[math-fun] Anti-aliasing photo detector arrays
Fujifilm has a square 6x6 RGB detector array pattern which is claimed to be better than the standard "Bayer" RGB pattern in eliminating Moire patterns: http://upload.wikimedia.org/wikipedia/en/thumb/f/ff/Xtranscolourfilter.svg/2... http://en.wikipedia.org/wiki/Fujifilm_X-Pro1 One additional interesting feature of this array is the slightly different % of RGB: 20 G's, 8 R's, 8 B's (56%, 22%, 22%) The more traditional "Bayer" pattern has 2 G's, 1 R, 1 B (50%, 25%, 25%) http://en.wikipedia.org/wiki/Bayer_filter This Fujifilm pattern would probably be better for large electronic displays than for sensors, because the pixels are so obvious. Both Bayer & Fujifilm patterns can be extended with 2 different Greens: G1 & G2, which gives better coverage of the color spectrum. Question: wouldn't some of the aperiodic/quasicrystal tiling patterns work even better for these purposes?
Yes, it looks like a very good camera, well, here is a thumbnail rule, the max ISO for the device is related to the price max ISO/3 = price in USD for the basic camera, ouch. Talking of light related matters, here is one problem, nowaday, there are very powerful lasers that can cut through just about anything, I was thinking Suppose we have an apparatus of many lasers or maybe one reflected laser in such a way to produce an envelope of a curve, for example a caustic, the question being : can we arrange some lasers this way to actualy sharpen a knife 'perfectly' ? the thing is : what would be the perfect geometrical shape of a steel blade for example that would be perfect for cutting let's say vegetables or meat ? Is there a known geometry for what would be the perfect blade ? We know that there are those japanese sabre that are very good but they are made of many 'plys' of steel like 32768 since they fold the blade 15 times to produce a particular shape which is optimal in this case. Is there a definite geometric argument for this ? Best regards, Simon Plouffe
Interesting questions. Japanese sword steel (which may have incorporated technology from the Middle East and/or India) is basically a composite material which is layered from hard iron & soft steel. The hardness comes from the hard iron, while the soft steel supports the hard iron to keep it from breaking. Think of plywood, except with alternate layers of hard iron & soft steel. I don't know the ideal shape for a cutting implement, and this ideal shape may vary depending upon what material it has to cut through, but I would imagine that Japanese swords are probably pretty close to the ideal shape for their intended purpose, since non-ideal sword owners tended not to live very long! In order to cut a tomato, which has a relatively tough skin covering a very delicate almost-liquid inner portion, the blade has to quickly pierce the skin without bruising the tomato. After the blade pierces the skin, the sides of the blade can't adhere to the skin, which may require some sort of wax or teflon on the side of the blade. At 08:13 AM 2/3/2013, Simon Plouffe wrote:
We know that there are those japanese sabre that are very good but they are made of many 'plys' of steel like 32768 since they fold the blade 15 times to produce a particular shape which is optimal in this case. Is there a definite geometric argument for this ?
I think the folding is more related to making the iron into steel (back in the days before they had good techniques for doing this) than to the gross geometry of the blade. Charles Greathouse Analyst/Programmer Case Western Reserve University On Sun, Feb 3, 2013 at 11:13 AM, Simon Plouffe <simon.plouffe@gmail.com>wrote:
Yes, it looks like a very good camera,
well, here is a thumbnail rule, the max ISO for the device is related to the price
max ISO/3 = price in USD for the basic camera, ouch.
Talking of light related matters, here is one problem,
nowaday, there are very powerful lasers that can cut through just about anything, I was thinking
Suppose we have an apparatus of many lasers or maybe one reflected laser in such a way to produce an envelope of a curve, for example a caustic,
the question being : can we arrange some lasers this way to actualy sharpen a knife 'perfectly' ?
the thing is : what would be the perfect geometrical shape of a steel blade for example that would be perfect for cutting let's say vegetables or meat ? Is there a known geometry for what would be the perfect blade ?
We know that there are those japanese sabre that are very good but they are made of many 'plys' of steel like 32768 since they fold the blade 15 times to produce a particular shape which is optimal in this case. Is there a definite geometric argument for this ?
