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New Camera Sensor Filter Allows Twice As Much Light
bugnuts writes "Nearly all modern DSLRs use a Bayer filter to determine colors, which filters red, two greens, and a blue for each block of 4 pixels. As a result of the filtering, the pixels don't receive all the light and the pixel values must be multiplied by predetermined values (which also multiplies the noise) to normalize the differences. Panasonic developed a novel method of 'filtering' which splits the light so the photons are not absorbed, but redirected to the appropriate pixel. As a result, about twice the light reaches the sensor and almost no light is lost. Instead of RGGB, each block of 4 pixels receives Cyan, White + Red, White + Blue, and Yellow, and the RGB values can be interpolated."
"We've developed a completely new analysis method, called Babinet-BPM. Compared with the usual FDTD method, the computation speed is 325 times higher, but it only consumes 1/16 of the memory. This is the result of a three-hour calculation by the FDTD method. We achieved the same result in just 36.9 seconds."
What I don't get is calling the FDTD (finite difference time domain) analysis as the "usual" method. It is the usual method in fluid mechanics. But in computational electromagnetics finite element methods have been in use for a long time, and they beat FDTD methods hollow. The basic problem in FDTD method is that, to get more accurate results you need a finer grids. But finer grids also force you to use finer time steps. Thus if you halve the grid spacing, the computational load goes up by a factor of 16. It is known as the tyranny of the CFL condition. The finite element method in frequency domain does not have this limitation and it scales as O(N^1.5) or so. (FDTD scales by O(N^4)). It is still a beast to solve, rank deficient matrix, low condition numbers, needs a full L-U decomposition, but still, FEM wins over FDTD because of the better scaling.
The technique mentioned here seems to be a variant of boundary integral method, usually used in open domains, and multiwavelength long solution domains. I wonder if FEM can crack this problem.
sed -e 's/Chuck Norris/Rajnikant/g' joke > fact
Seriously this was in the rags...months ago...not news now.
I've been hoping for 4-sensor cameras for ages. People only have three color sensors, but what those colors are vary a bit from person to person, and capturing 4 colors stands a better chance of getting images that look good for everyone.
This is a really cool new tech. Wonder when it will make it into consumer cameras? Also, could have done without the Gizmodo link - the third link is sufficient to get the information without giving click traffic to those whores.
Realistically light is not made up of R G & B, but humans see light (mainly) in those three wavelengths. As humans we can't tell the difference between light at one specific (within reason) frequency vs a mixture of colours making the same average frequency. How long do you think until we have technologies that can both capture and reproduce imagery made with more than 3 or 4 colour samples?
Why does this matter? Until things improve other animals are still going to think our photos look weird. Oh an the gamut of photos sucks, but really, while birds are judging the posters on my wall poorly I can't care about anything else.
Foveon has 3 photodiodes per pixel, and theoretically should have the most accurate colors and sharpness by avoiding moire and interpolation issues with bayer filters. In practice, though, a lot of light is lost by the time it reaches the 3rd photodiode.
There is indeed white light because not every pixel has a filter over it. Many pixels pass the light through a hole to the pixel, while a neighbor pixel funnels red light (e.g.) to it. Thus, you get white + 1/2 the neighbor's red. You also get half the neighbor's red on the other side, resulting in white + red for the three pixels in a line.
Cyan is part of the color spectrum as a "subtractive color". What remains under each neighbor pixel when you strip away the red, is the cyan.
From what I can tell, this will not get rid of the need for the anti-aliasing.
...we've switched from calculating rggb values based on attenuated rggb values sensed, to calculating rgb values from sensing cyan (usually a color of reflected light with red subtracted, white+blue ?, white+red ?, and yellow (again reflected white light minus the blue spectral light.)
I can see the resulting files having better print characteristics, if the detectors sense to the levels close to the characteristics of ink used for prints, but I don't think that's going to help at the display the photographer will be using to manipulate the images.
And of course neither variety of photo image capture is comparable to the qualities of light that our rods and cones respond to in our eyes.
You never know...
Remember how the Foveon X3 sensor was supposed to revolutionize digital photography and make the standard sensors obsolete? Tell me how many cameras you've used with those sensors in them.
In other words, technological superiority doesn't always win in digital photography.
Damn_registrars has no butt-hole. Damn_registrars has no use for a butt-hole.
