Comparison and validation of point spread models for imaging in natural waters.

It is known that scattering by particulates within natural waters is the main cause of the blur in underwater images. Underwater images can be better restored or enhanced with knowledge of the point spread function (PSF) of the water. This will extend the performance range as well as the information retrieval from underwater electro-optical systems, which is critical in many civilian and military applications, including target and especially mine detection, search and rescue, and diver visibility. A better understanding of the physical process involved also helps to predict system performance and simulate it accurately on demand. The presented effort first reviews several PSF models, including the introduction of a semi-analytical PSF given optical properties of the medium, including scattering albedo, mean scattering angles and the optical range. The models under comparison include the empirical model of Duntley, a modified PSF model by Dolin et al, as well as the numerical integration of analytical forms from Wells, as a benchmark of theoretical results. For experimental results, in addition to that of Duntley, we validate the above models with measured point spread functions by applying field measured scattering properties with Monte Carlo simulations. Results from these comparisons suggest it is sufficient but necessary to have the three parameters listed above to model PSFs. The simplified approach introduced also provides adequate accuracy and flexibility for imaging applications, as shown by examples of restored underwater images.

Why does the Secchi disk disappear? An imaging perspective.

The widely-used Secchi disk method is re-examined from the modulation transfer aspect. Namely, by assuming a volume scattering function and applying small angle scattering approximation, we show that the Secchi depth and horizontal visibility can be determined using the water modulation transfer function and the corresponding spatial frequencies associated with the disk. A basic equation of Secchi disk is reached that is comparable to the radiative transfer approach, in that the Secchi depth is inversely proportional to the attenuation coefficient (c). With typical values for parameters applied, we demonstrate that the modulation transfer technique produces a horizontal visibility range of about 4.8/c, which is inline with previous studies. The improvement lies in the fact that the current approach correctly addresses the response of all spatial frequencies according to the modeled optical transfer function of the water. In terms of Secchi disk theory, the current approach helps to understand the effect of disk size as well as the role of scattering on the Secchi disk depth. The approach presented provides an understanding of Secchi disk disappearance by showing that as the disk is moved away from the observer, the spatial frequencies corresponding to the disk size increase, while the modulation transfer dampens contrast at an increased rate.