Author Topic: Different Sources of Tracking Error  (Read 172 times)

rossbalfigen

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Different Sources of Tracking Error
« on: December 30, 2017, 12:05:59 AM »
After commenting on several threads about the various errors that lead to poor tracking over the years, I realized that for me I needed to nail down the exact definition of the different terms weuse to describe these errors. Chief among these terms is Periodic Error. I have probably been guilty in the past of inadvertantly using the term tracking error when I should have used the term periodic error and vice versa. So here is my breakdown of the different errors that lead to poor mount performance. For the purposes of this discussion, I am limiting the scope here to just tracking errors, not pointing errors.

First of all, if we can all agree that the total error in following a starin the sky (regardless of where it is located on the celestial sphere) is called "Tracking Error". The goal here is to track perfectly so that the result over a given time frame, let's say 10 minutes, is a perfectly round image of a stellar object. This tracking error is made up of several error terms that I split up into two groups, they are "IntrinsicTracking Errors" and ExtrinsicTracking Errors". Intrinsic Tracking Errors are related to the mountand include (but may not be limited to): "Sidereal Rate Error", "Polar Alignment Error", "Periodic Error", "Non-Periodic Error - Gear Related" and Non-Periodic Error - Flexure". ExtrinsicTracking Errors include (but may not be limited to): "Seeing Error", "Atmospheric Refraction Error", AKA"Astronomical Refraction Error" and "Non-Periodic Extrinsic Error" i.e., wind, or other vibration related issues.

Atmospheric Refraction causes a displacement in the apparent location of the stellar object from its calculated ALT/AZ position. Atmospheric Refraction also causes a chromatic image effect thatresults inoval stellar images. This is an optical error that can be corrected using an optical element called an "Atmospheric Dispersion Corrector" (ADC). Since this is not a tracking related error, per se, I am not going to include this effect.

When correcting for these various intrinsic and extrinsic mount errors, the frequency of the effect needs to be considered to respond effectively to the error and correct it. Here are the various time intervals involved with the various errors:

Intrinsic Tracking Errors:
​ Sidereal Rate Error - 24 hour period
​ Polar Alignment Error - Declination Drift - 24 hour period
​ Polar Alignment Error - RA Drift - 24 hour period
 Field Rotation - 24 hour period - very small
​ Periodic Error - Worm Period, - < 1 second
​ Non-Periodic Error - Gear Related - Random - 0.1 second to several seconds. Spiking behavior
​ Non-Periodic Error - Flexure Related - Random - several seconds to minutes. Spiking behavior
​Extrinsic Tracking Errors:
 Seeing Error - 0.05 seconds to 5 seconds
​ Atmospheric Refraction Error - 5 minutes
​ Non-Periodic Extrinsic Error - Random - Spiking behavior, i.e. wind and pier vibration

To correct these various errors, several methods can be used. First, to correct the intrinsic and extrinsic random non-gear related error, you need mechanical tightness and protection from the elements. For the intrinsic gear related non-periodic errors, youeither need excellent worm/wheel quality that provides a smoothPE, or somehigh-speed PE correction device such as ahigh-resolution incremental encoder drive corrector that detects and corrects this non-periodic random error. A mount controller that has a very accurate sidereal drive rate, to within a few seconds per day will solve the Sidereal Rate Error. A perfect polar alignment will correct the 2 Polar Alignment Error terms and the Field Rotation Error term. The final intrinsic error, Periodic Error or PE can be solved either intrinsically or extrinsically, An auto-guider system using a CCD camera and small scope can solve it extrinsically by measuring a star's position in real-time and sending corrections to the mount at a frequency of 1 second or slower. An intrinsic correction for Periodic Error, which is intrinsic to the mount, is toinstall a high resolution drive correction system to solve the PE. The correction rate for PE can be slower than that for non-PE errors.

To correct the extrinsic seeing error, the most effective control may beby applyingadaptive optics system (AOS). An alternative (although I have not tried this) may be to tune an auto-guiding system to attempt to "chase the seeing". This would require exposures of less than 200 ms I would suspect. Atmospheric Refraction Error can be corrected through a calculated rate correction that adjusts the sidereal rate to account for the change in apparent position based on the altitude of the object in the sky. This modified rate, first identified and calculated by King is called the King rate. This would be considered an intrinsic solution for an extrinsic error.

