Atmospheric Scattering Revisited

[bh]

Amazing... love the ocean renedering... maybe Celestia one day?

[t00fri]

Amazing... love the ocean renedering... maybe Celestia one day?

Indeed, ...imagine the methane lakes on Titan

Fridger

[bh]

I'd love to try Eric's demo... not for mac though... oh well.

[chris]

I wonder why the color is so yellow/orange in your new backlit display?

Because I've been focusing on getting this code in shape to share and haven't spent much time tweaking scattering parameters (except for Earth, where known physical quantities are used.)

Here's backlit Titan again, this time with Rayleigh scattering coefficients increased:

titan-ring-2.png

There's now a visible bluish-purple fringe. I'm sure that this can be improved further, ideally with parameters derived from actual measurements. I've been using this color image assembled by Gordan Ugarkovic as a reference: http://www.flickr.com/photos/ugordan/820494346/ I don't know for certain that this is more realistic that Matt's image, but Gordan has demonstrated a lot of skill and care in making other color composites of spacecraft images.

Currently, the scattering parameters are:

* Scale height for Rayleigh scattering molecules
* Scale height for Mie scattering aerosols
* Rayleigh scattering coefficients for three wavelengths (m^-1): 680nm, 550nm, and 440nm
* Mie scattering coefficient (m^-1)
* Absorption coefficients (m^-1): same wavelengths as for Rayleigh scattering
* Mie asymmetry parameter (g)

The Mie particles scattering particles are considered to be the same as the light-absorbing particles, i.e. their scale heights are the same. It's quite possible that additional populations of particles or different density profiles will produce a more realistic representation, though the current simple atmosphere model shows promise for Titan.

--Chris

[ajtribick]

Out of curiosity, does this code handle stars with different spectra yet? Earth with a red dwarf sun for example.

[chris]

Out of curiosity, does this code handle stars with different spectra yet? Earth with a red dwarf sun for example.

Yes. The scattering and transmittance are computed separately for three wavelengths. Incorporating star color is just a matter of multiplying by the star's brightness at each of these wavelengths. This assumes that light isn't being absorbed and then reemitted at a different wavelength, but as far as I know such effects don't contribute significantly to the appearance of planetary atmospheres.

Another nice thing: it will be quite easy to make this precomputed scattering technique work for planets illuminated by multiple stars.

--Chris

[t00fri]

I wonder why the color is so yellow/orange in your new backlit display?

Because I've been focusing on getting this code in shape to share and haven't spent much time tweaking scattering parameters (except for Earth, where known physical quantities are used.)

Here's backlit Titan again, this time with Rayleigh scattering coefficients increased:

titan-ring-2.png

There's now a visible bluish-purple fringe. I'm sure that this can be improved further, ideally with parameters derived from actual measurements. I've been using this color image assembled by Gordan Ugarkovic as a reference: http://www.flickr.com/photos/ugordan/820494346/ I don't know for certain that this is more realistic that Matt's image, but Gordan has demonstrated a lot of skill and care in making other color composites of spacecraft images.

Since the available CICLOPS raw images basically lack physics/hardware-based normalization, neither Matt McIrvin nor Gordan Ugarkovic can really know the truth. Matt carries a PhD in theoretical physics from Harvard. So no surprise that I tend to trust him . At least he must have had a thorough training in scientific methodology. Gordan is not a scientist by profession, while his imaging output has been indeed overwhelming. So no doubt about his imaging experience. I had my share of discussions with him about Mercury's colors...

Personally, I never had a go at R,G,B compositing those raw images. With high probability, one will get stuck before the end, since outsiders don't have all required info available. Since so far the status of Celestia's atmospheres was not in an advanced stage, I felt it was too early to get involved in that compositing job more seriously. I had intensive and fruitful contacts before with the leading scientist of the CICLOPS team. So retrieving the required information from the team shouldn't be hard.

Currently, the scattering parameters are:

* Scale height for Rayleigh scattering molecules
* Scale height for Mie scattering aerosols
* Rayleigh scattering coefficients for three wavelengths (m^-1): 680nm, 550nm, and 440nm
* Mie scattering coefficient (m^-1)
* Absorption coefficients (m^-1): same wavelengths as for Rayleigh scattering
* Mie asymmetry parameter (g)

These are more or less identical to what we had previously. Right?

