In April 2013 I removed the stock Takahashi manual focuser and the stock imaging train adapters entirely from my FSQ-106EDX. I replaced these parts with adapters from PreciseParts and an FLI Atlas digital focuser, shown below. The setup includes my QSI 683wsg camera, an SBIG ST-i guider, a Moxa UPort 404 USB hub, a PowerPole power splitter and a Kendrick Micro dew heater controller and strap mounted with Socal Astro rings and plates. This setup rides on my Takahashi EM-400 Temma2M mount using a Takahashi CCA-250 saddle plate.
The back focus calculations for the setup are shown in the following table. The maximum adapter length available from PreciseParts is 90 mm. Ideally, the length of the first adapter should be longer and the second shorter to reduce the torque that is supported by the bearings inside the Atlas. This could be achieved by using an additional front spacer adapter, at additional cost.
PreciseParts adapter (FSQ focuser removed to Atlas), 90.0 mm
FLI Atlas (middle position), 37.7 mm
PreciseParts adapter (Atlas to QSI), 72.0 mm
Filter refraction, -1.0 mm
QSI 683wsg with 2.156"-24 plate, 53.3 mm
Total backfocus, 252.0 mm
My goals with this focuser change include (1) reduce image train flexure, (2) provide electronic focusing and (3) support focus drift compensation during my 40 minute exposures.
Keeping my FSQ in focus during exposures as the night cools has been a challenge due to the FSQ's rather large temperature dependent focus position. Prior to installing the Atlas focuser, I compensated for the expected focus shift during an exposure by moving the camera position slightly inside of proper focus immediately prior to starting the exposure using the manual focuser. My goal was to achieve proper focus half way through the exposure. Typically at my imaging sites temperature decreases by about 1 degree Celsius during a 40 minute exposure. I estimated the focus shift caused by 1 degree of cooling using a Bahtinov mask, and used this information to help estimate the amount of manual compensation necessary. Of course, actual cooling rates vary and this approach was not always able to achieve a good result.
With the Atlas focuser, my goal was to automate this process and improve reliability by applying focus drift compensation during the exposure, in hopes of achieving better focus and smaller star full width at half maximum (FWHM) on average.
The first step I took was to model the focus position temperature dependency. The following chart shows data for 11 nights at 3 sites in California and Nevada. Each point represents a temperature, focus position measurement immediately prior to the start of an exposure using a Bahtinov mask to achieve proper focus as accurately as possible. Temperature values are provided by the Atlas' internal temperature sensor. I then fit a linear model to each night's data using the least squares method. The slopes of the best fit lines equal roughly 600 +/- 150 steps or equivalently 50 +/- 12 microns per degree C. The slopes appear to show a site dependency, which may be related to the difference between the average site weather conditions. I plan on experimenting with an external temperature probe mounted on the OTA to see if weather independent focus position versus temperature consistency can be achieved.
The critical focus zone (CFZ) of the FSQ operating at f/5 is approximately +/- 10 microns , shown in the chart above as dotted lines above and below each best fit line. A one degree C change of 50 microns represents a significant movement out of the CFZ and appears as a noticeable increase in FWHM.
The following chart shows a linear model fitted to the data using the weighted least squares technique.
With linear modeling completed, I wrote a Win7 application that performs focus drift compensation during an exposure, using the focuser ASCOM driver supplied by FLI. The application's configuration dialog is show below. The primary parameters are slope and hysteresis. The focuser is moved when the change in focuser temperature equals or exceeds the hysteresis value. With slope set to 600 and hysteresis value set to 0.25, focuser movements of 150 steps occur typically once every 10 minutes (1 degree of cooling every 40 minutes with a total position change of 600 steps). The bound and time span parameters constrain focuser movements. I will explain these parameters below. Finally, compensation can be performed in two ways, automatically or manually. I will explain these options below also.
The application's status dialog is shown below. Values of the focuser's current position and current temperature and the active compensation mode are displayed. Also, in parentheses, various additional values are displayed. For position, the total change in position since the start of compensation is displayed. For temperature, the change in temperature since the start of compensation and since the most recent compensation are displayed. Finally, for compensation, the time in minutes since the start of compensation and since the most recent compensation are displayed. The Move button allows the focuser to be repositioned manually. The Stop button stops compensation.
