Image of a Complex Object: OSU Physics Building Atrium

The gamma density function of Eq. 1 was first used to analyze the speckle at three areas of the unmodulated image of the Physics atrium shown in the upper panel of

. These areas were selected to have large, nearly uniform structures so that changes in scene geometry and reflectivity did not dominate the speckle statistics. The upper intensity distribution (orange box) is from a nearby wall (at ~10 m) made of painted drywall and returned a fit parameter $N = 3.63$. The middle intensity distribution (green box) is from a seminar room (at ~ 30 m) that is interior to the atrium and covered with rough tile and returned $N = 4.31$. The lower intensity distribution from a wall (at ~10 m), made of painted drywall, and returned $N = 3.84$. Since the contrast is inversely proportional to the square root of the fit parameter $N$, the average speckle contrast $C$ of each of these images is 0.51.

However, as we have noted above, the images of the physics atrium are complex, not only because of the angular variation that forms the image, but also in the nature and variety of its reflection. For a surface that has a surface roughness that is less than a wavelength, the resulting reflection will be part specular and part diffuse. The resulting signal will not create the "fully developed speckle" pattern of Eq. 1, but will follow a modified Rician density function \begin{equation}p_I(I)=\frac{1}{I_n}e^{-\left(\frac{I}{I_n}+\gamma\right)}I_0\left(2\sqrt{\frac{I}{I_n}r}\right)\end{equation} where $I$ is the intensity, $I_n$ is the average speckle intensity, $r$ is the ratio of the specular reflection amplitude to the average speckle intensity, and $I_0$ is the modified Bessel function of order zero. The contrast of the image is \begin{equation}C=\frac{\sqrt{1+2r}}{1+r}\end{equation} The same intensity distributions as above were fit to modified Rician density functions after normalizing to the average speckle intensity, shown in

show somewhat better fits for the Rician function, especially in the bottom two panels.