The Case for Autoguiding

Autoguiding issues appear frequently on the forums and it is easy to see why; it is a complex dynamic interaction of image acquisition, mechanics and increasingly, software, all of which differ from one user to another and even between imaging sessions. One of the frustrating aspects is that autoguiding can perform one night and play up on another, without any apparent reason. To understand why and what can be done about it, we need to understand what is happening. In a perfect system, there is already a lot going on, and when you add in all the sources of error in the mount and imaging system, it is a wonder that autoguiding works at all. Some premium mount manufacturers already improve their mount’s tracking accuracy by using closed-loop position feedback systems. This improves things to a point that autoguiding can be dispensed with or made considerably easier (depending on the individual setup and object position).

To start with, let’s look at what is meant to happen with autoguiding, then add in all the real-world effects, see how they affect performance and then develop some coping strategies. The first question should be, do we need autoguiding in the first place?

After careful polar alignment and using a mount with no appreciable periodic error (say less than 1 arc second) do you need autoguiding? Well, maybe. Let us assume for one moment that we are using a perfect mount and consider polar alignment again. Theoretically, a mount can be accurately aligned to a celestial pole. There is some debate on what “accurate” is in relative terms to the imaging scale but let us assume 2 arc minutes or better. If the celestial pole is visible, the ingenious QHY PoleMaster accessory achieves sub arc minute accuracy quickly and easily. To achieve this using traditional methods potentially erodes precious imaging time. Even so, the effect of a slight movement or sag in the mount or support can ruin any alignment: For example, a tripod has its feet 1 m apart. If the north foot sinks by 1 mm, it changes the RA axis altitude by 4 arc minutes, that will make a star drift by about 4 arc seconds during a 5-minute exposure at a declination of 10°. As one is blissfully unaware of the subsidence, only autoguiding can detect and recover the drift. If the imaging system is resting on a compliant surface, excellent tracking requires autoguiding for traditional telescope focal lengths (350 mm or above).

The perfect mount does not exist. A few mounts with shaft encoders achieve <1 arc second peak-to-peak periodic error (PE), the rest typically are in the range of 3–30 arc seconds peak to peak over a worm-gear cycle (without correction). Periodic error correction (PEC) only removes the principal worm error, leaving residual errors from the motor and transmission system. Excellent results are achievable with PEC. My Paramount MX achieves 1.2 arc seconds peak-to-peak, comparable to seeing noise and approaching the accuracy of encoder-based systems. Other mounts use toothed belt reduction drives and dispense with worm gears altogether. The nature of this transmission system gives rise to more complex tracking errors that exhibit no convenient cyclical nature to measure and correct. The case for autoguiding is growing.

If that was not enough, even if we have a perfect mechanical system, physics deals a body-blow; at low altitude, standard tracking does not take into account increasing atmospheric refraction that affects a star’s apparent position. Image registration during the calibration process will account for average shifts between exposures, but over a long exposure it may have an additional effect: For example, during a 10-minute exposure at an altitude of 30°, the effect of increasing atmospheric refraction introduces an apparent tracking error of about 7 arc seconds. Similar considerations apply to any optical flexure, especially those in moveable mirror systems (e.g. SCTs). The outcome therefore is that some form of autoguiding is needed in most situations, either to make up for alignment or mount mechanical errors or as a safety net in case there is some unexpected event that shifts the image.

fig.1 There is no escaping the fact that an autoguiding system is complex and one has to appreciate the many possible sources of error to consistently obtain good results. Understanding its behaviors is the fastest route to optimize performance.

Autoguiding in the Real World

The autoguiding process is a repetitive loop. After an initial calibration, which computes the scale and orientation of the image axis, it establishes a reference position for a guide star. An autoguiding loop has the following high-level cycle:

1expose image, typically 0.5–15 seconds

2download image or sub-frame and compute exact center of the guide star (centroid)

3calculate error between this and the reference position

4work out and issue correction movement commands to the mount for one or both axes

5mount moves by correction amount (in addition to tracking)

6delay / repeat cycle

This is a theoretical ideal and looks simple enough. With that in mind, it is time to meet the system in all its complexity. Fig.1 outlines a typical system; the salmon-colored boxes are the intended signal sources and processes, the grey boxes are the things that mess things up. Just as with any other classical system, we call these sources of error “noise”. The system has a number of issues:

1The system measures the apparent error in the guide star position. Our intent is to guide out the legitimate errors: drift, periodic error and common-mode flexure (affects both imaging and guide camera). At the same time, we are trying to avoid adversely reacting to the other inputs, namely astronomical seeing, differential flexure and other transient disturbances like ground vibration or a gust of wind. If PE, drift and common flexure are the signals, astronomical seeing, differential flexure (the guider and imaging camera flex indepen-dently) and other disturbances are considered as noise. An effective autoguiding system must prevent noise from influencing the movement corrections.

2The mount may not move as intended: As we discussed in the hardware sections, a mount is a complex machine. Every gear, belt, motor, bearing and worm has tolerances. These manifest themselves mostly as stiction, backlash and in a dynamic sense, delay.

3The system is a giant feedback loop, and like every other feedback loop the control signal is a reaction to an error signal. In an audio amplifier, this occurs faster than the ear can detect. In this system, the mount reacts to an error several seconds after the error event has occurred. If the error is slow to change, the system will keep pace or catch up. In the case of a rapidly changing error, it will likely struggle, since by the time the mount has corrected itself, the error will be something else again. This is one of the reasons that a mount’s peak to peak PE performance is not the whole story; the rate of change of PE is equally, if not more important on its guiding performance. In the worst case scenario, conditions reinforce the error and the corrections make matters worse and the mount oscillates.

All these issues conspire, in differing degrees for each user, to make autoguiding a challenge and ultimately a compromise. To resolve issues in the field, it helps to understand each of these in a little more detail. It is convenient to treat them separately but since their effects interact, there will be some inevitable cross-over and repetition throughout the discussion. In one sense, this is a simple engineering dynamic control problem, familiar to electronic and mechanical engineers. A degree in engineering is not a pre-requisite, however, but some of the diagnostic tools that engineers use, in simplified form, provide valuable insights into what is happening in the system and clues on the best control strategy. Taking this one step at a time, we first consider guider hardware followed by the input signal (tracking error) and noise sources (everything else). Finally we move on to the imperfect mechanical system that does not quite react in the way we want.

Guider Optics

Optical configurations fall into two main categories: independent optics (guide scope) or shared with the imaging camera (off-axis guider or OAG). The best is not a foregone conclusion and, as usual, there are several considerations that affect the best choice for your system. The implementation as well as the configuration is just as important too; for instance, guide scopes may be an inexpensive 80-mm f/5 doublet refractor, a 50-mm f/4 finder, a re-purposed camera lens or anything in between. The principal benefit an independent guide scope has over an off-axis guider is its broader field of view and the ability to independently aim and pick a guide star. In some cases too it is the only option, since there is insufficient space in the main imaging path to introduce an off-axis guider pickup (a common issue when one is using a DSLR as the imaging camera behind a field flattener).