In other words, technological superiority doesn't always win in digital photography.
This is very true, although the Foveon was superior in resolution and lack of color moire only - it terms of higher ISO support it has not been as good as the top performers of the day.
But the Foveon chip does persist in cameras, currently Sigma (who bought Foveon) still selling a DSLR with the Foveon sensor, and now a range of really high quality compact cameras with a DSLR sized Foveon chip in it. (the Sigma DP-1M, DP-2M and DP-3M each with fixed prime lenses of different focal lengths)
I think though that we are entering a period where resolution has plateaued, that is most people do not need more resolution than cameras are delivering - so there is more room for alternative sensors to capture some of the market because they are delivering other benefits that people enjoy. Now that Sigma has carried Foveon forward into a newer age of sensors they are having better luck selling a high-resolution very sharp small compact that has as much detail as a Nikon D800 and no color moire...
Another interesting alternative sensor is Fuji with the X-Trans sensor - randomized RGB filters to eliminate color moire. The Panasonic approach seems like it might have some real gains in higher ISO support though.
"There is more worth loving than we have strength to love." - Brian Jay Stanley
"From what I can tell, this will not get rid of the need for the anti-aliasing."
You ALWAYS need antialiasing when you discretize.
Simply use three sensors and a prism. The color separation camera has been around for along time and the color prints from it are just breath taking. Just use three really great sensors then we can have digital color that rivals film.
Check out the work of Harry Warnecke and you will see what I mean.
Hey KID! Yeah you, get the fuck off my lawn!
All the colors are in the color spectrum. Cyan is between green and blue. About 500 nm wavelength.
"You ALWAYS need antialiasing when you discretize."
That's my motto!
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Interesting comments from both, but I believe you both missed the point. The real question is, which one of these methods, FDTD or FEM-FD, will allow optimal reprocessing in the frequency domain that makes my dinner look prettier with an Instagram vintage filter?
Neither brown, black, nor white are in the color spectrum.
http://en.wikipedia.org/wiki/Spectral_color
"there is no cyan in the color spectrum"
You might want to open your eyes and look in the 490–520nm range on a representation of the visual range of the EM spectrum.
Still waiting on Serviscope_minor to wake up to fucking reality and realize that Jessica Price isn't going to fuck him.
Twice as much light equals one f stop. Significant, but not game changing.
Why not do it like the human eye does it: most sensor cells are only highly sensitive general censors with relatively infrequent color sensors in the mix. It seems the brain does fine with "spotty" color coverage.
Table-ized A.I.
quantize
Is that one of those colors only women can see? Like mauve?
We used to have a Bill of Rights. Now, with the rights gone, all we have left is the bill.
"From what I can tell, this will not get rid of the need for the anti-aliasing."
You ALWAYS need antialiasing when you discretize.
I think the word you are looking for is "quantize"
When working with designs meant for screen printing, the original artwork was done in RGB, then a team would separate the color channels (in Photoshop), one channel per ink to be used. They could technically do CMYK directly, but it didn't look good for a wide variety of purposes -- you can imagine a flat-filled cartoon character would be pretty much impossible. It would look a bit like comic book halftoning, probably. The shop would use that when they wanted to print Thomas Kincaide-esque sweatshirts for grannies. They would also use additional channels for things that weren't colors, like adhesive (for foil, usually) and clear inks.
I don't imagine that having more than three or four color channels is a new thing, or difficult to deal with. I would imagine even the prosumer technology would allow you to choose between various rendering intents. Probably the color separation is handled at the driver or device level, but TIFF, PDF, and DCS 2.0 (??) should handle extra channels natively.
A few more details on screen printing for those who might care: The actual screen printing process was not computer-controlled as a rule. The smaller shops I worked at printed a transparency which was transferred onto the screen by a photographic process, but the large one had a computer-controlled airjet "printer" that would knock out the design. Usually they would do a few samples by hand, to work out what ink and screen combination to use (different mesh sizes and ink thicknesses produce slightly different effects), and adjust finer details like when you would "flash" the shirt. That is, hitting it with a very high powered xenon lamp for a few seconds to dry the ink, before applying a new layer. You could do some interesting painterly effects with wet-on-wet ink; you can also make a hell of a mess that way. Flashing also tends to affect the color somewhat, especially for temperature-sensitive inks. After you get a few good samples, you send them off to the client as a proof. Then you would set up your automatic press for a run of a couple hundred. Color balance was something that the press operator kept an eye on after that point. After printing, the shirts are sent through a 400 degree open oven on a conveyor belt, for perhaps 10-20 seconds, to cure the ink.
