image distortion when taking a picture from space I'm trying to understand if there is a distortion of an image taken from space (i.e. from a satellite), and if there is, then how to model it mathematically (depending on the angle in which we take the photo).
So, is there such a distortion (I assume there is, and it increases with the angle of the camera relatively to the nadir angle), and why (mathematically)?
 A: Yes, there is such a distortion and there exist various methods to correct for it. Depending on the sub-field, it may be called nadir correction or limb correction.
One reason is the optical path length through the atmosphere. This is of major importance at wavelengths where the atmosphere is at least partly absorbing, such as in regions of the thermal infrared (outside of the 8–12 µm window region) and in most of the microwave. This is difficult to correct for in the situation of a single-channel instrument and a field of ongoing research. For example, you could check out this paper for infrared radiances:


*

*Teo, Chee-Kiat, Tieh-Yong Koh: Nadir Correction of AIRS Radiances. J. Atmos. Oceanic Technol. 27, 470–480, 2010.
doi: 10.1175/2009JTECHA1341.1.


or for microwave:


*

*Goldberg, Mitchell D., David S. Crosby, Lihang Zhou: The Limb Adjustment of AMSU-A Observations: Methodology and Validation. J. Appl. Meteor. 40, 70–83, 2001.
doi: 10.1175/1520-0450(2001)040<0070:TLAOAA>2.0.CO;2.


Another aspect is the actual angle of incidence on the surface. This applies at any wavelength and is related to simple geometric distortion. Additionally, in visible wavelengths (which I suppose you are mostly interested in), the incident angle of the Sun varies through the field of view of the camera. One paper on the subject is


*

*Leroy, M., and JL Roujean, Sun and view angle corrections on reflectances derived from NOAA/AVHRR data, IEEE Trans. Geosci. Remote Sens. 32, 684-696, 1994. doi: 10.1109/36.297985.


but there are many others.