What I don't understand at this point is the listing of Mie scattering and Rayleigh scattering as seemingly separate scattering processes. Actually, Mie scattering is the general framework here, while Rayleigh scattering can be derived from it in a particular limit.

I guess what is meant is that the scattering on molecules is only considered in the Rayleigh limit of Mie scattering, while for aerosols, a more general Mie approach is considered? Agreed?

The Mie particles scattering particles are considered to be the same as the light-absorbing particles, i.e. their scale heights are the same. It's quite possible that additional populations of particles or different density profiles will produce a more realistic representation, though the current simple atmosphere model shows promise for Titan.

--Chris

Before seeing what is really in your patch and what is missing, it's hard to make guesses, of course. One mentioned limitation of Bruneton's et al. approach is that the aerosol properties are assumed constant (for given altitude). In reality, they can change a lot depending on atmospheric conditions.

Fridger

[Chuft-Captain]

Good to see the DEVS incorporating some of Eric's techniques into Celestia. I've been impressed with his work ever since I first discovered his RAMA simulation a couple of years ago:
http://shatters.net/forum/viewtopic.php?p=103977#p103977

I was surprised however to see Fridger actually recommending a fictional work:

And last not least, a MOST beautiful video: Rendez-vous with Rama
3D animation of a spacecraft freely inspired from the book "Rendez-vous with Rama" from Arthur C. Clarke. Switch on your sound!

That's not your usual style Fridger !

[t00fri]

Good to see the DEVS incorporating some of Eric's techniques into Celestia. I've been impressed with his work ever since I first discovered his RAMA simulation a couple of years ago:
http://shatters.net/forum/viewtopic.php?p=103977#p103977

I was surprised however to see Fridger actually recommending a fictional work:

And last not least, a MOST beautiful video: Rendez-vous with Rama
3D animation of a spacecraft freely inspired from the book "Rendez-vous with Rama" from Arthur C. Clarke. Switch on your sound!

That's not your usual style Fridger !

Hey CC

well, my "soul" is a slightly more complex animal than what you might have anticipated ...

Actually in my youth I used to be a great SciFi fan and surely have read many of Arthur C. Clarke's novels. Unfortunately, the more I turned into a mature physicist during my (long) professional formation period, the more I recognized how much physical crap exists in this kind of literature. It simply takes a considerable knowledge about "how Nature works", before stupid contradictions can be avoided.

Thus, with time, I became considerably more critical towards many but not all SciFi tales.

In addition, when e.g. Celestia is concerned, I simply want fiction and scientific realism to be CLEARLY separated. Last not least, Eric Bruneton (and some of his INRIA fiends) are most talented computer graphics experts! It is just a pleasure to see what they have managed to achieve in the field of 3d visualization.

Fridger

[Chuft-Captain]

Actually in my youth I used to be a great SciFi fan and surely have read many of Arthur C. Clarke's novels. Unfortunately, the more I turned into a mature physicist during my (long) professional formation period, the more I recognized how much physical crap exists in this kind of literature. It simply takes a considerable knowledge about "how Nature works", before stupid contradictions can be avoided.

Thus, with time, I became considerably more critical towards many but not all SciFi tales.

I actually quite like hard science fiction such as some of Larry Niven's stories which are at least based on reasonably solid physics.
eg. 3 Hugo Award winning short stories:

"Neutron Star" .. about the effects of a close flyby of a neutron star on a spacecraft's occupants,
"The Hole Man"... murder story featuring a micro-black hole on Mars, ...
and "Inconstant Moon" .. a romance story set at the end of the world (with a twist).

Also not too bad, are:

"The Turing Option" ... about Machine Intelligence (by Harry Harrison and Marvin Minsky)
"Earth" by David Brin

... although these last 2 are both a little far-fetched and include some of the physical crap you so detest.

Have you read any of these?

In addition, when e.g. Celestia is concerned, I simply want fiction and scientific realism to be CLEARLY separated.

I tend to draw the distinction between fiction and scientific "feasibilty". ie. RAMA type structures and O'Neill cylinders as featured in Eric Bruneton's animation, though they don't currently exist, are not "fictional" per se, as it's been known ever since Gerard K. O'Neill's original 1970's studies that they could be built using 20th century science and engineering principles. (So they are "scientifically realistic")

Last not least, Eric Bruneton (and some of his INRIA fiends) are most talented computer graphics experts! It is just a pleasure to see what they have managed to achieve in the field of 3d visualization.

