Stephan Paukner :: syslog

This is no real surprise, as all sensors simply have this drawback—or, is it a feature?

The first video shows the infrared emitter of the remote control for my PicooZ, taken with my Nokia N73—that phone has 2 cameras, one with high resolution and another for video calls. Both show the same behavior. The second video has been taken with my Canon PowerShot A710 IS and shows the same emitter. The third video shows an ordinary TV remote control, taken with the same digital camera.

All sensors of digital cameras or camcorders on the market are covered by an infrared filter. Camcorders with the nightshot feature are able to deactivate it, so, sensors are very sensitive to infrared light in general. Some cameras have a too weak infrared blocker, like the expensive Leica M8, giving a red tint to black surfaces or black clothing. Customers have to use a separate infrared filter.

(Q34+44) If an operator S can be written as S = TT, then we abbreviate S^1/2 := T. In the mapping sequence x → Tx → TTx, clearly S^1/2 “lies between” S⁰ and S¹. We know that (AB)⁻¹ = B⁻¹A⁻¹, so far existant, and so S⁻¹ = T⁻¹T⁻¹. So we can abbreviate S^−1/2 := T⁻¹, and (S^1/2)⁻¹ = S^−1/2. It is now clear that S^−1/2SS^−1/2 = T⁻¹TTT⁻¹ = Id.

It remains to show that S^−1/2 is a limit of polynomials in S⁻¹ in the strong operator topology.