This particular status dialog shows that the compensation has been running 8 minutes with a total compensation movement of -150 steps. The total decrease in temperature during the 8 minutes is 0.38 degrees C. It has been 2 minutes since the last compensation, and temperature has cooled an additional 0.13 degrees C since that compensation. Note this particular example was from a test using synthetic temperature data with an accelerated cooling rate.
As of June 2013 I have use this application on about 30 hours worth of 40 minute exposures at imaging sites in California and Nevada. I feel that the compensation is working well and that subexposure star FWHM values on average have decreased, compared to my previous manual compensation technique. However, one unexpected problem has cropped up.
I have noticed a image shift when the focuser is moved by 150 steps. The image shift can be as large as 8 microns, and requires autoguiding correction to restore proper guide star position. The typical guiding error of my setup is 0.5 to 1.0 arcseconds RMS or equivalently 1.3 to 2.6 microns RMS. An 8 micron image shift represents a disturbance of at least 3 times typical RMS error. Such a large deviation sticks out like a sore thumb on my autoguiding charts, and the fact that it occurs immediately after a focuser movement clearly indicates that it is a focuser issue. I believe that this image shift is due to Atlas' bearing runout. FLI confirms that image shift due to runout is to be expected with the Atlas. Runout is variation in bearing race wall thickness. Runout values are classified by bearing manufacturing standards, and certain classes and types have values in the 1 to 10 micron range. My measurements are consistent with these standards.
On my setup, image shifts in the RA axis direction are quickly corrected by the autoguider. However, image shifts in the Dec direction are not corrected quickly if the direction of the shift is counter to the normal Dec drift direction due to polar misalignment and if the magnitude of the shift is large. Such delays are due to my mount's Dec axis backlash unwinding time. Dec backlash winding delays increase guiding RMS errors and compromise the quality of my subexposures occasionally. I have not been successful at reducing my mount's Dec backlash, which ranges up to about 20 arcseconds.
The chart below shows an image shift example. The RA and Dec axis guiding error in microns of each guider exposure for a 40 minute subexposure is shown as a point on the chart. The RMS error, equal to about 2.5 microns, is shown as a dashed circle. Dec drift is in the negative Dec direction. The furthest outlying point at the 11 o'clock position, in a direction opposite to Dec drift, corresponds to the guider exposure immediately following a focuser movement of 150 steps. The other outlying points in the same direction correspond to subsequent guider exposures. In this example approximately 1 minute was required to correct the image shift, part of the delay was due to Dec backlash unwinding.
My current workaround for this Dec axis image shift problem is as follows. Prior to making a focus movement, I let guiding error in Dec accumulate to its maximum uncorrected value due to drift. At that point I allow the focus movement to proceed. This delay reduces the impact of any counter drift direction image shift. I also have experimented with a variation that lets Dec error accumulate several microns beyond the normal limit by temporarily disabling Dec autoguiding corrections. These methods do not solve the problem entirely, but they have helped reduce the time required for image shift correction.
To help implement this workaround, I added a manual compensation mode to my Win7 application. In manual mode the application continues to monitor temperature and compute required corrections automatically. But it delays any required movements until the Attune button is clicked. In practice I wait for the Dec error to accumulate sufficiently and then click the button. The additional bound and time span parameters of the application help make this manual task easier. Prompts for movement occur no more often than time span minutes. And the magnitude of a movement is limited to slope times bound steps.
My current workflow involves accurately focusing immediately prior to each 40 minute exposure using a Bahtinov mask, and running focus drift compensation during the exposure with slope set to 600 steps per degree C and hysteresis set to 0.25 degrees C. Focus drift compensation movements equal 150 steps or 12 microns per 0.25 degrees C and occurs on average once every 10 minutes. Typically compensation movements are performed more frequently early in the night and less frequently later, due to the typically decreasing night cooling rate.
 Goldman, Megdal, "In Perfect Focus", Sky & Telescope, page 72, August 2010. Full version http://www.astrodonimaging.com/docs/GetFocusedPreprint.pdf.