Yes it is. Very realistic renderings of water and reflections has been possible for many years, so this is nothing new, but it is very exciting to see this sort of thing being done in real time on desktop level hardware.

CC

ps. Sorry if this post is a little off-topic.

[ugordan]

Since the available CICLOPS raw images basically lack physics/hardware-based normalization, neither Matt McIrvin nor Gordan Ugarkovic can really know the truth. Matt carries a PhD in theoretical physics from Harvard. So no surprise that I tend to trust him . At least he must have had a thorough training in scientific methodology. Gordan is not a scientist by profession, while his imaging output has been indeed overwhelming. So no doubt about his imaging experience. I had my share of discussions with him about Mercury's colors...

I appreciate the compliments, but would like to point out one thing. The truth is there is no truth when it comes to color representation. Any color appearance, both in real life as well as on screen depend way too much on outside factors such computer screen specifics, color temperature, white balance, etc. It doesn't take a theoretical physicist from Harvard to realize that, nor does it really imply that person's color renditions are by default more "accurate" or "valid".

Scientific methodology doesn't cut it in a subjective a field as color reproduction whether one likes to accept that fact or not. One can have personal preferences, but calls to authority are irrelevant, IMHO. I can tell you my images are set to D65 sRGB white balance meaning the solar spectrum is divided out and matched for viewing on computer screens so white material (i.e. fresh ice) really turns out white on the screen. Using non-corrected whitepoint for solar illumination would otherwise make such ice yellowish because solar spectrum looks yellow to our eyes on the ground, partly due to the fact the total illumination coming down is solar spectrum + a good bit of Rayleigh-scattered blue sky color.

I would like to know the method Matt McIrvin uses because his results obviously differ from mine.

I also take exception to the claim "CICLOPS raw images basically lack physics/hardware-based normalization", I calibrate the PDS raw data just as CICLOPS does and have achieved consistent I/F calibrated results for the past several years, it's not some ad-hoc playing around with histogram-stretched, raw jpeg files. I did tweak my procedures and channel mixes a bit over the years to match my (higher color fidelity) experiments with VIMS spectrometer data, to compensate for the fact the ISS GRN filter is actually more yellow than green. That very fact also makes really "accurate" color representation from Cassini impossible for anything but bodies with flat spectra, and Saturn falls into that category only partially.

[ugordan]

Here's backlit Titan again, this time with Rayleigh scattering coefficients increased:

<cut>

There's now a visible bluish-purple fringe.

I quite like this version and would probably also increase the depth of the Rayleigh scattering layer, if possible. Is it possible to mix the two effects to get a more "creamy" color at high phase angle - a mix of normal orange color and blue scattering? A further obvious improvement would be to add the detached haze layer that also exhibits the same scattering color.

[t00fri]

Have you read any of these?

Actually, it has been a long time since I read the last SciFi novel. Honestly, I cannot even make a clearcut statement whether I read or didn't read any of the stories you listed. One main reason is that in German translations, the titles are usually quite different, since literal translations from English (or other languages) often don't sound good.

Certainly, in a bookshop, I would want to avoid SciFi stories that involve black holes or neutron stars, since you can bet that the author did not really understand their subtle underlying physics, unless he also happens to be a proven researcher in the field of General Relativity or similar. There are a few such positive exceptions, fortunately.

So many people, notably so-called "science writers, WEB journalists, etc", keep writing utter nonsense with lots of self confidence about these highly non-trivial "animals" . In this field it is certainly not enough to just click a few respective WEB pages and/or listen to "educational" TV broadcasts ...

In addition, when e.g. Celestia is concerned, I simply want fiction and scientific realism to be CLEARLY separated.

I tend to draw the distinction between fiction and scientific "feasibilty". ie. RAMA type structures and O'Neill cylinders as featured in Eric Bruneton's animation, though they don't currently exist, are not "fictional" per se, as it's been known ever since Gerard K. O'Neill's original 1970's studies that they could be built using 20th century science and engineering principles. (So they are "scientifically realistic")

Well, also in my proper research field, quite many proposals of future experiments, future space missions etc are made through conferences and seminars. A long time ago I have decided not to attend such talks anymore, where all perspectives of realistic financing and scheduling are lacking. That also applies to the RAMA type structures and O'Neill cylinders. Here I am mainly interested in the real time coding aspects (cf EBruneton...)

