Jupiter has four inner moons that lie inside the orbits of the better-known Galilean satellites.  Amalthea is the largest of these and the 3rd closest to Jupiter. It was the last of the solar system's moons to be discovered visually and was first detected by Edward Barnard in 1892, nearly 300 years after Galileo's discovery of Io, Callisto, Europa and Ganymede. Subsequent observations by the Voyager and Galileo missions have shown that Amalthea is red in colour, irregularly shaped and measures approximately 250 x 150 x 120 km.

Barnard's original paper announcing the discovery appeared in the Astronomical Journal #275 (available here) and makes for interesting reading, including his descriptions of faulty equipment and emergency repairs! To make accurate micrometer measurements of position, he added a strip of 'carefully smoked' mica to reduce Jupiter's brightness and allow the planet and moon to be viewed in the same field. Readings were made to 0.01" and Barnard's estimate of Amalthea's orbital parameters are extremely close to modern values. 

Although imaging Amalthea electronically is easier than making a visual observation, it still proved a challenging object for a 4" scope. The problem of course is the overwhelming brightness of Jupiter. With over 16 magnitudes between the two, Amalthea is more than 2 million times fainter than its host planet.

Having made several previous unsuccessful attempts on Amalthea, I tried a few new things this time. I used a red filter to try to gain a contrast boost relative to Jupiter. A one second exposure time was selected and the camera gain adjusted to ensure that the sky at a distance of about 1-2 Jovian diameters from the centre of the planet wasn't saturated. Two hours of 1s exposures were collected.

Custom image processing software was written in Matlab, which included the following steps:

- Individual 1 sec images were summed in groups of 200. Images were aligned on the centre-of-mass of the grossly over-exposed image of Jupiter
- A co-added image of all 36 x 200 s summed exposures was created. Relying on Amalthea's motion during this period to blur it out from the summed image, this results in a background image that can be used remove background scattered light (see below)
- The background image was then subtracted from each of the 200 s frames. Due to small variations in seeing during the 2 hour exposure window, the size of over-exposed Jupiter image was found to vary slightly from frame to frame, which was handled by scaling the background image slightly.
- The corrected frames were heavily stretched to reveal Amalthea. A separate, correctly exposed and stacked image of Jupiter collected earlier in the evening using the same equipment was superimposed to show the scale and location of the planet.
- The first ten frames were combined into an animated GIF using the GIMP program.

In addition to faint Amalthea, Callisto can also be seen emerging around Jupiter's polar region.


Stretched raw image showing the complex light scattering pattern from the mag -2.7 Jupiter (centre). Ganymede and Europe  appear at the lower right; Amalthea at an angle of about 10 o'clock is completely overwhelmed. The star at the lower left is of 11th magnitude.

The two hour window was originally selected using the Stellarium app such that Amalthea should have reached maximum separation from Jupiter about halfway through. Initial examination of the frames at this time showed no sign of the moon. It was only after carefully going through all the frames that Amalthea was discovered in the early shots. Checking with the Jupiter Ephemeris Generator  confirmed the result, indicating that Stellarium has Amalthea incorrectly located in its orbit by a couple of hours. Lesson learned! Apart from its rapid motion, Amalthea's identity was confirmed by its accurate position relative to the centre of Jupiter (starting at a distance of 62" in the first frame) and the absence of any stars brighter than 16th mag that close to Jupiter.

Is Thebe possible in a 4" scope? Although 2-3 magnitudes fainter, it does have a larger orbit and reaches up to 74" from the planet centre. Seeing conditions for the Amalthea observations were very poor, with a strong wind blowing. So maybe!

Update! The answer on Thebe turns out to be yes! An image collected a few nights later showing both moons is here https://www.astrobin.com/hejrfb.