Very fun job, the ink is messy as hell. I would still be doing it, but working with computers pays better.
Those who advocate genocide deserve every protection afforded by law, and none afforded by common human decency.
Discretising is just quantising in the spacial domain!
This is very true, although the Foveon was superior in resolution and lack of color moire only
Foveon is only superior in resolution if the number of output pixels is the same. But if you count photosites, i.e. 3 per pixel in a Foveon, then Bayer wins. A Foveon has about the same resolution as a Bayer with twice the pixel count, but the Foveon has three times the number of photosites.
But the problem is colors.
Foveon has a theoretical minimum color error of 6%. Color filter sensors (eg. Bayer) have a theoretical minimum error of 0%. Color filter sensors can use organic filters that are close to the filters used by the human eye. Foveon is based on the filtering effect of metals. In addition, there is significant overlap between the sensitivities of the three layers (a red photon may excite any of the three layers, for example). This leads to metamerism, where two colors perceived the same to the human eye will look like two different colors to a Foveon, or vice versa. Good luck matching makeup to clothes for a fashion shoot.
In addition, the Foveon has horrible effects when colors clip. If you shoot a bright red flower and the red is overexposed, it will "blow out". On a Bayer sensor this looks like a very red flower. The detail might be gone and it's not pretty, but it's red. On a Foveon it turns grey. The image processor tries to fix this, but even that's a recent advancement.
The sad thing about the Foveon is that it would make a great video sensor. It has good on-chip binning and could do live-view or movies long before anyone else could. Sigma threw away this competitive advantage.
boldly going forward, 'cause we can't find reverse
Magenta?
Tedious Bloggy Stuff - hooray?
a 3-ccd camera has awful color rendition.
The extra space between lens and sensor also makes for worse lenses (wide-angle at least, telephotos don't care).
boldly going forward, 'cause we can't find reverse
Actually you'd see those too and more if you took out the part of your eyeball that filters out UV and a few other wavelengths.
Still waiting on Serviscope_minor to wake up to fucking reality and realize that Jessica Price isn't going to fuck him.
Magenta is a combination of colours just like white isn't "in the colour spectrum".
Indigo/violet however is in the spectrum but as it's outside of the range of values which can be created with red green and blue we approximate it using magenta which is a mixture of blue and red.
Slashdot, can I buy this RIGHT NOW? No? Then wake me up when I can.
"From what I can tell, this will not get rid of the need for the anti-aliasing."
Which was not the goal, nor is it a goal of a Foveon sensor. Aliasing exists whenever there is frequency content greater than a sensor can handle.
"Foveon has 3 photodiodes per pixel, and theoretically should have the most accurate colors and sharpness by avoiding moire and interpolation issues with bayer filters."
Foveon does not promise more accurate colors. Sharpness is a function of a number of things, not just photosite layout. Foveon is a loser in the market because it doesn't perform.
Not when you can handle all frequencies that you will encounter. There are cameras on the market without anti-aliasing filters. When you stop down enough your aperture limits resolution to potentially less than the aliasing limit anyway.
If you signal is already low pass filtered you don't need to low pass filter it. Sure, I'll give you that. You've still got antialiasing, you're just not doing it with a piece of glass.
Why is RGB used for filtering at all? Wouldn't it be better to use the inverse (i.e., CMY or no-red, no-green, no-blue) instead? Wouldn't that allow twice as much light to pass through? I must be missing something obvious, someone care to explain what I am missing here?
My karma ran over your dogma
That's "SPATIAL domain"!
Uhh...you insensitive clod?
"To be fair, I was left completely unsupervised." ~Anon
Foveon is only superior in resolution if the number of output pixels is the same.
That is a pretty bad way to measure things, because it ignores things like color moire and other artifacts you get with bayer sensors. As I stated, resolution is not everything. And a Foveon chip delivers a constant level of detail, whereas a bayer chip inherantly will deliver levels of detail that vary by scene color.
In a scene with only red (say the hood of a red car) you are shooting with just 1/3 of the camera sensors capturing detail when you shoot with a bayer chip. So the red flower you are about to bring up is converting your 30MP bayer camera into a 7.5 MP camera. This is easy to see when you shoot a color resolution chart.
