Pitch and roll characterization

After I chased down all the known alt/az problems, I then turned to the other two axes of the telescope, pitch and roll.

I knew that roll would offer a few problems because I did not have an encoder on the roll axis. In hindsight, I should have installed an encoder at the roll axis pivot and mounted it over the secondary mirror external structure. Instead, I added an encoder which was in friction contact with the roll shell, close to where the stepper motors were driving. Here is that encoder temporarily clamped in place while I designed and built a bracket for it:

For a mechanical reference, I added a magnetic relay slightly above the roll shell and embedded a small magnet in the roll shell counterweight. In the left photo is the small spherical magnet, epoxied into a hole in the lead counterweight, just below the piece of blue tape. In the right photo is the magnetic relay on a bracket that is epoxied to the telescope tube. The bracket elevated it above the roll shell (the shell was not installed in this photo) so that the magnet could pass close by. The bottom photo shows the relay assembly, circled in red, positioned above the roll shell.

I could have used just the stepper counts as an encoder, but any slippage would have caused a loss of reference. I found that the magnetic reference point worked fairly well. The magnetic relay would trigger at a repeatable roll position, but only if the magnet had approached the relay from a given direction (hysteresis). So in my software I had to be sure that the indexing of the roll axis was handled carefully.

Because the roll angle entered into the positioning of the target but not into the calculations in the final catalog, I did not pursue perfecting the roll encoder accuracy. During actual observing runs for measuring separations, I found that after I found the first pair of stars of the run, I was able to use those offsets for the rest of the run, and the scope would reliably drop both stars of the pair into the camera FOV.

In the pitch axis, I had the benefit of the dual FOVs to establish a zero point for the separation measurement. As shown on the optics page , by rotating the pitch mirror so that the same star was seen by each FOV, I could set the zero point of pitch rotation by noting when the two stars were at the minimum distance apart (or overlapping).

Separations were then accomplished by rotating the pitch mirror to the expected separation value, and rotating the roll axis by the calculated amount, until the second star in the pair appeared. Once the two star images were in the common camera FOV, small steps in the pitch rotation were made until the minimum separation had again been achieved. At this point, the pitch angle was noted for later analysis.

Separation shortfall:

Data analysis showed that the pitch measurement was working almost as planned, but comparisons to predictions showed that my measurements were short by a part or two in a thousand. Here is a typical late era dataset showing the shortfall:

The errors seemed to grow linearly with the separation angle (degrees), but I would have expected a sinusoidal error, so I checked the accuracy over a much wider span of separations. Here, with separations up to three times as large as my typical measures, I found the relation to still be linear:

On top of that, over time, I found that the slopes of these fits were growing steadily. The following combined graph shows, over the 6000+ separations measured, the slow growth of the slopes as found in groups of time sequential sets, each having a thousand data points. The time spans cover from June 2020 to December 2021. Because I did not use a common vertical scale, the slopes cannot be compared visually. The important item to note is the slope of the fitted equation in each different plot.

A plot of these errors showed an average zero point of about -0.007, and a slope growing more negative by about -2E-6 per day. I used this plot (below) to provide the only correction to my separation data.

The equation I used for separation correction was: final_sep = raw_sep+0.007+raw_sep*(mjd*2E-6). The constant term in the slope fit was ignored. The only exception to this correction was a brief interval (23 minutes) on one night when the zero point changed to 0.045 (from mjd=722.22754 to 722.24371), unexplained.

I have no explanation for the cause of this small overall separation shortfall or its change in time.

I did one more test to try to identify the separation shortfall. I set the altitude to zero, and the roll to 90, which brought the pitch axis parallel to the az axis. A distant target was placed in the center of the camera FOV. The scope was then rotated through a series of 5 or 10 degree steps in az. The scope was then stopped after each step, and the pitch axis was then rotated to reacquire the target. The pitch and az rotations should have canceled each other out. I expected to see a slowly growing pitch shortfall as the az axis rotation increased. This would have identified the cause as coming from the pitch optical train. I found no such shortfall in this test:

The pitch measurement is much more robust than the altitude measurement. The altitude measurement is derived from the mechanical rotation of the altitude axis and the centering of the star in the direct optical path. Because of the axis misalignment, the altitude rotation encoder needs corrections, and the direct optical path is subject to flexure in any of its optical components.

The pitch axis involves only a rotation of a small, lightweight, balanced mirror. This pitch mirror is not likely to be affected by flexure. Flexure is driven primarily by changes in the telescope altitude, and the overall pitch errors do not show a dependence on altitude.

Here is a video of the pitch mirror in motion.

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