# Closed formula Fourier transform of complex exponential

Is there a closed formula for the Fourier transform of the function $$f(t) = e^{2\pi i \sqrt{1-t^2}},$$ where the square root for $|t|>1$ is $i \sqrt{t^2-1}$. This function emerges in Fourier optics.

• How do you define the square root for $|t|>1$? – Start wearing purple Sep 1 '13 at 11:39
• I added the definition. – Guido Kanschat Sep 1 '13 at 11:54
• This would give exponential growth at infinity. Are you sure about the sign? – Start wearing purple Sep 1 '13 at 12:09
• Good point. It had to be the decaying function – Guido Kanschat Sep 1 '13 at 15:48