# Lens design.

Discussion in 'Camera Building, Repairs & Modification' started by nhemann, Apr 18, 2011.

1. ### nhemannMember

Messages:
203
Joined:
Jan 21, 2011
Location:
NJ - Near NY
Shooter:
Multi Format
I am slowly thinking my way through a homebuilt camera: I have a good source for loose lenses, good handle on how to make a bellows, plenty of skill with the tools, wood and etc. The question of the day is - how the heck do I determine what the image circle will be for a given focal length? Is it dependent on the lens diameter? There has to be an equation or something, right? Any light you LF or DIY-ers could shed would be most appreciated; reference material that you can direct me too? Even better. I'm planning on a single element on to start with - the engineer in me is dying to understand how to set up a multi-element as well - but first things first.
Thnks
neil

2. ### Ian CMember

Messages:
724
Joined:
Feb 8, 2009
Shooter:
Large Format
The diameter of the image circle at infinity is a function of both the focal length and the projection angle of the lens. We cannot calculate coverage unless we know both of these parameters.

If the projection angle of the lens is θ and the focal length = f, then the diameter d of the image circle at infinity focus is

d = 2f*tan(θ/2)

3. ### nhemannMember

Messages:
203
Joined:
Jan 21, 2011
Location:
NJ - Near NY
Shooter:
Multi Format
awesome, Ian - now we are getting somewhere. I assume that the projection angle is a design parameter from the OEM? I'm looking at a typical spec from the supplier and they look like this:

Manufacturer's part# 01 LAM 138, original unit price: \$54.00. Made of SF8 glass, design wavelength is 546.1nm. Clear aperture of 36mm, center thickness is 7mm, edge thickness is 5.2mm. Surface quality is 60-40 scratch and dig, centration is 3 arc minutes. Edges are .25-.50 bevel. Manufacturer's companion doublet for this lens: 01 LAO 138. Aplanatic lenses are free of spherical aberration and coma.

Would it just be a matter of getting ahold of the OEM or can this be determined otherwise - assuming that I am working in the world of horse shoes, if a decent estimate determines that its going to cover 4x5, 8x10 etc with some margin I am in good shape, eh?

4. ### ToffleMember

Messages:
1,848
Joined:
Mar 27, 2007
Location:
Point Pelee,
Shooter:
Multi Format
Thanks for throwing that out there, Ian. I was just about to start making stuff up.
Is it safe to say, though that the projection angle is a product of the rear element/group, or can the other groups affect this as well?

Supplimental question.... if, as the OP indicates, he is dealing with loose lens elements, (I've got a box full, too) how do you calculate the projection angle?

(I suppose you could reverse the calculations from the focal length and image circle, but any time I've tried to measure an image circle, I have come up with very fuzzy numbers... about as fuzzy as the edge of my circle. The last thing I want to promote here is fuzzy math. You can get eaten by dragons here when you talk fuzzy math. )

5. ### nhemannMember

Messages:
203
Joined:
Jan 21, 2011
Location:
NJ - Near NY
Shooter:
Multi Format
Its not nearly as dangerous as fuzzy logic, but just like The New Math, you need to be careful with the fuzzy stuff.

6. ### Ian CMember

Messages:
724
Joined:
Feb 8, 2009
Shooter:
Large Format
The projection angle is determined by the lens design. If the supplier cant provide the projection angle, then your only recourse is to test the lens when you get it to determine the angle and diameter of the image circle at infinity.

Youd have to set up the lens so that you focused a distant scene (infinity focus) onto a white surface and mark the boundaries of the projected circle with pencil.

This is most easily done by placing the lens and white surface in a darkened room and projecting a distant sunlight scene thorough a relatively small opening in a cardboard covering over the window.

Then youd know the diameter of the circle and can calculate the projection angle (although by then youd already know the diameter of the circle).

θ = 2*arctan(d/2f).

The circle not only has to cover the diagonal of the film holder, but you need to judge the quality of the projection as well. It might be that you judge, say, 70% of the diameter of the circle as usable, but the outer part might be too fuzzy or the light might falloff too much for a practial image.

7. ### Ian CMember

Messages:
724
Joined:
Feb 8, 2009
Shooter:
Large Format
I don’t think that there’s an easy way for us to determine ahead of time what the result would be of assembling multiple elements into a compound-element design.

The lens making companies have that ability, of course, but that’s beyond what we can do with the simple formulas available to us.

8. ### nhemannMember

Messages:
203
Joined:
Jan 21, 2011
Location:
NJ - Near NY
Shooter:
Multi Format
wow - I've just had a lot of floundering around the internets get prevented. Thank you so much. And boy, the neighbors are going to love watching as I crawl into a calibrated camera obscura to figure that one out. lol.

Ok then next issue: large vs small lens - as I see it from what you said above - given two lenses identical in quality and performance - I would pick a larger lens be able to keep my subsequent range of useful apetures larger i.e a low f of say 1.2 vs f4.5 or something? Is there a reasonable lower limit to f-stop in LF, I have seen a few pics here - Andrew Moxom's shot of that gun barrel comes to mind where where the DOF appears to almost literally be a plane.

