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I've heard Astronomers talking about backlit CCD sensors, and talking about how much better they are than other types. What are they, why might I want to get one, and what are the pros/cons of this compared to related technologies?

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A backlit sensor isn't really a new kind of sensor, it's just a different arrangement of the imaging elements to allow more light into the sensor. From Wikipedia:

A traditional digital camera sensor consists of a matrix of individual picture elements. Each element is constructed in a fashion similar to the human eye, with a lens at the front, sensors at the back, and wiring in between. The front of the detectors require an active matrix to be placed on their front surface. The matrix and its wiring reflects or absorbs some of the incoming light, thereby reducing the signal that is available to be captured.

A back-illuminated sensor moves this wiring behind the sensors, similar to a Cephalopod eye.

They're not without issues though:

Moving the active matrix transistors to the back of the photosensitive layer normally leads to a host of problems, such as cross-talk, which causes noise, dark current, and color mixing between adjacent pixels.

Backlit sensors improve the low-light performance of a CCD chip, reducing the ISO needed for low-light conditions (and thus reducing noise). This is a clear benefit to astrophotographers, allowing them to use shorter exposures with less noise to get equivalent shots.

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Back-illuminated CCDs also have their peak sensitivity shifted to a different wavelength- somewhat bluer, I think. –  Andrew Jun 13 '11 at 14:24

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