On the other hand, the rigidity of the guider focus assembly and the mounting hardware leave much to be desired in many cases, adding to the problem. Differential flexure can occur in a side-by-side mounting arrangement and crucially within the main optical system. The most notorious source is caused by mirror movement in reflector telescopes but also may occur less obviously in the main telescope’s focus tube and camera assembly. The flexure problem becomes more acute at long focal lengths and this is when an OAG comes into its own. Since they share the same optical path as the imaging camera, they see the same angular flexures and record them accurately for correction. OAGs do not have it all their own way, and have to cope operating at the periphery of the imaging circle via a small pick-up mirror and in some cases behind the imaging filters, further attenuating the light level of distorted stars. Their smaller field of view is often locked with the main imaging camera. Guide star selection is restricted and is often a compromise between the perfect imaging camera framing and angle and a position that offers a suitable guide star both before and after a meridian flip.

The focal length and guiding resolution is also a consideration but less important than one might think: Since the guider software can determine sub-pixel star centroid accuracy, as a rule of thumb, if the imaging focal length is no more than 10x the imaging focal length, you should have sufficient tracking resolution.

Guide Cameras

Like optical configurations, there are two main camera styles in common use for autoguiding; low-noise, sensitive CCD still cameras, epitomized by the Starlight Xpress Lodestar and increasingly low-noise CMOS video cameras, with a long-exposure capability. In some cases the guide camera is integrated within the imaging camera body, or the camera is part of a stand-alone guider system with optics, software and control. Traditional guide cameras have an ST4-compatible guider port or link via USB to a parent imaging camera that has one. The ST4 interface, provides a set of relay (or more typically, opto-isolated) switched outputs that tell the mount to move N, S, E or W. If the telescope mount has a guide port, it will typically be to the same specification, utilizing a 6-way RJ-12 connector. The ST4 pinout is allegedly a standard but over time, a few variations have manifested themselves on guide cameras and mounts. The most common deviation is a simple reversal of the pinout (fig.2) obtained by flipping the connector over at one end of the flat cable. This traditional interface is increasingly being replaced by software-based guiding controls that are integrated with their tracking control systems. At the same time, an increasing number of small-pixel CMOS cameras, based on a 1.25-inch diameter body and at a much lower price-point, are being used for guiding. The sensitivity and noise level is not yet that of the CCD sensors but they work well enough with bright guide stars and as a bonus many generate video too, through the Windows DirectShow interface, to act as a virtual eyepiece or planetary imager.

Sensor Noise

The key to effective autoguiding is to first minimize the input’s “noise” level and then find a way to minimize its effect on the output signal (motor movement command). Assuming you have taken the necessary precautions to ensure a rigid mount and optical assembly, the principal “noise” sources are sensor noise and astronomical seeing. Sensor noise affects the accuracy of the apparent star tracking error. Autoguiding exposures are short and although we can discount thermal noise, read noise, hot pixels and bias are very noticeable, compared to the brief exposure of a few dim guide-stars. The algorithms that determine the center of a star can confuse it with a nearby bright pixel. Image noise in the vicinity of a guide star also affects the reliability of the centroid calculation. It seems unlikely that a few pixels can have that much effect but they do.

fig.2 A typical ST4 guider RJ-12 connector with two common alternative pinout implementations. So much for a standard!

The autoguiding software does not simply identify the brightest pixel in the image of the star, that is far too coarse, but also measures the surrounding dimmer pixels and uses the light fall-off to calculate the precise center to sub-pixel accuracy. In this way, autoguiding programs resolve to 1/10th of a pixel or better. If a star is represented by a single pixel, the guider software does not have much to work on and it actually helps if the star intensity fades off gradually over the surrounding pixels. If there are only a few pixels associated with a star image, a little sensor noise is more likely to affect the centroid calculation. In a paper by Craig Stark, the author of the original PHD guiding program, he suggests that sensor noise can introduce a calculation error of 0.2 pixels, equivalent in my system to 0.6 arc seconds. Maxim DL and PHD2 usefully display the signal to noise ratio of each exposure to highlight the guide star’s general suitability and have filtering and binning options to improve the signal to noise ratio.

Hot Pixels

In addition to thermal and read noise, most CCD cameras have hot pixels (whose number increase slowly with age). These are the cause of more headaches. A hot pixel close by a guide star can skew the calculation or worse, as they may be interpreted as an unmoving star (and you believed that flat-line tracking graph)! Just as with imaging cameras, there are strategies to minimize the effect of sensor noise and hot pixels shown in fig.1. The simplest solution is to calibrate each exposure before assessing the guide star location. Both PHD2 and Maxim DL allow you to calibrate the guide exposure by subtracting a dark frame. PHD2 has a utility that exposes and averages several dark frames over a range of exposures and then during guiding, subtracts this from each guide exposure.

Applying a bad pixel map is better still as it is more robust to changes in exposure duration and temperature. (PHD2 also measures the SNR of each guide exposure and has an option that can additionally adjust the exposure to reach a minimum setting.) Maxim DL also has the option to apply a full image calibration to each guider exposure. These techniques are often sufficient to calibrate guide camera images and maximize the signal to noise ratio so the star centroid calculation is as robust as possible.

There is also a little trick that effectively deals with hot pixels in Maxim DL5. The steps below were suggested in a forum post by Terry Platt of Starlight Xpress:

1Take a zero length exposure using the “dark” setting in Maxim and save it to the calibration folder.

2Take a 2-second dark exposure, open up Maxim’s calibration dialog and select it to generate a bad pixel map.

3Create a calibration group using the zero exposure dark image as a dark frame and select the hot pixel map in the box provided.

4Turn the dark frame autoscale option off, if the guide camera has no temperature control.

In operation, set “no calibration” for the main imaging camera (camera 1) and “full calibration” for the guider (camera 2). In effect, each guide camera exposure has a bias frame subtracted from it (using the zero exposure dark frame) and then the hot pixels are removed. (If these terms are unfamiliar, we cover calibration later on in its own chapter.)

Sensor Focus

Ironically, the surrounding pixels are perhaps more important than the central one and explains why a small amount of de-focus on an under-sampled guide camera improves centroid determination and helps with saturated guide stars. This is not an excuse for poor focus, however, especially with a centrally-obstructed telescope, such as New-tonians, SCTs and RCTs. In these instruments, a de-focused star quickly becomes a donut. The smallest amount of seeing noise will change the location of the hot spot around the donut and can make the tracking jump about. My 10-inch RCT has some field curvature that is quite apparent in the field of view of the off-axis guider. I also own several refractors which have flatter fields and in this case, the off-axis guider tube is optimized for focus with the RCT. Diffraction provides the necessary blur and the small amount of coma with the shorter refractors is of little consequence.

Astronomical Seeing and Tracking Error

After optimizing your location and conditions and choosing high-altitude subjects, there is not a lot more you can do about seeing, other than wait for a better night. For effective autoguiding, we need some help to minimize its effect. Fortunately the clue lies within the apparent tracking error data. The graph in fig.3 shows the measured tracking error for a bright star on a NEQ6 mount running with its ST4 guide cable unplugged. It was measured with a free utility, PERecorder, using a webcam, operating at about 25 frames per second. (TheSkyX PE/PEC utility performs a similar function using a still camera, normally with 1-second exposures to reduce the latency.) The tracking graph in the top left window shows several versions of the data; light grey for the actual tracking error, dark blue for the PE without the drift, green for the noise (most of which is seeing) and red for the filtered and smoothed error resulting from the worm drive in the mount. The most significant thing is the relative changes in error over a given period. The graph in fig.3 measures the apparent tracking error over 9 worm cycles, each of 8 minutes’ duration. The vertical scale is in arc seconds. From this it is possible to measure the individual contributions to the apparent tracking error:

•The drift rate is about 15 arc seconds over 6 cycles, or 0.005 arc seconds / second, or 3 arc seconds in 10 minutes.

