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<!-- comment -->
<!DOCTYPE html>
<html lang="en">
<head>
<meta charset="utf-8">
<title>Microscope objectives: Numerical aperture</title>
<link rel="stylesheet" href="stylesheets/style.css">
<link rel="stylesheet" href="stylesheets/prism.css">
<script src="javascript/python-highlighting/prism.js"></script>
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<script src="javascript/update_figures.js"></script>
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</head>
<body>
<section>
<a href="https://amsikking.github.io/">Home page</a>
<h1>amsikking: Microscope objectives</h1>
<a href="./index.html">Index</a>
<h2>Numerical aperture</h2>
<p>
The numerical aperture \(NA\) is usually provided by the manufacturer:
\[ NA = n \sin\theta \tag{1}\]
where \(n\) is the refractive index of the object and \(\theta\) is the
collection half angle
(<a class="citation" href="https://www.pearson.com/en-us/subject-catalog/p/Hecht-Optics-5th-Edition/P200000006793/9780137526420"
title="Optics, 5th edition; E. Hecht;
p220, ISBN-13: 9780133977226, ISBN-13: 9780137526420 (eBook),
(2016)">Hecht 2016</a>). The \(NA\) is often used to calculate other properties
of an objective, but this should be done with caution:
</p>
<ul>
<li>The objective should, at minimum, <em>collect</em> at the specified \(NA\)
on the <em>optic axis</em> (or to within a tolerance of a few %). However, it may
not image stigmatically at this \(NA\) and so the <em>effective</em> angular
collection for a given property of the lens (e.g. resolution) may be lower.</li>
<li>The <em>off axis</em> \(NA\) may be further reduced, not only from the limits
of the optical design, but by purposeful <em>vignetting</em> from a physical stop
or aperture, which directly removes the aberrated light that is often most
pronounced at the highest angles and away from the optic axis.</li>
<li>Whilst the <em>design</em> may indeed show (via simulation) that a perfectly
made lens would deliver a certain \(NA\). Real world manufacturing and
tolerancing may further limit or reduce the final angular range that gives
diffraction limited imaging.</li>
</ul>
<figure>
<img src="figures/objective_numerical_aperture.png" alt="objective_numerical_aperture.png">
<figcaption>
(<a href="figures/objective_sketches.odp">.odp sketch</a>)
</figcaption>
</figure>
</section>
</body>
</html>