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Osche G.R. Optical Detection Theory for Laser Applications (2002)(T)(418s)_EO_.djvu |
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by imagining the turbulent medium to consist of a series of thin slabs through
which the beam propagates...
C-174) can be
inverted to yield20
*^ 1 /-"singp d Г 1dDn(j>)-\J
Ф„(К) = — 1— \dp C-175)
4tt2K2 Jo Kp dp I dp J
If the Kolmogorov inertial subrange model given by Eq...
Correlation function for a weak turbulent field versus transverse separation p normal-
normalized to the Fresnel length 4
are within the inertial subrange (i.e., ?0 <&
obtain for the case of plane waves (y = 1),
Lo)...
C-192) and C-193) leads to
D(p) = 8x2k2 drj с1ккФп(к)[1-Ыкру)] C-215)
Jo Jo
Inserting the Kolmogorov spectrum given by Eq...
As stated earlier,
numerous experiments have confirmed that the log intensity obeys a normal
distribution, that is,
pit) = —L^-^-WJ^ C.222)
Here I = ln(//(/)) is the log intensity, I the optical intensity at a point, and of
the variance of log intensity...
Historically, the aperture-averaging
factor was originally introduced by Fried24 in lieu of a more complete theory
describing atmospherically induced speckle analogous to that for surface-induced
speckle and mathematical limitations associated with using log-normal statistics...
C-248), a simple interpolation formula
suitable for engineering applications can be developed...
In this section we follow Fried's27 original analysis
of the problem that relates the coherence diameter of the field to the aperture
diameter of the system...
Once again we may conclude that there is little to be gained in
sensitivity from further increases in aperture diameter beyond D = r0...
Thus propagation of short wavelengths
over long ranges can result in saturation even for small-to-moderate values of C%...
Note that the I-K and К distributions are deter-
determined by the parameters m, к, and m, respectively...
C-304) can be obtained and is
given by
Both the I-K and log-normal Rician models are two-parameter models that
require fitting to at least the first three moments of measured normalized intensity
data to obtain a valid solution...
Indeed, the process of parameter selection in
Figure 3-28 was not obvious, corresponding to more of a trial-and-error process
than one would like to see in a rigorous theory...
Many of the target and receiver classes discussed in this and later chapters
achieve significant speckle noise reduction through various types of diversity
techniques...
SINGLE-PULSE DIRECT-DETECTION STATISTICS
For a large number of scatterers, the central limit theorem can be invoked to
obtain zero-mean Gaussian probability density functions for the real and imagi-
imaginary components (cf...
In direct-detection systems, which respond to the intensity of the field,
the effect might be better characterized as exponential fading...
Cumulative gamma distribution with the speckle count M as a parameter,
where Wq = x'Q/a and y(M, Wq) is the incomplete gamma function, defined by
y(a,t)= I xa~le-*dx a>0 D-35)
Jo
Equation D-34) represents the probability that Wo will be less than or equal to
W^...
Equation D-70) can now be written as
D-77)
248 SINGLE-PULSE DIRECT-DETECTION STATISTICS
where z = ~Nn(M + Ns)/Ns...
Indeed, it is not too difficult to show by expansion that
D-82)
such that pr{\ - q)'r = 1...
It will be useful for later comparisons to develop expressions for the mean
and variance of the negative binomial distribution...
The analysis is accomplished by first generalizing the joint probability density
function given by Eq...
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