Rangefinder Design - Framelines
to get framelines in focus, an element has to be added to bring them in focus for the rear element of the viewfinder. In terms of optics, this means that the framlines either have to be at one focal length from the element so that:
1/f = 1/o + 1/i
1/f = 1/f + 1/i
0 = 1/i
i = ∞
Hence the light is collimated, same as for the rest of the rays in the viewfinder. Alternatively, another element has to be added to bring the virtual image of the framelines to that distance. The trick is, for a PCX element if o is shorter than f1 then the virtual image i is still on the object side, but further than o. Essentially the image is being projected outside of the camera at the correct distance so that f2 can colimate it.
This whole assembly should be placed so that d + i (positive) is equal to the focal length of the eyepiece, f2. The issue thus arises that the rangefinder and framelines occupy the same ray path, with the former in the center and the later along the sides. In the M3 Leica solved this problem by directing the rangefinder path infront of the framelines.
Japanese Manufacturers often made a hole in the magnifying lens (f1) for the rangefinder patch to pass through, and used a beamsplitter to reflect the light for the framelines, where only the center part would let through light for the patch. The Nikon SP uses two sets of beamsplitter prism infront of each other instead of side to side, it also uses a porro-prism to offset it’s wide angle viewfinder. It’s a wonderfully odd and beautiful beast. All of this to say that there’s more than one way to skin a cat.