The Math Behind the Rolling Shutter Phenomenon

"I remember seeing the photo above on Flickr once, and having my brain melt slightly from trying to figure out what went wrong." reports Jason Cole, PhD student from London with a passion for math, physics, and data visualization.

Photo: Flickr

The issue was the propeller was rotating as the camera detector ‘read out’, i.e. there was some motion during the exposure of the camera. This is an interesting thing to think about, lets have a look.
 
Many modern digital cameras use as their ‘sensing’ device a CMOS detector, also known as an active-pixel sensor, which works by accumulating electronic charge as light falls upon it. After a given amount of time, the exposure time, the charge is shifted row-by-row back to the camera for further processing. There is then a finite time where the camera scans down the image, saving rows of pixels at a time. If there is any motion over this timescale the image will be distorted.

To illustrate, consider photographing a spinning propeller. In the animations below the red line corresponds to the current readout position, and the propeller continues to spin as the readout proceeds. The portion below the red line is saved as the captured image.

First, a propeller which completes 1/10th of a rotation during the exposure:
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Source: PetaPixel