But the problem is colors.
The solution is Foveon, which has more accurate colors overall and treats all colors equally in terms of capturing detail.
This leads to metamerism, where two colors perceived the same to the human eye will look like two different colors to a Foveon,
In nine years of shooting with Foveon sensors I have never once seen that happen. In nine years of seeing people like you claim that none have ever been able to show a single image that exhibits this effect.
That's the problem with people that live in a world of theory vs. understanding what cameras can (and cannot) do by shooting them. Instead you pretend you understand what they will do because of your THEORY of how they will work, compared to the real world where the whole camera is a series of many different components and software, any one of which may compensate for issues that arise in one part of the system.
If you shoot a bright red flower and the red is overexposed, it will "blow out". On a Bayer sensor this looks like a very red flower.
Sorry but it goes pink regardless of camera.
Again, if you shot real cameras instead of just leaning on theory you would understand this.
The sad thing about the Foveon is that it would make a great video sensor.
In reality all of the strengths of the Foveon chip do not matter in video, bayer works well there because of inherent color and detail smoothing helping in a scene with motion. That's why it has never been considered seriously for consumer video applications (it has some place in scientific video capture).
"There is more worth loving than we have strength to love." - Brian Jay Stanley
There is really also no "R" in the color spectrum; anything a digital camera captures is going to involve measuring the response of some wide band color filter. Terms like "R", "cyan", and "white" describe roughly what kind of filter we are talking about, enough so that people get an idea of how this and other cameras work.
As for Foveon, it measures "RGB" directly at each pixel, but that's a bad tradeoff: it gives you lower resolution than interpolation, loses a lot of light, and actually doesn't give you much control over the spectral response. And what I really find annoying about "Foveon" is that the name suggests that it has something to do with the "fovea", when in reality a Bayer sensor actually works much more like the human eye.
That's wrong too. For example, if your image consists of widely spaced point light sources, it isn't low-pass filtered, but you still don't need or want an anti-aliasing filter to reconstruct the position of the point light sources. Not only don't you need an anti-aliasing filter, the image will look better without it. That's the case in astrophotography.
Whether you need anti-aliasing filters depends on what kinds of pictures you take, what you know about the scene, and what you are trying to get out.
Discretising is just quantising in the spacial domain!
First I've heard of it. 20 years of farting around with sampling systems and the associated DSP, I've never heard it called anything other than quantizing. Is this some alternate universe I've slipping into?
I should use this sig to advertise my book ISBN-13 : 978-1501515132.
Foveon is a loser in the market because it doesn't perform.
Er.. And it costs more.
I should use this sig to advertise my book ISBN-13 : 978-1501515132.
Nope. Stars are essentially point sources, and so have a very high spatial frequency. If you had a hypothetical telescope that had a flat and infinite modulation transfer function your unfiltered star field would look like crap with all the aliasing. It's possible you could still measure distances between stars, depending on how extended those stars really are, and the distribution of the starfield, but it would look like crap and you'd get a better measurement with an appropriate low pass filter.
In reality there's no such thing as a lens or mirror (or microphone, or any other sensor) with a flat and infinite MTR so your lens itself is acting as a... wait for it... low pass filter. There are some examples of MTFs on this page: http://photo.net/learn/optics/mtf/. For doing realistic separation measurements in astronomy you want to make damn sure you're using an appropriate filter because you're generally looking at sources that are close together and hard to resolve. A little bit of aliasing will completely screw that up.
Actually, an efficient optical system has a sensor with a maximum frequency response that is similar to the rest of the system. There's no point in measuring resolution that your lens can't pass, and no point in passing frequencies your sensor can't detect. So the aliasing you'd see if you hacked the low pass filter out of a camera isn't anything like the aliasing you'd see if there wasn't any filtering at all.
It's quite possible there is some edge case where my broad generalization isn't quite true. An artist who likes pictures of featureless walls comes to mind. Or one who likes aliasing artifacts for their artistic value. It's fun watching you get more and more pedantic trying to find it though.
Nope, it's not. Quantization is the process of taking a continuous valued measurement and rounding, truncating or otherwise cramming it onto a discrete scale. For example, taking the value 5.382... and recording it as 5.
