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midtskogen
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30 May 2018 21:58

Yes, maybe we need an "optimal climate" thread.  It sounds like what you want is the dewpoint to be fairly stable throughout the year, and to that I agree.  I prefer the dewpoint to stay below 10 °C and above 15 it's really uncomfortable.  It shouldn't be too low either.  If the dewpoint goes below -20 °C outside, all sorts of problems with static electricity and itchy skin become very annoying.  A year-round dewpoint of -5 °C would be ideal, if I had to pick a single point.
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Watsisname
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03 Jun 2018 00:55

At the very center of every shadow, lies a small point of light.

Well, that's almost never true.  But it actually can be true if you have the right conditions. If the object is sufficiently circular and smooth, illuminated with rays of sufficiently parallel light, then the center of the shadow does in fact contain a bright spot.  The spot is caused by the diffraction of light around the edge of the object, constructively interfering at the center, and destructively interfering almost everywhere else.  It is a powerful demonstration of light's wave-like property, and there is a neat history behind how it was first theorized and experimentally proven.

Nowadays this experiment is not too difficult to do using lasers, and I really wanted to try it using our lab equipment.  We used a laser and spatial filter to expand and clean up the beam (there are significant artifacts introduced by imperfections in the laser and dust on the lens, which made the spot impossible to see otherwise), and a common Canadian coin to cast the shadow.  It was surprisingly beautiful in person and my photograph doesn't really do it justice.  There is also a bright diffraction maximum around the edge of the shadow which was very brilliant to the eye.

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FastFourierTransform
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03 Jun 2018 03:45

The first time I heard of it at university I was staggered. Is such a mental break for our intuition...
If you were at the Arago spot looking at the coin you would see light of the source behind it even if that coin is blocking straight light rays. Its just incredible.
 
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03 Jun 2018 04:41

Yes, it's such a counter-intuitive thing.  That what you would expect to be the darkest part of a shadow actually ends up being the brightest, and in theory can be as bright as if the object were not even there!


FastFourierTransform wrote:
Source of the post If you were at the Arago spot looking at the coin you would see light of the source behind it even if that coin is blocking straight light rays.

Speaking of which... :)

I just repeated the experiment again at home, using my 120mW green laser and a ridiculous improvised setup.  Actually I wasn't really expecting this to work but it ended up working quite well.  And I was also very curious to see what it would look like from inside the spot.  The spot intensity would have been low enough to be eye safe, but the surrounding beam was definitely not, even after being expanded, so I did not dare try to view it directly.  But I figured it would be safe enough for the camera.  It was, and it's gorgeous:




Picture of the spot I obtained this time.  Some other interesting diffraction effects show up at the bottom corners due to how I support the coin.  I think the diffraction rings around the shadow also came out really nicely here.

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03 Jun 2018 05:51

Watsisname wrote:
Source of the post And I was also very curious to see what it would look like from inside the spot.

Just spectacular. Really impressive. It resembles Baily's beads in a solar eclipse (just that is a completely different phenomenon). The experimental setup was done by trial and error or you started with some calculations?
Here I found another example of what you did.



Now I'm wondering if this can be generated naturally in a planetary scale. I mean, during a lunar eclipse this can't be because the Sun is far from a point-like source and we are probably to close to the moon for the diffraction to occur. But I'm wondering (too lazy today for the calculations) if there are places where this configuration can be accomplished. If we use a luminous star or maybe the light comming from an accreting black hole then we can get extremely far away and still have a lot of light (maybe a neighbouring stellar system) while keeping the angular size of the source sufficiently small (point-like). Then a planet with a round moon at large distances from the planet could have some eclipse shadow with an arago spot inside?
 
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03 Jun 2018 09:54

Wow, that video is spectacular too!

For what I did no calculation was needed; the effect is fairly independent of the size of the object casting the shadow, or the distance behind it that you project it to.  I passed the laser through a magnifying glass so that the beam would be expanded (past the focal point) to a few times the size of the coin after a few meters, and then placed the coin in the beam and projected the shadow.  The spot begins to become visible in the middle of the shadow not too far beyond the coin -- a few meters.  You'd be surprised how quickly the spot can form afterward, since the light can actually spread perpendicularly to its direction of travel!  Every point on the wavefront essentially acts as a source of new spherical wave fronts. 

It is important that the surface of the object casting the shadow be very smooth.  A coin with ridges, like the US quarter or dime, does not work.  A spherical object like a marble will work (it's the profile seen by the incoming wave fronts that matters).  

I thought as well about whether the effect could occur in eclipses.  For the Earth and Moon, the biggest problem is that the lunar surface is too rough.  We can use the equations from the wikipedia page to check.

Assuming parallel rays of light (which is fairly true of the Sunlight), Arago's spot will form if:
1) [math]
2) [math]

For Moon casting the shadow, eq 1) imposes the condition that the observer must be less than a few thousand light years away.  No problem.

Eq 2) imposes the condition that, for Earth being about 360,000km away during total eclipse, then to form a spot on it the Moon's roughness must be less than about 50 micrometers.  Absurdly smooth... this is the real reason why we don't see the effect in solar eclipses, or anywhere else in the solar system.  (And a good thing, too, or else it would greatly interfere with viewing the Sun's corona). :)

For comparison with the coin (diameter ~ 1cm, spot projection distance ~4m), the maximum size for roughness is about 0.1mm.  Very reasonable for a coin.


