<?xml version="1.0"?>
<feed xmlns="http://www.w3.org/2005/Atom" xml:lang="en">
	<id>https://en.formulasearchengine.com/w/index.php?action=history&amp;feed=atom&amp;title=Truncated_6-cubes</id>
	<title>Truncated 6-cubes - Revision history</title>
	<link rel="self" type="application/atom+xml" href="https://en.formulasearchengine.com/w/index.php?action=history&amp;feed=atom&amp;title=Truncated_6-cubes"/>
	<link rel="alternate" type="text/html" href="https://en.formulasearchengine.com/w/index.php?title=Truncated_6-cubes&amp;action=history"/>
	<updated>2026-09-06T12:58:04Z</updated>
	<subtitle>Revision history for this page on the wiki</subtitle>
	<generator>MediaWiki 1.47.0-wmf.7</generator>
	<entry>
		<id>https://en.formulasearchengine.com/w/index.php?title=Truncated_6-cubes&amp;diff=25248&amp;oldid=prev</id>
		<title>en&gt;Tomruen at 09:21, 23 October 2013</title>
		<link rel="alternate" type="text/html" href="https://en.formulasearchengine.com/w/index.php?title=Truncated_6-cubes&amp;diff=25248&amp;oldid=prev"/>
		<updated>2013-10-23T09:21:01Z</updated>

		<summary type="html">&lt;p&gt;&lt;/p&gt;
&lt;p&gt;&lt;b&gt;New page&lt;/b&gt;&lt;/p&gt;&lt;div&gt;[[File:Afocal photography.png|thumb|right|350px|An afocal setup with a digital camera and a [[finderscope]] with optical diagram:&amp;#039;&amp;#039;&amp;#039;&amp;lt;br&amp;gt;&lt;br /&gt;
&amp;#039;&amp;#039;&amp;#039;1&amp;#039;&amp;#039;&amp;#039; - Telescope &amp;lt;br&amp;gt;&lt;br /&gt;
&amp;#039;&amp;#039;&amp;#039;2&amp;#039;&amp;#039;&amp;#039; - Camera&amp;lt;br&amp;gt; &lt;br /&gt;
&amp;#039;&amp;#039;&amp;#039;3&amp;#039;&amp;#039;&amp;#039; - Film or CCD plane&amp;lt;br&amp;gt;&lt;br /&gt;
&amp;#039;&amp;#039;&amp;#039;L1&amp;#039;&amp;#039;&amp;#039; - Telescope objective&amp;lt;br&amp;gt;&lt;br /&gt;
&amp;#039;&amp;#039;&amp;#039;L2&amp;#039;&amp;#039;&amp;#039; - Eyepiece&amp;lt;br&amp;gt;&lt;br /&gt;
&amp;#039;&amp;#039;&amp;#039;L3&amp;#039;&amp;#039;&amp;#039; - Camera lens]]&lt;br /&gt;
&amp;#039;&amp;#039;&amp;#039;Afocal photography&amp;#039;&amp;#039;&amp;#039;, also called &amp;#039;&amp;#039;&amp;#039;afocal imaging&amp;#039;&amp;#039;&amp;#039; or &amp;#039;&amp;#039;&amp;#039;afocal projection&amp;#039;&amp;#039;&amp;#039; is a method of [[photography]] where the [[camera]] with its lens attached is mounted over the [[eyepiece]] of another image forming system such as an [[optical telescope]] or [[optical microscope]], with the camera lens taking the place of the [[human eye]].&amp;lt;ref&amp;gt;[http://books.google.com/books?id=uk9WAAAAMAAJ&amp;amp;q=%22Afocal+photography%22&amp;amp;dq=%22Afocal+photography%22&amp;amp;lr=&amp;amp;cd=12 The British journal of photography, Volume 150, Issues 7410-7422 by The Liverpool Photographic Society]&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
==Overview==&lt;br /&gt;
Afocal photography works with any system that can produce a [[virtual image]] of parallel light, for example telescopes and microscopes. Afocal photographic setups work because the imaging device’s eyepiece produces [[collimated]] light and with the camera&amp;#039;s lens focused at infinity, creating an [[afocal system]] with no net convergence or divergence in the light path between the two devices.&amp;lt;ref&amp;gt;[http://books.google.com/books?id=WTKcbdR-2h8C&amp;amp;pg=PA76&amp;amp;dq=afocal+photography&amp;amp;cd=5#v=onepage&amp;amp;q=afocal%20photography&amp;amp;f=false Michael A. Covington, Astrophotography for the amateur, page 75]&amp;lt;/ref&amp;gt; In this system the device is focused on the object and the camera is placed above the eyepiece as close as possible. The drawback is the system will have a high [[focal ratio]], with a correspondingly dim image, and some [[vignetting]]. A high focal ratio also means the [[field of view]] will be narrow. Field of view can be calculated using:&lt;br /&gt;
&lt;br /&gt;
Focal [[field of view]]/[[angle of view]]:&lt;br /&gt;
