|Phys 198||April 14, 1997|
Laser Speckle is the result of coherent light reflecting from a diffuse surface. A random distribution of bright and dark spots is obtained as shown in the photograph at the right.
The two basic types of speckle fields are specified as objective and subjective: Speckle patterns are called objective when there is no lensing involved. The speckle distribution can be observed by simply holding a piece of paper in the region surrounding the reflecting surface. The average size of the speckles in these patterns is determined primarily by the wavelength of the coherent light, the width of the original illuminating beam or equivalently, the size of the illuminated surface area, and the geometry involved. If the object distance to the detecting surface is L and the illuminated area has diameter D, then the statistical average diameter of the speckles is
On the other hand, if a lens is used to image the reflecting surface onto a screen, the speckle pattern shown in the image is called subjective, and the average speckle size is related to the imaging lens characteristics, such that if M is the image/object magnification, f is the focal length and a is the lens diameter, the average speckle diameter in the image is given by
In the reflecting surface, of course, the speckle size will be the image speckle size divided by the magnification of the imaging system.
The use of speckle metrology is divided into two classes,
depending on whether the measurement merely depends on the simple
translation of speckle patterns with no use of phase information,
or whether a coherent reference beam is added to the speckle
pattern and phase information is utilized. In the first case, the
measurement is called speckle photography, and in the second
case, speckle correlation or speckle interferometry. For the rest
of this discussion, speckle photography will be the method
analyzed; speckle correlation methods will be taken up later.
One of the advantages of using speckle photography is the simplicity of acquiring the data images. The figure at the right shows the basic layout involved. The film plate is first exposed to the speckle pattern on the object surface when the surface is in its initial or preloaded state. The surface is then loaded so as to produce in-plane deformation of such a size that the movement of points on the surface is larger than the speckle size (this is required in speckle photography, forbidden in speckle correlation methods), and yet not so large as to cause deformation of the speckle pattern for small regions on the surface. This produces a double exposure of two speckle patterns which is called a specklegram. Notice that no surface preparation is required, no physical contact with the surface is needed, and information is gained for all points within the illuminated area. A small region of the specklegram might look somewhat like the small sketch at the right. Notice that because of the deformation, each speckle has a twin and these pairs all have the same separation and orientation.
There are two common methods of analyzing such a specklegram. The first uses a point by point application of the Young's fringes technique to determine the direction and motion of each small region or point. The setup is sketched at the right. Here the spacing between fringes is d, D is the specklegram-screen separation, and the Airy disk indicated in the figure represents the diffraction of the small circular area of the specklegram illuminated by the narrow laser beam. Using the Young's fringes equation and noticing the orientation of the fringes gives the direction and the magnitude of the separation between the speckle pairs being illuminated by the laser beam. (All the pairs in the beam are assumed to have undergone the same translation.) It should be noted that there is still a sign ambiguity, the specklegram does not determine the sign of the displacement, only the magnitude and direction. Given the speckle displacement, it is relatively simple to examine the imaging setup and determine the actual displacement of points of the surface under test. The main problem with this method of analysis is that it quickly becomes tedious to move the laser position and repeat all the calculations for a large number of points.
An alternative method uses Fourier filtering techniques to get full-field displacement readings. The setup required is shown in the sketch below.
In this setup a laser beam is expanded and collimated and the
wide beam is used to illuminate major areas of the specklegram. A
lens (called the transform lens) is placed just after the
specklegram so as to produce the Fourier transform of the
specklegram in the focal plane of the lens. At the location of
the transform, a solid disk with a movable hole is located so as
to allow only light passing throught the hole and therefore
coming from specklegram regions which have a particular grating
spacing and orientation (due to the speckle twins) can be imaged
by a second lens (the imaging lens) on a screen. The image formed
on this screen will be an image of the original specklegram with
fringes indicating the locus of points that have a common spatial
shift and orientation such that light from them passed through
the hole. Of course, this would produce a dark image with bright
fringes; if the screen is a film plate, development will produce
a light image with dark fringes. This method gives information
over the whole image, but is much more complicated to obtain than
by using the Young's fringe method because of the difficulty of
correctly locating the filter aperture in both radial distance
from the center and at proper orientation around the central
axis. Also, if the filtering aperture is made small to produce a
narrow frequency fringe, the amount of light transmitted through
it will be small and long time exposures will be required to
obtain a reasonable final image.
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