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07-28-2011, 08:08 PM   #1
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Interesting GPS astrotracer mathematics.

What the astrotracer function does is simply to keep startrails out of the picture. Those startrails happen because the earth is rotating 15 seconds of arc each second of time. What the gps does is move the sensor in the camera to compensate this startrailing which makes a star picture elongated. To emulate an equatorial mount, the sensor has to move up and down, sideways and also rotate. We are tempted to think that these movements have to be big but that's not the case at all. I have done some calculations for the worst case which is a star on the horizon. The biggest sideways movement that the sensor has to do would be 1.19 mm which is not a lot. The formula for startrails at the horizon is (Lens focal length X exposure time in seconds X .00007). I have used the data given by Pentax for the astrotracer function. What I find fascinating is the huge amount of calculations that the software inside the camera has to do to correct the three movements of the sensor, it's simply incredible that it works at all. Correct me if I'm wrong. Comments appreciated.

07-29-2011, 07:42 AM   #2
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Too much computation, It gives me headache. That's why some time I use approximations, interpolations using known values. I think the formula is not very complex and must be applied only once, at the start of the exposure, the result should be the amount of shift per second for example. Then it shifts each second the respective amount of mm and voila.
Or there could be some predefined values and according to current focal length and position it could interpolate. Anyway the position and orientation is not 100% correct, GPS and SR's gyroscopes are not pinpoint accurate...I think.
my 2c.

Last edited by valy; 07-29-2011 at 07:51 AM.
07-29-2011, 09:16 AM   #3
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I haven't checked your math, but on a rough order-of-magnitude basis, I'd say that sounds about right.

The absolute magnitude of motion undertaken by the SR mechanism, for the astrotracer or its primary shake reduction function, is quite small. Only 1-2 mm for the most extreme cases. But think about it on a relative basis, this way: 1.19 mm of sensor movement represents about 7.5% of the length of the sensor along its short axis. That's serious compensation.
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