Lens math

[cyrus]

So could someone double check my math

Say we're talking about a rather large process lens - the 1070mm Apo Ronar

I understand that conservatively, it covers 40 degrees at infinity (I also see claims of 43 degrees) so
you get the diagonal at infinity = 778mm or 30inches


So it would cover a 21 inch square format at infinity. that not right is it?
Am I right? It seems like a fishy coverage and I have a nagging feeling I missed something.

Bellows draw would be 1070mm = 42 inches

[Nathan Potter]

Well, I don't quite follow. If you have a 1070 mm Ronar thats about a 42 inch focal length. That then is the approximate distance along the optical axis on the image side of the lens - say at infinity. If the angle of coverage is 40 degrees then 1/2 the diameter of the image circle will be 42 X tan 20 degrees = 42 X .325 = 13.6 inches. The image circle is twice that or 27.2 inches or 690 mm. Looks like it might cover a 20 X 20 inch square format or whatever format you would choose to fit in a 27.2 inch image circle.

Nate Potter, Austin TX.

[Leigh]

The 480mm Apo-Ronar has an IC of 396mm,

... so a 960mm version would have twice that or 792mm (31 inches).

The data sheet that I have only goes up to 480mm. It says the angle of view is "around 48 degrees".

For the lenses in that table, the flange focal length is slightly less than the optical focal length, so your bellows draw at infinity would be about 1070mm.

- Leigh

[cyrus]

Three different results so far. . . :)
Is this (http://www.prograf.ru/rodenstock/largeformat_en.html#table1) the table you were talking about Leigh?

OK let me see if I can do this math thingy (and I have a science degree! I should try to get a refund.)

The forumula is
diameter=2 x f x tan((angle in radians)/2)

So 40 degrees is 0.698 radians
Half of that is 0.349
tan(.349) =0.3638
Multipled by focal length 1070 = 389.2
multiplied by two = 778.5mm or 77.85cm
which when divided by 2.54 = 30.6 inches.

And that would cover about a 21" square format at infinity. (21.6 squared + 21.6 squared = 30.6 squared)

Right?

Assuming an angle of view of 40 degrees, of course. I have read 43 degrees and now Leigh suggests 48 degrees (I remember reading somewhere that there was a drastic fall in angle of view when you go over 900mm in process lenses, for some reason.)

If it was 43 degrees, that would come out to 842.72mm or 33.17 inches, and would cover a 23.45 inch square.

I think.

[Leigh]

You don't really need the radians conversion, although I suppose you can use it if you wish. :D

The simple right-triangle solution is tan(half angle) = opposite / adjacent. In this case 'opposite' is the distance from the center of the film to one corner, while 'adjacent' is the focal length.

We use the 'half angle', being the angle of view divided by two, since we're measuring from the optical axis, thus half of the AoV.

Solving we get opposite = tan(half angle) * adjacent = tan(20°) * 1070 = 0.36397 * 1070 = 389.5mm.

The film diagonal would be twice that, or 779mm = 30.7".

This is the same as your solution, with an explanation of the derivation.

It never hurts to use a smaller AoV in the calculations, to be conservative.

I thought the waffling about the AoV on the spec sheet was rather odd.

- Leigh

[Leigh]

1/2 the diameter of the image circle will be 42 X tan 20 degrees = 42 X .325
Correct statement, but

... the tangent of 20° is 0.363970, not 0.325.

- Leigh

[cyrus]

I think the "waffling" regarding the AoV is due to what was actually usable in process work vs. what was technically true. I'm sure that technically there is a wider AoV if you don't mind distortions/falloff/low resolution etc.

In any case a 20x24 format would require a diagonal of 31.24 inches so this lens would fall short if we assume a 40 degree angle of view.

[Leigh]

I think the "waffling" regarding the AoV is due to what was actually usable in process work vs. what was technically true. I'm sure that technically there is a wider AoV if you don't mind distortions/falloff/low resolution etc.
Yes, I expect each focal length was designed for a very specific process, so the specs may have been tailored accordingly. :cool:


In any case a 20x24 format would require a diagonal of 31.24 inches so this lens would fall short if we assume a 40 degree angle of view.
That diagonal (31.24" = 793.5mm) only requires an AoV of 40.7 degrees, which seems reasonable given the values discussed above.
I would certainly try it, if you have the option of not buying it if it doesn't work.

- Leigh

[cyrus]

OK so the next question is how that compares to a 750mm APO-Germinar's coverage.
I'm not sure what the weight difference is but we are comparing an f/14 to an f/9 so there's a mark in favor of the APO-Germinar and it requires less bellows extension to focus at infinity. However I can't find reliable figures on the AoV for the Apo Germinar.
Arne Croell says 46 degrees which means it has a diagonal of 636mm or 25 inches. That's substantially short of what an 20x24 would require, yes?

[Leigh]

I think the Apo-Germinar is way short of what you need.

As I mentioned previously, I think the 1070mm would be worth trying.

Lack of suitable lenses is one of the major problems with ULF, unfortunately.

- Leigh

[cyrus]

Even the 35" Red Dot Artar falls short - at 1:1 it is reported (http://www.largeformatphotography.info/forum/attachment.php?attachmentid=19647&d=1227076768) to have a coverage for 36x45. That means at infinity it would cover about 18x22.5

However all of these are regularly recommended for 20x24 ULF cameras, no? What's up with that?

