Rotation is the enemy

Last week I have published a simple tool that calculates (among a few other things) motion blur resulting from camera movement relative to the photographed object. Looking at the results of those calculations, one could say that motion blur is a very minor issue in UAV photography: at a platform speed of 30 km/h and a shutter speed of 1/1000 s, motion blur is as low as 0.8 cm. Flying a Canon G12 at the wide angle limit (28 mm) and 200 m above ground, this amounts to only 0.25 image pixels. From the calculation results of UAVphoto, motion blur does not appear to be a relevant issue. The need to take images at short intervals to achive sufficient overlap appears to be much more important when using a UAV. But why do I even get blurred images when using a kite that is almost immobile relative to the ground?

The point is that motion blur due to translation (i.e. linear movement of the camera relative to the object) is only one reason for blurred images. Another (and much more relevant) reason is rotation of the camera. Unfortunately, this is also much harder to measure and to control. To show how important rotation is for image blur, I have added the calculation of rotation blur to the new version of UAVphoto. Two types of rotation have to be distinguished: rotation about the lens axis and rotation about the focal point but perpendicular to the lens axis. I am not using the terms pitch, roll and yaw here because the relation of platform pitch, roll and yaw to rotation about different camera axes depends on how the camera is mnounted to the platform.

Rotation about the lens axis results in rotation blur that is zero at the image centre and reaches a maximum at the image corners. Rotation about an axis orthogonal to the lens axis results in rotation blur that is at first sight indistinguishable from motion blur due to high speed translation movement. Of course, all types of blur combine to the total image blur. Rotation blur about the lens axis is independend of focal length. Orthogonal rotation blur, on the other hand, increases with increasing focal length. In both cases an increase in shutter speed will result in a proportional decrease in image blur.

Most UAV rotation movements are due to short-term deflections by wind gusts or steering. Wind gusts are also the main source of rotation movements of kite-carried cameras. Let’s say we’re using a Canon G12 at the wide angle limit (28 mm). The maximum rotation rate which will not result in image blur (using a 0.5 pixel threshold) is 12.4 °/s (or 29 s for a full circle) for rotation about the lens axis and 8.1 °/s (or 44 s for a full cirlce) for rotation orthogonal to the lens axis. At a focal length of 140 mm, the maximum rotation rate orthogonal to the lens axis is only 1.9 (or 189 s for a full circle). If all this sounds very slow to you, you’ve got the point: even slow rotation of the camera during image capture is a serious issue for UAV photography, in most cases much more important than flying speed.

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