•Periodic error is about ±5 arc seconds peak to peak, maximum rate of change can be calculated from the maximum slope of the worm drive graph on the right hand side, about 6 arc seconds over 120 seconds or 0.05 arc seconds / second.

•Seeing is about 2–3 arc seconds in magnitude and changes rapidly between individual samples.

fig.3 This screen grab from the free utility PECPrep, shows the actual guide star error in pale grey in the top left graph and a number of filtered results too in different colors. The smooth red trace represents the assumed worm periodic error, the blue trace is the raw trend and the residual noise, represented by the green trace, principally caused by seeing and other errors. The graph on the right hand side shows frequency filtered errors to select the worm induced tracking error. The successive errors from each worm cycle are overlaid to show the correlation. When they are averaged and inverted they can be applied as a periodic error correction curve in EQMOD (fig.9).

This performance is typical of a modest telescope mount that has been polar aligned and operated in a typical suburban environment. These figures tell an interesting story:

•The apparent tracking error is very different from the actual tracking error between measurements.

•The real tracking error changes at a slow rate.

•The real tracking error will eventually become large enough to require correction.

•The effect of astronomical seeing on the measured star position (compared to the last sample) is up to 50x greater than caused by the underlying tracking error caused by PE and drift.

Between successive exposures, the apparent tracking error is almost entirely due to seeing arising from atmospheric turbulence. Its effect on the apparent star position completely swamps the real tracking error. For that reason it is essential that the autoguiding system does everything possible to distinguish and correct the real tracking errors and ignore the comparatively large and random measurement errors caused by seeing. The traces in fig.3 suggest that seeing rapidly changes the apparent position of a star. The phenomenon is complex; not only are there extremely quick shifts, in the 10–100 ms range, but it has a localized effect too. At any one instant, different parts of the image will have different displacement errors, explaining why a high magnification 30 fps video of a planet wobbles around like Jell-O between successive frames.

The effect of seeing has a random effect on the measured star position; the image shift is equally likely to occur in any direction and the probability of a big shift is progressively less likely than a small shift. In practical terms, a long exposure of a small, tightly focused star becomes a diffuse circular blob over time. Thankfully, the randomness works in our favor and the center of the blob formed by a long exposure is coincident with the center of the star.

So, to reduce the effect of seeing on the measured tracking error, we need to lengthen the guider exposures. A long exposure averages all the micro shifts of the star over time and produces a diffuse blob, centered on the actual star position. In other words, a longer exposure lowers the effect of seeing noise on the tracking error measurement. In fig.3, the camera was exposing a subframe at a breezy 25 fps but even at much longer exposures, there are clear differences in the sensitivity to seeing. Fig.4 compares the seeing noise with exposures of 0.5, 3 and 10 seconds. There is still a clear improvement between 3 and 10 seconds.

fig.4 These three guider graphs from Maxim DL were taken with the guider outputs disabled and show the apparent error in arc seconds over a few minutes. They were all generated in a half-hour period, the only difference between them is the guide exposure time. From the left these are 0.5, 3 and 10 second exposure settings. You can easily see the effect of exposure time on seeing noise. The 10-second trace is smooth and shows a slight drift in DEC and very little noise in either trace. Even with a 3-second exposure the middle graph still has some seeing noise, smoother and at about half the peak variation of that in the session using 0.5-second exposures. All guide exposures were fully calibrated and in this case, the guide image SNR was high in all cases, at 150, 545 and 690 respectively. If I had chosen a faint guide star then the sensor noise would have contributed further to the apparent tracking error and would have also been improved by increased exposure time.

With longer exposures, however, the signal or the real tracking error is growing. In this case it has some way to go before the noise from seeing is reduced to the same level as that from the real tracking error. The tracking graphs in fig.4 give an indication. In this case, by my reckoning, it requires an exposure between 5 and 10 seconds to reduce the seeing noise to a level comparable to the PE error. Before we all start using 20-second guide exposures, we must recall that the whole purpose of autoguiding is to eliminate drift and PE. Long exposure times also have the potential to under-call the true tracking error, since, in the case of drift, the star moves during the exposure and the guider will work out a mid-position, rather than the end position of the star. Long exposures may also saturate a star and cause errors in the centroid calculation. (If the mount generally tracks well and has low drift, one can use a moderate guide exposure of say 5 seconds, with a 10-second delay or more between guider commands.) The question is, how long can we expose for and still maintain an acceptable tracking error?

If the seeing conditions effectively increase the star size to 3 arc seconds, one way to set the exposure time is to keep the underlying tracking error to say 10% of that figure, or 0.3 arc seconds. (The PHD guiding assistant computes an optimum value.) That is equivalent to 60 seconds of drift or 6 seconds of PE in my example. (The PE error rate is 10x greater than drift in this example and it caps the maximum exposure time.) To increase that exposure time, there are two choices; relax the tracking error specification or find a way to reduce the rate of PE in the mount. (This same EQ6 mount, after using the Periodic Error Correction feature in EQMOD, halves the maximum PE rate to 0.02 arc seconds / second.)

Assuming an otherwise perfect signal, if we simply take a single measurement every 6 seconds and correct 100% of the error, the maximum error will exceed 0.3 arc seconds due to the delays in the system. If we take 2 samples in 6 seconds and correct 50% of the residual error, there will be a slight lag, not exceeding 0.3 arc seconds. If we attempt to correct 70% of the measured error, the error settles at about 0.2 arc seconds. There is a clear trade-off between maximizing the exposure time and the real residual error. The 100%, 75% and 50% values above are often called the guider aggressiveness setting. The equivalent settings in Maxim DL use a 0–10 point scale, representing 0%–100% error correction each cycle. It is tempting to select 100%, but when we factor in the measurement noise caused by the seeing conditions, there is a danger of over-correcting the perceived error. In any system, a low aggressiveness value usually makes a system run smoother. The conclusions so far are:

•The effect of seeing is reduced by increasing the guide-camera exposure time.

•The unguided tracking error rate sets a cap on the maximum guider exposure time.

•The residual tracking error increases if the guider cycle time (exposure) is increased.

•A mount with a smaller PE rate is easier to guide, since it allows longer exposure times (or moderate exposures with a pause in between) to reduce the effect of seeing, without compromising actual tracking errors.

If the mount is polar aligned and has modest periodic error, it is unlikely that the guide camera exposure time will ever be long enough to reduce the effect of seeing to a level less than that of the true tracking error. Most systems operate with apparent tracking errors, caused by seeing, that are larger than the actual tracking error.

As a consequence of these and especially the last point, it makes sense that if our tracking corrections are still largely based on guesswork, with an underlying trend of reality, the best course of action is to do the minimum amount of correction. In other words we must not react to noise, add a further tracking error into the system and make matters worse.

