Adventures in Differential Flexure

How’s that for a thrilling title? But this topic really does encapsulate a lot of what I love about astrophotography, despite the substantial annoyance it’s caused me lately…

Long exposure of M51 in Hydrogen Alpha – 900s

My quest for really nice photos of galaxies has, inevitably, driven me towards narrowband imaging, which can help bring out detail in galaxies and minimise light pollution. I bought a hydrogen alpha filter not long ago – a filter that removes all of the light except from a hydrogen emission line, a deep red narrow band of light. This filter has the unfortunate side effect of reducing the total amount of light hitting the sensor, meaning that long exposures are really required to drive the signal far above the noise floor. In the single frame above, the huge glow from the right is amplifier glow – an issue with the camera that grows worse the longer my exposures. Typically, this gets removed by taking dozens of dark frames with a lens cap on and subtracting the fixed amplifier glow from the frames, a process called calibration. The end result is fairly clean – but what about these unfortunate stars?

Oblong stars are a problem – they show that the telescope failed to accurately track the target for the entire period. Each pixel in this image (and you can see pixels here, in the hot pixels that appear as noise in the close-up) equates to 0.5″ of sky (0.5 arc-seconds). This is about two to four times my seeing limit (the amount of wobble introduced by the atmosphere) on a really good night, meaning I’m over-sampling nicely (Nyquist says we should be oversampling 2x to resolve all details). My stars are oblong by a huge amount – 6-8″, if not more!

My guide system – the PHD2 software package, an ASI120MC camera and a 60mm guidescope – reported no worse than 0.5″ tracking all night, meaning I should’ve seen perfectly round stars. So what went wrong?

The most likely culprit is a slightly loose screw on my guidescope’s guiding rings, which I found after being pointed at a thing called “differential flexure” by a fantastic chap on the Stargazer’s Lounge forums (more on that later). But this is merely a quite extreme example of a real problem that can occur, and a nice insight into the tolerances and required precision of astronomical telescopes for high-resolution imaging. As I’m aiming for 0.5″ pixel accuracy, but practically won’t get better seeing than 1-2″, my guiding needs to be fairly good. The mount, with excellent guiding, is mechanically capable of 0.6-0.7″ accuracy; this is actually really great, especially for a fairly low-cost mount (<£1200). You can easily pay upwards of £10,000 for a mount, and not get much better performance.

Without guiding though it’s not terribly capable – mechanical tolerances aren’t perfect in a cheap mount, and periodic error from the rotation of worm gears creeps in. While you can program the mount to correct for this it won’t be perfect. So we have to guide the mount. While the imaging camera takes long, 5-10 minute exposures, the guiding camera takes short 3-5 second exposures and feeds software (in my case, PHD2) which tracks a star’s centre over time, using the changes in that centre to generate a correction impulse which is sent to the mount’s control software (in my case, INDI and the EQmod driver). This gets us down to the required stability over time.

My Primaluce Lab 60mm guidescope and ASI120MC guide camera on the “bench”, in PLL 80mm guidescope rings on ADM dovetails

The reason why my long exposures sucked, despite all this, is simple – my guide camera was not always changing its orientation as the imaging camera was. That is to say, when the mount moved a little bit, or failed to move, while the imaging camera was affected the guiding camera was not. This is called differential flexure – the difference in movement between two optical systems. Fundamentally, this is because my guidescope is a completely separate optical system to my main telescope – if it doesn’t move when my main scope does, the guiding system doesn’t know to correct! The inverse applies, too – maybe the guidescope moves and overcorrects for an imaging system that hasn’t moved at all.

With a refractor telescope, if you just secure your guidescope really well to the main telescope, all is (generally) well. That is the only practical potential source of error, outside of focuser wobble. In a Newtonian such as the one I use, though, there’s plenty of other sources. At the end of a Newtonian telescope is a large mirror – 200mm across, in my case. This is supported by a mirror cell – pinching the mirror can cause huge deviation (dozens or hundreds of nanometers, which is unacceptable), so just clamping it up isn’t practical. This means that as the telescope moves the mirror can move a little bit – not much, but enough to move the image slightly on the sensor. While moving the mount isn’t an ideal way to fix this movement – better mirror cells reduce this movement – it’s better than doing nothing at all. The secondary mirror has similar problems. The tube itself can also expand or contract, being quite large – carbon fibre tubes minimise this but are expensive. Refractors have, broadly, all their lenses securely held in place without issue and so don’t suffer these problems.

And so the answer seems to be a solution called “Off Axis Guiding”. In this system, rather than using a separate guide scope, you use a small prism inserted in the optical train (after the focuser but before the camera) to “tap” a bit of the light off – usually the sensor is a rectangle in a circular light path meaning this is pretty easy to achieve without any impact to the light that the sensor receives. This light is bounced into a camera mounted at 90 degrees to the optical train, which performs the guiding function. There are issues with this approach – you have a narrower (and hard to move) field of view, and you need a more sensitive guide camera to find stars – but the resolution is naturally far higher (0.7″ rather than 2.5″) due to the longer focal length and so the potential accuracy of guide corrections improves. But more importantly, your guiding light shares fate with the imaging light – you use the same mirrors, tube, and so on. If your imaging light shifts, so does the guiding light, optically entwined.

The off-axis guiding route is appealing, but complex. I’ll undoubtedly explore it – I want to improve my guide camera regardless, and the OAG prism is “only” £110 or thereabouts. The guide camera is the brunt of the cost – weighing in at around £500-700 for a quality high-sensitivity guide camera.

But in the immediate future my budgets don’t allow for either of these solutions and so I’ve done what I can to minimise the flexure of the guidescope relative to the main telescope. This has focused on the screws used to hold the guidescope in place – they’re really poorly machined, along with the threads in the guidescope rings, and the plastic tips can lead to flexure.

Before and after – plastic-tipped screws

I’ve cut the tips almost back to the metal to minimise the amount of movement in compression, and used Loctite to secure two of the three screws in each ring. The coarse focus tube and helical focuser on the Primaluce guide scope also have some grub screws which I’ve adjusted – this has helped considerably in reducing the ability for the camera to move.

Hopefully that’ll help for now! I’m also going to ask a friend with access to CNC machines about machining some more solid tube rings for the guidescope; that would radically improve things, and shouldn’t cost much. However, practically the OAG route is going to be favourite for a Newtonian setup – so that’s going to be the best route in the long run.

Despite all this I managed a pretty good stab at M51, the Whirlpool Galaxy. I wasn’t suffering from differential flexure so much on these exposures – it’s probably a case of the pointing of the scope being different and so not hitting the same issue. I had two good nights of really good seeing, and captured a few hours of light. This image does well to highlight the benefits of the Newtonian setup – with a 1000mm focal length with a fast focal ratio, paired with my high-resolution camera, I can achieve some great detail in a short period of time.

M51, imaged over two nights at the end of March
Detail, showing some slightly overzealous deconvolution of stars and some interesting features

Alongside my telescope debugging, I’m working on developing my observatory plans into a detailed, budgeted design – more on that later. I’ve also been tinkering with some CCDinspector-inspired Python scripts to analyse star sharpness across a large number of images and in doing so highlight any potential issues with the optical train or telescope in terms of flatness, tilt, and so on. So far this tinkering hasn’t lead anywhere interesting, which either suggests my setup is near perfect (which I’m sure it isn’t) or I’m missing something – more tinkering to be done!

Map of sharpness across 50 or so luminance frames, showing a broadly even distribution and no systemic sharpness deviance