Uncertainty Analysis of Calculated Extinction From Apparent Contrast Measurements

1.0 Introduction The contrast of a given feature at a specific wavelength of light is determined by the radiance of that feature and the radiance of the background or adjacent feature against which it is viewed. Target/Sky contrast (C) is defined as the ratio of the difference between the feature (target) and the background sky radiance to the background sky radiance: where N stands for radiance, t and s represent target and background sky respectively. Two important definitions are: Inherent Contrast: C o The contrast of the target at zero distance Apparent Contrast: C r The contrast of the target as viewed at a distance r For an atmospheric sight path with average an extinction coefficient = b ext , the apparent contrast (C r) to an observer who is viewing an object of inherent contrast (C o) is rigorously defined: where s N o and s N r represent the radiance of the identical sky reference position as measured at the target location (distance = 0) and at the observation point (distance = r) respectively (Malm, 1979). Equation 2 can be rearranged to solve for b ext : Equation 3 can be simplified by defining a sky radiance ratio as r s o s N N N R / = : () N N N C s s t − = (1) () r b N N C C ext r s o s o r −         = exp (2) r o r s o s ext C C N N r b ln 1 (3)         = r o N ext C C R r b ln 1 (4)