Before we move on to discuss the mechanical system, there is another way to reduce the effect of localized seeing conditions. If a dozen stars are separately and randomly affected by seeing conditions, then if their individual apparent tracking errors are averaged, it should reduce the “noise” level up to about 3x. Most autoguider software works by sampling a single star but in recent years, plug-ins for Maxim DL and other advanced autoguiding routines have introduced multiple star sampling. Early results show that by sampling several stars the measurement error, induced by seeing, reduces by about 2x. The benefit is not as high as it might be, simply because air turbulence at one time may similarly affect more than one star and is therefore not locally random. It is also worth mentioning that there is a small benefit too to guiding through a red filter, since the longer red wavelengths are less affected by atmospheric refraction and hence seeing.

Periodic Error Control

Periodic error and its control have been mentioned a few times in passing but so far not in any particular detail. Unless a mount has a highly-accurate shaft encoder, with a resolution measured in sub-arc seconds, every mount, no matter how expensive, will have appreciable PE. There are two aspects of the nature of PE that cause concern:

•the rate of error change (affects guided accuracy)

•the peak to peak error (affects unguided accuracy)

fig.5 The PEC utility in TheSkyX can analyze its own guider log (fig.6) and filter out high-frequency seeing noise, the effects of drift and other periodic error to leave behind the principal tracking error arising from worm anomalies. In this case the PE is 1.8 arc seconds peak to peak.

Most mount systems have a mechanism to store a set of PE correction values for each worm angle. The motor control system uses these values to alter the rate of the RA worm rotation, to compensate in real time for the major source of PE; the worm itself. This is called Periodic Error Correction or PEC and the values are either stored within the mount electronics or by the driver/application on the computer. For this to be successful requires an accurate tracking error assessment at each worm angle. (The “worm gear” is the large circular disk around the RA or DEC axis, the “worm” is the smaller gear resembling a screw.)

There are several methods to measure tracking errors. Most autoguider programs record a blow by blow account in a text log file. If the guider outputs are disabled, these values can be used for PEC analysis. There are also dedicated utilities that measure the tracking error using a video or high-speed camera. Some mounts, like iOptron, monitor guider corrections over a worm cycle and calculate their own PEC. All these tracking error logs, however, are also affected by the seeing noise. To isolate the tracking error in the presence of this noise uses a familiar technique that averages several measurements together. Well, almost. The standard practice is to measure the tracking error over four or more worm cycles and use a special program to average the errors together. It does this in a unique way that isolates those tracking errors that are caused by the worm cycle. In effect, the tracking error exhibits compound errors of different periodicity, which are caused by the rotations of gears, belts, pulleys and motors. Armed with the knowledge of the worm-cycle period, a mathematical technique known as the Fast Fourier Transform (FFT) can isolate the tracking errors that synchronize with the worm cycle. It is these errors that are averaged, as can be seen in fig.3 and 5. Crudely, this error signal is then inverted and stored as a correction signal, to be applied whilst the mount is tracking (figs.7, 8).

fig.6 A sample log file, generated by the TheSkyX autoguider for calculating Periodic Error. PHD2 will generate a similar log file for use by other programs, such as PEMPro and PECPrep.

fig.7 An example of a calculated Periodic Error Correction over a worm cycle for a Paramount MX mount, using TheSkyX.

The second hurdle is to measure and deploy the error correction at the same precise worm angle. This requires a mechanical or electronic means of knowing the orientation of the worm (either continuously or relative to a reference position) and ensure the measurement and correction is applied without delay. To do this, most worms are either synchronized to a position-activated switch, have a rotary encoder or are manually aligned by the user and parked/un-parked with each use.

Although lengthy exposures are good at removing seeing noise, PE measurement normally uses an exposure duration of 1 second or less to minimize the measurement latency. (The FFT isolates the worm cycle effects and takes care of the high frequency seeing noise.) When applied, PEC is intelligently combined with autoguider commands using a technique generically called pulse guiding, rather than cause potentially conflicting commands through alternative interfaces.

fig.8 This screen shot from EQMOD shows the periodic error correction at work on the left and the guider settings for guide rate, along with the maximum and minimum movement times on the right-hand side. In this case, EQMOD is set up for pulse guiding, a technique that elegantly combines the RA guider correction inputs with the periodic error movement commands and sends an overall movement command to the mount. Other options are available, including using the traditional guide relays. This method may, at any one time, have conflicting inputs from the autoguider algorithm and the periodic error corrections.

Up to this point the discussion has concentrated on measuring the actual star location as accurately as possible. This is a compromise between sufficient exposure time to overcome noise sources and ensuring one keeps up with the real underlying tracking error. The level of compromise changes with the quality of the polar alignment and the mount’s rate of periodic error. Successive measurements still show a high degree of randomness caused by seeing and this is before we send a control instruction into the great unknown; the mount. Even before we go there, we need to translate the star position error into RA and DEC corrections using a guider calibration.

Guider Calibration

The calibration process calculates how a star movement relates to a RA and DEC angle. The guide camera will have a certain pixel pitch and orientation, by which we mean angle, to the RA and DEC axis. If the guide camera is attached to an off-axis guider, or imaged via a mirror, the image will be flipped too. Guiding commands are specified in terms of method, duration and guiding rate (specified as a fraction or percentage of the sidereal tracking rate or a simple 1–10 value, depending on the application). Before guiding, it is necessary to calibrate your system, using the guider interface you will use in practice and with the same settings. This requires a knowledge beforehand of the best guider rate and physical method. As this may have not yet been determined, a few iterations may be necessary to trial different options. One has to start somewhere, however, so in the absence of any general consensus from a user-forum or the like, assume a 0.5x guide rate (50% of the sidereal rate of 15 arc seconds per second) and choose the ST4 interface as a starting point.

fig.9 This crop from a Maxim DL guider calibration screen shows the four completed movements, indicated by the red lines. The star should be centered on the apex. The fact that it does not indicates a degree of DEC backlash, in this case about 1 second’s worth at the guiding rate. If this calibration is repeated (with a backlash value applied) the star position at the end of the calibration moves towards the apex.

Calibration determines the pixels per second movement along RA and DEC axis, at the guiding rate and the sensor orientation. There are two principal methods of calibrating:

 

1Deliberately move the mount back and forth in DEC and RA for a specified time and measure the star movement and angle.

2Plate-solve the image from the guide camera and determine the guider angle and pixel scale in arc seconds per pixel.

 

PHD(2), TSX and Maxim DL employ the first method. These programs move the mount in both directions on each axis using the same control method employed for guiding and take exposures to determine the star movement. There are several control methods, including ST4 guider relays, various forms of pulse guiding, or direct mount commands; more on those later. In the case of Maxim DL, it moves the mount back and forth for a user-specified time. PHD2 moves the mount in about a dozen steps until the star has moved sufficiently to make a reliable measurement. From the relative positions of the star, the pixel / second movement (at the guide rate) is determined. There are a couple of points of note:

fig.10 PHD2 has effectively superceded PHD and offers enhanced control options and interoperability with external imaging programs. A key feature is DEC compensation, allowing for a single calibration to apply for all the sky. This program is under active development and is being updated regularly to accommodate a growing range of needs and offers a number of alternative guiding algorithms to suit a range of hardware configurations.

