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Discussion of stray light in Juno Earth flyby images
Gerald
post Aug 27 2015, 10:02 PM
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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:
Attached Image

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

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:
Attached Image

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

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Gerald
post Aug 28 2015, 09:35 PM
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After horizontal point noise filtering of the 0th "ghost flatfield",
Attached Image

and application to the masked ghost images, e.g. with this result,
Attached Image

8-fold vertical condensing of 0th-flatfielded ghosts
Attached Image

reveals three types of ghosts which can easily be distinguished:
- a sharp ghost below the bright object,
- a blurred ghost below the bright object,
Attached Image

- and a vertically close to structureless ghost above the respective bright object.

Attached Image

The ghosts below an object appear to be decomposed into five columns.
Columns 1, 3, and 5 contain the sharp ghost,
columns 2 and 4 contain the blurred ghost.
The ghost above a bright object isn't obviously decomposed into columns.

The 8-fold vertical compressed sharp ghosts of EFB12 are sufficiently clearly structured, that they can be identified with features on Earth.
Attached Image

The blurred ghosts are sufficiently sharp to show that they originate in vertically displaced strips of the source object relative to the sharp ghosts.

The three thus far identified types of ghosts are to be investigated separately in more detail.
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Gerald
post Aug 29 2015, 06:12 PM
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Subframes 0 and 81 show the same part of Earth, with an inaccuracy of about 20 pixels near the center of the subframes:
Attached Image

That's roughly corresponding to a full 360 rotation of Junocam, and an offset due to the relative motion of the spacecraft.
(Nominally a rotation takes about 30s / 0.38s = 79 subframes. Based on this, the offset is about 2 subframes of the 81 subframes difference.)

The ghost at the left in subframe 71
Attached Image

shows features visible in the green framelet of subframe 76, and it almost fills in part of the masked strip between the blue and the green filter in subframe 75.
Attached Image

That's near the presumed vertical optical center. The horizontal offset of the ghost in this example is about 32 pixels to the right.
As a first estimate, the origin of the sharp ghost is vertically 4 subframes off the center, or about 4 * 360/81 = 18 (considering the average relative motion of spacecraft).

Same exercise with subframes 67 (ghost)
Attached Image

and 71, offset of the ghost about 12 pixels to the left:

Attached Image

And just to be sure, a crosscheck with subframes 66 (ghost)
Attached Image

and 70, again offset of the ghost about 12 pixels to the left:
Attached Image


So, the sharp ghosts seem to be distorted horizontally. This doesn't fit well to the small change of perspective by a difference of just 4 subframes.
Optical distortions (pinhole / barrel) would be of a similar order of magnitude as the observed distortions.

This step provides a basis to decide, whether the analysis of the ghosts can be continued with 2d methods allone, or whether map projections and 3d simulations become necessary at this point.
Now, continuing merely with 2d methods appears feasible, with the advantage, that less a-priori knowledge about the target is needed.
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Gerald
post Aug 31 2015, 10:41 AM
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An idea of the draft pinhole simulation of the geometry of the sharp ghosts, derived from the raw color version of a merged efb12:
Attached Image

It needs further geometric refinement (by about an accuracy factor of 5 to 10), e.g. by considering the Brownian K1 parameter, to be useful for cleaning.
These two gifs may provide an idea of the remaining distortion, first the bright portion of the image:
Attached Image

The (more subtle) sharp ghost portion (best visible in the leftmost of the five columns) :
Attached Image
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Gerald
post Sep 2 2015, 03:21 PM
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It took me some time to improve the geometric distortion of the images needed as a starting point for the simulation of the sharp ghosts.

Another ingredient is a ghost-type specific "flatfield". It's summarized in the following gif.
The idea is specific averaging of the "flatfield" from the sharp ghosts, followed by manual selection and copying of the central column to the first and fifth, since it appears to be of the highest quality.
Intermediate steps are averaging of the approriate subframes, decomposition in horizontal and vertical average with consecutive composition, horizontal point noise filtering, clipping of the two columns with the blurred ghosts, manual selection of the highest quality column as a prototype:
Attached Image

The next gif shows steps to narrow down the simulation of the sharp ghosts by using the "flatfield" as an intensity mask; the first frame is a distorted crop of the raw color merged efb12; the last frame is a subframe made of three raw framelets.
The gif shows steps to (approximately) derive the sharp ghost in the raw framelets from a distorted crop of the merged efb12:
Attached Image
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Gerald
post Sep 3 2015, 11:48 PM
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12 ghost images, cropped from the raw subframes (#64 - #75), flatfield-enhanced with the 0th "ghost flatfield", 8-fold vertically condensed, and composed to an overview image:
Attached Image

As a comparison: Ghosts, simulated from the raw color merged EFB12, based on the thus far achieved modeling of the "sharp" ghosts, also 8-fold vertically condensed:
Attached Image

The geometry is roughly ok, it may however need some further refinement. Two not yet modeled properties of the original ghosts are going to emerge:
- The sharp ghosts seem to be superposed with other ghosts or scattered light.
- The sharp ghosts aren't perfectly sharp, but blurred a bit.

The bright vertical lines in the enhanced original ghosts are probably due to hot pixels, to be investigated separately.
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Gerald
post Sep 4 2015, 08:25 PM
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A first estimate of "how" blurred the ghosts are.
To get an idea, I've blurred the raw merged EFB12 with Gauss blurs of exponentially increasing radii starting with radius 1 pixel with multiplicative steps of about sqrt(2), more formally radii sigma_n = sqrt(2)^n, for n = 0,...,10, the largest radius being 32 pixels.
The relative weight for the blur is exp(-r^2/(2 sigma^2)), with r the pixel distance to the central pixel; the blur is calculated over a square from -(3 sigma + 1) to +(3 sigma + 1), decomposed into two consecutive blurs, a horizontal and a vertical one.
As color values I've used the linearized values, which have been square root encoded again, after applying the blur.

