Estimating the image spectrum signal-to-noise ratio for imaging through scattering media

Characterizing the Degrading Effects of Scattering by Atmospheric Fog on the Spatial Resolution of Imaging Systems

“…Moreover, the image spectrum SNR provides a means of estimating the noise effective resolution of an imaging system, hence providing a useful metric of evaluating the effects of various sources of noise on the image quality. The SNR of an image obtained with a deterministic MTF and a photon-limited image detection system is given by [4],…”

“…where SNR(υ) is the image spectrum SNR, H(υ) is the MTF of the imaging system, O n (υ) is the normalized Fourier spectrum of the target irradiance distribution, K dir (λ) is the mean number of photons directly transmitted to the imaging system from the target, and K sca (λ) is the mean number of photons scattered by the atmospheric aerosols before reaching the imaging system. K dir (λ) and K sca (λ) are given by [4],…”

“…Paper: ASAT-16-140-SP Where PSF dir (0,λ), PSF sca (0,λ) and PSF t (0,λ) are the direct, scattered, and total effective PSF, respectively, at the central portion of the imaging plane; PSF t (0,λ) = PSF dir (0,λ) + PSF sca (0,λ),and K avg (λ) is the average number of photons detected by the imaging system is given by [4], , spectral wavelength bands, where λ c is the central wavelength of the given spectral band, using the radiometric model described in [4]. Also, another parameter to be defined is the noise effective cutoff spatial frequency, υ noise [cycle/rad], of the image spectrum SNR, which is the spatial frequency that corresponds to an image spectrum SNR value of 1.…”

“…The diffraction-limited plots, shown in figure (4), assume the absence of atmospheric aerosols; K sca = 0. [rad], of the image spectrum SNR for the atmospheric aerosol models, at each spectral band as shown in figure (4). The values of θ th which is listed in Table (3) indicate that for each atmospheric aerosol model θ th at the visible spectral band is less than θ th is at the NIR spectral band, indicating a better spatial resolution of the imaging system at shorter wavelengths, and also a better SNR.…”

“…Blurring is attributed to optical turbulence and small-angle forward scattering (Mie scattering) caused by large sized aerosols, r ≥ λ, which is known as the adjacency effect, since photons are imaged in pixels adjacent to those in which they ought to have been imaged [2]. Scattering has the effect of de-correlating the light leaving the target from the unscattered light reaching the imaging system; i.e., the scattered and direct path radiation received at the imaging system entrance pupil, after propagation through a scattering medium, are uncorrelated [3,4].…”