The first is the guide star needs to move several pixels to obtain a reliable measurement. Maxim DL rejects the calibration if the movement is less than 5 pixels. Ideally it should be more. If a low guide rate, say 0.1x, is specified, it will take a long time to move the guide camera sufficiently. (In Maxim DL, you can cheat by performing the calibration with a high guide rate setting and then reduce the guide rate and the x and y speed values by the same factor afterwards.) The second is that a basic RA guider calibration made at high declination is very different to one made at low declination. This is an important point that requires further discussion but for now, be sure to check your calibration declination and DEC compensation settings are as you intend them to be.

Returning to our two calibration methods, the second one is to use plate-solving. A plate-solve not only calculates the center of an image, it also reports the image scale, in arc seconds per pixel and its orientation. It only takes a few seconds to generate a calibration. Since the sidereal tracking rate is 15 arc seconds / second, dividing the image scale into 15 gives the calibration value in pixels per second. If the guide rate is 0.5x, halve the calibration value and so on. This is very effective using stand-alone guide scopes but becomes more difficult in the restricted field of view of an off-axis guider image (The standard GSCII catalog used by PinPoint / Maxim 5 may have insufficient stars to plate-solve the few stars in say an off-axis guider image. The latest versions of Maxim and PinPoint can use the more detailed UCAC4 or USNO-A2.0 catalog, although they take considerable time to download their 8 GB multi-file structure.) Assuming one can plate-solve the guider image, a Maxim DL plug-in by John Winfield calculates the guider calibration with a few button presses.

There is a catch though: This method assumes a perfect system and may give the wrong results. Since it does not measure the actual star movement it can be caught out by system anomalies: I discovered pulse guiding with my EQ6 mount moves the mount further than it should, but moves correctly if I use the ST4 guide port. On my 10Micron mount, the pulse guide movement is accurate but the ST4 port is configured differently and one of the guiding directions is reversed. (As a result, I quickly discovered that far from being a single standard, the industry uses a number of ST4 pinouts that swap over connections for N<>S, E<>W and so on. If you do not believe me, just do an Internet search!) In the case of the 10Micron it is a simple matter to manually change the sign of one of the calibration values.

Calibration Declination

At high declinations, as a result of trigonometry, an image is less sensitive to periodic error and RA drift arising from polar misalignment. At first this seems confusing, when our field of view or pixel scale remains the same. To conceptualize, consider the logical extreme of a guide star at the celestial pole. It is immune to periodic error, or even if the mount stops tracking. In practical terms, a periodic error or RA drift of a few arc seconds at low declination moves the guide star position on the sensor by more pixels at low declination than at high. Conversely, a small pixel movement in RA at a high declination is more significant than at a low declination. The original PHD did not communicate with the mount and did not know the declination of the guide star. It was designed to be calibrated at the same declination as the imaging target for natural compensation.

Modern autoguiding algorithms automatically compensate for this, but only if they know the guide-star declination. These applications (including TheSkyX, Maxim DL and PHD2) have the facility to connect to the mount and read its current DEC position and an option to change the RA calibration for alternative declinations: When connected to a telescope they read the declination telescope property and normalize the guider calibration values (the x and y speeds in pixels per second) to a declination of 0° (on the celestial equator). In this way these applications calculate new guiding parameters for any other declination, using the equation above, without repeating the entire calibration process. This is called DEC compensation and seems a savvy thing to do, but it has a sting in its tail. For now, the recommendation is to calibrate your autoguider at a low declination. This provides the most accurate reference.

fig.11 Maxim DL’s guider setting controls allow DEC corrections in one direction (shown) as well as stiction and backlash controls. The calibration values are shown as well as the physical guider method, communication port and exposure settings. Note the displayed calibration values are calculated for 1x1 binning and DEC=0, irrespective of the actual DEC and binning used for the calibration. Maxim uses these calibration values and the current DEC and guider binning to establish the actual calibration, allowing one to change binning and DEC without the need for a new calibration.

Control Method

In the beginning, there was ST4, and it survives to this day. It was ideally matched to the basic mounts at the time but today’s modern mounts with their complex electronics, optical encoders and just as importantly, software, provide an opportunity for interesting alternatives. These are colloquially referred to as pulse guiding and are generally available through the ASCOM telescope device interface. Their concept is to introduce the RA and DEC corrections using software instructions rather than a direct hardware interface. It is easy to combine both guiding and PE corrections in software and issue one aggregate command to the motors. (Some mounts hijack the ST4 port, monitor it and combine with PEC in software.) The benefits are one less cable, diagnostic log files of every movement and smoother control, since the magnitude of the combined correction is potentially less than the two separate signals.

Pulse guiding implementations vary between mount models. Most rely upon modifying the tracking rate by the guiding rate for a specified duration. For example, a 100 ms 0.25x guide pulse to the RA axis would result in the RA moving either at 1.25x or 0.75x sidereal rate for 100 ms (depending on the polarity) and then would return to the sidereal rate. (Since the DEC axis is normally stationary, the rate and duration is simply applied directly.) Other implementations introduce an arc second equivalent positional error into the control software and let the existing control system accommodate it. My various mounts have displayed everything from severely over-damped (the mount takes several seconds to fully adjust its position) to virtually instantaneous. The former case is interesting; since even with a low aggression setting, if further guiding errors are measured and instructions issued before the mount has completed its initial movement, overshoot and oscillation occur very easily.

Clearly one chooses the method that performs best for your particular setup. When changing methods it is advisable to re-calibrate at the same time. Note too that guiding polarities before and after a meridian flip are sometimes treated differently and may require a change to the DEC reversal option in the autoguiding software. In practice, I find the performance differences between methods subtle and difficult to detect from an autoguiding trace or RMS error readout alone, especially in the presence of variable conditions. An alternative approach is to compare the mount’s dynamic response to a single artificial correction (using a simple script or manual guide control) and look for tell-tale signs of delay, overshoot, consistency and crosstalk between the axis. Comparing this response at different guide rates and magnitudes provides valuable insights into the way the mount moves (or doesn’t). This is not as artificial as it seems, as this is precisely what an autoguider-implemented dither command does and in practice, the settling period after a dither command is very informative.

fig.12 This small screen grab of a Maxim DL autoguider shows the (upper) RA error and (lower) DEC error traces. At about 3,570 seconds, the exposure ended and a dither command was sent to the mount. The dither command effectively moves the stars reference position and waits for the autoguider system to catch up and provides useful diagnostic information: The RA axis moves quickly to the new position in about 15 seconds but the DEC axis does not move for about 30 seconds, as its backlash is slowly removed by successive autoguider commands. It then overshoots slightly and takes another 90 seconds to finally center up (as a result of the corrections being less than the minimum move setting).

Min and Max Movement

Minimum and maximum movements limit the extent of an individual guiding correction and can be independently set for the RA and DEC axis (fig.10). In the prior example, a 50 ms minimum movement is equivalent to 15 x 0.05 x 0.5 = 0.37 arc seconds. That means that for any error less than 0.37 arc seconds, no mount correction is issued. The maximum movement sets a cap on the largest and although it reduces the likelihood of the mount responding to a rogue sample, it can also slow down the response to dither and centering. The minimum creates a threshold beneath which the seeing noise (and tracking error) is effectively ignored. The trick is to limit this range as much as possible and in doing the calculations, rationalize the guide rate for the RA axis:

1Lower the maximum RA movement to say twice the highest possible PE error within a guide cycle. In the example used here, assuming a 2-second exposure and 3-second cycle, that is 0.3 arc seconds movement per cycle. That implies a time of moving time 40 ms at a guide rate of 0.5x, which is probably not feasible (Maxim’s lowest value is 100 ms). If we assume a guide rate of 0.25x and a maximum movement of 100 ms, that gives 0.1 x 0.25 x 15 = 0.37 arc seconds.

