I took a few shots of Jupiter at the end of February (my solar system weekend). Seeing the transit of the GRS across the pictures made me think: can I measure the size of structures on Jupiter (and especially the GRS) using these pictures taken from an amateur telescope ?

My system:

Celestron C8 + televue PowerMate 2.5x

Skywatcher AZ-EQ6 + TheSkyX Pro + EQASCOM

BackyardEOS (BYE)+ EOS 6D

The flow used to acquire and process the data was:

movie acquired through BYE, planetary mode (1500 frames, around 25fps) alignment and stacking using Registax6 final processing done in PixInsight

I was able to extract the following 13 images out of all the data acquired during the GRS transit.

When I tried to calculate the polar and equatorial diameters of Jupiter, I quickly found out that I can’t easily use values (or ranges) from the manufacturer(s) in order to obtain the total focal length of my optical system. The main formula used was:

Which means, if I know the focal length of my optical system, I can calculate the diameter of Jupiter. Or I can use the known value of the equatorial diameter of Jupiter in order to calculate my focal length. Of course, as soon as I choose to use the known value of the diameter I don’t really need to calculate my focal length in order to know the dimensions of one pixel on Jupiter (for example, if 10 pixels map to 10000 kms on Jupiter, then 1 pixel is 1000 kms). I still want to know my focal length so starting from the original equation, the focal length for my system is:

The next step is to measure both the equatorial and polar diameters in pixels and find out my focal length from this equation.

The idea is to get an average value for the focal length, so for every picture I did:

measure in pixels the polar diameter and get a value for my focal length (let’s call it my “polar” focal length)

measure in pixels the equatorial diameter and get a second value for my focal length (let’s call it my “equatorial” focal length)

Then I average the values and verify everything is consistent. I used OpenOffice calc in order to do that :

I found my focal length for this particular setup is 4355 mm and the associated resolution per pixel on Jupiter is 987kms.

The last and most interesting step is to get an estimation of the size of the GRS: I can count for example how many pixels I have on the East-West direction, multiply this number by the average resolution and then find the size of the GRS in kms (E-W direction).

As seen in the screenshot below, this is quite easy to say but a lot more difficult to do: where does the GRS start and stop ?

I tried/thought about few things:

wavelet filter in order to expose the GRS structure : not successful as the wavelet filter had to be adjusted for every picture and did not give great results

resize the picture (make it bigger) so it will be easier to “find the edge” based on colour change: not practical

find a way to plot the 3D intensity profile so it may be easier to “find the edge”, probably using something like Scilab

This is a generic structure detection problem. Can we say for example that if the lightness of the pixel’s first neighbour drops or increases by 30%, then we are “at the edge of the structure” ?

I was at the same time trying to find online articles about the GRS hoping to find some “official method” to characterize the boundaries of the GRS but was not successful. After few days, I started to explore all the masking generation functions in PixInsight and ended up with RangeSelection. From the documentation:

RangeSelection allows you to generate a mask by defining a range of pixel values. Those pixels whose values fall within the selected range will be rendered as white pixels on the mask, while pixels outside the selected range will be rendered as black mask pixels. This simple mechanism can be combined with a fuzziness parameter. Fuzziness can be used to introduce a degree of uncertainty in the boundaries of the selection range, as described below. RangeSelection allows you to generate either a binary mask or a mask from source pixels through a mechanism that we call screening, also explained later in this document. Finally, you can generate a mask from the nominal RGB/K image components or from the lightness (CIE L*) component of a color image, with optional smoothening and inversion of the output mask.

I used it on a resized picture of Jupiter:

And once I find the right set of parameters that allow me to “close the loop”, like in the screenshot below, I can count my pixels and get the size of the GRS.

The mosaic below is made of the 13 pictures of Jupiter, each of them with 2 inserts:

a crop of the GRS, resized 200% – top right

the mask generated via the RangeSelection function (building the mask using the Lightness value and inverting the final result) – bottom right

Finally, I measured the dimensions of the GRS in pixels, averaged it and converted it into kms and the result is: 16587 kms (equatorial) and 10020 kms (polar). The latest value measured by NASA in 2014, using the Hubble Space Telescope (article here and original article here) is 16500kms !