When the drizzle technique can bring you better resolution
Drizzling for higher resolution images
Hubble also experiences this problem: how does undersampling arise and which software helps to solve the problem?
20 images, each with 300s exposure time, of the globular cluster M5 - on the left with normal stacking, on the right with drizzle stacking. The normal version has been scaled to the same aspect ratio as the drizzled image for comparison. The setup for the process was in the undersampled area, recognizable by the presence of many star forms that are not perfectly rendered, they appear somewhat pixelated. A refractor with 105mm aperture and 670mm focal length was equipped with a camera with 9μm pixels. Sampling is therefore at 2.77"/pixel with a theoretical resolving power of 1.14". With the drizzle technique (result on the right), a finer depiction of the densely-packed stars is possible – star pairs that are close together are more clearly separated. M. WeigandUsing a large-format sensor to photograph a large section of the sky may result in undersampling – a problem that also affects the Hubble space telescope. A clever process can provide a remedy: the drizzle technique.
Besides the observing conditions, the detailed resolution of a photograph is determined by two instrument-driven factors: the telescope’s resolution and the fineness of the camera’s pixel grid. Not every camera/telescope combination can fully exploit your optics’ resolution. If, for example, you use a large-format sensor with relatively large pixels to capture the largest possible area of the sky, you will encounter undersampling. The Hubble telescope with its Widefield Planetary Camera is also in this situation, which is why an algorithm was developed to retrieve at least something from the lost resolution: the drizzle technique.
The basic idea behind the drizzle technique developed by A. Fruchter and R. Hook is the use of several images, in which the input pixel grid is shifted slightly from image to image relative to the object. This offset enables sampling of the object at the subpixel level.
To do this, the pixels of all images are reduced in size and projected onto a finer pixel grid. The brightness values are drizzled onto the new grid and distributed in proportion to the overlap of the two pixel grids. The brightness values of all images in the series are averaged for each pixel in the output image. If you select the drizzle factor relatively low, superimposing many shots will result in a more consistent image with finer sampling.
Dithering and multiple images
The slight offset between the frames of a series of images required for the drizzle procedure can be generated by dithering. The position of the telescope is randomly and automatically adjusted by a few pixels after each exposure. Dithering is usually used to eliminate noise during the stacking process. This can be achieved, for example, using the autoguider, which moves position by a few pixels after each frame. All common autoguiding software offer this option.
In addition, you will need as many images as possible to reconstruct the lost information. Only then can the gaps created by the redistribution of the brightness values be filled.
The same star from different frames, between which the position has been slightly changed. The star’s profile appears unsymmetrical, which allows the undersampling to be detected. Furthermore, the profile changes from image to image, which is used in the drizzle process. M. WeigandLimits of the process
Of course, the drizzle technique also has its limits. The drizzle factor is not arbitrary, because sampling cannot be increased at will. The number of images required for a consistent image would be very large and practically impossible to achieve. A factor of 2 is usually recommended. In addition, the resolution of the telescope and the seeing limit the technique’s results. For the seeing typically experienced in Germany, the drizzle technique is rarely worthwhile for long exposure times with sampling of around 1.5"/pixel or finer. The method is particularly useful for situations where undersampling arises, such as overview images of the Moon and Sun, as well as in the deep sky range at shorter focal lengths. It should also be noted that the drizzle technique cannot be combined with stacking methods such as median stacking or sigma stacking. This is because only alternate finer grid pixels have content, which is similar to the appearance of noise, which is filtered out in these stacking procedures.
On the principles of the drizzle technique: in the left image, a star has landed exactly at the intersection of four pixels and its brightness values are evenly distributed across the pixels. This makes the star appear pixelated and its actual profile is not correctly rendered. The original image pixel grid (blue) is now reduced (red) and projected onto a new grid (second image). The new grid is finer by a factor of 2. Of course, with only one image there are gaps in some places, as can be seen in the resulting value distribution in the third image. That's why a large number of images with small and varying offsets are required. After their averaging, the star profile is now hopefully rendered more accurately (right image). M. WeigandSoftware
Unfortunately, only a handful of stacking programs offer a drizzle option or similar algorithm. The function can be found, for example, in AutoStakkert! And RegiStax software for videos of objects in the solar system. Fitswork and DeepSky Stacker also offer this facility for deep sky images. These programs are all available free of charge on the Internet.
The bottom line
Drizzling offers the possibility to better utilize a telescope’s resolution with a given degree of undersampling and can improve stars’ definition. This results in advantages in detail rendition. The procedure works when the following conditions are met: the camera-telescope combination produces undersampling, there are as many single images as possible, and there is an offset between the individual images (dithering).
Author: Mario Weigand / Licence: Oculum Verlag GmbH