2Raise the minimum movement and set the error correction threshold to about 10% of the best likely seeing conditions. In my case this is about 0.2 arc seconds, or a minimum guide time of about 50 ms assuming the 0.25x guide rate. This can also be applied to the DEC axis setting.

DEC Compensation

As briefly mentioned, the declination of the guide star has an effect on the RA tracking error and although a sensor or pixel sees a fixed angle, this FOV is projected onto an imaginary equatorial grid. The FOV overlaps more RA grid lines as they get closer together and meet at the pole. In effect, the rate of star movement (in pixels) reduces at higher declinations and follows a simple rule:

rate at DEC = rate at celestial equator . cos(DEC)

If we take two points, one on the celestial equator (DEC= 0°) and another 10° from the celestial pole (DEC=80°), although the RA axis moves at a constant angular rate of 15 arc seconds per second, it sweeps out more sky near the equator than near the pole. If the image scale is 2 arc seconds per pixel and the mount were to suddenly stop tracking, a star would move 7.5 pixels each second, for an object on the celestial equator but move just 1.3 pixels at DEC=80°. Similarly the effect of any PE is similarly scaled back. Happy days? Not necessarily; in an autoguiding system, the actual tracking error shrinks with higher DEC values (that is, the signal gets smaller). At the same time, the seeing conditions have the same effect on the star appearance and measured position, in pixels. In other words our signal to noise ratio is lowered, just by increasing the declination of the subject, and the system is more likely to react to seeing conditions. To make matters worse, some mount software and the guiding software’s DEC compensation option mentioned earlier, compensate for the decreasing sensitivity of error detection at high declinations and increases the gain of the RA guider correction. (This correctly assumes the principle that the required physical angular corrections to compensate for periodic error, are the same, regardless of where it is pointing, but the measured RA tracking error appears smaller at higher declinations.) The intent is to ensure the degree of mount correction is not underestimated for correcting RA tracking issues.

This reasoning, however, completely ignores the effect of seeing conditions. Seeing conditions, in terms of measured pixel centroid error, are the same for any declination. Far from helping, DEC compensation can make the system more reactive to seeing conditions. For example, at DEC=0°, a pixel error of 0.1 pixels may translate to a guider movement of 0.3 arc seconds but at DEC=80°, after compensation, it translates to: 0.3 /application cosine (80°) or 1.72 arc seconds.

If we pause to consider this for a moment, we quickly realize that DEC compensation acts precisely the same as if you calibrated the autoguider software at the target’s DEC in the first place (the approach that was implicit in the original PHD guider calibration routine.) In the case of good seeing, the RA corrections will be automatically scaled and there will be no issue. Alternatively, in the case of less than ideal conditions and at high DEC, the errors caused by seeing conditions increasingly swamp your mount tracking errors and the autoguider has to work harder. In this case the autoguider software may try to chase seeing and the mount will receive continual, random corrections of quite high amplitude, limited by the maximum move parameter. A quick experiment will determine which case is prevalent; calibrate at low DEC and simply compare the guiding performance at high DEC with DEC compensation enabled and disabled.

The following, admittedly controversial suggestions, may help to reduce the sensitivity to seeing at high declinations and keep the mount under better control at high declinations:

1increase exposure time for high declinations

2calibrate at DEC=0 and disable DEC compensation

3turn off guiding (in the case of a well-corrected mount)

In 1, the argument goes: Since the effect of drift and PE is less at high declinations, less guiding is needed and therefore a longer guide exposure time can be used to lower the influence of seeing conditions without compromising image appearance. In 2, we effectively lower our guide rate setting by cosine(DEC) and although the mount continues to react equally to seeing conditions, those movements at high declination have less effect on the image appearance as a result of the now familiar cosine relationship. Note: The original PHD user instruction notes the issue and suggests one uses its low-pass filter option, at high DEC settings, to reduce the effect of seeing noise.

In 3, it might be possible to disable guiding altogether at high DEC altogether. These recommendations are novel but the data-driven approach makes some sense, as long as you have an idea of the signal contribution from your mount and environment.

Guiding Algorithms

The simplest systems measure the tracking error and issue a guiding command to fix some of the error, determined by the aggression and guide rate settings. The more sophisticated offer a number of alternative algorithms for RA and DEC control. These are designed to minimize the number and magnitude of incorrect guiding corrections. Some are linear in design, combining and weighting prior errors with the current error to form an effective new value and others are non-linear, in so much that they uses math to generate a linear value but then switch behavior, based on preset conditions. The linear algorithms anticipate the kind of tracking error mechanisms we see with drift and seeing noise, namely an underlying error trend and randomness. For example, in PHD2, “LowPass” and “Hysteresis” algorithms statistically combine several recent tracking errors with the current error. They are subtly different; LowPass computes the median of recent errors and adjusts it in the presence of a underlying trend. Hysteresis is simpler and blends a user-defined proportion of the recent errors with the current one, allowing considerable flexibility. Predictive algorithms are also being developed to overcome latency and included in the latest PHD2 snapshot builds.

fig.13 When choosing a guide star, make sure that the longest exposure you are likely to use does not clip. Here, the star is diffuse and the star profile shows a sharp peak. A flat top indicates the central pixels are saturated. (The latest version of PHD2 gives a clipping warning.)

I typically start with the hysteresis method for both RA and DEC. If the mount shows signs of backlash, I evaluate one of the legacy PHD algorithms like, “resist switch”. This non-linear filter is frequently used with mounts that have some DEC backlash (a non-linear problem). It avoids changes in DEC direction by statistically working out the underlying drift direction. This filter ignores tracking errors in the same direction as the same correction until the statistical likelihood of seeing noise being unidirectional compels it to change its mind. Not all mounts exhibit DEC backlash but it can also be useful when the DEC bearing has some lateral play (which translates into an apparent RA movement) that is triggered by a DEC reversal (fig.14). Choosing an optimum guiding algorithm usually starts by evaluating a default value and then, after some appreciation of the way the mount is drifting or reacting, making informed guesses and evaluating alternatives. (PHD2 usefully has a tool to measure DEC backlash.)

Star Mass

I often use PHD2 with SGP to do my guiding. On a few occasions the ‘star lost’ warning has come up whilst I’m sleeping and the system has shut down, fearing the worst. The cause is one of the PHD2 settings that is enabled by default. This is the Star Mass Detection option in the Guiding settings. This is designed to detect and prevent the guide star flipping between close stars of different magnitudes, most frequently found at shorter guiding focal lengths. It can also trip due to changes in transparency or a passing vapor trail. In practice, I disable this feature when using an off-axis guider.

