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I’m not trying to call you guys out. Just curious for more information. I would say I have enough knowledge about signal processing to be dangerous, as it’s qui

I’m not trying to call you guys out. Just curious for more information. I would say I have enough knowledge about signal processing to be dangerous, as it’s quite adjacent to my job. But this isn’t clicking with me. Assuming we’re not including cameras outside the visible light spectrum, are there cameras that actually have enough dynamic range to capture a recoverable amount of information about stars against a bright sky? Beyond that, the original commenter takes about oversampling, but oversampling of what exactly? Intuition says that even with a high resolution sensor (like a modern iPhone) the visual size of a star would still be less than a single pixel. If my intuition there is correct, aren’t we spatially under sampling? The shutter is open for some period of time, so I guess you could say we’re temporally oversampling, but then we’re applying the same gain both to the stars and the sky, so that doesn’t seem to helpful. I feel like taking a high pass filter of a daylight sky would leave you with next to nothing save some of the sensor’s inherent noise. Are you discussing exquisite sensors or optics here? Genuinely curious. I tried some basic google searches on the matter of recovering stats in daytime images but didn’t get much back.

pifm_guy 4y ago
> oversampling, but oversampling of what exactly? If you have 3 million pixels of sky, and 3 variables to find, then you have oversampled by 1 million times. In the ideal noise-free world with no other unknowns, any 3 of those pixels would be enough to solve the problem perfectly.
protastus 4y ago
About planets and stars in daytime: https://www.skysurfer.eu/daystars.php https://www.skysurfer.eu/daystars.php The concept here is processing gain, which is algorithmic. It's what enables the miracle of GPS, even though satellites are 20000km far away, there may be clouds, rain, etc and your phone doesn't come with a satellite dish. Also used in CDMA radio for civilian and military communications, it allows reliable transmission at negative SNR by spreading the message over a huge space. In the case of GPS/radio, the space is frequency. Here, the message is coordinates of a rectangular crop of the sky, encoded in the (huge) space of few million pixels. On a per-pixel basis, the SNR can be negative -- looking at a single pixel I can't tell you with confidence if it contains a star, because the shade of blue is just too close to average. But correlating the entire image against the correct "code" (a clean star field), tells me whether I got the location of the sky correctly. Intuitively: accumulated over the entire image, the noise statistics are such that the noise stays bounded, and the tiny amount of signal adds up. Appropriate optics will increase the SNR so that bright stars can actually become visible. Per the link above, mag 2-3 stars are visible with a 10cm telescope (looking through the eyepiece; no filters or digital sensors needed). So if the conditions are right and the optics are good, you may actually see a few stars reliably, and the scenario reduces to the B-21 hangar scenario. Finally, it's worth noting that even a consumer grade CMOS sensor will sample at 12 bits per pixel (4096 linear levels) with low noise. The human eye cannot discriminate a luminance difference of 1/4096 relative to full scale, not even close. Using the naked eye for intuition here is misleading, because this is a scenario where a sensor is far better at registering the small additive contribution of a star under daylight, and this is the key to enabling the processing gain through math.

pifm_guy 4y ago

> oversampling, but oversampling of what exactly? If you have 3 million pixels of sky, and 3 variables to find, then you have oversampled by 1 million times. In the ideal noise-free world with no other unknowns, any 3 of those pixels would be enough to solve the problem perfectly.

protastus 4y ago

About planets and stars in daytime: https://www.skysurfer.eu/daystars.php https://www.skysurfer.eu/daystars.php The concept here is processing gain, which is algorithmic. It's what enables the miracle of GPS, even though satellites are 20000km far away, there may be clouds, rain, etc and your phone doesn't come with a satellite dish. Also used in CDMA radio for civilian and military communications, it allows reliable transmission at negative SNR by spreading the message over a huge space. In the case of GPS/radio, the space is frequency. Here, the message is coordinates of a rectangular crop of the sky, encoded in the (huge) space of few million pixels. On a per-pixel basis, the SNR can be negative -- looking at a single pixel I can't tell you with confidence if it contains a star, because the shade of blue is just too close to average. But correlating the entire image against the correct "code" (a clean star field), tells me whether I got the location of the sky correctly. Intuitively: accumulated over the entire image, the noise statistics are such that the noise stays bounded, and the tiny amount of signal adds up. Appropriate optics will increase the SNR so that bright stars can actually become visible. Per the link above, mag 2-3 stars are visible with a 10cm telescope (looking through the eyepiece; no filters or digital sensors needed). So if the conditions are right and the optics are good, you may actually see a few stars reliably, and the scenario reduces to the B-21 hangar scenario. Finally, it's worth noting that even a consumer grade CMOS sensor will sample at 12 bits per pixel (4096 linear levels) with low noise. The human eye cannot discriminate a luminance difference of 1/4096 relative to full scale, not even close. Using the naked eye for intuition here is misleading, because this is a scenario where a sensor is far better at registering the small additive contribution of a star under daylight, and this is the key to enabling the processing gain through math.