Geometry whizzes, I need your help with a rhombus!

[Hops]

I'm not so great at geometry, but I imagine this will be an easy problem for someone...

I'm repairing a Nikon FM that I got for peanuts. It works perfectly, but has some cosmetic problems, so I am swapping parts from a couple other dead FM bodies. I needed to replace the focusing screen, and while removing it, I failed to notice that there are shims under the four screws that hold the focus screen/prism assembly. These shims adjust the height of the focus screen, and thus, focus calibration. I don't know which shims go where, so I need to recalibrate.

So my idea is to create a test target that when viewed from 45 degrees, appears square in the viewfinder. I would use a macro lens, or even a reversed lens with at least a 1:1 magnification so as to have as shallow a DOF as possible.

So here is a rough draft of my idea for a rhomboid test target.

Can someone provide me with the calculations to make this appear precisely square in a viewfinder that is tilted 45 degrees?

I tried making a rectangle and running it through the Photoshop lens correction filter, applying a vertical tilt, but it does not use degrees as it's unit. If it did, then negative 90 would be an invisible 2D line, but it still shows a rhombus.

 

[Hops]

Oops! It is a trapezoid! Thanks Ian. (told you I wasn't good at geometry)

 

[Ian C]

I and many others here might calculate what’s needed if the problem was well defined. But as you’ve stated it, I don’t know what you mean by the words you’ve used.

Can you clarify this statement?

“Can someone provide me with the calculations to make this appear precisely square in a viewfinder that is tilted 45 degrees?”

I know that the idea is clear to you, but it isn’t to me and it likely isn’t clear to other readers as well.

Literally, it sounds like you want to tilt the viewfinder 45° and see the target as a series of rectangles.

The shape you’ve provided appears to be a trapezoid.

Or instead, do you mean: how do you draw a trapezoid that appears rectangular when tilted 45°? If so, it can’t be done. A trapezoid drawn in a plane and tilted 45° from its horizontal axis as shown will still appear as a trapezoid that is not as tall as it is in the plane.

I’ve just draw several and tilted the paper both forward and back until the paper becomes a single line. Until it vanishes the trapezoid remains a trapezoid to my vision.

It strikes me that the focus screen must be parallel to the bottom of the prism and every horizontal reference plane in the camera and that it must be at a definite distance from the prism and from the mirror.

Obviously, the distance from the nodal point of the lens to the film must be the same distance as from the nodal point to the mirror + the distance from the mirror to the roughened surface of the FS to achieve the same focus on the screen as at the film plane.

You claim that the shims are for adjustment, but how do you know this? I wonder if you’re misinterpreting their purpose.

It seems unlikely that the shims are employed as a method of adjusting the screen angle or its height above the mirror. Rather, it seems more likely that these “shims” are simply intended to grip the FS without damaging it.

Are the “shims” fiber, rubber, metal?

I’d expect that the positioning of the mirror is foolproof with respect to the location and orientation of the FS. If I was the designer I’d want the system as foolproof as possible. By engineering a fixed position for the screen, all sorts of unnecessary problems would be avoided. Of course, I might be wrong.

I have Thomas Tomasy’s somewhat generic Nikon Repair book at home. When I go home this evening I’ll look at it and see if Tomasy says anything about this and report back tomorrow. At one point I believe he covers the FM. But this book is generic. Nothing is covered in great detail.

 

[Hops]

Thanks Ian. I'm quite sure the shims are used to adjust the height of the focus screen so that it matches the registration distance of the film plane. The shims are metal washers, and in my Nikon FM2 repair manual, they are referred to as shims and parts are available in many tiny increments. There is also a description of the calibration method, which uses a collimator and a test jig.

Yes, I want it to appear in the viewfinder as a series of concentric rectangles. I would then be able to see the DOF cutting across the center of the frame, and get it level across the frame. I would then adjust it so it matches a piece of ground glass on the film rails.

I got this idea by putting the camera on a tripod, aiming it 45 degrees at a piece of paper, and then using a pencil to trace the outline in the viewfinder. I got a trapezoid shape that was skewed because the focus screen is off. I suppose some of this skew could be because of the angle I look through the viewfinder.

But I've just realized that the dimensions of the trapezoid would depend on the distance to it! The side of the trapezoid closest to the camera will appear shorter than the opposite side, proportional to the distance from the ground glass.

Correct?

 

[Steve Smith]

But I've just realized that the dimensions of the trapezoid would depend on the distance to it!

I was about to mention that.

Instead, could you focus on a piece of squared or graph paper which is aligned perfectly parrallel to the film plane?

If so, if the focusing screen is out of alignment (i.e. at an angle to its optimum position, The pattern may not appear perfectly square.

This won't help if it is uniformly out of position though.


Steve.

 

[Mike Wilde]

why not a test negative in a slide copier as an alignment tool. You indicate that you have a macro lens so you are familiar with shallow dof that macro presents.

 

[Ian C]

If you have the repair manual then you already have some good information to begin with.

Your comments make sense with respect to the size distortion we see when viewing the near and far sides of a flat rectangular sheet of paper viewed at an angle to the axis of the lens.

However, I don’t understand how the proposed trapezoidal test target will help you to set the position and angular orientation of the focusing screen.

Why not use a concentric pattern of rectangles in a flat target set parallel to the film plane? Isn’t that closer to the procedure given in the manual? It should accomplish what you want with the advantage that it’s much simpler.

 

[Christopher Walrath]

Just a 0.02 here. The focus screen needs to be the distance from the nodal point equal to that of the film plane as this is where the image is focused. As to the exact spacing required for the prism above the focusing screen, no idea. But the nodal point focal distance definitely needs to be the same to the film plane and to the focusing screen.

 

[Ian C]

Additional comment to #7:

By viewing both through the finder, and then with the shutter set at B or T, through a small ground glass with the roughened side resting on the film rails, you could see when the two images match in terms of parallelism. When they do, the focusing screen is in the correct angular configuration.

When the focus at the viewfinder and ground glass agree, then the position of the screen is correct.

 

[Hops]

Well, my idea of calibrating at a 45 degree angle was to minimize DOF, thus revealing alignment.

Thanks to your ideas, I am now thinking this is unnecessary

I think I need as shallow a DOF as possible. What if I used a reversed lens to get something like a 4:1 magnification and just focussed on a piece of graph paper? Would the DOF be shallow enough to make adjustment obvious? I guess I'm after a paper-thin DOF, literally!

If I need to enhance the target further, I could place four small screws, standing on end, in the four corners of the frame. The threads would serve as a ruler.

I have a Nikon PB-4 bellows with the slide copier attachment. I suppose that will be a square enough reference.

 

[ic-racer]

45 degrees, Huh?
Use infinity (distant object)

 

[Hops]

At infinity, the DOF will be too large to determine alignment. I am making no adjustments to the film plane, so should not affect infinity focus. Thanks!

 

[Bob-D659]

Grab a piece of exposed and developed film, with a very sharp knife, scribe an X from corner to corner and a cross thru the center. Put it in the slide copy attachment and focus on the center using a ground glass or your messed up focus screen so all corners and the center are in focus. Now close the shutter and shim the screen until it matches the image at the film plane. No need to worry about infinity focus or anything else, unless you removed the lens mount.