Fridger

[t00fri]

...
The truth is there is no truth when it comes to color representation.
...

Pleeeease, no lectures about basics in optics or rendering... I really don't need that as a Senior Scientist with a PhD in Theoretical Physics. . Above, I just used the term "truth" as a shortcut to refer to the apparent discrepancy between Matt McIrvin's and your rendering of backlit Titan. I thought this was obvious, ...sorry.

Scientific methodology doesn't cut it in a subjective a field as color reproduction whether one likes to accept that fact or not. One can have personal preferences, but calls to authority are irrelevant, IMHO.

As became evident also in our previous discussion about Mercury's colors, your respectable imaging work is actually a typical example for violating "scientific methodology". The latter implies first of all well documented procedural transparency and reproducability of the results by others (e.g. by the peers reviewing scientific work before publication in scientific journals!).

Given your vast output of color imaging as generated from raw data of space missions, good scientific methodology would require a concise documentation of ALL the corrections inherent in ALL your imaging results. Already in case of Mercury I asked you in vain to make the details of the many corrections public that you applied here and there to your imaging.

Only then, your images acquire scientific value besides (undisputed!) aesthetical beauty.

Perhaps I missed such a published documentation. If so I apologize, of course. Yet, from looking through a good part of your images on the web, I noticed many "on the fly" modifications within subsequent image "generations".

As a further illustration, you tell here in passing:

my images are set to D65 sRGB white balance, ..., I calibrate the PDS raw data just as CICLOPS does , ..., I did tweak my procedures and channel mixes a bit over the years to match my (higher color fidelity) experiments with VIMS spectrometer data, to compensate for the fact the ISS GRN filter is actually more yellow than green.

The net result is: You keep claiming that you got the best colors, since you have all relevant corrections included. Yet no-one is able to reproduce and also check the results from documented info AND the raw data.

So far concerning the background for my above remark about "scientific methodology". Every mature theoretical physicist -- including e.g. Matt McIrvin and myself-- has been tought over many years of professional formation the rules and virtues of "scientific methodology"! That's why I trust Matt in the first place, NOT because he got his PhD from Harvard

I would like to know the method Matt McIrvin uses because his results obviously differ from mine.

I wrote that I "trust him" and that I never went into compositing backlit Titan myself. So you will have to contact him and ask, if you are interested. I suppose he applied a quite simplistic procedure, since there was not much accompanying documentation. While such simplified and thus imperfect procedures are perfectly acceptable from a methodology point of view, more sophisticated and "accurate" ones (like yours) will require concise public documentation to have lasting value.

Fridger

[ugordan]

Given your vast output of color imaging as generated from raw data of space missions, good scientific methodology would require a concise documentation of ALL the corrections inherent in ALL your imaging results. Already in case of Mercury I asked you in vain to make the formulas public for the many corrections you applied here and there to your imaging.

Only if these are mady public, your images acquire scientific value besides (undisputed!) aesthetical beauty.

Perhaps I missed such a published documentation. If so I apologize, of course. Yet, from looking through a good part of your images on the web, I noticed many "on the fly" modifications within subsequent image "generations".

<cut>

The net result is: You keep claiming that you got the best colors, since you have all relevant corrections included.

I'm not claiming anything of the sort nor am implying that anywhere (if anything, I get the feeling your choices are implied to be the "best colors"). I'm just mildly amused you tend to dismiss my work on account of no meticulous documentation on my procedures, no scientific methodology, etc. yet are willing to accept another poster's image (and I mean absolutely no disrespect to him) as reference without questioning it whatsoever.

I wrote that I "trust him" and that I never went into compositing backlit Titan myself. So you will have to contact him and ask, if you are interested. I suppose he applied a quite simplistic procedure, since there was not much accompanying documentation. While such simplified and thus imperfect procedures are perfectly acceptable from a methodology point of view, more sophisticated and "accurate" ones (like yours) will require concise public documentation to have lasting value.

So, without actually also knowing anything about the way he produced his image, how does your "scientific methodology" arrive at "trusting him"? Is appeal to authority the scientific method?
Does that "trust" mean Chris should take your pick of choice and word for it? Otherwise why point out one of us has a doctorate from Harvard?