: Approximate: &amp;lt;math&amp;gt;\alpha = {d \over f} \times {180 \over \pi} \equiv {180 d \over \pi f}&amp;lt;/math&amp;gt;&lt;br /&gt;
: Precise: &amp;lt;math&amp;gt;\alpha = 2 \arctan {d \over 2 f}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
==Use with optical telescopes==&lt;br /&gt;
One method of afocal photography is to mount a  [[camera]] with its lens attached behind the [[eyepiece]] an [[Refracting telescope#Keplerian Telescope|Keplerian]] optical telescope, the combination giving the photographer a [[long focus lens]]. Historically afocal photography with 35&amp;amp;nbsp;mm SLR or large format film cameras was a very difficult method of photography. With film cameras the bulk and mechanical shake had to be taken into consideration, with some setups employing a separate tripod for the camera (adding the complexity of setting up the camera in relationship to the eyepiece). The general difficulties of focus and exposure with film cameras, along with the detailed mathematical calculations, combined with the time lag of waiting for the film to be developed, meant film afocal photography could be pretty hit and miss.&amp;lt;ref name=Cicco&amp;gt;di Cicco, Dennis. [http://www.skyandtelescope.com/howto/astrophotography/3304336.html &amp;quot;Afocal What?&amp;quot;]. SkyandTelescope.com. Retrieved 2011-04-16.&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
[[File:Nikon digiscoping set.jpg|thumb|left|[[Spotting scope]] with a digital camera mounted afocally using an adapter.]]&lt;br /&gt;
&lt;br /&gt;
===Digital afocal photography===&lt;br /&gt;
The advent of [[digital single-lens reflex camera]] and, moreover, compact [[Point-and-shoot camera|point and shoot]] digital cameras has made the afocal method far more popular since this type of camera is small enough to mount directly on to telescopes or other devices, is for the most part a [[Solid state (electronics)|solid state device]] with minimal moving parts, has auto focus, has auto exposure adjustment, has some capacity for time exposure, usually has a zoom mechanism to crop vignetting, and has a video screen on the back side of the camera so you can actually see the image hitting the image plane.&amp;lt;ref name=Cicco/&amp;gt; A whole new industry has sprung up selling couplers and other devices for mounting digital cameras afocally. Simply holding the camera up to the eyepiece and snapping a picture can obtain usable results. Most popular types of consumer digital cameras have non-removable lenses so afocal photography is also the only method available for these types of cameras.&lt;br /&gt;
&lt;br /&gt;
=== Afocal astrophotography ===&lt;br /&gt;
Afocal photography is a form of [[astrophotography]] long practiced by astronomers. Afocal setups with film and digital cameras are not the preferred system for astrophotography since astrophotographers have many ways of coupling a camera to an astronomical telescope, the simplest being prime focus (using no camera lens and allowing the image to fall directly onto the film, or image plane of a digital single-lens reflex camera or purpose built [[Charge-coupled device#Use in astronomy|astronomical CCD camera]]).&amp;lt;ref&amp;gt;[http://books.google.com/books?id=tzXv4WrvZ-EC&amp;amp;printsec=frontcover&amp;amp;dq=astrophotography&amp;amp;cd=2#v=onepage&amp;amp;q=projection&amp;amp;f=false Michael A. Covington, Astrophotography for the amateur, page 69]&amp;lt;/ref&amp;gt; Almost from their invention amateur astronomers were adapting compact digital still and video cameras for use in afocal astrophotography.&amp;lt;ref&amp;gt;[http://books.google.com/books?id=WTKcbdR-2h8C&amp;amp;pg=PA243&amp;amp;dq=afocal+photography+digital&amp;amp;lr=&amp;amp;as_drrb_is=b&amp;amp;as_minm_is=1&amp;amp;as_miny_is=1994&amp;amp;as_maxm_is=1&amp;amp;as_maxy_is=2000&amp;amp;as_brr=0&amp;amp;cd=3#v=onepage&amp;amp;q=afocal%20photography%20digital&amp;amp;f=false Michael A. Covington, Astrophotography for the amateur, page 243, afocally video imaging from 1997]&amp;lt;/ref&amp;gt; &lt;br /&gt;
