Math doesn't check out for me: plane flies at ~700mph or 0.2 miles per second. Satellite speed is on the order of 5 miles per second. Sensors separation is on the order of a few inches. It would take about 15 microseconds between first and last sensor passing over the same spot. The plane can only move around 5 millimeters in this amount of time. It looks like it's moved several hundred feet.
I believe that what you are missing is the distance between the satellite and the plane. planes are at ~10,000 m altitude, GPS flies at 20,000,000 m altitude. A very small angle of distortion creates a very large distance at the plane.
I think you're missing optics. Each pixel maps to a perhaps meter wide spot on the Earth. Which means that each color line which is separated by maybe a few hundred pixels of distance on the sensor maps to hundreds of meters of distance different on the Earth. A plane travels at hundreds of meters per second, which is hundreds of pixels per second in sensor space.
My understanding is that these satellites are using push broom scanning [1]. So I don't see any meaningful sense in which the different scanners are separated by "a few hundred pixels". They're separated by inches, which corresponds to time.
For this same reason, I don't see why the altitude of the satellite is important. But I've never really studied this so I'd be happy to be corrected.
They're not mapping the Earth to a resolution of microns though. Does that help make sense of the fact that there isn't a 1-to-1 scale mapping between the Earth and the sensors? Each image sweeps each pixel across a length along the Earth of nearly a meter. If you try to imagine how this maps onto the sensor head it rapidly breaks down. Each pixel seemingly overlaps with other pixels, each line seemingly overlaps with other lines. But that's not what happens, instead there are optics which effect spreading the image plane over a large area on the Earth with a separation of several meters between each color line.
Think about the optics in reverse. Imagine turning the satellite's sensor head into a hologram then sending it backwards through the optics until it reaches the Earth, where it would be magnified to an enormous size and each pixel would be the size of a human.
I do not understand your description in terms of push broom scanners. Scanning is done by a linear array of sensors that detect at varying angles that go off perpendicular to the angle of motion of the satellite. Imaging in the direction of motion of the satellite is done by physically moving the satellite - which of course is happening quite quickly. This is like looking through a slit in a door frame - you move the light sensor perpendicular to the slit to see the objects inside (except not a perfect analogy: it would be more like carrying the doorframe with you as you move so that you need to move x distance to see something x distance from what you were first seeing). The image is being taken orthographically along one direction. So for the red sensor to see what the green sensor is currently seeing, the satellite must move forward by a few inches so that the red sensor is above the same spot as the green sensor was earlier.
This is not how traditional photography works. There is actually a one-to-one correspondence of motion of the sensor with displacement of the imaged object (in one direction). This is similar to how a "photo finish" is done [1] Since the satellite moves much faster than the plane and the displacement between the sensors is small, it seems that the plane should not have traveled very far.
You are assuming that the lines of sight of each of the arrays are parallel with one another, so that their separation on the ground is the same as the separation of the arrays on the satellite. If they are at an angle to one another, the separation of these lines at the surface will be different from (and possibly in a different order than) the separation of the arrays. It is the surface separation, divided by the speed of the satellite, that determines the time between images of the same point on the surface by different arrays.
If the arrays all share the same lens, that would cause this effect.
I'm not sure what you're saying. I think you are either saying the same thing as InclinedPlane (see my response) or are suggesting that either intentionally or due to tolerances in machining or some such, the red and green sensor units are at some small angle from each other. Assuming you're saying the latter, since the distance is large, this small angle contributes a large displacement on the ground. Afterwards the image would be stitched together to compensate for that via some calibration routine which would work for only stationary objects.
That is entirely plausible, I hadn't considered that before and had just been assuming that the satellite construction was 'ideal'. This sounds like the most likely reason for such an artifact to occur, though I still wonder whether this particular imperfection would be done given the high level of precision necessary for the entire project.
It's not due to imprecision, it's due to design and fundamental optical constraints. There's nothing special about the optics used for a push broom imager, it's just an ordinary lens. If you put a full frame sensor at the focal plane you could take an image of a several kilometer square patch of Earth. If instead you put several different lines of sensors in the focal plane and put each behind a color filter then you'd have a multi-spectral push broom sensor. But each line does not view the same part of the Earth at the same time. Because the sensors scan the Earth they end up imaging the same spot within a fairly short delay. But optically it's not possible to have each color line viewing the same horizontal slice of the image of Earth at the same time, that's not the way lenses work.