9. ### Chris LangeMember

Messages:
780
Joined:
Aug 17, 2009
Location:
NY
Shooter:
Multi Format
I've ground my own lens before (as part of a glassworking studio at my university), and I ended up with a fixed focus ~65mm/1.4 single element optic, mounted inside an M2 extension ring for my Nikon.

It wasn't horribly difficult, just a time consuming process. Granted, I can make nearly any type of element I may need, since we have a full blowing and casting shop at our disposal.

10. ### Jim JonesSubscriber

Messages:
2,390
Joined:
Jan 16, 2006
Location:
Rural NW MO
Shooter:
Multi Format
I vaguely remember that the lowest practical f/ number for photographic lenses is around f/.7. As early as 1934 Leitz made a 75mm Summar f/0.85, but it was not used for traditional photography. Photographers had to be satisfied with the 73mm f/1.9 Hektor of 1931. I have one, and it is a very compact lens for that speed.

11. ### DenverdadSubscriber

Messages:
274
Joined:
Apr 20, 2009
Location:
Superior, Co
Shooter:
Medium Format
Neil,

The short answer is that there really isn't any simple formula for determinging the image circle of a lens based on focal length, f/#, etc. For example, two lenses with the same focal length and maximum aperture could project very different image circles depending on the details of their respecive lens designs. Factors such as the diameter of the elements (especially the front and rear elements) and the length of the overall assembly relative to those diameters come into play; but there is a lot more to it and there is no simple relationship.

If you want to empirically determining how big the image circle is for a given lens, I think someone already suggested putting together a sort of camera obscura setup to test it. This should be relatively simple to do.

For multi-element photographic lenses, you may be able to get a manufacturer's spec for image circle or projection angle (or alternatively, infer a minimum value from on the format for which the lens was designed since the image circle usually has to be at least as big as the diagonal of that format). But the idea of an image circle usually isn't applied to single element lenses. The reason is that light can make its way through a singlet lens at almost any angle - basically, there just isn't anything that prohibits light being transmitted through the lens until you get to pretty extreme angles (approaching 90 degrees, half angle). Of course that doesn't mean you can get sharp results at those more extreme angles! For a singlet lens the angle over which you can get acceptable image quality tends to be much smaller than whatever the maximum angle is, with increasing blur at larger angles. Just how blurry it is depends on the relative aperture (f/#).

Yes and no (as usual with optics!). Generally the larger aperture buys you better low light capability, higher shutter speeds for less subject or camera movement, shallower depth of field , etc. But as as you implied with the notion of a minimum useful f/#, a lens may have prohibitively high aberrations at low f/#'s and the meniscus lens certainly needs to be stopped down big time if your goal is to produce detailed images. Having said that, it is surprising just how good your image quality can be with only a meniscus lens when stopped down sufficiently. For what it is worth, my experience in medium format (6x6 usually) is that stopping down to the range of roughly f/16 to f/32 produces sharper results than most people would expect, even approaching the edges of the frame.

I think another criteria you should be thinking about is what your ultimate goal is as far as image characteristics. On the one hand, you may be looking to produce images of high technical qualiity and detail which you can print large. But at the other extreme, maybe reasonably sharp in the center of the image is "good enough" and you value image artifacts such as vignetting and blurring of the edges on artistic grounds. For the latter objective, the meniscus lens you mentioned would be a great place to start. However for the former, you might be somewhat disappointed in the results.

If you do experiment with a meniscus lens, there are some image characteristics you can play with in your design. For example, depending on whether you place your aperture stop in front of or behind the lens, you will get either barrel or pincushion distortion (I forget offhand which gives which). There may also be an optimal spacing between the lens and the aperture to consider.

Finally, you might be interested to know that the lens you mentioned was produced by Melles Griot (I recognize the numbering system). Actually, they are now called CVI-MellesGriot and use a new numbering sequence for their lenses. But they are still the same lenses and if you are interested about the application and use of their meniscus lenses you can find some interesting information here: http://www.cvimellesgriot.com/Products/Documents/Catalog/MENN_MENP.pdf

I hope that helps,

Jeff

12. ### nhemannMember

Messages:
203
Joined:
Jan 21, 2011
Location:
NJ - Near NY
Shooter:
Multi Format
Hi Jeff
Wow, you bet that helps. I am always impressed by this community's collective knowledge. I definitely have some further questions of a technical nature but, unfortunately no time to type them all at right now. The site that I found those lenses on is here http://www.surplusshed.com/lens.cfm The prices are good enough that I can definitely afford to do a little experimenting with, they even sell unmounted triplets and achromats - and while I can't speak intelligently about that now, I hope to soon. From a basic design theory, I'm not looking for razor sharp image (at least in a first iteration) but I don't want to end up with a LF Diana either. I think my goal is a camera lens with style and character, but not an attitude - if that makes sense.
Thank you for your time to write that up, and please keep an eye on this thread. I can feel a brain trust assembling
Neil

13. ### raoulMember

Messages:
120
Joined:
Mar 8, 2005
Location:
Melbourne
Shooter:
Medium Format
Can I recommend "Primitive Photography"? This book has some good simple lens designs for DIY. Made a triplet from lenses from surplusshed. quite easy and remarkably good quality!

14. ### nhemannMember

Messages:
203
Joined:
Jan 21, 2011
Location:
NJ - Near NY
Shooter:
Multi Format
yes you may and thank you, I'll check into it!