Phase Imaging
The PCHOLO software has been modified to allow real-time display of wrapped phase images for static displacements and vibration modes. The conventional static hologram display program provides an image of the object that is multiplied by a fringe function:
I(x,y) = Io(x,y) [1 + cos(f (x,y))]
where Io is the irradiance of the object
and f is the fringe
locus function which is also
referred to as the phase of the fringe function. Typically
f(x,y) = L(x,y)
[cos(q1) + cos(q2)] 2p/l (1)
where L is the displacement of the object, q1 is the angle between the displacement vector and the illumination direction, q2 is the angle between the displacement vector and the observation direction, and l is the wavelength of light.
The conventional fringes are sinusoidal variations of brightness that modulate the irradiance of the object. The new phase imaging program provides an image that is
I(x,y) = f(x,y) modulo 2p
The fringes are geometrically identical to the conventional fringes, but their irradiance profile is a sawtooth rather than sinusiodal. This means that as the displacement of the object increases, the fringe irradiance increases from black to white. When the maximum irradiance of 255 is reached it then resets back to black. The object irradiance is now no longer part of this display.
This type of display is very useful for nondestructive testing applications where bonding flaws are detected by subjecting the test object to vacuum or heat stressing. Such stresses cause small localized deformations of the object surface that perturb fringe patterns. With conventional fringes, such perturbations can be hidden if they occur near the middle of a white or black fringe because they do not generate a brightness change. Such perturbations are easily detected with a continuously moving fringe pattern, but it is not possible to capture a moving pattern in a static display. With phase imaging, there is always a brightness change associated with a perturbation of the fringe pattern, so flaws are always apparent.
Phase imaging is also the first step toward processing interferograms for data extraction. Capture of a phase image automatically stores the interferogram, and three additional files from which an unwrapped phase image can be extracted, that is, an image where appropriate multiples of 2p have been added to the pixels so that the result is a continuous function. A new and highly robust phase unwrap program has been developed and is available with the PCHOLO software for this operation. Unwrapped phase images may be used in Eq.(1) to solve for the object displacement, L(x,y), with a limiting resolution of 0.2 nanometers. Such deformation maps can be useful in determining the response of structures to static loading, and comparison to finite element programs.
The four images on the right sidebar show a typical experimental output of an Aluminum plate subject to a static deflection load pushing on the left edge.
Static Mode Cosine Fringes
On Aluminum Plate
A constant deflection load is
placed on the plate, the resulting cosine fringes show the deflection.
Static Mode Wrapped Phase Image Display of the Aluminum Plate
The same cosine fringes as
above are now displayed as wrapped phase fringes.
Unwrapped Phase Image
Fringes
The unwrapped phase image
fringes shows the deflection at the left end of the plate. The degree of deflection is
directly proportional to the intensity.
3-D Surface Plot of Unwrapped Phase Data
The 3-D surface plot graphically shows the deflection at the left end of the plate that is resulting from the static load being applied.