Each sensor will be on the focal plane of the lens it uses. If they are all are looking through the same lens, their lines of sight will all cross one another at the optical center of the lens, and so will be at an angle to one another. Therefore, each sensor has a different view of the surface - it is an example of parallax.
(EDIT: I have changed 'lens system' to 'lens', because I think the former might be misleading. All I meant by 'lens system' is that to make a decent camera, you have to have several lens elements along the optical axis. Subsequently, I realized 'lens system' might be taken as implying an array of lenses. What I actually mean by 'lens' is simply as in 'telephoto lens'.)
did a quick BOE calculation based on this assumption. The idea was to see if the implied focal length for the lens is plausible.
I actually used the green-blue pair for the calculation, because I think it is slightly more likely that each pair share a lens, than that they all do.
The green and blue images seem to be something more than a wingspan apart. We don't know what type of aircraft these are, so I picked a 737 as a mid-sized example. The latest models have a 34m wingspan, so let's say the aircraft has moved about 50m between images.
Assuming the aircraft are moving relatively slowly, because they are searching, I used 100 m/s (200kts) for their speed, which means there is 0.5 sec between the images.
The satellite is moving at "almost 5 miles per sec", so let's say 7 km/sec. That means the views of the two sensor arrays have a 3.5 km separation at the surface.
Zizzer gives the satellite altitude as about 630 km. The ratio of the focal length of the lens to the separation of the sensor arrays is the same as the ratio of the altitude of the satellite to the distance between what part of the surface each array is imaging: f/a = 630/3.5, or f = 180a (a is the array separation).
From the picture of the sensors, and principally using the connectors' pin-holes for a sense of scale, I guess the blue and green arrays are about 0.5 cm apart, implying f = 90cm, which seems plausible to me.
To be clear: you're saying that each of the the sensor lines are at slightly different angles and that this is due to sharing (at least for some of them) the same lens?
If so, that shared lens would be exactly the part of this that I was missing. Honestly, it doesn't look like there's a shared lens between the red and the other two, as you point out, but I guess it could be sharing a lens with the "unused lines" marked in the diagram that puts it at a distinct angle.
As a test of my understanding - would I be correct in saying that when the article says "The red and infrared rows are paired on one CCD array, while the green and blue sensors are on a second array, which is why the red plane often seems much further ahead than the green and blue planes." it's going a little too far: there's no reason that the red line would have to be inherently at a greater angle than the other three? I used to interpret this line as just meaning "the green and blue are closer together than the red is, so the red image will be further apart" but that should be insignificant.
I'm curious - does anyone know how they calibrate this kind of equipment or are the tolerances good enough that they don't really need to? Do they take passes over known objects to calibrate or do some algorithmic test for how well the three colors match up (in a non-moving example).
To the first question: yes, and after a bit more thought, I realize that this assembly must be designed to use a single lens, as the sensor arrays are close together, which would make it difficult to have any other optical arrangement. The pictured assembly would form the back of the camera, where the rectangular CCD array (or film) goes in a conventional camera.
The picture shows that the red sensor is further from the green one than the blue is, simply because it is on a separate sub-assembly. If the infra-red image showed on the pictures, it would be as far from the red one as the green one is from the blue. Given the order of the arrays on the camera, the IR image of the plane would be ahead of the red image, meaning that the IR is the last of the four images taken.
Incidentally, the pictures show the aircraft are experiencing considerable wind drift, especially in the case of the top-left picture, where you can see the contrail. This indicates strong winds, and probably also a relatively low airspeed for the aircraft. The orientation of the waves suggests a head- or tail-wind, but to get that drift, it must be different at the airplane's altitude (which probably is not high if it is searching.)
Yes, there is a one to one correspondence in displacement but because the sensor elements view parts of the Earth that are farther apart the delay between lines is larger on the Earth than for the sensor elements in orbit. Just as the size of the pixels on the camera are larger than the size of the pixels on the sensor. That's because the view line of each sensor element is at an angle relative to the others. And that's what allows the sensor to see a multiple kilometer wide swathe of the Earth in each pass instead of just a few centimeters.