Best regards,
Simon Plouffe
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Why not simply skip the blade & use the laser for cutting? (I was involved in one of the first tests of using lasers for cutting wool in the clothing industry. Yes, everything smelled like burnt hair!) I would imagine that the ideal laser would be at a wavelength/frequency/color such that the photons would have just the right amount of energy to disrupt the chemical bonds of the material being cut. If there are multiple types of bonds, then perhaps the laser would have to have multiple "colors". At 08:13 AM 2/3/2013, Simon Plouffe wrote:
nowaday, there are very powerful lasers that can cut through just about anything, I was thinking
Suppose we have an apparatus of many lasers or maybe one reflected laser in such a way to produce an envelope of a curve, for example a caustic,
the question being : can we arrange some lasers this way to actualy sharpen a knife 'perfectly' ?
the thing is : what would be the perfect geometrical shape of a steel blade for example that would be perfect for cutting let's say vegetables or meat ? Is there a known geometry for what would be the perfect blade ?
* Henry Baker <hbaker1@pipeline.com> [Feb 03. 2013 19:48]:
Why not simply skip the blade & use the laser for cutting?
(I was involved in one of the first tests of using lasers for cutting wool in the clothing industry. Yes, everything smelled like burnt hair!)
That was infrared, right? Because ...
I would imagine that the ideal laser would be at a wavelength/frequency/color such that the photons would have just the right amount of energy to disrupt the chemical bonds of the material being cut. If there are multiple types of bonds, then perhaps the laser would have to have multiple "colors".
Ultraviolet does what you want, just better. I once visited a company called "Lambda Physics" (IIRC), they had exactly that. They showed a video of writing put on the head on a match. It did not ignite! Could write on glass without any remnant stress caused by heating (chemical disintegration cause the frosting). Had a 50W (pulsed "continuous" operation) UV laser plus a set of lenses, all you could see was that elongated pulsating (noisy!) blue flash about 40 centimeters from the laser, 5cm long. Boy's toys at its very best (OK, explosives aside). (Sadly the 800W equivalent was out of operation when I was there ...)
At 08:13 AM 2/3/2013, Simon Plouffe wrote:
nowaday, there are very powerful lasers that can cut through just about anything, I was thinking
Suppose we have an apparatus of many lasers or maybe one reflected laser in such a way to produce an envelope of a curve, for example a caustic,
the question being : can we arrange some lasers this way to actualy sharpen a knife 'perfectly' ?
Put them into the required angle and happyly burn away?
the thing is : what would be the perfect geometrical shape of a steel blade for example that would be perfect for cutting let's say vegetables or meat ? Is there a known geometry for what would be the perfect blade ?
I'd need a definition of "perfect" here (this will depend on material of knife and material to be cut, optimality conditions for the cut, cutting techniques actually used (there are a *lot*), and probably much more, so I suggest to not even try). Best, jj
Yes, the cutting was done primarily with heat. That experiment was a failure, because there was no way to get rid of the smell after the cutting was done. At 11:13 AM 2/3/2013, Joerg Arndt wrote:
* Henry Baker <hbaker1@pipeline.com> [Feb 03. 2013 19:48]:
(I was involved in one of the first tests of using lasers for cutting wool in the clothing industry. Yes, everything smelled like burnt hair!)
That was infrared, right?
"SP" == Simon Plouffe <simon.plouffe@gmail.com> writes:
SP> the question being : can we arrange some lasers SP> this way to actualy sharpen a knife 'perfectly' ? SP> the thing is : what would be the perfect geometrical SP> shape of a steel blade for example that would be perfect SP> for cutting let's say vegetables or meat ? Is there a SP> known geometry for what would be the perfect blade ? The profile of the katana's blade os of two round curves meeting at a sharp point. This differs from the typical euro blade which was sharpened to a 90 degree corner. The round profile is said to keep the edge from blunting in use. I have no idea what curve best matches the best-sharpened katana. I beleive there are only one or two families left passing down the sharpening technique. (The above data was all learned from documentaries, most recently including episodes of Modern Marvels and How Its Made. One hopes that they were reasonably accurate.) -JimC -- James Cloos <cloos@jhcloos.com> OpenPGP: 1024D/ED7DAEA6
participants (5)
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Charles Greathouse -
Henry Baker -
James Cloos -
Joerg Arndt -
Simon Plouffe