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George,

After some additional thoughts I do now understand that you referred
here to the conversion function:

> With centred optics, any radial plot, of pixel count from the centre point
> of the array, Px, against offset angle A from the optical centre-line, MUST
> pass through the origin, at (0,0), and MUST be antisymmetric about that
> origin. When the pixel count from the centre is expressed as a function of
> angle Px = f (A), then f (-A ) must equal - f (A), when we consider light
> arriving with opposite offsets from the centre-line.

You are right that theoretically this function has to go through the
origin (0,0). However, a polynomial like
a Px^3 + b Px
shows only a slightly better correlation than just a linear regression
with the "wrong" constant off-set. In order to get a real improvement
one would have to use even higher terms. But how practical would then
such function be for being tagged on the lens cover? The best fits
have been obtained with the arc-tan-function. In order to obtain those
parameters one has to use the Solver tool. For those who don't have
this tool or are not familiar how to use it the next best option
compared to the linear regression was thought to be the quadratic
equation with the "wrong" constant which can be shown "automatically",
i.e. without using Solver.

Marcel

   

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