What data did Mr. McIrvin use to produce that composite, what calibration procedure, if any? How carefuly did he align the filters to eliminate inevitable color fringing at diffuse edges otherwise? You have no problem accepting it, yet you apparently question Chris' choice of image because it differs from that one, never mind the fact virtually all other reproduced Titan high phase images (including the bulk of CICLOPS ones) look more similar to my version than his. I don't have to contact him any more than you apparently didn't so I don't see why I should defend my work by a different standard.

I tend to shy away from posting anything here since the last "episode" about methodology, science, whatsoever, but this apparent double standard irked me to reply. And I still maintain that color is a subjective issue and depends upon viewing conditions, individuals, etc. If you really think there is a scientifically correct color for every scene, I have to say I think you're being naive. Even having piles of documentation on how you arrived at that representation is irrelevant.

Spectra are scientifically useful, applying scientific methodology when working with them is absolutely valid and noone is debating that. That goes for your optics knowledge and whatnot.
Color is a human, subjective representation of a spectra. The scientific method breaks down there. At most, it can determine how the majority of the people perceive that spectra in certain condidions, but it is not an absolute. Change the assumptions or change the viewing conditions and the whole approach is rendered moot.

[t00fri]

So, without actually also knowing anything about the way he produced his image, how does your "scientific methodology" arrive at "trusting him"? Is appeal to authority the scientific method?

I wrote it most explicitly already: it's the lack of documentation of all your imaging sophistication that creates a problem with accepted "scientific methodology". Noone wants to appeal to "authority".

Matt and I both underwent the same type of long theoretical physics training at excellent institutions. That naturally creates trust... That's about all I meant to say here. This doesn't mean that from today's point of view Matt's colors are more "accurate" visually. I think I never claimed that, despite trusting Matt's work in general.

When I questioned Chris about his orange backlit colors, I actually was (still) unaware of your Titan rendering. Only Chris' link made me look it up. Your imaging output is so large that it is hard to keep up with it

My relation to Matt's work is actually historical: Matt's color composition of backlit Titan to my knowledge was the first one available (Dec 2004): http://mmcirvin.livejournal.com/179356.html?mode=reply
Note that my tuning of the Mie parameters (before the present new efforts!) are similarly old!
Here is my old result. Nothing changed since.





Since Matt didn't add much info to his image, I guess that he just composed the three R,G,B filtered raw images (visual light) without adding any additional correction "magic". Assuming this is correct, his result may be eventually inaccurate, BUT the procedure was at least simple and transparent. I explicitly wrote above that Matt doesn't know the "truth" .

Since we were aware that Celestia's Mie atmospheres were physically incorrect/incomplete in many aspects, it wasn't worth going into big discussions about "scientific methodology" at the time. It was just encouraging that we managed to get the Titan atmosphere into a qualitatively correct behaviour. This was the purpose of my above matching exercise at the time.

But now we want to improve Celestia's atmospheres considerably by using recent work of Eric Bruneton et al., based on largely precomputed Mie atmospheres. One important new aspect is to eventually relate the underlying Mie parameters directly to observable quantities. The methodology aspect now also becomes a more central issue.

Does that "trust" mean Chris should take your pick of choice and word for it?

This remark I don't understand. Chris seems to trust your Titan atmosphere colors (see his posts) and at least used them for tuning the forthcoming patch he is working on. Eventually we will be sorting this issue out together. He is not a scientist and may have different criteria. As a longstanding co-author of Celestia, I did indeed add my share of "scientific methodology" to the official Celestia distribution during the last 8.5 years...

Fridger

[chris]

Currently, the scattering parameters are:

* Scale height for Rayleigh scattering molecules
* Scale height for Mie scattering aerosols
* Rayleigh scattering coefficients for three wavelengths (m^-1): 680nm, 550nm, and 440nm
* Mie scattering coefficient (m^-1)
* Absorption coefficients (m^-1): same wavelengths as for Rayleigh scattering
* Mie asymmetry parameter (g)

These are more or less identical to what we had previously. Right?

Almost. The current implementation in Celestia doesn't use different scale heights for Mie and Rayleigh scattering particles.

What I don't understand at this point is the listing of Mie scattering and Rayleigh scattering as seemingly separate scattering processes. Actually, Mie scattering is the general framework here, while Rayleigh scattering can be derived from it in a particular limit.

