[X] My Assistant

[Gerald]

This is now a first step of a somewhat sophisticated analysis of the ghosts, the success of which is to find out.
The ghosts are best feasible outside the bright Earth. So I've masked all efb12 subframes to just show the ghosts in front of dark background.
Example:

This is the average of all these masked subframes, constraint to the non-black pixels:

This average shows remnants of the source images. Most of this can be averaged away by decomposing the image in a horizontal and a vertical mean brightness function.
For averaging, the brightness values are temporarily gamma-corrected with gamma = 2, considering the square-root encoding of the raw image.
The two functions can then be composed to result in this mean ghost image:

This image is intended to serve as a 0th approximation of a flatfield for the ghosts.

[Gerald]

Some more explanations regarding the above article:

As described in the article, I've applied methods related to the Newton method to fit peaks into the EFB03 data. The idea is, to find a local minimum of the square error sum. For differentiable functions, the derivative is zero at the minimum of a function. The Newton method can find such a point efficiently, if the derivative is locally sufficiently similar to a linear function. Unfortunately, the error functions defined immediately by the RMS error of a ("power-law") peak with respect to the actual data isn't that well-behaved at the guessed starting points of the iteration. But by using a sufficiently high power of the RMS error, the resulting function can be made sufficiently well-behaved. The following graphics visualizes the underlying principle for the 1-dimensional case:

PDF version:  NewtonMethod_and_Modification.pdf ( 118.43K ) Number of downloads: 1012


An explanation of zeta has been pending:
Here two attempts to give the parameter zeta an intuitive meaning, visually (Fourier series and effect on peak)

and audible, with each "beat" starting a new damping by increasing zeta in a linear way. Parameter u1 varies with each "beat" in a total of two cycles. The audio version samples only the Fourier series, not the respective derived peak. (The file is packed twice with 7-zip, for effective compression, and to obtain a .zip extension.)
 ZetaSamples1.0_2.0_0.2_1.01_1.41_0.004_400_400_2.wav.7z.zip ( 269.26K ) Number of downloads: 439


And back to EFB03:
This graphics shows linear regression data ("raw") of vertical stripes of width 100 pixels obtained from near the left and from near the right side of EFB03,
the best-fit "power-law" peaks with zeta=1, and the residuals (remaining errors).


There appear to be systematic errors with respect to the considered family of peaks. This effect is more distinct near the right of EFB03 than near the left side. I'm presuming, that these deviations can be reduced a little, but not considerably by including zeta as variable peak parameter. Inferring zeta is rather fragile and probably time-consuming, therefore I'm looking for other options first.

My favored approach will be a description by a sum of two peaks, a narrow high and a wide shallow one. Since the horizontal variability of the peak parameters clearly cannot be described by a single peak, I'm considering to investigate multi-peak approaches as the next step to narrow down the 2d-structure of EFB03 stray light.

The additional math needed to feed into some modified Newton method doesn't look difficult at first glance. Although I don't know yet, how well-behaved the approach will be numerically. I guess, that dedicating another about two weeks will return first (continuous) 2d approximates.

Other related tasks appear at the horizon, e.g.
- writing a ray tracer to explain/model the 2d structure of the stray light physically, and
- pinning down the effect of TDI regarding integration over some neighboring color filter (probably responsible for horizontal substripes within framelets).

[mcaplinger]

As described in the article, I've applied methods related to the Newton method to fit peaks into the EFB03 data.

Keep in mind that EFB03 was taken in a mode that is unlikely to be duplicated for Jupiter observations (lots of TDI in a visible channel). We will probably only use a lot of TDI for the CH4 channel.

In the diagram you show above of the CFA, be aware that there is a light shield between the top of the CCD and the back of the optics with an aperture nominally 0.231x0.473 inches centered on the center of the sensor. This is intended to block stray light paths from the sensor bond wires and metallization on the sensor package, though there could be some misalignment and some small paths could still exist.

Mods: it might make sense to create a subforum for this material, much as was done with the MSL discussion of technical details about the cameras.