-
Notifications
You must be signed in to change notification settings - Fork 3
/
Copy pathoptical_pixels.html
85 lines (68 loc) · 2.83 KB
/
optical_pixels.html
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
<!-- comment -->
<!DOCTYPE html>
<html lang="en">
<head>
<meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1.0">
<link rel="stylesheet" href="stylesheets/style.css">
<link rel="stylesheet" href="stylesheets/prism.css">
<script src="javascript/python-highlighting/prism.js"></script>
<script async src="javascript/Minimal-MathJax/MathJax.js?config=TeX-AMS_CHTML"></script>
<script src="javascript/update_figures.js"></script>
<script src="javascript/reference_list/reference_list.js"></script>
<title>amsikking: Optical pixels</title>
</head>
<body>
<header>
<nav>
<ul>
<li><h1 style="margin-top: 0rem; margin-left: 1rem; margin-right: 1rem">amsikking:</h1></li>
<li><a href="https://amsikking.github.io/">Homepage</a></li>
<li><a href="https://github.com/amsikking/microscope_objectives">GitHub</a></li>
</ul>
</nav>
</header>
<main>
<h1>Microscope objectives</h1>
<p>An introduction to 'infinity' corrected microscope objectives.</p>
<a href="./index.html">Contents</a>
<section>
<h2>Optical pixels</h2>
<p>
According to the <em>Nyquist criterion</em>
(<a class="citation" href="https://doi.org/10.1007/978-0-387-45524-2"
title="Handbook of Biological Confocal Microscopy, third edition;
J. Pawley; p64 , Springer US, ISBN 978-0-387-25921-5,
eBook ISBN 978-0-387-45524-2, (2006)">Pawley 2006</a>), the interval
between intensity measurements (the pixel size) should be less than or
equal to half the smallest feature size:
\[ r_{px} \leq \frac{1}{2} r_{min} \tag{1}\]
and,
\[ z_{px} \leq \frac{1}{2} z_{min} \tag{2}\]
If the smallest features are sub-diffractive, then (in a traditional
imaging regime) we can use the expected size of the diffraction
limited point spread function to determine the correct pixel size:
\[ r_{px} \leq \frac{1}{2} \frac{0.61 \lambda_0}{NA} \tag{3}\]
and,
\[ z_{px} \leq \frac{n \lambda_0}{NA^2} \tag{4}\]
In this case, the <em>voxel aspect ratio</em> scales with the
collection half angle according to:
\[ \frac{z_{px}}{r_{px}} = \frac{3.28}{\sin\theta} \tag{5}\]
For most objectives \( 0.1 \leq \sin\theta \leq 0.95 \),
and so in this regime the axial pixels are significantly
<em>longer</em> than the radial pixels:
\[ 3.5 \leq \frac{z_{px}}{r_{px}} \leq 32.8 \]
When considering optics and camera chips it is often useful to
calculate the number of pixels in the field of view:
\[ N_{px} = \frac{FOV}{r_{px}} \tag{6}\]
</p>
<figure>
<img src="figures/optical_pixels.png" alt="optical_pixels.png">
<figcaption>
(<a href="figures/objective_sketches.odp">.odp sketch</a>)
</figcaption>
</figure>
</section>
</main>
</body>
</html>