I have an automated telescope that I have written some software for. I am currently using TPoint to compensate for some of the irregularities of my system.

However with TPoint you apply an offset (based off of the given coefficients and the telescopes pointing position) to the target and that is where you point to acquire the target in your viewfinder.

Does anyone know how to invert this process, such that given your known telescope point position, you evaluate your "true" pointing position.

There are 6 parameters:

  • IA = Azimuth axis index error (encoder offset).
  • IE = Elevation axis index error (encoder offset).
  • NPAE = Az/El axis non-perpendicularity.
  • CA = Elevation axis / Pointing axis non-perpendicularity.
  • AW = E-W misalignment of Azimuth axis.
  • AN = N-S misalignment of Azimuth axis.

And the offset equations come out to be:

azimuth_Correction = (-IA) + (-NPAE * Tan(boundedElevation)) + (-CA / Cos(boundedElevation)) + (-AN * Sin(azimuth) * Tan(boundedElevation)) + (-AW * Cos(azimuth) * Tan(boundedElevation));


elevation_Correction = (IE) + (-AN * Cos(azimuth)) + (AW * Sin(azimuth)));

Where: boundedElevation is the "capped" value so that the elevation value gives the correct value for Tangent. This is:

  • MAX_TANGENT_Q1 = Atan(10);
  • MAX_TANGENT_Q2 = (Atan(-10) + PI);

The TPoint can be found documentation HERE


The corrections are so small that simply changing the signs in the formulas may give a sufficiently accurate result. In any case the formulas you quote are already a first order approximation, whereas TPOINT implements the NPAE, CA, AN and AW terms using rigorous vector expressions - for example AN and AW are part of a 3D rotation.

  • $\begingroup$ Welcome to Stack Exchange! It's always better to add a supporting link or two to answers; it can help readers judge the veracity of an answer. Thanks! $\endgroup$
    – uhoh
    Jun 25 at 4:06

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