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![]() ![]() ![]() ![]() Next: Evaluation Up: Geometrical calibration of ALIS Previous: System and requirements   Contents Calibration methodsFor studies of the atmosphere and the ionosphere it is appealing to use calibration images made under the same conditions with exactly the same rotations and use background stars as a way of determining the lines-of-sight. In this way the refraction of light in the atmosphere is automatically accounted for.
The requirement that the determination of the viewing directions
should be accurate to within
To proceed with determining the pixel lines-of-sight it is necessary
to be able to identify a large number of stars in an image,
preferably more than 100 evenly distributed over the image plate. For
these ``star pixels'' we know the lines-of-sight to within the
required accuracy. For the intermediate pixels we can choose either to
interpolate between the lines-of-sight from neighbouring star pixels or use an optical
transfer function that describes where the light from a direction in
space
For practical work the first approximation of an optical transfer function is the pinhole camera model, which is described in most textbooks on optical imaging ( Gonzalez and Woods, 1993); see Figure 4.2. The incident light from a direction in space ![]()
where ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]()
After a new fit of the optical parameters for the modified optical model, it appears that the systematic error has been removed (see Figure 4.4).
For the auroral and atmospheric studies which are the focus of ALIS, where the aim is to determine the position of objects at altitudes between 15 and 500 km, the required parameter is the path of the light through the atmosphere.
Due to the variations in density and temperature with altitude, the
refractive index of the atmosphere varies from 1 in free space to
approximately 1.0003 at sea level. This variation in refractive index
causes an object outside the atmosphere to appear closer to zenith than
it actually is. An everyday example of this is that
when the sun disappears from the horizon its centre is
already For a flat plane parallel atmosphere the total change in zenith angle is easily calculated by Snell's law: where ![]() ![]() ![]() ![]() ![]() This simple relation is correct to within ![]() ![]() ![]() In order to determine the path through the atmosphere there are three choices: to use the apparent zenith angle and to perform a path tracing in order to calculate the true path of the light, to use the apparent zenith angle and assume that the light travels in a straight line, or to use the true zenith angle and use that angle for calculating the line-of-sight. If we use the true zenith as the zenith angle of the light ray there will be an error between that ray and the true path of light due to the refraction in the atmosphere as can be seen in Figure 4.5,
![]() For zenith angles of up to ![]() ![]() If we were to use the apparent zenith angle, the error between the infered and the true paths of light would be: For a zenith angle of 45the difference between true and apparent zeniths is approximately 1 arc minute which gives an error of approximately 60 m at 200 km distance. Here it can be concluded that use of the true zenith angles and approximations of the light path with a straight line gives errors that are within the acceptable accuracy. The small error that results from this approximation can be compared with all other errors in the analysis and weighted against the computationally heavy and cumbersome task of performing a path-tracing through an atmosphere whose refractive index structure as a function of altitude is, at best, only roughly known.
![]() ![]() ![]() ![]() Next: Evaluation Up: Geometrical calibration of ALIS Previous: System and requirements   Contents copyright Björn Gustavsson 2000-10-24 |