Mathematics of Field Rotation in an Altitude over Azimuth Mount

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by Bill Keicher

This article was originally published in the Sept 2005 issue of AstroPhoto Insight astrophotography newsletter.

The origin of field rotation in an altitude over azimuth mount is due to the fact that the coordinate system of the mount is not aligned to the earth’s axis of rotation. In this case, rotation of the earth couples or projects that rotation into all three axes of the telescope’s coordinate system. Since an alt/azimuth mount typically only has two drives, rotation on the third axis goes uncompensated. When a field rotator is added to the alt/azimuth mount, then rotations on each axis can be removed.

The amount of field rotation depends on the amount of “misalignment? introduced by telescope pointing. The equation for field rotation in degrees per second is:

Image:Alt-Az equation 1 - Bill Keicher .jpg

where: Azimuth = 0 when pointing North Azimuth = 90 degrees when pointing East, etc.

In order to calculate how far the focal plane (CCD) rotates during a given exposure, simply multiply the rotation rate in radians per second by the exposure time and then multiply that result by one half the size of the diagonal (effectively a radius) in micrometers. This blurring can be compared to size of a CCD detector (pixel), the size of the optical system’s blur circle or the size of the optical blur caused by atmospheric turbulence. If we set the maximum blur caused by field rotation to, say, Dmax, then an expression for the maximum altitude as a function of azimuth, integration time, Dmax and latitude can be written as shown below.

Image:Alt-Az equation 2 - Bill Keicher .jpg

Note that this is for a maximum blur of 10 micrometers, what I have termed the image quality constraint. This equation is used in the polar plots above.

Click here for Bill's article on using the above equations to plot exposure times based on your latitude.