Some of the resulting blurred EFB12 images contain insets of cropped and 8-fold vertically condensed raw subframes. Here two excerpts of cropped versions as animated gifs:
Attached Image
Attached Image


For the "sharp" ghosts a sigma of 1.4 pixels looked similar, for the "blurred" ghosts a sigma of 22.6 pixels. The values for sigma should be ok within a factor of two as an error estimate.

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Gerald
post Sep 6 2015, 02:17 AM
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The source of the blurred ghosts seems to be about 0.44 less displaced than the source of the sharp ghosts, hence about 17.56, preliminarily assuming the source of the sharp ghosts being displaced by 18.00.

Here a separate simulation of the sharp ghosts (Gauss blur with a sigma of 1.4 pixels), the blurred ghosts (Gauss blur with a sigma of 22.6 pixels), and the merged efb12 in raw colors.
I didn't apply intensity filters for the ghosts in this simulation. Images are cropped to the upper (southern) fragment.
I'm posting the three individual images as JPGs instead of an animated gif to avoid considerable loss of quality.
Attached Image
Attached Image
Attached Image

The three images may look displaced at first glance, but they are aligned up to the accuracy of the simulation, a few pixels for most parts of the images.

The comparison shows, to which extent the simulation applies. Particularly the overlap will require additional considerations.
But before, the third identified type of ghosts can be investigated in more detail, at least, and some refined intensity analysis should be possible.
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Gerald
post Sep 30 2015, 10:10 PM
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Some regions of the efb images can be assumed to be colored almost exclusively by ghosts.
If these ghosts can be assumed to be known except their pixel-wise weight, the weight being the same for all framelets at a given CCD pixel position, the weights can be calcuated in most cases, provided a sufficient number of subframes are available.

After applying this method, I'm rather sure, that in addition to the sharp and the blurred ghost below an object, other types of ghosts below an object need to be assumed.

From right to left in this visualized equation are a column vector of 2 raw subframes, a 2x2 matrix of simulated ghosts with constant weight 1, and a column vector of the calculated weights:
Attached Image

You may note, that the column (at the left) with the weights looks rather heterogenious, which shouldn't be the case for the correct weights.

The next obvious step is hence to narrow down the remainig ghosts / stray light, such that the calculated weights get reasonable.

Here an article summarizing some of the theoretical background:
Attached File  junocam01_some_related_algebra.pdf ( 105.77K ) Number of downloads: 248
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Gerald
post Oct 9 2015, 03:19 AM
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A preliminary analysis of EFB03 hints towards the structure of the target object being relevant for the poorly structured stray light.
Attached File  junocam02_about_efb03_straylight.pdf ( 117.54K ) Number of downloads: 239

The test tries to determine the degree of linear dependence of framelets showing mostly stray light.
Linear dependent framelets would indicate few relevance of the structure of the target object.
EFB03 is particularly well-suited for this purpose.

According matrices of correlation diagrams, mentioned in the above article, cases 1x1, 2x2, and 3x3:
Attached Image
Attached Image
Attached Image

Clear diagonal lines in these diagrams would point towards the structure of the target object being not relevant for the stray light.
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Gerald
post Oct 24 2015, 12:14 PM
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A fist step towards an empirical description of the stray light in EFB03:

Decomposing the framelets respectively into three appropriate horizontal substripes allows linear regression for these substripes, if constrained to averages within vertical stripes.
The regression parameters can then be approximated by Gauss functions.
Graphical synopsis:
Attached Image


An animated gif of six images, indicating the dependence of the parameters of the linear regression fragments on the selected vertical stripe:
Attached Image


More detailed technical description:
Attached File  junocam03_empirical_efb03_straylight_I.pdf ( 195.17K ) Number of downloads: 191


Next steps will probably be an attempt to refine the 1-dimensional approximations, and to extend the approximations to a closed 2-dimensional description over the whole image.
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Gerald
post Dec 22 2015, 01:52 PM
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Evaluating a simple function at a small number of points is rather easy.
Finding a simple function, which fits well to a time series, however, can be hard.
So this article is a moderately tough one:
Attached File  junocam04_empirical_efb03_straylight_II.pdf ( 263.87K ) Number of downloads: 243

It's about finding a family of functions able to fit into a 1-dimensional time series of grey values, as derived from EFB03.
The functions are designed to overcome some of the weaknesses of Gauss functions, especially to provide periodicity, skewness, and kurtosis.

I hope, I'll find time the next few days, to create several diagrams visualizing some of the methods and data.
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Gerald
post Dec 24 2015, 09:04 PM
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This graphics visualizes some properties of a family of peaks:
Attached Image


These diagrams show the horizontal variability in EFB03, of properties similar to the above:
Attached Image

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Gerald
post Dec 29 2015, 06:12 PM
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Possible physical root cause for sharp ghosts in Junocam images:
EFB12 subframe compared with camera CCD:
Attached Image

Path of light ray including possible reflection, z-axis (optical axis) as vertical:
Attached Image

Both attachments use distorted and cropped versions of figure 12 of this paper.
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Gerald
post Jan 4 2016, 06:14 PM
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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:
Attached Image

PDF version: Attached File  NewtonMethod_and_Modification.pdf ( 118.43K ) Number of downloads: 267


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)
Attached Image

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.)
Attached File  ZetaSamples1.0_2.0_0.2_1.01_1.41_0.004_400_400_2.wav.7z.zip ( 269.26K ) Number of downloads: 41


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).

Attached Image

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).
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