设椭圆\( \frac{{x}^{2}}{{a}^{2}}+\frac{{y}^{2}}{{b}^{2}}=1(a＞b＞0)\)的两个焦点为\( {F}_{1}{F}_{2},{F}_{2}\)作椭圆长轴的垂线交椭圆于点P\( ,\)若\( {F}_{1}P{F}_{2}\)为等腰直角三角形\( ,\)则椭圆的离心率为 ( )
A. \( \frac{\sqrt{2}}{2}\)
B. \( \frac{\sqrt{2}-1}{2}\) C. \( 2-\sqrt{2}\) D. \( \sqrt{2}-1\)
