Math to calculate vignetting?

[MTGseattle]

The background: I recently got myself a Mamiya 6mf again after about a 12-year gap since I sold my last one. I did not source the Mamiya dedicated hoods for both lenses, so I bought a silly collapsible rubber one. I went with the first one on the shelf that had the required thread diameter. It causes a fair bit of vignetting on the G 50mm lens. Is there a way to calculate the distance off of the front of the lens barrel where vignetting will occur? My thought is to take a known quantity (some B&W skylight 1A) and just keep stacking them until I get vignetting. The problem here is 1. having to buy a bunch of 1A filters, 2. the delay in shooting and processing to get the results.
To do the proper math, would I need the very specific measurements from Mamiya regarding the lens if available? Another known quantity is obviously the proper hood designed for the lens which I could measure with a caliper and then have a distance within which no vignetting occurs.
The reason I am even asking this is I would like to try some techniques that would require my Lee filters.

https://lens-db.com/mamiya-g-50mm-f4-l-1989/ If the link works, it should be an image of 8 elements in 5 groups lens cell configuration. 76.4 degree stated angle of view.

Ultimately, if I have to "waste" another roll of film or 2 figuring this out, that's fine as I've already "wasted" 3 rolls just goofing up having been away from film for a while.

Any thoughts are appreciated.
-MG

 

[Dan Daniel]

I know this takes the fun out of it, but I check vignetting by focusing at infinity, lens wide open, open shutter. Open back, sSight from the corner of the film gate. Slide something forward until I see it cut off light at the corner. Put a shade on and off, seeing what happens when sighting from a corner.

Similar to one of the reasons that view camera glass often has the corners snipped- so you can see vignetting due to movements, etc.

 

[eli griggs]

Try to tubes by cutting them into sections with black paper or painted insides, then cut them longwise, and using a small section you can squeeze the cut black tubes into so they can slide back and fourth in, which is taped on either side to the lens.

By selecting different lengths of the blackened, sliced tubes, you should be able to find the correct lenght for a narrow lens shade, in a little time.

I doubt you'll need more than an inch of forward movement to to make a proper shade with.

Or,
you can consult a 1970's Morgan and Morgan for charts and how too's.


Good luck,

Eli

 

[BradS]

Seems like it might be better to simply get the proper OEM lens hood.

Stacking filters is not good. Each filter will reduce the light transmitted. To see the effect, stack a few on top of a clean white sheet of paper.

Maybe I'm missing something but the math in this case seems deceptively simple. If the angle of view of the lens is ~80 degrees, wouldn't a lens hood with an "angle of view" of (slightly) greater than 80 degrees be what you want?

 

[reddesert]

Brad has the right idea, but vignetting depends on the front element diameter and how deeply the front element is set behind the filter thread, so there's no simple answer like filter size X means hood size Y. As Dan says, you don't need to use any film to do this, you can check by looking through the lens to the film gate with the shutter open.

You probably bought a normal rubber lens hood, which will typically work for any lens with a "normal" angle of view (like 45-50mm on 35mm format). But your lens is a wide angle, so it vignettes. You need a wide angle rubber lens hood (although it may obscure part of the viewfinder), or the OEM hood. If you want to use Lee filters, put them on the front and remove the hood.

 

[MattKing]

There might be a mathematical solution, but I believe that you would need to be able to identify where the nodal points are for the lens in order to employ it.

 

[Nodda Duma]

It’s the diagonal FOV projected forward from the edges of the wide open entrance pupil as seen through the front lens. That is going to be the edge of the clear aperture of the front lens. Brad’s pretty close. Keep that cone clear and you’ll get no *additional* vignetting beyond what’s inherent in the design itself.

 

[Sirius Glass]

There might be a mathematical solution, but I believe that you would need to be able to identify where the nodal points are for the lens in order to employ it.

Finding the nodal point of a lens is more work than is needed. Follow post number 2 to converge on your answer faster.

 

[OAPOli]

You can compute that with good precision if you can locate the entrance pupil of your lens. The minimum hood diameter D at a distance L from the entrance pupil is D = f/fno + L*S/f where S is the sensor diagonal, f the focal length and fno the aperture. If you want a rectangular hood, S = sensor sides.

To find the entrance pupil. Secure the lens, open to bulb and close the diaphragm. Take a second camera on a tripod + nodal slide. Focus it on some landmark of your lens (e.g filter mount) and note the position of the nodal slide. Without changing focus, slide the camera until the aperture opening is in focus. The distance moved is the distance of the entrance pupil to the landmark.