I think this covers all the different errors that we have to deal with, although I may have missed something. It's important to understand that PE isonly one, but significant, source of error that auto-guiding can correct. I prefer to approach the correction of inherently intrinsic errors by applying an intrinsic correction, and extrinsic errors, extrinsically. In that regard, auto-guiding would be used to correct Atmospheric Refraction and Extrinsic Non-Periodic Error, and in the case of gear relatedPeriodic, and Non-Periodic Error, theywould be solved using an encoder based drive correction system. The nice thing about an encoder based drive correction system is that it can also be used to solve the Non-Periodic Extrinsic Error caused by the wind impacting the telescope tube if you are in a windy environment. It will not correct for vibrations that are transmitted via the pier or tripod though. Auto-guiding can correct for rate and drift errors caused by imperfect polar alignment that occurs when using a portable system. These rate and drift errors related to polar alignment should be virtually non-existent in a permanent installation.

I think that for most people, auto-guiding systems are a good overall correction system that can solve many errors at once except for seeing and field rotation, it does not correct for non-periodic errors where the encoder drive corrector can correct for most periodic and non-periodic errors. If you apply atmospheric refraction modeling, and perfect polar alignment with an encoder drive corrector, you can solve all the error terms except for seeing error and pier vibration. Neither auto-guider nor encoder drive correctors can solve flexure issues.



Brandon Costello

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Re: Different Sources of Tracking Error
« Reply #1 on: January 01, 2018, 02:06:47 AM »
Quote
​ Periodic Error - Worm Period, - < 1 second


This kind of error have period much larger than one second - typical valuesare 4 or 8 minutes, depending of worm gear ratio.

chlorleifilwhirl

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Re: Different Sources of Tracking Error
« Reply #2 on: January 04, 2018, 06:21:09 PM »
Quote
Quote

​ Periodic Error - Worm Period, - < 1 second


This kind of error have period much larger than one second - typical valuesare 4 or 8 minutes, depending of worm gear ratio.
I think he meant that the correction frequency needed to neutralize is less than one second.

Lasaro Tourabi

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Re: Different Sources of Tracking Error
« Reply #3 on: January 09, 2018, 06:14:54 AM »
Quote
Quote

​ Periodic Error - Worm Period, - < 1 second


This kind of error have period much larger than one second - typical valuesare 4 or 8 minutes, depending of worm gear ratio.
The < 1 second time I have listed there is related to the time to detect the error the worm period is of course as you say, 4 or 8 minutes.

rissubssimpsat

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Re: Different Sources of Tracking Error
« Reply #4 on: January 11, 2018, 03:05:56 PM »
Quote
Quote

Quote

​ Periodic Error - Worm Period, - < 1 second


This kind of error have period much larger than one second - typical valuesare 4 or 8 minutes, depending of worm gear ratio.
I think he meant that the correction frequency needed to neutralize is less than one second.

Yes, that is right.

Joe Mallard

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Re: Different Sources of Tracking Error
« Reply #5 on: January 12, 2018, 06:58:50 AM »
Quote
The amateur accessible AO do the same as autoguiding quicly "chasing the seeing".
Unfortunatly this is not the way the seeing can be fully adressed ad it only relies to one star in the field, and mainly on the tip/tilt error.
The seeing act differently across the fov.
So a very small part of the field will be corrected (typicaly, ten's of arcsec)

<p class="citation">QuoteNeither auto-guider nor encoder drive correctors can solve flexure issues.

[/quote]
It depends from what you are talking about : an on axis autoguider can correct for nearly every errors (not seeing or wind...)
An on axis (mount axis) encoder, can, throught modelisation compensate all errors (but no unrepetable flexure or seeing)By the way, thanks for your nice writting and quite good analysis/synthesis of a not so easy to understand problem.

Daniel Lacasse

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Re: Different Sources of Tracking Error
« Reply #6 on: January 13, 2018, 11:59:07 PM »
An off axis guider can correct for a bit of flexure as well.  I guess not correct so much as not be effected.
Sent from my SAMSUNG-SM-G925A using Tapatalk

tradneedcoegen

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Re: Different Sources of Tracking Error
« Reply #7 on: January 25, 2018, 02:08:12 PM »
Dear Jerry,

I would not say that flexure related errors are necessarily spiking and/or random. We do have several sources for tracking errors where flexure is a issue. One is clearly random and spiking: wind.
However, since there is no such thing as a infinite stiff mount the mechanics do change during tracking and so does flexure. The reason for this is, that in the absence of external sources, like wind, cows or the occasional observer to bump into the mount during exposure, the main force that deforms the mechanical system that holds the optics is gravity. Gravity does not change its direction - the force is always directed straighty downwards. So it is constant in an altaz system. But we have a moving equatorial system. So the effective force changes if the telescope is not perfectly balanced in all relevant means. This is never the case - the gravity induced flexure for the optical tube assembly and the guidescope does change during long exposures. It does so very smoothly and slowly, following the changing angles relatively to the ground.
Since the flexure in the telescope is not constant for all angles from all dimensions the drift is different for different object positions.
If we have a mount system that is not balanced, like for example a equatorial fork mount, this differential flexure is even bigger. A fork will behave a lot differently for a object just above the horizon than it will for a object at the meridian where the fork arms are parallel to the ground.
So having mechanically stiff telescope does not only help to control amplitude and duration of external shocks, but also keeps the differential flexure low and avoids tracking errors due to that cause. Since a encoder will not detect those slow flexure induced tracking errors it is important to have a overall stiff system to deal with this.

