Originally posted by kamayok3 Hi,

Can someone point out what is the math that applied behind this great tools? Especially in Astrophotography side.

Thanks.

I think some abstract reasoning gives you the quickest start. I assume you have minimal knowledge in math as otherwise, you wouldn't have asked your question

Well, the sensor has to rotate during the exposure to do its trick. As it counters the Earth's rotation. What the camera needs to know is the virtual axis of rotation and rotational (angular) speed. If the virtual axis of rotation (e.g., near polar star) is very far off the sensor, the sensor movement will almost look like a translation.

It derives it from the Earth's axis rotation (known, 24h), camera optical axis and focal length.

The focal length f is transmitted via the lens mount to the camera and is a known.

The camera optical axis is described by 6 parameters where only 4 parameters do actually matter:

- the position in space (3 parameters, but altitude with respect to Earth's surface can be ignored, leaving 2 parameters): x, y

- the angle of the optical axis (3 parameters, rectascension, declination and roll where roll can be ignored): r, d

Now, the camera measures 4 knows to determine x,y,r,d:

- the GPS coordinate delivering x,y (using the O-GPS1 gps receiver).

- the camera pitch p (using roll only if the camera isn't level), using the built-in level meters.

- the camera yaw or heading h (using the O-GPS1 compass).

A formula returns x,y,r,d from x,y,p,h. From x,y,r,d,f follows the virtual axis of rotation for the sensor (and speed).

I would assume that the compass provides the most inaccurate measure. However, the sensor can only move that much (limiting max. exposure time depending on focal length and r,d) and therefore, may have been tuned to be exact enough.

As a first approximation, max. exposure time should decrease inversely proportional to the focal length ~1/f.

However, the real charme of the O-GPS1 is that you can take starry night images with a (slightly blurred) foreground. Therefore, the focal length wouldn't be too high. With a higher focal length, one may assume no foreground and it then is no problem to stack multiple images to achieve arbitrarily long exposures.