 

[MTGseattle]

good suggestions all. I had a similar drawing roughed out to what @BradS posted above.
Some more info: This all is regarding the 50mm lens for the Mamiya 6/6MF. The way the in-camera electronics work, I can't trip the shutter with the loading door hanging open. I will double check when I complete my roll, but I am almost sure the safety interlocks do not let one do this.
I do own the "proper" Mamiya hood for the lens. I was going to try some pretty long daylight exposures so I'm trying to figure out if my Lee system will cause vignetting or not. In the near term, I will simply measure the Mamiya hood stand-off from the front of lens barrel and compare that with the stack of stuff a Lee system entails.
The idea of stacking skylight filters was just to get some easy measurements, i,e; if the filter is 3mm wide and I attach 4 of them and get vignetting, then 12mm added to the lens barrel is too much.
In @BradS image above, imagine the left and right side of the lens barrel getting longer. At a certain point they cross into the angle of view. The math of this point is all I am trying to avoid with a reasonable guess before I start wasting film.
I'm going to go put calipers on some of my gear...

 

[OAPOli]

For the Mamiya lens the pupil will be very close to the shutter blades. You can also guesstimate the location by eyeballing. Move a rule or card back and forth and you can tell when it's in the same plane as the aperture or shutter.

I'll add that the the formula I posted above is basically what @BradS showed. Just that the point of the FOV triangle is located at the entrance pupil, and the "point" is actually a segment representing the entrance pupil diameter. If that makes any sense.

 

[MTGseattle]

Here's a fairly non-scientific (or very light math) solution for now. The projection of the Mamiya hood from the end of the lens barrel is 18mm (there's a few decimal points in there but for my purposes I'll call it 18 mm) My current setup needed to hang a Lee 100 holder on the Mamiya 50mm is; a. 58-67mm step-up ring. b. Lee 67mm filter holder adapter. c. Lee 100 filter holder. This 3-piece combo stacked up to 19mm
If I order the Lee 58mm standard adapter, I can get rid of 2.5mm of step-up ring. This is all close enough that I'm not worried about wasting a whole roll of film due to equipment issues. Whether the film is "wasted" on a gimmicky technique and/or questionable compositions will remain to be seen.

 

[eli griggs]

A calculator for cone dimensions could help with this.

 

[gone]

There is no ready made formula, mainly because hoods have different flares, different OD's, and when you add a filter or two to things......

Dan and others have some good ideas. My philosophy is simple: w/ all things optical, use my eyes and a loupe, not a pencil or a calculator.

 

[AgX]

Seems like it might be better to simply get the proper OEM lens hood.

Stacking filters is not good. Each filter will reduce the light transmitted. To see the effect, stack a few on top of a clean white sheet of paper.

Maybe I'm missing something but the math in this case seems deceptively simple. If the angle of view of the lens is ~80 degrees, wouldn't a lens hood with an "angle of view" of (slightly) greater than 80 degrees be what you want?

View attachment 317164

You basically got the right approach: construct it graphically.

One needs three main points, at center of the edges and at the corner, the location of the principal point, the location of the filter thread. Projections of these points through the principal point are constructed and then parallel and longitudinally shifted from the cardinal point to the thread. From there on you construct the optimum shade.

 

[OAPOli]

There is no ready made formula, mainly because hoods have different flares, different OD's, and when you add a filter or two to things......

Dan and others have some good ideas. My philosophy is simple: w/ all things optical, use my eyes and a loupe, not a pencil or a calculator.

There is a formula I posted above. It was distilled from this document https://www.bbc.co.uk/rd/publications/rdreport_1962_20 which is a bit dense.

But what's annoying about hoods is that they have to be designed for the wide-open aperture otherwise they will vignette. Which limits their effectiveness because one rarely shoots wide-open. I've made custom hoods with a 3D printer for fun. But in the end I simply use my hand when there is a strong glare.

 

[eli griggs]

By calculating the dimensions of a cone, you can cut a piece of metal or paper that conforms to the 'Official' parameters of an OEM lens hood.

If you are still worried about vignetting, design the cone shaped hood to one or two filter sizes larger.

You can figure out how to mount the hood as you go.

Manufactures of camera lenses self published many lens designs in pamphlets touting the resolving power of their lenses with computer and blueprint semantics and there is no reason no to ask each other for measurements, tips and pdfs that many of us may have accumulated over the years.

Sigma and Tokina, etc made some nice posters of their lenses designs and that might be a good item to search out any Lens Makers might have published the year your lenses were made.

IMO.

 

[MTGseattle]

I appreciate all of the replies everyone. I do own the proper lens hood for the Mamiya 50mm. What started all of this was mounting an improper hood and wasting a roll of film. The vignetting caused by the improper hood had me wondering just where/how the vignetting occurred and whether or not I can use my Lee 100 series filters. I have film at the lab currently which will provide the answers.
Additionally, the "B" setting on one 6MF body doesn't work, which sucks.