Inverse Fourier Transform in the Gamma Coordinate System

<table>The circles on unit sphere and a helix in 3D space. (a) The illustration of <svg height="10.9125" id="M252" style="vertical-align:-0.17555pt" version="1.1" viewbox="0 0 36.5 10.9125" width="36.5" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,10.9125)">
<g transform="translate(72,-63.27)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝜎</tspan>
<tspan style="font-size: 12.50px; " x="10.802592" y="0">=</tspan>
<tspan style="font-size: 12.50px; " x="22.842981" y="0">0</tspan>
</text>
</g>
</g>
</svg> and<svg height="10.9125" id="M253" style="vertical-align:-0.17555pt" version="1.1" viewbox="0 0 41.712502 10.9125" width="41.712502" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,10.9125)">
<g transform="translate(72,-63.27)">
<text transform="matrix(1,0,0,-1,-61.24,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">̇</tspan>
<tspan style="font-size: 12.50px; " x="-6.5390692" y="0">𝜎</tspan>
<tspan style="font-size: 12.50px; " x="4.2635231" y="0">=</tspan>
<tspan style="font-size: 12.50px; " x="16.303911" y="0">0</tspan>
</text>
</g>
</g>
</svg>, (b) a circular locus on the unit sphere and the motion of the frequency plane, and (c) the helix in 3D space and the motion of its TNB frame. The figure is not drawn to scale.</table>

International Journal of Biomedical Imaging

Inverse Fourier Transform in the Gamma Coordinate System

Figure 4