No speck of brown. Very bright blue eyes, just like mine.
Eye color is very subjective (and dependent on skin/hair color) and patterns vary.
In rare cases, melanin (the brown) can be there and be overpowered by the blue, so while a person is genetically a "hazel," they appear to be a true blue.
Here is a heredity predictor based on a blue-eyed mom, an alleged blue-eyed dad, and a brown-eyed child --- the result being that the alleged father is "likely excluded" as the father. (You can play with the various iternations of this calculator.)
http://genetree.com/resource/CalculatorResults.php?T=2