I guess what is meant is that the scattering on molecules is only considered in the Rayleigh limit of Mie scattering, while for aerosols, a more general Mie approach is considered? Agreed?

They are treated separately for pragmatic--not physical--reasons. Since the scattering table is 3D (or 4D, if you include the viewer-sun angle), it's crucial to keep the size of each element in the table as small as possible. In the simulation, Rayleigh scattering is wavelength dependent while Mie scattering is treated as wavelength independent. This permits storing the inscattering factors into a 64-bit texture element: 4 16-bit half precision floats, 3 for Rayleigh RGB, 1 for Mie. The wavelength dependence of Mie inscattering is approximated using the proportionality rule described in section 4 of Bruneton's paper. Without this little shortcut, we'd have to store to use a separate 3D texture for Mie inscattering. The scattering shaders also perform better if we can use the simple (1+mu^2) phase function for the Rayleigh scattering rather than the more general Cornette-Shanks.

Before seeing what is really in your patch and what is missing, it's hard to make guesses, of course. One mentioned limitation of Bruneton's et al. approach is that the aerosol properties are assumed constant (for given altitude). In reality, they can change a lot depending on atmospheric conditions.

Yes, the whole approach of precomputed scattering tables relies on spherical symmetry. Without it, we have to resort to volume tracing.

--Chris

[t00fri]

These are more or less identical to what we had previously. Right?

Almost. The current implementation in Celestia doesn't use different scale heights for Mie and Rayleigh scattering particles.

What I don't understand at this point is the listing of Mie scattering and Rayleigh scattering as seemingly separate scattering processes. Actually, Mie scattering is the general framework here, while Rayleigh scattering can be derived from it in a particular limit.

I guess what is meant is that the scattering on molecules is only considered in the Rayleigh limit of Mie scattering, while for aerosols, a more general Mie approach is considered? Agreed?

They are treated separately for pragmatic--not physical--reasons. Since the scattering table is 3D (or 4D, if you include the viewer-sun angle), it's crucial to keep the size of each element in the table as small as possible. In the simulation, Rayleigh scattering is wavelength dependent while Mie scattering is treated as wavelength independent. This permits storing the inscattering factors into a 64-bit texture element: 4 16-bit half precision floats, 3 for Rayleigh RGB, 1 for Mie. The wavelength dependence of Mie inscattering is approximated using the proportionality rule described in section 4 of Bruneton's paper. Without this little shortcut, we'd have to store to use a separate 3D texture for Mie inscattering. The scattering shaders also perform better if we can use the simple (1+mu^2) phase function for the Rayleigh scattering rather than the more general Cornette-Shanks.

Before seeing what is really in your patch and what is missing, it's hard to make guesses, of course. One mentioned limitation of Bruneton's et al. approach is that the aerosol properties are assumed constant (for given altitude). In reality, they can change a lot depending on atmospheric conditions.

Yes, the whole approach of precomputed scattering tables relies on spherical symmetry. Without it, we have to resort to volume tracing.

--Chris

Thanks, your explanations fit well with my own views at this point. Approximations are fine so long as they have some physical justification. I think they are done quite clevely in Bruneton's et al. approach.

Fridger

[chris]

Here's backlit Titan again, this time with Rayleigh scattering coefficients increased:

<cut>

There's now a visible bluish-purple fringe.

I quite like this version and would probably also increase the depth of the Rayleigh scattering layer, if possible. Is it possible to mix the two effects to get a more "creamy" color at high phase angle - a mix of normal orange color and blue scattering? A further obvious improvement would be to add the detached haze layer that also exhibits the same scattering color.

Increasing the height of the Rayleigh scattering layer is simple to do. As for getting a less saturated color at high phase angles, that may naturally result from deeper Rayleigh layer. I'll try some experiments...

As for the detached haze layer, it should be possible to create it by using some distribution of Rayleigh scattering particles that has a peak at the height the haze. However, the precomputed scattering tables that I'm experimenting with require that the atmosphere be spherically symmetric, i.e. the particle distribution varies with altitude, not longitude or latitude. So, the haze layer would It would appear as a perfectly circular blue halo around Titan. I'm not convinced that it's worth adding detached haze unless we can also find a way to simulate the irregularities seen in Cassini and Voyager images of the moon.

--Chris