams. Both beams are then focused onto the object from opposing angles as indicated in the diagram below. The speckle pattern is produced by the intereference of the light from both beams reflecting off the object and is captured by the video camera.  In plane object displacement causes the relative beam path lengths between both laser beams to vary, which results in an alteration of the speckle pattern.  Out of plane displacement is cancelled out as both beam path lengths are altered by the same amount.  

To perform an ESPI inspection process, a speckle image of the unstressed object is first captured and stored in the computer. The object is then stressed causing the object's surface to displace. This causes the beam path length of the light reflected off the object surface to alter,  which in turn causes the unique speckle pattern to change. When compared with the original stored speckle image, a final image containing the familiar zebra-like fringe patterns is produced. The process for out-of-plane ESPI is highlighted by the equation below: 

The fringe sensitivity of in-plane displacements is of the order of  is the angle of incidence of the illuminating beams, which ideally should be the same for both beams. 

 

From the equations above it becomes evident that the object displacement magnitude is constant along a fringe contour, but changes between consecutive fringes due to the increase or decrease in the magnitude of n