Questions on the Fresnel integrals.
Different normalizations are done for the Fresnel integrals. One normalization is
$$\begin{align*} S(x)&=\int_0^x \sin(t^2)\,\mathrm dt \\ C(x)&=\int_0^x \cos(t^2)\,\mathrm dt \end{align*}$$
and a different normalization is
$$\begin{align*} S(x)&=\int_0^x \sin\frac{\pi t^2}{2}\mathrm dt \\ C(x)&=\int_0^x \cos\frac{\pi t^2}{2}\mathrm dt \end{align*}$$
Check your reference to see which normalization is being used.
