Drizzle and dithering: recovering resolution from undersampled astro images

What drizzle does

Drizzle, formally Variable-Pixel Linear Reconstruction, was developed for Hubble Space Telescope work, first to combine the dithered images of the Hubble Deep Field North. Fruchter and Hook’s 2002 paper describes it as a linear reconstruction of an image from undersampled, dithered data that preserves photometry and resolution, can weight each input pixel by its statistical significance, and removes geometric distortion.

The method is easier to picture than its name. Each input pixel is shrunk into a “drop” and rained onto a finer output grid, after the shifts and rotations between frames are accounted for; its value is shared among the output pixels it overlaps, in proportion to the area of overlap. Two parameters control it, as defined in the arXiv version of the paper:

drop size = pixfrac × input pixel  ·  output pixel = s × input pixel

With pixfrac near 0 the method approaches interlacing, placing samples directly into output pixels; with pixfrac = 1 it becomes shift-and-add, which blurs the image again by the pixel’s own footprint. For the Hubble Deep Field North the drops were half the input pixel, slightly larger than the output pixels. The authors stress that drizzle is reconstruction, not restoration: it does not sharpen detail suppressed by the optics, it avoids adding a second convolution by the pixel.

Watch the convention. Siril uses “scale” the other way round: its scale 2.0 means an output grid with twice the resolution, which is s = 0.5 in the paper’s notation.

Why it needs dithered, undersampled frames

Fruchter and Hook describe the detected image as a continuous blurred image sampled at the center of each pixel. A small shift of the detector between exposures, a dither, produces offset samples of the same image. If every frame lands on the same pixel grid, there are no new samples to interlace. Siril’s documentation adds the practical side: with enough frames and suitably scattered dither positions, every output pixel receives data; with too few, null pixels show up as moiré patterns.

Undersampling is the other condition. The paper’s motivating case was a Hubble camera whose pixel was as wide as the star’s FWHM in the near infrared, against about 2.5 pixels per FWHM for a well-sampled detector. Siril states that if your sampling already matches what the telescope can resolve, drizzle cannot add detail.

Dithering in practice

The PHD2 manual describes dithering as moving the telescope by very small amounts between exposures, which imagers do to reduce fixed-pattern noise and hot pixels. The imaging program controls it, because only it can pause the main camera; PHD2 shifts its guide-star lock point and guides the mount to the new position. The maximum size is usually set in pixels, and PHD2 picks random amounts below it so the pattern does not repeat or return to earlier positions. A spiral mode with fixed steps is offered for cameras with strong fixed-pattern noise. The imaging program then waits for guiding to settle before the next frame; the guiding math guide covers the guider’s image scale.

Which setups in our data are undersampled

The AAVSO photometry guide treats fewer than 2 pixels across the FWHM as probably undersampled. With 3.76 µm IMX571 pixels and stars of 2.5″ or 3.5″, the ends of the range Diffraction Limited gives for non-alpine sites (computed):

Setup	Focal length	Image scale	Pixels per 2.5″ FWHM	Pixels per 3.5″ FWHM
William Optics MiniCat 51	178 mm	4.36″	0.57	0.80
William Optics Mighty Cat 71	230 mm	3.37″	0.74	1.04
William Optics Cat 51	250 mm	3.10″	0.81	1.13
Askar FRA400 with 0.7× reducer	280 mm	2.77″	0.90	1.26
Sharpstar 13028HNT	364 mm	2.13″	1.17	1.64
Celestron RASA 8	400 mm	1.94″	1.29	1.81
Sky-Watcher Esprit 100ED	550 mm	1.41″	1.77	2.48
Celestron RASA 11	620 mm	1.25″	2.00	2.80
Celestron EdgeHD 8	2032 mm	0.38″	6.55	9.17

Every setup at 400 mm or shorter is undersampled with these pixels in both seeing cases, and the Esprit 100ED only in the better seeing; the EdgeHD 8 is heavily oversampled and gains nothing from drizzle. With Siril’s scale 2, the Cat 51’s output pixel becomes 1.55″, still only 1.61 output pixels across a 2.5″ star. The sampling calculator runs this check for other pixel sizes, and the image scale calculator gives the scale itself.

Color cameras are a special case. Siril points out that a Bayer sensor’s red and blue channels are already undersampled by the spacing of their pixels, so it recommends drizzling color data at scale 1.0 and pixel fraction 1.0; the mono vs color guide shows the numbers.

What drizzle costs

Noise. Siril warns that a larger scale spreads fewer input pixels over each output pixel, so the result is noisier and needs more integration time. Fruchter and Hook add that drops spread each input pixel’s power over several output pixels, so neighboring output pixels have correlated noise, and noise measured pixel by pixel underestimates the noise on larger scales.

Disk space. Output pixels grow with the square of the scale. Siril’s own example takes a 1024 × 512 input to 2048 × 1024. For an IMX571 frame (computed):

Image	Pixels	32-bit mono size
Original, 6248 × 4176	26.1 million	104.4 MB
Siril scale 2, 12,496 × 8,352	104.4 million	417.5 MB

Siril runs drizzle as a registration step followed by stacking, so the drizzled frames exist on disk as a sequence. If each of 76 frames, the four-hour example in the storage calculator, is kept as a 32-bit image, that intermediate step alone is 31.7 GB (computed; check what format your software writes). Siril also notes that drizzle is a little slower than interpolation.