Guide Exposure and Star Selection

Although we have discussed increasing the guider exposure duration to smooth out seeing noise and improve the signal to noise ratio, too much can be a problem if the combination of the guider exposure and the star intensity overloads the sensor well-depth. The centroid detection algorithms work best when the intensities are within the sensors range. Check your guide star choice with the longest likely guide exposure by sampling its peak value or reviewing its star profile, such as the one in PHD2, shown in fig.13 and which displays “Sat”, for saturation.

fig.14 This is a 60-second image capture of a bright star, during which the mount has been successively moved N, S, E and W from a central position using manual guider commands (5 seconds at the guiding rate). The imaging sensor is aligned with the RA and DEC axis and you can see that when the DEC correction reversed, there is a small shift in RA too, shown by the double vertical trace and possibly caused by insufficient DEC bearing pre-load. In practice, however, it may not necessarily manifest itself unless one is heavy-handed with the guiding corrections. This mount routinely achieves sub 0.3 arc second RMS tracking accuracy with 2,000 mm focal length optics and on account of the highly accurate polar alignment, has frequent DEC reversals.

Unique DEC Axis Issues

Both the RA and DEC motor and gear assemblies have tolerance issues that manifest themselves as periodic error, backlash, play and static friction. These do not equally apply: Since the RA system is continuously moving in the tracking direction, it should never encounter backlash or stiction (the one exception is in an unbalanced configuration when the OTA tips over). The DEC motor on the other hand is basically stationary and potentially has backlash and stiction but does not encounter periodic error. Play, however, sometimes the effect of insufficient bearing pre-load, can cause either axis to wobble and cause an apparent shift on the other axis (fig.14). A few microns of play can cause several arc seconds of movement. So far though we have generalized on issues common to both axes and we should additionally consider the special cases of backlash and stiction on the DEC axis. These are non-linear effects and require a non-linear treatment.

Static friction and dynamic friction are the terms given to the force required to move a body from rest and keep it moving. Static friction is always higher; the force to move your computer mouse is less than that to keep it moving. In a mount, the label stiction is given to that initial force to get things moving. For a small movement, the applied forces by the motor and gear assembly may be insufficient to overcome stiction, or worse still if you are changing direction, the energy stored in the flex within the bearing and gear assemblies may temporarily reverse the intended movement. After further movement commands are issued, the forces in the system are overcome, the full motor torque is applied to the head and things start to move (and in the right direction). If the mount does not move, it simply introduces a further lag. Since the input signal is mostly noise, the mount will either catch up on the second cycle, or the error nulled out by subsequent random commands in the opposite direction. If the mount temporarily moves in the wrong direction, it creates the potential for over-correction on successive guider cycles. One solution is to disable any DEC corrections in the direction of drift; this can either be done manually (fig.11) or alternatively PHD2 and Maxim DL have a facility to detect the drift direction and minimize DEC commands that add to it. With the right telescope fore-aft balance, this can be very effective but may falter when the telescope is pointing near the zenith, as there is no angular moment and the scope is “floating”, for want of a better word.

Backlash is another non-linear affect and occurs when the DEC gears try to change direction. Unlike the RA gear, which is constantly tracking in one direction, the DEC motor is mostly stationary and gear backlash cause guiding commands in a reverse direction to have less than the desired effect. The guider calibration image in fig.9 actually shows it up: The red line traces the star position at the end of the four calibration moves. If you look closely, the star does not return back to its initial position. The backlash is the small remaining distance. Judging from the length of the red lines and the calibration time, the backlash in this case is just under 1 second (at the guiding rate). This number may be useful later on. PHD2 has a more sophisticated method of measuring backlash within its calibration tools. The same unidirectional movement strategy used for stic-tion can help here too. Again we can selectively disable certain directional commands. This might be the end of the story until you execute a meridian flip or use dither. In the case of a meridian flip, the guider software must reverse the RA commands and swap over any disabled settings. (It is explained elsewhere but briefly, dither is a small deliberate image shift between exposures. Each exposure is in a slightly different position and after they are aligned and combined, the random distribution of hot pixels facilitate their removal during image processing.) In Maxim DL, when guiding, the dither movement is executed via guider commands. If it happens to request a movement in the DEC drift direction it can take an age for the mount to move by the correct amount. In effect, the drift has to catch up with the dither amount. You can prevent the main exposure starting until the tracking is back on target (within an error threshold) or after an elapsed time. PHD2 has an option to dither only in RA, to avoid this potential hang-up.

In these circumstances, one alternative is to enable backlash compensation. This is a feature of Maxim DL, PHD2 and some telescope mount drivers. If mount-based backlash is available it is usually a single parameter hysteresis value designed for visual observation purposes and if set too high, will cause DEC oscillation. PHD2 backlash compensation is more sophisticated, not only does it measure the backlash, it also dynamically adjusts the required amount based on real-time guiding performance.

Backlash creates a dead band with DEC reversal. In my SkyWatcher mount, DEC backlash was apparent during its calibration (fig.9) at about 10 arc seconds, or 1 second at a guiding rate of 0.7x. If the mount had both DEC movements enabled, it potentially set a rather large lower limit on tracking error. It is a bit like setting a minimum movement value of 1 second. The backlash compensation feature essentially skips over the dead band by adding additional guider movement time if, and only if, its direction is opposing the last.

The backlash value is measured in time (at the guider rate) and should be set to a value less than the actual backlash. The remaining backlash value is effectively the difference. If you set its value too high, the mount will oscillate in DEC and the guider graph will show alternating large positive and negative tracking errors. Backlash compensation is tricky to get right and its avoidance is better than its cure. With backlash compensation, less is more. Lastly, if it is available, the “resist switch” or equivalent guiding algorithm, which requires several tracking errors to occur in the same direction as the last correction before electing to change the DEC correction polarity, will reduce the number of reversal instances.

Guider Settings

Autoguiding is not a trivial matter to get right and creates numerous practical compromises. The autoguiding programs go a long way to solve most issues but it still requires some work on the part of the astrophotographer to understand their system and set exposure times, guide rate, movement limits and establish if stiction and/or backlash compensation is required. If the inherent mount tracking errors are small to begin with, it allows longer guider exposures and a gentle touch to keep any remaining errors in check. As tracking errors become larger, a careful balance of correction versus over-correction is required. The autoguider tracking graphs give a clue if the mount is over-reacting to seeing conditions or if drift and PE are creeping in.

Good RA guiding results in a tracking graph that does not produce successive large corrections in opposite directions and only makes a few corrections in one direction before doing nothing (until the PE accumulates above the minimum movement value). If the autoguider requires many corrections in the same direction, especially with a high aggression setting, it is likely the system is not catching up. It is unlikely to be the guide rate or the maximum movement setting; even at their minimum settings they should keep up with all but the worse mount PE. It is more likely that the minimum movement is set too high or a result of excessive measurement latency (the centroid measurement of a 10-second exposure is 5 seconds old already). Since successive corrections in the same direction are an indication that seeing noise is not dominant; it should be safe to lower the minimum movement and exposure.

On the DEC axis, the guiding should only correct for drift and ideally, send out commands in one direction (and the opposing direction after a meridian flip). This behavior can be forced, by disabling corrections in the direction of the prevailing drift, or through long exposure and minimum movement settings. (This, however, does not allow you to dither between exposures on the DEC axis.) In general I disable the DEC compensation feature in the guider controls and calibrate the autoguider at a low declination. In practice I find this gives greater stability when the seeing conditions are poor. Before I rationalized my guider parameters, my first attempt to image M82 at 70° DEC produced a tracking graph that resembled the Swiss Alps!