Imagine a different satellite that instead of looking down looked out toward the Earth's horizon, as seen from orbit. And imagine it has two sensors, one which looks forward and one that looks backward, very nearly a 180 deg. difference. At the height of a satellite in low Earth orbit that could be a 1,000 km difference in what each sensor sees. Now, every millimeter the satellite moves the view moves as well, but because the views are separated by 180 deg. or 1,000 km of ground that means it takes much longer for one view to catch up to where the other was, even though the track of the sensor elements themselves in space do the same thing much quicker.
Or, just imagine if the satellite rotated so the sensor was sideways, parallel to the direction of motion. It still views the same multiple kilometer wide slice of the Earth, but now it reimages the same thing line as it moves, shifting just one pixel forward each image. The sensor is only a few cm wide so it takes a tiny fraction of a second for the satellite to translate the position of the rearward most sensor pixel to where the forwardmost sensor pixel was, but it does not take the same amount of time for the viewed slice of the Earth to translate by an entire frame, because the frame is many kilometers wide.
No, I believe that you are still mis-interpretting the push broom scanners. A greyscale push broom scanner would have a single row of pixels that are lined up perpendicularly to the direction of travel and whose rays are in the plane perpendicular to the direction of travel. So yes, these rays would span many kilometers, but only in one direction. In order to image a 2D area of the planet the entire satellite would need to traverse down it linearly - which is something that satellites happen to be quite good at given how fast they are moving. This is almost like how a document scanner works - it translates a line of sensors across a document to construct a full 2D image.
For a full color image, three linear sensors are used, each displaced some distance along the direction of motion. So the fact that the rays are spreading out in the perpendicular doesn't change the distance the satellite must travel to image the next part.
For example, your second paragraph doesn't hold. The large separation of rays only occurs in the direction perpendicular to that of travelling. Note how your method would be imaging the same place multiple times on each pass whereas a push broom scanner would capture each one just one.
For your third paragraph, I agree that this could be done but that's simply not how the sensors are aligned and that difference is important. In particular, it's the very difference that I'm trying to point out.
I'm not quite sure why you aren't getting this. The view of the Earth that each pixel has isn't separated by the same distance as their separation on the sensor. Do you agree with that?
The important part is that it's also true for the different color lines as well. That's what I'm trying to explain.
The view of each color line may traverse 1mm for every 1mm the satellite moves in orbit, but that has nothing to do with the separation of the lines. The important thing is that the view of, say, the green color line will not be identical to the view of the red color line when they are at the same relative physical position in orbit (e.g. a fraction of a second apart in the orbital motion) because the view of each color line is at a different angle through the optics. And because of that the portion of the Earth that each line is viewing at a given time is separated by a considerable distance, and there is then a considerable time separation between when a given spot on the Earth is imaged by each color line.
My other examples are trying to provide hypothetical scenarios to help get you to understand why your preconceived ideas about how push broom scanning works have important gaps, they're not meant to explain how things work in this particular example.
Since there shouldn't be too much moving around the open ocean besides planes, couldn't you use this artifact to build a semidecent search algorithim rather than going through all the data by hand?
This particular type artifact is created because the plane is bright and moving FAST enough that it isn't in the same position relative to the sensor from the beginning of the image to the end. My best guess is that you need something moving at least 100MPH to see this effect at all and the position of the double image (assuming the same sensor) should be a function of the speed of the object. Islands of garbage moving fast enough to be mistaken for a plane are probably interesting in their own right.
As it turns out that the real problem here is that the all of the data from the 8th is in a pretty useless spot given what we know now. So what is useful to find is wreckage not planes. After looking at the data I'm also unconvinced that speed has anything to do with it and that the more likely cause is altitude.
You do realize that the surface of the ocean is moving around rather drastically? That part of the ocean, because of how wide open it is, has some of the largest swells of any ocean. I feel that this would make things rather difficult.
Out of all the news coverage showing the search crews manning the planes, never once did I see anyone wearing sunglasses. Wouldn't polarized glasses actually help with reflection/glare?
