Rotational Gradient (Larson Sekanina Filter)
The rotational gradient, also called Larson Sekanina filter, is a filter that allows to remove circular structures from an image, to better highlight other details. This technique is particularly effective to show the jets coming out of the nucleus of a comet.
The principle is quite simple: this image processing consists in subtracting two copies of the image from each other, one of the two copies having been previously rotated with respect to a point defined in the image.
If there are circular structures around this point they are not modified by rotation and will disappear after rotation.
If there are non-circular structures, like jets in the coma, they will be shifted in relation to each other between the two copies and the subtraction will amplify the contrast of this structure in the result.
If the comet moves in the image, it is possible to add a radial shift.
Dialog box of the Rotational Gradient filter.
Theory
Starting from an input image, the filter generates two images, each with a radial shift (\(dr\) in pixels) and a rotational shift (\(d\alpha\) in degrees) relative to the point (\(x_c\), \(y_c\)). These shifts have the same magnitude but opposite signs between the two images. The two images are then combined to produce the final image. In polar coordinates \((r, a)\) with respect to the point \((x, y)\) we have:
with \(B\): the starting image, \(B'\): the resulting image, \(d\alpha\): the radial shift and \(dr\): the rotational shift
In the example below, concerning the comet C/2022 E3, the alignment was made on the comet and the stars show important trails. The coma is very circular and it is difficult to see details about its activity. Therefore, it is not necessary to define a radial shift. For the rotation, an angle of 15° was chosen (this choice was made after several attempts and using the undo button to go back). To choose the coordinates of the center of rotation, just make a selection around the cometary nucleus and click on Use current selection. This action will copy the coordinates of the centroid to the desired location.
Image of a comet (C/2022 E3 (ZTF)) showing a coma and a tail (courtesy of Stéphane Garro).
A simple click on Apply will apply the filter. In our example, a jet becomes visible.
After applying the filter, we notice a jet emerging from the core.
Siril command line
rgradient xc yc dR dalpha