ESTIMATION OF THE ATMOSPHERIC REFRACTION EFFECT IN AIRBORNE IMAGES USING RADIOSONDE DATA

Abstract. The influence of the atmospheric refraction on the geometric accuracy of airborne photogrammetric images was already considered in the days of analogue photography. The effect is a function of the varying refractive index on the path from the ground to the image sensor. Therefore the effect depends on the height over ground, the view zenith angle and the atmospheric constituents. It is leading to a gradual increase of the scale towards the borders of the image, i.e. a magnification takes place. Textbooks list a shift of several pixels at the borders of standard wide angle images. As it was the necessity of that time when images could only be acquired at good weather conditions, the effect was calculated using standard atmospheres for good atmospheric conditions, leading to simple empirical formulas. Often the pixel shift caused by refraction was approximated as linear with height and compensated by an adjustment of the focal length. With the advent of sensitive digital cameras, the image dynamics allows for capturing images at adverse weather conditions. So the influence of the atmospheric profiles on the geometric accuracy of the images has to be investigated and the validity of the standard correction formulas has to be checked. This paper compares the results from the standard formulas by Saastamoinen with the results calculated from a broad selection of atmospheres obtained from radiosonde profile data. The geometric deviation is calculated by numerical integration of the refractive index as a function of the height using the refractive index formula by Ciddor. It turns out that the effect of different atmospheric profiles (including inversion situations) is generally small compared to the overall effect except at low camera heights. But there the absolute deviation is small. Since the necessary atmospheric profile data are often not readily available for airborne images a formula proposed by Saastamoinen is verified that uses only camera height, the pressure at the ground and the camera level, and the temperature at the camera level.