Polarized glasses help with reflection at a shallow angle, but the observers will be looking down, not across the surface, and when the sun is low on the horizon, all observers will be looking away from the sun, as it would be a waste of time to try to see anything up-sun, even with polarized glasses.
In addition, using polarized glasses might lead to seeing the colored bands of stress birefringence in the window, depending on what material it is made of.
Thus far, have we found even a single piece of debris that we know came from the MH370?
I just don't buy the idea that the plane ended up as far south as it did and I haven't really read of any solid evidence to support this other than one blurry satellite image with a large but unidentifiable object. If that object was in fact part of the plane, I have yet to hear of any explanation as to why the plane was that far south of it's last known position instead of continuing north west.
It's a multitude of satellite images, combined with a Doppler analysis of satellite pings of the aircraft, plus a fuel-range analysis, plus a radar analysis of the northern half of the potential travel routes...
I have yet to hear of any explanation as to why the plane was that far south of it's last known position instead of continuing north west.
No one knows that, yet (possibly ever). But they do know that the plane did not travel north west, as it didn't show up on the civilian or military radars of multiple countries.
Do we have any good theories explaining why the plane would have even traveled in that direction? AFAICT there is nothing in that direction on the map. What were they flying towards?
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[ 3.5 ms ] story [ 78.4 ms ] threadWhat am I missing?
[1] http://en.wikipedia.org/wiki/RapidEye
For this same reason, I don't see why the altitude of the satellite is important. But I've never really studied this so I'd be happy to be corrected.
[1] http://en.wikipedia.org/wiki/Push_broom_scanner
Think about the optics in reverse. Imagine turning the satellite's sensor head into a hologram then sending it backwards through the optics until it reaches the Earth, where it would be magnified to an enormous size and each pixel would be the size of a human.
This is not how traditional photography works. There is actually a one-to-one correspondence of motion of the sensor with displacement of the imaged object (in one direction). This is similar to how a "photo finish" is done [1] Since the satellite moves much faster than the plane and the displacement between the sensors is small, it seems that the plane should not have traveled very far.
[1] http://en.wikipedia.org/wiki/Photo_finish
If the arrays all share the same lens, that would cause this effect.
That is entirely plausible, I hadn't considered that before and had just been assuming that the satellite construction was 'ideal'. This sounds like the most likely reason for such an artifact to occur, though I still wonder whether this particular imperfection would be done given the high level of precision necessary for the entire project.
(EDIT: I have changed 'lens system' to 'lens', because I think the former might be misleading. All I meant by 'lens system' is that to make a decent camera, you have to have several lens elements along the optical axis. Subsequently, I realized 'lens system' might be taken as implying an array of lenses. What I actually mean by 'lens' is simply as in 'telephoto lens'.)
did a quick BOE calculation based on this assumption. The idea was to see if the implied focal length for the lens is plausible.
I actually used the green-blue pair for the calculation, because I think it is slightly more likely that each pair share a lens, than that they all do.
The green and blue images seem to be something more than a wingspan apart. We don't know what type of aircraft these are, so I picked a 737 as a mid-sized example. The latest models have a 34m wingspan, so let's say the aircraft has moved about 50m between images.
Assuming the aircraft are moving relatively slowly, because they are searching, I used 100 m/s (200kts) for their speed, which means there is 0.5 sec between the images.
The satellite is moving at "almost 5 miles per sec", so let's say 7 km/sec. That means the views of the two sensor arrays have a 3.5 km separation at the surface.
Zizzer gives the satellite altitude as about 630 km. The ratio of the focal length of the lens to the separation of the sensor arrays is the same as the ratio of the altitude of the satellite to the distance between what part of the surface each array is imaging: f/a = 630/3.5, or f = 180a (a is the array separation).
From the picture of the sensors, and principally using the connectors' pin-holes for a sense of scale, I guess the blue and green arrays are about 0.5 cm apart, implying f = 90cm, which seems plausible to me.
If so, that shared lens would be exactly the part of this that I was missing. Honestly, it doesn't look like there's a shared lens between the red and the other two, as you point out, but I guess it could be sharing a lens with the "unused lines" marked in the diagram that puts it at a distinct angle.
