Hi all,
in the subject of mapping from the air, it is important to know how many pixels fall per cm on the ground.
Following
http://en.wikipedia.org/wiki/Angle_of_view
we got the following angles of view from equivalent focal length and we can compute aspect ratio from them:
| Focal Length (mm) | 24 | 28 | 35 | 43.3 | 50 |
| Vertical (°) | 53.1 | 46.4 | 37.8 | 31 | 27 |
| Horizontal (°) | 73.7 | 65.5 | 54.4 | 45.1 | 39.6 |
| 1.38794727 | 1.41163793 | 1.43915344 | 1.45483871 | 1.46666667 |
On the other hand you have sensor resolution:
Canon S90 is 3648 x 2736 = 9980928 roughly 10MPIX
this is aspect ratio 3648/2736=1.333...
It is said to be equivalent to focal length 28...105mm.
On the other hand all aspect ratios calculated above are well above 1.33.
Conclusion: even standard lens are generating wider view than the sensor is,
resulting in less horisontal than vertical resolution.
True or false?
Comments
You are now entering the world of photogrammetry!!
All of the problems you mention (and much more) have already been solved by these people (there are whole faculties for this topic...).
A search for "digital photogrammetry" should give you many hits and a good reading for some days :-)
Very demanding math sometimes but it gives you a feeling for the processes needed to e.g. produce orthorectified pictures and map projections.
Basic projection math may be simple (given ray hits ground at tan(x) or similar)
But what is the math for georectification in the language of a graphics processor - which turns this around and solves (at the surface point) what is the color (or image xy) of the pixel _AT_THIS_POINT?
The reason the numbers in the table don't work out to exactly 1.5 is that the distance on the image plane (i.e the sensor) is proportional to the tangent of the angle, not to the angle itself. This becomes significant for wider angles (i.e. shorter focal lengths) - if you looked at values for f past 50mm you would find that they converged on 1.5.
Fisheye lenses are different. They do have a linear relationship between distance on the image plane and angle, but this ends up transforming straight lines into curves when you look at a picture taken with such a lens.
On the other hand, assuming that the camera is aimed straight down, the relationship between distance on the image plane and distance on the ground will be linear so that, for a given altitude, one pixel will always represent the same number of cm on the ground both horizontally and vertically. If the camera is aimed forward rather than down then the pixels will be stretched along the ground in the direction the camera is aiming, with the effect being very significant for shallow angles towards the horizon.