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Fix typo in PSF width
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kmdouglass committed Oct 17, 2023
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Expand Up @@ -100,7 +100,7 @@ \subsection{The Point Spread Function} \label{sec:psf}
I \left(X\right) = I_{0} \left[ \frac{2 J_{1}\left(X\right)}{X} \right]^2
\end{equation}

\noindent where $ X = 2 \pi r \text{NA} / \lambda $, $r$ is the radial coordinate in the image plane, $\text{NA}$ is the numerical aperture of the microscope, and $\lambda$ is the wavelength of light. $J_{1}\left(X\right)$ is called the first-order Bessel function of the first kind. Its first zero, which is important for defining resolution as we shall see later, is at $\Delta X = 3.8317$. In terms of the radial coordinate, it lies at $\Delta r \approx 0.61 \text{NA} / \lambda$.
\noindent where $ X = 2 \pi r \text{NA} / \lambda $, $r$ is the radial coordinate in the image plane, $\text{NA}$ is the numerical aperture of the microscope, and $\lambda$ is the wavelength of light. $J_{1}\left(X\right)$ is called the first-order Bessel function of the first kind. Its first zero, which is important for defining resolution as we shall see later, is at $\Delta X = 3.8317$. In terms of the radial coordinate, it lies at $\Delta r \approx 0.61 \lambda / \text{NA}$.

\subsection{Image Formation in Linear Shift Invariant Systems}

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