One other thing to watch out for is the combination of low aggressiveness, low guide rate and a large minimum movement that can prevent guider corrections and lock in an error threshold, calculated by the following equation:

A 50 ms minimum move at 0.5x guide rate and 50% aggression setting locks in a ±0.75 arc second error guiding dead band, within which there are no corrections. (This is twice as large as the RMS tracking error of my Paramount.) On the other hand, a maximum move of 50 ms in PHD2 for DEC at 0.5x guide rate will keep up with the drift caused by a large polar alignment error of 15 arc minutes.

Case Study: Avalon Linear

It is useful to lay out the evaluation of the guiding parameters for a new mount. As we have seen, there are many variables and experimentation is always necessary. The trick is to narrow the range down using information about the mount’s construction, conventional wisdom and intuition. The Avalon Instrument mounts are unique in that they use toothed belts to transmit and reduce the drive ratio from the motors to both axis. The belts are very durable and due to the large contact area around the various pulleys, do not exhibit a classical short-term periodic error. There are tracking errors, however, but they are hard to characterize (fig.16). With no gears, there is effectively no backlash but being a belt, which bends, there has to be a little elasticity. Some mount designs exhibit obvious play in worm drives or reducing gears. In this case, the drive yields elastically to an externally applied force. An Internet search from user forums is always a good place to start and in this case indicate a range of user-recommendations ranging from 100% aggression, 1-second exposures to 10-second exposures with less aggression. They all agree on using a slow guide rate and a small minimum movement value (presumably on the basis that lots of small, slow adjustments are better than a large fast one). This unique mount design should therefore make an interesting case study.

The first step with any mount is to analyze the underlying tracking error (without any guiding). This gives an indication of the polar alignment, the peak to peak error and most importantly the tracking error’s maximum rate of change. After setting up an accurate polar alignment of less than 1 arc-minute, I measured the tracking error over a 10-minute period. To reduce false measurements arising from seeing noise, the exposure was extended to 3 seconds. The all important parameter is not the peak to peak tracking error, but the rate of change of tracking error. In this case, the worse-case rate measured 0.32 arc seconds/second, suggesting that short guider exposures (or more accurately guide intervals) of 4 seconds or less were required to minimize the peak guided tracking error. Short-exposure, high-aggression guide settings are unusual and traditionally lead to erratic mount movement as the system tries to chase seeing noise. On the other hand, a low aggression value would be insufficient to keep up with the maximum rate of tracking error change, especially if used with longer guider intervals.

fig.15 The test rig for establishing the Avalon Linear autoguider parameters. A medium refractor was fitted to the mount along with a high-speed guide camera and polar aligned with a QHY PoleMaster. The counterweight position indicates this is a lightweight imaging system and it may be necessary to additionally tune the autoguider parameters when using a heavier scope.

fig.16 The unguided tracking graph for the Avalon shows the level of tracking error, its magnitude and most importantly, the rate of change, which is a function of the slope or the tracking error characteristic. This sets an expectation for the maximum guider interval. If the slope changes rapidly, this can catch out guider parameters that rely on heavy filtering to remove seeing noise. These important characteristics correspond to the first and second derivatives of the tracking error. Newton would be proud.

Using an autoguiding program to measure tracking error is very useful but becomes less accurate with short guider exposures in the presence of seeing noise. Anything less than a few seconds is likely to be give an overly pessimistic indication of tracking performance. The ultimate measure are the star’s appearance in the image. The FWHM and the eccentricity are excellent measures to get the very best out of the system. A software utility like CCDInspector can monitor a folder and plot these attributes in real time, say for a sequence of 5-minute exposures using a range of guide exposure, hysteresis and aggression settings.

I also wondered if the mount would “bounce” with an impulsive movement. I visualized the mechanical behavior by considering a ball suspended from an elastic string and how I might lift and lower the ball without making it behave like a yo-yo. The answer is to use small moves, with low acceleration and in a time frame that does not reinforce any natural oscillation. I realized too, that the guiding parameters will be particular to the imaging system, since the mass affects any oscillation period.

In guiding terms, this empathetic approach suggests a slow guide rate ( < 0.25x) and small minimum move (to prevent a dead-band). To avoid unnecessary movements from chasing seeing, it suggests guider exposures in the range 1.0–4.0 seconds, with no delay, and high aggressions setting of 75% or higher, with some hysteresis for filtering. Within these confines, there are several combinations that trade exposure time with aggressiveness and hysteresis, providing an opportunity to avoid oscillation over a range of equipment masses. It also occurred to me that in a system with allegedly no backlash and a compliant drive, symmetrical guider responses would benefit from precise equipment balance, a view supported by several recommendations from user forums.

Before trying these out, I tried an unusual experiment to understand the dynamics of the mount. Movement around DEC and RA axis can be quite different on account of the angular momentums involved. Any RA move swings the considerable counterweight and telescope masses about its axis but a DEC moves rotates the counterweight and telescope tube on-axis.

To get a feeling for how the mount would respond to a stimulus, I mounted a digital SLR to a 600-mm focal length lens and took a 10-second exposure of a bright star as the mount slewed in RA. During the exposure, I tapped the telescope lightly in the DEC movement direction and then examined the image. If the mount was going to “ring” in DEC, this would be seen as a wiggle in the star trail. Assessing this in RA required repeating the experiment, only this time, with the mount slewing about the DEC axis during the exposure (using the handset) and tapping the end of the telescope about the RA axis. In practice, the best conditions for this experiment were when the stimulus was confined to one axis. This is most easily achieved when DEC is close to zero and pointing at the meridian. The results can be seen in fig.17 and fig.18. In both cases the ringing decayed to negligible levels within 1 second, with the additional mass of the RA axis extending the decay period. The results suggest guider exposures of less than about half a second should be avoided as it might cause oscillation.

After a little experimentation, the final result proved the initial hunch was not far off (fig.19). The trick was to put as little energy transfer into the mount as possible and the guider responded with respectable guiding errors over indefinite periods, achieving a respectable RMS tracking error of 0.44” RMS in good seeing conditions.

The current SkyWatcher ASCOM driver permits guide-rate settings down to 0.1x. The new Avalon StarGo controller goes down to 0.05x. (This can be retro-fitted as an upgrade accessory.) There is room for further improvement and if the ASCOM driver is similarly updated, I will try 0.05x and zero the minimum move settings. As mentioned before, using the PHD2 graph to measure tracking performance with short exposures is undermined by poor seeing and my next step will be to do the final fi ne-tune by comparing star FWHM and eccentricity from using 2-minute imager exposures taken at different guider settings (or wait for excellent seeing conditions).

fig.17 This star trail of 2 seconds, taken with the mount slewing in RA, shows the effect of a light tap on the telescope about the DEC axis of rotation. It gives an indication of how the mount might respond to DEC guider pulses.

fig.18 As fig.17 but this time evaluating how the mount might react to a RA guider input. In this case, the mount is being slewed in DEC (using the handset over a 2 second period). The light tap is this time aimed about the RA axis.

fig.19 The guided tracking graph for the Avalon, close to its optimum setting and confirmed by checking the FWHM and eccentricity in CCDInspector. The RMS tracking error is 0.44”, using the hysteresis algorithm, set to 15% with 2.5 second exposures, small minimum move and an aggression of 75%. The Lowpass2 algorithm works well too, using shorter exposures and zero min. move.