As a test of my understanding - would I be correct in saying that when the article says "The red and infrared rows are paired on one CCD array, while the green and blue sensors are on a second array, which is why the red plane often seems much further ahead than the green and blue planes." it's going a little too far: there's no reason that the red line would have to be inherently at a greater angle than the other three? I used to interpret this line as just meaning "the green and blue are closer together than the red is, so the red image will be further apart" but that should be insignificant.
I'm curious - does anyone know how they calibrate this kind of equipment or are the tolerances good enough that they don't really need to? Do they take passes over known objects to calibrate or do some algorithmic test for how well the three colors match up (in a non-moving example).
The picture shows that the red sensor is further from the green one than the blue is, simply because it is on a separate sub-assembly. If the infra-red image showed on the pictures, it would be as far from the red one as the green one is from the blue. Given the order of the arrays on the camera, the IR image of the plane would be ahead of the red image, meaning that the IR is the last of the four images taken.
Incidentally, the pictures show the aircraft are experiencing considerable wind drift, especially in the case of the top-left picture, where you can see the contrail. This indicates strong winds, and probably also a relatively low airspeed for the aircraft. The orientation of the waves suggests a head- or tail-wind, but to get that drift, it must be different at the airplane's altitude (which probably is not high if it is searching.)
Imagine a different satellite that instead of looking down looked out toward the Earth's horizon, as seen from orbit. And imagine it has two sensors, one which looks forward and one that looks backward, very nearly a 180 deg. difference. At the height of a satellite in low Earth orbit that could be a 1,000 km difference in what each sensor sees. Now, every millimeter the satellite moves the view moves as well, but because the views are separated by 180 deg. or 1,000 km of ground that means it takes much longer for one view to catch up to where the other was, even though the track of the sensor elements themselves in space do the same thing much quicker.
Or, just imagine if the satellite rotated so the sensor was sideways, parallel to the direction of motion. It still views the same multiple kilometer wide slice of the Earth, but now it reimages the same thing line as it moves, shifting just one pixel forward each image. The sensor is only a few cm wide so it takes a tiny fraction of a second for the satellite to translate the position of the rearward most sensor pixel to where the forwardmost sensor pixel was, but it does not take the same amount of time for the viewed slice of the Earth to translate by an entire frame, because the frame is many kilometers wide.
For a full color image, three linear sensors are used, each displaced some distance along the direction of motion. So the fact that the rays are spreading out in the perpendicular doesn't change the distance the satellite must travel to image the next part.
For example, your second paragraph doesn't hold. The large separation of rays only occurs in the direction perpendicular to that of travelling. Note how your method would be imaging the same place multiple times on each pass whereas a push broom scanner would capture each one just one.
For your third paragraph, I agree that this could be done but that's simply not how the sensors are aligned and that difference is important. In particular, it's the very difference that I'm trying to point out.
The important part is that it's also true for the different color lines as well. That's what I'm trying to explain.
The view of each color line may traverse 1mm for every 1mm the satellite moves in orbit, but that has nothing to do with the separation of the lines. The important thing is that the view of, say, the green color line will not be identical to the view of the red color line when they are at the same relative physical position in orbit (e.g. a fraction of a second apart in the orbital motion) because the view of each color line is at a different angle through the optics. And because of that the portion of the Earth that each line is viewing at a given time is separated by a considerable distance, and there is then a considerable time separation between when a given spot on the Earth is imaged by each color line.
My other examples are trying to provide hypothetical scenarios to help get you to understand why your preconceived ideas about how push broom scanning works have important gaps, they're not meant to explain how things work in this particular example.
In addition, using polarized glasses might lead to seeing the colored bands of stress birefringence in the window, depending on what material it is made of.
I just don't buy the idea that the plane ended up as far south as it did and I haven't really read of any solid evidence to support this other than one blurry satellite image with a large but unidentifiable object. If that object was in fact part of the plane, I have yet to hear of any explanation as to why the plane was that far south of it's last known position instead of continuing north west.
I have yet to hear of any explanation as to why the plane was that far south of it's last known position instead of continuing north west.
No one knows that, yet (possibly ever). But they do know that the plane did not travel north west, as it didn't show up on the civilian or military radars of multiple countries.