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-------------------------------- Optics Primer - Focal Reducers

--------------------------------------------------------- By Bill Claff

We have seen that adding a positive lens to a main lens will reduce the focal length.
In the case of attaching a close-up lens to the front of our lens we are able to focus closer but lose the ability to focus at infinity.
This same principle can be used to take a lens that focuses at infinity at a particular Flange to Focal Distance (FFD) and allow it to focus at infinity at a shorter FFD.
So, something can be attached to the rear of the lens to accomplish this and such attachments are generally called focal reducers.

Let's examine the focal reducer described in patent US 8,879,901.
The patent shows several variations of a focal reducer using an example lens but that lens is not fully described.
The patent does say it's a 60mm Nikon F or Canon EF lens so for the purposes of our example I'll use this Nikon 60mm f/2.8 lens:

with the close-up lens article I've highlighted the exit pupil.

Here's the focal reducer:

Here I've highlighted the entrance pupil; notice how far to the object side the entrance pupil has been placed. This is an important aspect of the design.
The specifications say this has a focal length of 102.6mm and the Optical Bench reports a pretty close 101.8mm value.

Now, let's stick the two together:

The resulting system has entrance and exit pupils that are pretty close the separate exit and entrance pupils although the roles are now reversed.
The Optical Bench reports the combination is f/2.03 with a focal length of 43.16mm.
Since this is designed to be a 0x71x let's check these results.
43.16mm / 59.99m = 0.72 and 2.03 / 2.82 is also 0.72; it certainly appears that the focal reducer works as advertised.

The design of the focal reducer relies on the exit pupil of the main lens being near the entrance pupil of the focal reducer.
If the exit pupil moves significantly the amount of focal reduction is affected.
At normal distances this isn't usually an issue, but since we've attached a 60mm "macro" lens let's push the boundaries as an experiment.
Here at 1x we see that the pupils have moved well away from the image plane:

In this extreme scenario the focal length actually increases slightly from 49.43mm to 54.54mm.
It would appear that focal reducers are not well suited to close-up work.

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