Diophantine Optics

Diophantine optics
What I call Diophantine optics is the exploitation in optics of some remarkable algebraic
relations between powers of integers. The name comes from Diophantus of Alexandria, a
greek mathematician, known as the father of algebra. He studied polynomial equations with
integer coefficients and integer solutions, called diophantine equations. Since constructive
or destructive interferences are playing with optical path differences which are multiple
integer (odd or even) of λ/2 and that the complex amplitude is a highly nonlinear function
of the optical path difference (or equivalently of the phase), one can understand that any
Taylor development of this amplitude implies powers of integers. This is the link with
Diophantine equations.
I have explored how remarkable
relations between powers of integers can help to solve several problems, especially in
the field of interferometry, such as achromatization of a phase shifter or deep nulling
efficiency.
It appears that all the
research that was conducted in this frame of thinking, relates to the field of detection
of exoplanets, a very active domain of astrophysics today.
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 Publications