I COULD have said "sampling." Sampling is measuring a signal at several points. The measured values are on the same scale the original was - if you're sampling sound with a microphone, for example, the samples are on a continuous scale. We almost always then quantize the samples, putting them on a discrete scale that's suitable to store in a computer. But sampling/discretization and quantization are two separate things.
Discretization is a term used more in math and statistics, but I used it here because it specifically refers to going from a continuous representation to a discrete representation. Sampling can also be done on a signal that is already discrete. We usually call that "resampling." If you're sampling a discrete signal and your sampling rate is equal to or higher than the original you don't necessarily need to low pass filter.
Discretization: http://en.wikipedia.org/wiki/Discretization
Quantization: http://en.wikipedia.org/wiki/Quantization_(signal_processing)
Seriously... ? Hands in the air; those people who think more megapixels is a good thing? No-one? Good.
Now for the idiots who buy oversized-censor-pro-amature camera's; you're an idiot:
http://press.nokia.com/wp-content/uploads/mediaplugin/doc/nokia-808-pureview-whitepaper.pdf
Eh, even if he made up this usage case for discretizing, it's a reasonable interpretation of the word, especially given the context - take something that is continuous (say, the range of possible values a thing being measured) and transform it to something that is a series of discrete values (the actual measurement of that thing).
Communication happened in that post, and the use of the word in that context does not preclude its usage in other contexts with more precise meaning, so other communication was not prevented or limited by the connotations established. Does there need to be an issue over this?
Can you be Even More Awesome?!
Foveon does not promise more accurate colors.
Actually, that is one of the things that it was heavily-promoted as providing. The reason is that in a conventional Bayer-design sensor, you only get accurate green levels for every other pixel, and accurate red and blue levels for every fourth pixel, and everything else is interpolated. With the Foveon design, you get all three at every pixel.
Foveon is a loser in the market because it doesn't perform.
I think it's more the case that Sigma have kept it proprietary. As a smaller company, they don't have the funds to build a truly groundbreaking camera with it, or to continue improving the sensor design to e.g. keep pace with the megapixel count of other manufacturers. I would love to try a camera with a Foveon sensor, but Sigma's lackluster bodies mean it's probably not going to happen. It was only about two years ago that they finally introduced a model with LiveView, and that was some ridiculously-overpriced model targeted at professionals, but without most of the other features that professionals would want.
You might want to open your eyes and look in the 490–520nm range on a representation of the visual range of the EM spectrum.
To nitpick, that's actually not cyan. Cyan is a combination of green and blue light. The wavelength you're describing stimulates the green and blue receptors in our eyes in a way that looks (to us) identical to cyan, but it's not the same thing. Sort of like how violet (in the sense of being around 400nm) light stimulates the red and blue receptors in our eyes, similar to (but distinct from) certain shades of purple.
This becomes important when discussing things like optical filters. A cyan filter passes green and blue light. In other words, it is a red-blocking filter. This is very different from a filter with a bandpass of 490-520nm, which would also block most green and blue light.
Where the Foveon failed was in the marketing. You cannot produce 2048x1536 pixel images which are clear as day 3 megapixels, and insist that they are 9 megapixels "just because". This attitude persisted and with great pomp a newer, bigger Foveon would be announced - everyone else is at 14MP, and Foveon too - _but_ only 1/3 of the pixels you were expecting to see are in the image. They should have stuck with the popular "standard" way of counting pixels and concentrated on keeping pace with the industry and making a genuine 14MP sensor (42MP in Foveonic).
The new tech now from Panasonic, per the article, can be easily applied to the existing sensor production (3 types), and says the article, can be expected in cameras sooner rather than later. This year's September camera clustershow should have something, or the manufacturers are sleeping or dead.
While I'm here: "Hello Canon. Stuff video and wifi (hacked baby, very hacked) in-camera. Don't stuff this new sensor into a crapmatic "power"shot A350, but (also) into a 7Dii or a 5Div EOS body. GPS, with a selectable ON/OFF setting is a must in an EOS too. Every other little point-n-hope has it already, but not the prosumer or full 'pro' models."
