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What is the difference between an Optical Corrector (OC) and a standard Barlow?

In short. If you buy a true optical corrector or OCA the maker will tell you how to use it and what magnifications you will get in a Binoviewer..

 
Now in long. A Barlow is just that.  Usually a telenegative type lens that is used with a single eyepiece to achieve a certain amount of magnification.  You never use an optical corrector with a single eyepiece.  The term "optical corrector" or the acronym "OC" usually followed by an additional acronym for the different specific companies' almost exclusively refer to Binoviewer use.  This term became popular when binoviewers started to be supported by specific optical devices rather than barlowing a telenegative lens from a Barlow.  Hence the term "Optical Corrector" as it relates to binoviewing was born.  So in short an optical corrector is a lens system specifically designed for a Binoviewer regardless of the manufacturer.  The magnification amount is not specifically important, although most "OC's" start at lower magnifications then is possible when a simple Barlow is used.  OC's can be a simple telenegative doublet if that doublet is designed and specifically made to offset the optical path of a Binoviewer with a preset magnification factor.
 
Here I will try to help you understand better why simple Barlow elements respond the way they do when introduced to a Binoviewer application.  Most standard x2 Barlow's of average length  use an element "telenegative" of roughly -100mm's focal length.  That negative value represents the overall strength of the element or the effect it will have on the optical train.  It's placement in the telescope optical path and distance in relation to the eyepiece will determine the magnification factor that you finally get.  There are two ways to change the magnification factor.  Increase the distance between the eyepiece and Barlow element.  When focus is then achieved the magnification will be higher.  If you keep the distance relatively the same extra magnification can also be achieved by increasing the strength of the negative element.  A typical shorty Barlow is trying to achieve a greater magnification factor in a shorter distance.  These elements are typically -50mm to -75mm fl lens.  Because of the extra power or greater divergence of the element less of a distance is required to achieve x2. 
 
In a 1.6x Barlow of normal length the focal length is likely in the -140mm fl.  This explains the less magnification of that particular Barlow.  Now make a 1.6x in a shorty Barlow and likely you have started out with a normal -100mm fl in a typical Barlow and simply shortened the optical path between the eyepiece and element.  Now 1.6x is achieved because of not having a full optical path as would be the case in a x2 Barlow.   If this element is applied to a Binoviewer it's effect will be likely the same as a standard length x2 Barlow. 
 
Not to get overly windy, but more sophisticated optical correctors will use additional elements normally a positive and a negative set to first increase the focal length entering the corrector and then reducing the focal length exiting the corrector.  This makes the intervening space take the place of the binoviewers optical path.  This makes it possible to offset greater distances such as in the case of the optical path of the Binoviewer, but at a lesser magnification factor.  The formulas for these type of correctors can be somewhat complicated which makes it necessary for special optical elements to be used. 
 
So there you have it.  A mostly complete explanation of what an optical corrector is.
 

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