Question
I have a Nikon d90 and have often found that the camera reaches focus faster, with less re-adjusting and missing the focus, when I have a speedlight (the Nikon sb-600 in my case) attached.
Why is this the case? I don't know enough about autofocusing systems inside the camera but I recognise that a red light is emitted from the speedlight while focusing and that this is likely involved.
Answer
The phase detect autofocus on your D90 works by measuring the displacement between two 1-dimensional images formed on the autofocus sensor. By detecting features in these image strips and measuring their offset, the distance to the subject can be estimated. In low light it is difficult to for the camera to identify features and make a measurement as the image strips will be very dim.
Most modern speedlights (such as your sb-600) have an "auto assist lamp", which is usually implemented as a red LED matrix that projects a grid pattern over your subject. The projected grid lines are easy for the AF system to pick up and measure displacement as you get a sharp peak on your image strip where a grid line crosses.
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