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Modifier Disks

Can someone explain to me just what a modifier disk does to the image through a scope? I get it that it reduces the incoming light and increases depth of field, and is evidently helpful in dealing with mirage, but I'm having difficulty in envisioning how the sight picture would change,
 
The sight picture doesn't change.. If your riflescope is focused on the target, it stays focused on the target. The image in the scope is not larger or smaller, it's just a little darker and if it's the middle of a nice sunny day, it won't make much of a difference in picture brightness.

As you already stated, the DOF will increase but that will be difficult to discern when you're focused 1000 yards away at 30X or more. Some people believe that the larger DOF allows you to detect mirage closer to you. I'm at 50X all the time and the DOF is not very deep, especially in front of the target line. Using a modifier equivalent to 1 f-stop, doesn't make a discernable difference in DOF to me. I paid lots of money for the 56mm objective, I try to extract from it all the resolution that I can (and paid for.)
 
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The modifier disk reduces the clear aperture which in turn reduces the image resolution (detail visible in the image)(about 33% reduction for the March Modifier Disk). That is how the modifier disk use will reduce the visible 'mirage' but maintain magnification. In extreme cases of atmospheric problems ('mirage', dust, smoke, haze, fog, air pollution) modifier disk use may be necessary to be able to shoot at all. However, this is a compromise of image clarity potential.

Us old radar guys refer to such practices as "smoothing the truth out of the data".
 

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