K¼
r
hiI¼ b
expð2T=scÞ 1 þ2T=sc
2TðÞ=sc^2"# 1 = 2
ð 10 : 18 ÞHere the coefficientβ(0≤β≤1) is determined by the ratio of speckle size and
pixel size at the detector and by the polarization characteristics and coherence
properties of the incident light. The theoretical limits of K range from 0 to 1.
A spatial speckle contrast value of 1 means that there is no blurring of the speckle
pattern, which indicates that there is no motion. For particle velocities corre-
sponding to values ofτcless than about 0.04 T, the speckle contrast is very low
because the scattering particles are moving at such a high speed that all the speckles
have become blurred.
Example 10.8Consider a laser speckle imaging systems operating at
532 nm. (a) Suppose the exposure time of the camera is T = 10 ms. If the
speckle coefficientβ= 0.5, what is the speckle contrast factor K if the speckle
correlation time isτc= 100μs? (b) What is the value of K ifτc= 20 ms?
Solution: (a) Using Eq. (10.18) yields the following value for K when the
ratio T/τc= 10 ms/100μs = 100K¼ bexpð2T=scÞ 1 þ2T=sc
2TðÞ=sc^2"# 1 = 2
¼ 0 : 5
expð 200 Þ 1 þ 200
2 ð 100 Þ^2"# 1 = 2
¼ 0 : 071
(b) Using Eq. (10.18) yields the following value for K when
T/τc= 10 ms/20 ms = 0.5K¼ 0 : 5
expð 1 Þ 1 þ 1
2 ð 0 : 5 Þ^2"# 1 = 2
¼ 0 : 61
A number of factors must be considered carefully when making measurements
with speckle patterns. These issues are described in detail in the literature [ 29 – 34 ].
One factor deals with proper spatial sampling of the speckle pattern. A key point
involves the speckle sizeρspecklerelative to the camera pixel sizeρpixel. When the
speckle pattern is viewed by a camera, the minimum speckle size will be given by
qspeckle¼ 1 : 22 ð 1 þM)(f=#Þk ð 10 : 19 Þwhereλis the wavelength of the detected light, M is the image magnification, and
f/# is the f number of the system (e.g., f/5.6), which is the ratio of the focal length of
a camera lens to the diameter of the aperture being used. To satisfy the Nyquist
10.3 Laser Speckle Imaging 309