&lt;br /&gt;
But since most celestial objects require a long exposure, compact consumer digital cameras are somewhat problematic due to their high inherent sensor noise. This noise limits their usefulness, especially since point-objects, such as stars, can be obscured by even one &amp;quot;hot&amp;quot; [[pixel]]. The narrow field of view for this type of photography lends itself to lunar and planetary objects. Continuing advancements in digital camera and image manipulation have somewhat overcome this limitation and digital afocal astrophotography has become more popular.&lt;br /&gt;
&lt;br /&gt;
[[Image:Mergus merganser m.jpg|thumb|right|A &amp;quot;&amp;#039;&amp;#039;digiscoped&amp;#039;&amp;#039;&amp;quot; photo of a [[Goosander]], taken with a [[Fujifilm]] digital camera and a [[Kowa (optics)|Kowa]] [[spotting scope]]]]&lt;br /&gt;
&lt;br /&gt;
===Daytime afocal photography===&lt;br /&gt;
{{See also|Digiscoping}}&lt;br /&gt;
Since the development of compact digital cameras, afocal photography is also widely used by [[birdwatching|birdwatchers]], [[naturalist]], and other photographers. In the birdwatching community it quickly acquired the coined name of “[[digiscoping]]”. Birdwatchers and naturalist found a digital camera used afocally with a [[spotting scope]] to be a particularly effective technique since it gave them an easy way to record their subjects (sometimes by simply holding the camera up to the eyepiece) as well as allowing them to take relatively high quality photographs. Since these types of photographs are usually single subjects (narrow field) in daylight hours, the light loss and narrow [[angle of view]] are not a hindrance, and the high effective focal lengths are a plus. It also gives the photographer the use of a very [[Long focus lens|long lens]] without buying and lugging around extra equipment (except maybe a small afocal adapter). &lt;br /&gt;
 &lt;br /&gt;
This technique has lent itself to many other types of photography including photographing plants (for example, wild orchids growing in the canopy of a jungle), insects (for example, wild bees near their beehive), other shy or dangerous wild animals, or details in old buildings (for example, statues/gargoyles on the roof of old churches/castles).&lt;br /&gt;
&lt;br /&gt;
==Afocal secondary lenses==&lt;br /&gt;
Besides combining a Keplerian telescope with a camera, there are also dedicated [[secondary lens]] afocal attachments that mount on the front of a camera lens to work in the role of a [[teleconverter]], technically called [[teleside converter]]s. These lenses are usually [[Galilean telescope]]s that alter the width of the entering beam of light without affecting the divergence of the beam, so they can change the effective focal length 1 to 3 times without increasing [[focal ratio]]. There are models that are 6x or 8x and even Russian made 12x to 14x [[Gregorian telescope|Gregorian]] [[Maksutov telescope|maksutov]] designs that can be used as long lenses and microscopes.&amp;lt;ref&amp;gt;{{cite web |url=http://www.cs.mtu.edu/~shene/DigiCam/User-Guide/Odd-Stuff/6X-and-8X/6X-8X.html |title=The CrystalVue 8X and Kenko 6X Combo |accessdate=May 14, 2012}}&amp;lt;/ref&amp;gt; Like their Keplerian counterparts these can be universally adapted to most camera lenses with the proper type of adapter.&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
{{reflist}}&lt;br /&gt;
&lt;br /&gt;
==External links==&lt;br /&gt;
* [http://www.barrie-tao.com/afocal.html barrie-tao.com/afocal.html Afocal photography]&lt;br /&gt;
&lt;br /&gt;
{{Photography}}&lt;br /&gt;
&lt;br /&gt;
{{DEFAULTSORT:Afocal Photography}}&lt;br /&gt;
[[Category:Astrophotography]]&lt;br /&gt;
[[Category:Photographic techniques]]&lt;br /&gt;
[[Category:Birding]]&lt;br /&gt;
[[Category:Ornithological equipment and methods]]&lt;br /&gt;
[[Category:Photography by genre]]&lt;/div&gt;</summary>
		<author><name>en&gt;Tomruen</name></author>
	</entry>
</feed>