The Second-Order Born Approximation in Diffuse Optical Tomography

<table><svg height="14.67" id="M305" style="vertical-align:-2.29482pt" version="1.1" viewbox="0 0 158.29124 14.67" width="158.29124" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,14.67)">
<text transform="matrix(1,0,0,-1,0.498,2.786)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝐽</tspan>
<tspan style="font-size: 12.50px; " x="6.7516847" y="0">𝑖</tspan>
<tspan style="font-size: 12.50px; " x="10.640155" y="0">𝑛</tspan>
<tspan style="font-size: 12.50px; " x="16.854206" y="0">𝑑</tspan>
<tspan style="font-size: 12.50px; " x="23.505865" y="0">𝑒</tspan>
<tspan style="font-size: 12.50px; " x="29.069754" y="0">𝑥</tspan>
<tspan style="font-size: 12.50px; " x="39.409836" y="0">=</tspan>
<tspan style="font-size: 12.50px; " x="51.45034" y="0">𝑁</tspan>
<tspan style="font-size: 12.50px; " x="62.090492" y="0">𝑥</tspan>
<tspan style="font-size: 12.50px; " x="71.742905" y="0">∗</tspan>
<tspan style="font-size: 12.50px; " x="81.070229" y="0">𝑁</tspan>
<tspan style="font-size: 12.50px; " x="91.710388" y="0">𝑦</tspan>
<tspan style="font-size: 12.50px; " x="100.68762" y="0">∗</tspan>
<tspan style="font-size: 12.50px; " x="110.00245" y="0">0</tspan>
<tspan style="font-size: 12.50px; " x="116.25401" y="0">.</tspan>
<tspan style="font-size: 12.50px; " x="119.37979" y="0">4</tspan>
</text>
</g>
</svg>, <svg height="14.8575" id="M306" style="vertical-align:-2.29482pt" version="1.1" viewbox="0 0 157.425 14.8575" width="157.425" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,14.8575)">
<text transform="matrix(1,0,0,-1,0.498,2.786)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝐽</tspan>
<tspan style="font-size: 12.50px; " x="6.7516847" y="0">𝑎</tspan>
<tspan style="font-size: 12.50px; " x="13.028251" y="0">𝑙</tspan>
<tspan style="font-size: 12.50px; " x="17.004244" y="0">𝑝</tspan>
<tspan style="font-size: 12.50px; " x="23.118269" y="0">ℎ</tspan>
<tspan style="font-size: 12.50px; " x="30.332569" y="0">𝑎</tspan>
<tspan style="font-size: 12.50px; " x="40.072498" y="0">=</tspan>
<tspan style="font-size: 12.50px; " x="52.113003" y="0">6</tspan>
<tspan style="font-size: 12.50px; " x="58.364563" y="0">.</tspan>
<tspan style="font-size: 12.50px; " x="61.490345" y="0">5</tspan>
<tspan style="font-size: 12.50px; " x="67.741905" y="0">0</tspan>
<tspan style="font-size: 12.50px; " x="73.993462" y="0">2</tspan>
<tspan style="font-size: 12.50px; " x="80.245026" y="0">9</tspan>
<tspan style="font-size: 12.50px; " x="86.496582" y="0">𝑒</tspan>
<tspan style="font-size: 12.50px; " x="94.836166" y="0">−</tspan>
<tspan style="font-size: 12.50px; " x="106.189" y="0">0</tspan>
<tspan style="font-size: 12.50px; " x="112.44056" y="0">0</tspan>
<tspan style="font-size: 12.50px; " x="118.69212" y="0">9</tspan>
</text>
</g>
</svg>, <svg height="12.57625" id="M307" style="vertical-align:-0.23825pt" version="1.1" viewbox="0 0 28.54875 12.57625" width="28.54875" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,12.57625)">
<text transform="matrix(1,0,0,-1,0.498,0.736)">
<tspan style="font-size: 12.50px; " x="0" y="0">1</tspan>
<tspan style="font-size: 12.50px; " x="6.2515602" y="0">0</tspan>
</text>
<text transform="matrix(1,0,0,-1,13.001,0.736)">
<tspan style="font-size: 12.50px; " x="0" y="0">%</tspan>
</text>
</g>
</svg> noise, sources (*), and detectors (o).</table>

Journal of Applied Mathematics

The Second-Order Born Approximation in Diffuse Optical Tomography

Figure 4