What would it take to view a natural Arago/Fresnel/Poisson spot from a celestial body?  Perhaps it happens in wide binary systems containing a cool neutron star (although the cooling time of a neutron star might be an issue).  Neutron stars have a radius of about 10km and, using the maximum terrain height formula, can probably have surface features of up to about 1mm high.  Assuming the partner star is sufficiently far away to act as a point source, how far must the viewer be from the neutron star to see the spot in the shadow?  Solve eq 2) for [math] and plug and chug, and it's 40,000km.  Again reasonable, and could work with a sun-like star ~100AU away.


One last experiment I tried was to use a non-circular coin.  I tried the Canadian 1-dollar Loonie.  It does not produce Arago's spot.  However, because edge is still smooth and regular (11-sided), it does produce a really neat interference pattern: an 11-sided star, although only 9 points are visible here due to obscuration.  

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midtskogen
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03 Jun 2018 13:36

Bigger scale (aragoscope):
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03 Jun 2018 16:55

Made a short game in RPG Maker MV using some screenshots from Space Engine. The game was for a one map challenge going on in the RPG Maker community forums.I mentioned Space Engine in the credits so anyone who plays would know about it.

My game's page on ITCH.IO
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FastFourierTransform
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04 Jun 2018 04:58

Watsisname wrote:
Source of the post What would it take to view a natural Arago/Fresnel/Poisson spot from a celestial body?  Perhaps it happens in wide binary systems containing a cool neutron star (although the cooling time of a neutron star might be an issue).  Neutron stars have a radius of about 10km and, using the maximum terrain height formula, can probably have surface features of up to about 1mm high.  Assuming the partner star is sufficiently far away to act as a point source, how far must the viewer be from the neutron star to see the spot in the shadow?  Solve eq 2) for l and plug and chug, and it's 40,000km.  Again reasonable, and could work with a sun-like star ~100AU away

That is a wonderfull sight. I didn't thought about roundness. I suppose that the neutron star has to be a very slow rotator also (something that would make sense if it has been there for the time needed to cool down to be a nearly black object) to avoid the spreadding of Arago's spot due to the shape of the object.
That said, I think a farther away source would be preferable. A sun like star would be very very dim at 100 AU but a blue star located in a nearby system would be brighter and still point-like. Also, the formation of a wide binary that has a component so old that has cooled down to blackness and a companion in the main sequence (or any fusion burning stage) seems quite improbable, both would have completely different origins with that difference in age.
For the distance of the planet (the screen where we want to project the shadow and Arago's spot) it could be much closer to the neutron star. Gravitational lensing could play a huge rol here, diffracting light even further to the gravitational focus of the neutron star. If I'm correct, that would make the shadow of the eclipse shrink and the arago spot to be much more concentrated and bright. If too far away, the planet might don't have even the eclipse shadow (if it is farther away from the gravitational focus in the moment of alignment they would see a bright Einstein ring and not complete darkness). I wonder if this conditions make the distance between the neutron star and the planet too short for this to happen (roche limit short).
If this is possible, I wonder if this configuration is going to take place even once, somewhere, across the entire history of the Universe. It would be a very very very delicate and exclusive event to witness.
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Since I'm speculating a lot and doing nothing to have at least some order of magnitude I want to talk also about another optical system of astronomical scale I have been thinking about: Single-slit diffraction using planets. I think this is impossible but maybe someone has an idea as to how. Two planetary objects could align to make a single slit from the perpective of a third using a star as a source. The alignment would be extremely serendipious and the duration would be very brief. Would there be an instant (just before the two shadows make contact) on which a difraction pattern could be projected in the "screen planet"? I suppose this is impossible because of the distances involved and the necessity of a separation in the order of the wavelengths of visible light. Also, the planets that make the slit should be in the same plane right? We would need them to collide? I think this is obviusly absurd but just to make a little brainstorming about it.
Here I have the two planets been bombarded with low frequency radio waves. Put the Color Scheme 3 and watch as the waves interfere with themselves. There is a difraction pattern emerging to the left. These are radio waves so nothing to do at all with the optical phenomena I'm searching for.



Another interesting topic could be that of rings as diffraction gratings. Periodic 100-meter scale patterns have been observed in Saturn's rings. These patterns can be viewed as diffraction gratings for radio waves. Something that has been detected using Cassini. I wonder if there could be a situation on which colourfull difraction patterns emerge in the visible range near planetary rings. I suppose this is absurd also since there would have to be some periodicity in ring structure with repetitions every 0.1 micrometers, and even the grains themselves are too large for that. But hey, an interesting idea, and also interesting to see that in the radio range.
 
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05 Jun 2018 13:50

I'll show my ship (the Charioteer) when I figure out how to get it to convert it's files.
I'm good when it comes to Physics, Algebra, Relativity, Space, and SpaceEngine. But I could still use a LOT of help on the things I still don't know. So I hope I get a lot of help on how all that works, here!

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