Compared to Bayer-filtered sensors, Foveon does far better at avoiding spurious color from aliasing artifacts along sharp transitions (which create a "speckling" of wrong-colored spots all over reconstructed Bayer-filtered images). Color accuracy in "smooth" areas (where interpolation between Bayer color sites works well), however, is significantly compromised. Thus, Foveon is much better at portraying fine high-color-contrast detail, but poor for subtle tonal transitions over extended areas (though noise-reduction tricks can hide a lot of this). The sensors are also highly sensitive to the angle of entering light rays from the lens, which makes designing a desirable interchangeable lens system more difficult (lens designs that work fine on Bayer SLRs can be unacceptably non-telecentric for Foveon, causing severe color shifts across the image frame).
An ideal imaging system projecting point light sources onto a digital sensor will project each point source onto a single pixel. That's perfectly predictable, though it may or may not be what you want in a particular application.
Which part of "widely spaced point light sources" did you not understand?
I'm used to you twisting other people's words and then accusing them of stupidity. It is mainly a reflection on your own stupidity.
Finally, a DSLR that can detect squant!
/. zen: Imagine a Beowulf cluster of Beowulf clusters...
Regarding antialiasing, foveon does promise to avoid color antialiasing which is generally required for bayer filters.
This new sensor "filter" splits colors into a pattern, which will have a similar effect as a bayer filter. Thus, it will need the colors antialiased to prevent bizarre moire color effects.
Sharpness is reduced by demosaicing and color antialiasing, thus Foveon kind of does promise sharper images because it needs neither of those. If their sensor tech had kept up with the quickly emerging tech of Canon or Nikon, they would be in the running. A 24Mpx Foveon sensor that actually worked in light extremes would really rock.
But with this new filter allowing a decent SNR and a ton of light to be gathered accurately (two big weaknesses for Foveon), I believe it will be the end for that struggling sensor.
The Pixel Qi LCD screen does exactly this to get high-efficiency color; splitting the RGB colors from the LED backlight to direct it to individual LCD cells. The idea of applying the same ideas to cameras are not new.
A big challenge with this idea, and many others, is that for cameras with variable focal lengths, the light hitting the edge of the sensor might come from almost straight in front (for a long lens); or from an extreme angle (for a wide-angle lens) causing significant issues with this kind of optics-in-front-of-the-sensor camera. For a fixed-focus lens as on a cellphone (like 90% of cameras built today) it's not an issue.
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The reason that color accuracy in smooth areas is compromised is that the depth-stacking of diodes, which performs color separation, does a poor job of color separation. Significant electronic processing is required to regain pure color channels, which results in more hue noise. Also, the poor separation makes it easier to "trick" the system into estimating the wrong color.
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The Panasonic sensor tech in the article will suffer this same effect: the actual purity of color separation in the deflected "red" and "blue" spectra is quite low (these are really "slightly pinkish" and "slightly blueish" being deflected, not red and blue). Add this to the already greater color uncertainty produced by mixing even "perfectly separated" RGB primaries into a W+B,W-B,W+R,W-R sensor, and the result will be very low color sensitivity --- plus the artifacts from Bayer-filter color interpretation. This sensor technology is aimed at tiny, light-starved cellphone cameras, where color is going to suck anyway and a >=2x increase in luminance info is extremely desirable (at nearly any other image quality cost). Unlike Foveon, the Panasonic tech can be added in a layer on top of a "traditional" sensor architecture, with the best available readout electronics (the Foveon sensors seem to be lagging a few generations behind in readout noise, and also don't scale down to the tiny pixel sizes for cellphones).
Brown is a form of orange. Black and white aren't colors.
This is great news if the innovation makes it into the low end of CCD detectors. It means that people with more modest cameras could shoot in very low light and get the response you could get from ASA 400 speed film like ekectachrome to shoot exosures of the sky. I was able to report pretty good constellation photos using very modest equipment, an OM-2 F 1.4 35mm lens to capture stars, including bright Messier objects, 35 years ago. I got M44 in Cancer once.
You play hell with a camera under $600 to get that amount of sensitivity from a digicam. I used to shoot 20 second exposures and get stars down to 7th magnitude on slide film. I'd love to do that again with a digicam and not pay a fortune.
Does anyone know some discretization or quantization technique which doesn't need antialiasing ?
I'm thinking of a non periodic array of sensors for cameras
Thanks for reminding that a DSP guy isn't a mathematician ;)
Actually I morphed from a computer science guy to a DSP guy to a crypto guy over my career.
I should use this sig to advertise my book ISBN-13 : 978-1501515132.