Backyard Astronomy


Differential Flexure

Why is the left image – taken with a premimum APO refractor – blurred, while the right image – taken with a 9¼" SCT – is much sharper?

Sharpness comparison

The answer is differential flexure – bad news for anyone trying to guide a mount with a separate scope and camera. But there's good news too.

Differential flexure occurs when one part of the imaging system shifts slightly, while other parts do not. These parts may be the guide scope, the guide scope focuser, the guide camera, the main telescope, the main focuser, and/or the main imaging camera. As the telescope tracks across the sky, gravity causes equipment to sag very slightly. Some items sag more than others, so the guide scope and the main scope no longer point precisely at the same spot in the sky. The autoguider valiantly keeps the guide star centered, but the image on the main camera moves relative to it, resulting in smeared stars and blurred details. Look at this example:

Smeared stars

This is a stack of 17 five-minute sub-frames. They were not registered (stars aligned) prior to combining. Explanation: Sum-combining without registering brings each star's full brightness value into the final image, so any movement that occurred while the shutter was open for each sub-frame shows up as trailed stars. The movement is very small – visually, the stars in each of the sub-frames appear round. But they are not round. The trailing is too small to see in the sub-frames, but summing the sub-frames reveals the movement.

Of course, when the subframes are registered (aligned) during processing, the registration software aligns the centriods of the stars, making them appear nearly round, but the non-stellar objects are smeared, as in the lefthand image at the top of this page.

Close inspection of this composite image in Photoshop shows the total displacement is roughly 11 pixels horizontally and vertically, or about 16 pixels diagonally. The image scale is two arc seconds per pixel, so something moved about 32 arc seconds over the total 85-minute exposure, or just under two arc seconds during each of the 17 five-minute sub-frames.

Just how much mechanical movement does two arc seconds (1/1800 of a degree) represent? Very little! Assuming the guide scope or imaging train is 12" (304mm) long, simple trigonometry reveals that two arc seconds represents a movement of 0.000116 inches – that's 116 micro-inches (0.00295mm), or about 1/32 the thickness of a human hair. Folks, precision machinist instruments can't measure this, and you certainly can't feel it by wiggling the equipment with your hand. You don't know the movement is there until it ruins an image.

Flexure – Hard to track down

So what does this all mean? It means you can never pay too much attention to eliminating differential flexure. Even after making several modifications to the guide scope, and replacing the Pyxis camera rotator with a tube of the same length to eliminate it as a suspect, a series of five-minute exposures still showed movement of about two pixels during a single sub-frame exposure. This is the same two arc seconds described above – no improvement at all.

Here is a single sub-frame showing an elongated star with an ideal star (pink circle) superimposed over the brightest pixels. The diim pixels beyond the pink circle on the right and bottom are obvious.

Star elongation

Flexure – Finally some good news

I'm pleased to report that my flexure problems are fixed! This hydrogen-alpha image of NGC6992 (reduced 50%) is a stack of 30-minute (not 5-minute, as above) sub-frames that were made after performing the modifications described in the table below. Here is a full-size version of this nebula in false-color (opens in a new browser window).

This is a single star enlarged from the NGC6992 image. Compare this 30-minute exposure with the 5-minute elongated-star image above. No elongation is evident over this long exposure.

No star elongation

What Eliminated Differential Flexure?

I made these modifications in my quest to eliminate differential flexure. I can't say for sure which one (or ones) did the trick, but I'm confident each was worth the effort.

Modification Why?
Installed a Robin Casady Triad Bar.


Perching the guide scope on top of the main OTA rings means that any movement of the rings is amplified at the guide scope. The Triad Bar places the guide scope low on a very solid bar, so movement is eliminated. Furthermore, the Triad Bar is superior to the typical side-by-side (tandem) bar because the main OTA is mounted in the center of the bar, not out on one end where it must be balanced by the guide scope on the other end.

Added a second 2½” (63.5mm) threaded extension tube between the focuser and the camera.


Originally I had a single 2½” extension tube, but this required the focuser drawtube to be racked-out nearly three inches. The extra extension tube allows 2½” more of the drawtube to be supported inside the focuser housing, reducing droop.

Replaced the original Delrin spacer blocks under the main telescope mounting rings with new ones made of aluminum.


Two people suggested the Delrin might be expanding or contracting at a different rate than the aluminum in the rest of the system. Or, being a slippery plastic, the blocks might be sliding. I wasn't convinced these were factors, but I replaced the Delrin with aluminum anyway.

Milled-flat the bottoms of the main telescope mounting rings.


After machining the new aluminum spacer blocks, I set the base of a mounting ring on one and was astonished to see it rock back-and-forth. There was a 0.010" (0.254 mm) hump in the center of the ring base. The second ring had a similar hump. I milled both ring bases flat, and now they rest firmly on the spacer blocks.

Replaced the felt lining in the main telescope mounting rings with solid styrene strips.


A friend suggested that the felt lining in the mounting rings might compress as the telescope weight shifts while tracking across the sky. Given the extremely tiny movement needed to produce elongated stars, this seemed very likely. I measured the thickness of the rubber-backed felt and found it would compress more than 0.005" (0.127mm) with only light finger pressure. I removed the felt, cleaned off the adhesive residue, cut strips from 0.030" (0.762mm)-thick sheet styrene (available at hobby shops), and affixed them to the inside of the rings with super glue.

I was fortunate that the 0.030" styrene was just right. Otherwise, I would have combined several layers of styrene to reach the needed thickness.

Added a metal strap to the guide scope mounting.


Originally, the 300mm guide scope was mounted on two short aluminum posts. A friend commented he once used something similar but needed a metal strap, so I added a hose clamp over the scope, with the cut ends screwed to the dovetail mounting bracket. In addition, as described above, I moved the guide scope from atop the OTA to the Triad Bar.

Notice that the guide camera is clamped securely to the dovetail rail, not supported by the guide scope focuser. Hanging a amera off a small focuser like this can cause major flexure.

Updated September 7, 2016