Drizzle and Undersampling: When It Helps and When It Wastes Your Night

Drizzle is probably the most misunderstood option in a stacking program. It is offered as a checkbox, it makes files four times larger, and roughly half the people who switch it on gain nothing from it.

Whether it helps depends on one number you can work out in about a minute.

Sampling

Your telescope delivers a star as a small blob. The atmosphere and the optics decide how large it is; 2 to 4 arcseconds across at half maximum is typical.

Your sensor divides the sky into pixels. The sky each pixel covers is:

arcseconds per pixel = 206.265 × pixel size in µm ÷ focal length in mm

A 3.76µm pixel behind a 400mm scope gives 206.265 × 3.76 ÷ 400 = 1.94 arcsec/pixel.

Now compare that with the blob. The useful ratio is roughly how many pixels span one star’s width:

• Fewer than about 1.5 pixels per star: undersampled. Stars land on one or two pixels and look square and blocky. Detail finer than a pixel is present in the light, but the grid throws it away.
• Around 2 to 3: well sampled. This is where you want to be.
• More than about 4: oversampled. Each star is spread over many pixels that carry no new information. The same photons are divided among more pixels, so each one is noisier.

In the example above, with 2.5 arcsec seeing, 2.5 ÷ 1.94 ≈ 1.3 pixels per star. That is undersampled, and the setup is a candidate for drizzle.

Short refractors with large-pixel cameras are the classic undersampled combination. A lot of people end up with exactly that, because short refractors are forgiving and easy to recommend.

What drizzle does

Drizzle (properly, variable-pixel linear reconstruction) was built for Hubble’s undersampled cameras, and the idea behind it is sound.

If every frame landed on exactly the same pixels, undersampled data would stay undersampled. The grid would be the limit.

Frames do not land identically, though. The mount drifts, and if you dither the frames are deliberately scattered by a few pixels. That scatter includes sub-pixel offsets: frame 12 is shifted by 3.4 pixels, not exactly three.

So each frame samples the sky on a slightly different grid. Combine them onto a finer output grid, placing each frame’s flux at sub-pixel precision, and you recover detail that no single frame contained. This is reconstruction from different samples, not interpolation or upscaling.

The three conditions

Drizzle helps only when all three hold.

1. The data is undersampled. Oversampled data has no sub-pixel detail to recover, because the grid was never the limit. Drizzling it gives you a file four times the size, no extra detail, and more noise.

2. The frames are dithered, or drifted. Sub-pixel variation is the raw material. Frames that land on the same pixels give it nothing to reconstruct from. Perfect guiding without dithering is the worst case here, which is a little ironic.

3. There are enough frames. Each output pixel needs contributions from many inputs. Below about 20 frames the result is patchy and noisy. It starts to look right at fifty or more.

Miss any one and drizzle costs you disk space, time and noise for nothing.

The costs

File size and time. 2× drizzle means four times the pixels. On a 26-megapixel sensor with 200 frames, that is a lot of disk and a much longer stack. Akastroid estimates the space before starting and tells you, since finding out 40 minutes in is the worst way to learn.

Noise. Spreading the same photons over four times the pixels leaves each pixel with a quarter of the signal, so drizzle is noisier per pixel. With enough frames that is a fair trade. With too few it is just noise.

It cannot fix bad data. Out of focus, trailed or poorly guided frames come through drizzle with all their faults intact. It is a sampling tool, not a sharpening one.

Deciding, in practice

Work out your arcsec/pixel with the formula above and compare it with your typical seeing. Use the FWHM your stacking software reports, since that is measured rather than guessed.

• Under ~1.5 px per star, dithered, 50+ frames: drizzle 2×. Expect a real improvement.
• 1.5 to 2: try both and compare at 100%. Sometimes it is worth it.
• Over 2: don’t. You may be oversampled, in which case binning (combining pixels) will improve your signal-to-noise. That is the opposite operation, and the right one.

Akastroid makes this decision from the frames. It reads the dithering pattern and how finely the field is sampled, chooses, and reports what it picked and why. The AUTO chip lets you override it if you disagree. The reasoning is shown in the same way as the frame quality scores.

A note on focal length

Undersampling is one of the few problems in this hobby with a simple hardware fix. The same camera on a longer telescope is better sampled, because arcsec/pixel scales directly with focal length.

Going longer brings tighter tracking demands, a smaller field, and more atmosphere in the way. Drizzle lets an undersampled short refractor recover much of the resolution a longer scope would have given, without those costs. That is a good trade, and a good reason to understand what the checkbox does.

Summary

• Work out arcsec/pixel: 206.265 × pixel µm ÷ focal length mm.
• Compare with your measured FWHM. Under ~1.5 px per star is undersampled.
• Drizzle needs all three: undersampled, dithered, and 50+ frames.
• It reconstructs from sub-pixel offsets. It is neither upscaling nor sharpening.
• If you are oversampled, bin instead. That is the opposite problem.