clear skies
Tassilo

Michael Dinelli

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Re: Different Sources of Tracking Error
« Reply #8 on: January 30, 2018, 06:35:30 AM »
Quote
Dear Jerry,

I would not say that flexure related errors are necessarily spiking and/or random. We do have several sources for tracking errors where flexure is a issue. One is clearly random and spiking: wind.
However, since there is no such thing as a infinite stiff mount the mechanics do change during tracking and so does flexure. The reason for this is, that in the absence of external sources, like wind, cows or the occasional observer to bump into the mount during exposure, the main force that deforms the mechanical system that holds the optics is gravity. Gravity does not change its direction - the force is always directed straighty downwards. So it is constant in an altaz system. But we have a moving equatorial system. So the effective force changes if the telescope is not perfectly balanced in all relevant means. This is never the case - the gravity induced flexure for the optical tube assembly and the guidescope does change during long exposures. It does so very smoothly and slowly, following the changing angles relatively to the ground.
Since the flexure in the telescope is not constant for all angles from all dimensions the drift is different for different object positions.
If we have a mount system that is not balanced, like for example a equatorial fork mount, this differential flexure is even bigger. A fork will behave a lot differently for a object just above the horizon than it will for a object at the meridian where the fork arms are parallel to the ground.
So having mechanically stiff telescope does not only help to control amplitude and duration of external shocks, but also keeps the differential flexure low and avoids tracking errors due to that cause. Since a encoder will not detect those slow flexure induced tracking errors it is important to have a overall stiff system to deal with this.

clear skies
Tassilo

Hi Tassilo,

Yes you are correct in your statements about flexure. A more precise way of talking about flexure and the impact on the system while using an optical auto-guiding system is to call it "Differential Flexure". This accounts for the mechanical issues you speak of even while auto-guiding. I include spiking behavior in differential flexure error because I have seen where, much like the buildup of seismic pressure in the Earth's crust and is relieved as an earthquake. This pent up strain is relieved in the mechanical fittings used to secure the auto-guider, or mirror, or other optical component in the system. This is of course due to the gravity vector not being constant while driving and/or slewing the mount as you stated.AOVs correct for high-frequency, very low amplitude movements locally at the image plane, and are designed primarily to correct for Seeing through a tip tiltoptical mechanism as discussed by famax.

Troy Clayton

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Re: Different Sources of Tracking Error
« Reply #9 on: February 02, 2018, 09:24:36 PM »
Things that I’ve not seen mentioned here:

 Observatory mounted systems can pick up vibrations in the building and ground being transmitted to the telescope; things like astronomers with big feet clomping around, closing doors, and 18-wheelers driving past on a nearby road. Just like any other vibration there might be a harmonic effect where this error is at a max one time, and gone another.

 Systems set up on soft grassy surfaces can slowly ( or not so slowly ) sink into the soil. You might be tracking will - and a few hours no - because your rig has shifted.

 Large temperature changes over a night or season can impact everything from gear mesh to the attachment of camera to telescope. If it works in summer, it might not in winter without mechanical adjustments.

rennlispuring

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Re: Different Sources of Tracking Error
« Reply #10 on: February 09, 2018, 12:53:58 AM »
Quote
Things that I’ve not seen mentioned here:

 Observatory mounted systems can pick up vibrations in the building and ground being transmitted to the telescope; things like astronomers with big feet clomping around, closing doors, and 18-wheelers driving past on a nearby road. Just like any other vibration there might be a harmonic effect where this error is at a max one time, and gone another.

 Systems set up on soft grassy surfaces can slowly ( or not so slowly ) sink into the soil. You might be tracking will - and a few hours no - because your rig has shifted.

 Large temperature changes over a night or season can impact everything from gear mesh to the attachment of camera to telescope. If it works in summer, it might not in winter without mechanical adjustments.

Yes George, you are correct, I have left out the diurnal temperature effect on mechanical equipment and the changes in focus position. The period for this effect is the same as that for polar alignment. Thanks!Seasonal changes always require some tune up from month to month, or even week to week. We have had a temperamental dome position encoder wheel causing us issues when the temperature gets really cold and the spring tension does not keep up with the contraction. total PITA!