(Maybe I'm making a mistake and the regular non-Red Dot artar has more coverage somehow? Seems unlikely)

[genotypewriter]

OK so the next question is how that compares to a 750mm APO-Germinar's coverage.
I'm not sure what the weight difference is but we are comparing an f/14 to an f/9 so there's a mark in favor of the APO-Germinar and it requires less bellows extension to focus at infinity. However I can't find reliable figures on the AoV for the Apo Germinar.
Arne Croell says 46 degrees which means it has a diagonal of 636mm or 25 inches. That's substantially short of what an 20x24 would require, yes?Going in reverse... a 750mm lens would need a 56 degree AOV to just cover 20x24 :) Does it look similar in shape (not size) to other 55 degree lenses like a 150mm f/9 for 4x5 or 300mm f/9 for 8x10?

G

[Leigh]

However all of these are regularly recommended for 20x24 ULF cameras, no? What's up with that?
You may be encountering a case of 'over-spec-itis'.

The process industry relies on extremely high technical standards.

The specs provided for lenses in that service may be much more stringent than those used for continuous-tone work.

For example, some process lenses operate at a fixed aperture (f/9 or ???).

It can be adjusted, but changes are made by a technician using special instruments, then the lens is locked for subsequent use.

- Leigh

[cyrus]

Oh I'm sure these lenses cover more than their official stats esp when closed down But the question is if I was in the market for a lens for a 20x24 wetplate camera, to be used mostly in the studio at about 1:1, what should I buy? The cheapest of the lot thus far is the 1070mm Apo Ronar but the only concern I have about that is the significant bellows draw. They'll all more than cover at 1:1 but the day may come when I go outdoors with a 20x24...nah, unlikely. the apo germinar is sooooo heavy but is an f/9 nice and bright and in great shape with a flange. The RDA looks like in great shape too but twice the price of the other two. Anyway, hard choice. Tips welcome :)

[Dan Fromm]

Cyrus, if you're going to shoot 20"x24" at 1:1 at f/22 or smaller, Rodenstock's Process Lens Handbook says that any Apo-Ronar CL from 485 mm up will do. The suffix CL indicates a modern Apo Ronar with elements cemented in place ("C") and a linear aperture scale ("L"). Plain old Apo Ronars should do as well for you.

The 1070 you're thinking of won't quite cover 20x24 at infinity at f/32.

[cyrus]

Cyrus, if you're going to shoot 20"x24" at 1:1 at f/22 or smaller, Rodenstock's Process Lens Handbook says that any Apo-Ronar CL from 485 mm up will do. The suffix CL indicates a modern Apo Ronar with elements cemented in place ("C") and a linear aperture scale ("L"). Plain old Apo Ronars should do as well for you.

The 1070 you're thinking of won't quite cover 20x24 at infinity at f/32.

It will have to do since, 1- I bought it, and 2- it has a 7 foot bellows draw and there's no way I can think of that anything could go longer and still be the least bit practical.
Nevertheless if anyone comes across a 1200mm or 1800mm Apo-Ronar, keep me in mind!

[Jan Normandale]

I love these lens discussions. No wonder most of us are puzzled by the question of "lens coverage"

[Bob Salomon]

The Apo Ronar CL lenses longer then 480mm covered 40 - 46° according to Rodenstock.

[Bob Salomon]

Oh I'm sure these lenses cover more than their official stats esp when closed down But the question is if I was in the market for a lens for a 20x24 wetplate camera, to be used mostly in the studio at about 1:1, what should I buy? The cheapest of the lot thus far is the 1070mm Apo Ronar but the only concern I have about that is the significant bellows draw. They'll all more than cover at 1:1 but the day may come when I go outdoors with a 20x24...nah, unlikely. the apo germinar is sooooo heavy but is an f/9 nice and bright and in great shape with a flange. The RDA looks like in great shape too but twice the price of the other two. Anyway, hard choice. Tips welcome :)

Rodenstock 360mm Apo-Gerogon f9 at 1:1 covers 24x36" and the 300mm Apo-Gerogon covers 22x26" at 1:1.

The Apo-Gerogons, according to Rodenstock, covered between 70 and 78°, are optimized at f22 and the focal lengths are ±1% whereas the Apo Ronar CL were ±0.5% of their effective focal length. The Eff. Focal Length of the 1070mm was 1070.5mm where the EFL of the 300mm Apo-Gerogon was 308.3mm and the 360mm was 354.6mm.

Recommended scale of reproduction for the 1070 was 1/10x to 10X and for the 300 and 360mm 1/5x to 5x.

[cyrus]

See Bob, that's why we need you to always be online!
So the Apo Ronars have an AoV of 40-46 degrees and the Apo Gerogons have an AoV of 70-78 degrees
If we even take the low end of the AoV for the longer lenses (1070 and 750) then they should both cover at infinity, and of course more than cover at 1:1. In fact at 1:1 I may get a shorter lens just to avoid the huge bellows draw for studio work. Maybe I'll try my schneider 360mm enlarger lens...?

[cosmicexplosion]

what would be a good lens to chase for 30"wet plate>?

short, as i want a ritter to travel with

i am not up to speed with the math, but i have a 24" artar, a 455mm nikkor proccess and a 19 dagor,

any of them come close

[Dan Fromm]

30" x 30"? 30" x what? It makes a difference.

If 30x30, you need a lens that will cover 42 inches. Used at infinity none of the three lenses you named will come close. The 1800/16 Apo Ronar will cover 30x40 at infinity, no shorter Apo Ronar will.

A lens that covers 90 degrees will cover twice its focal length. So if you want a short (relatively) 90 degree lens that covers 42" it will have to be a 21 incher. Schneider's Fine Art XXL 550/11 won't do it.

A 450/14 or 500/14 Perigraphe would do for you, but these are pre-WWI lenses and very scarce nowadays.

Good luck in your search.

[cosmicexplosion]

thanks dan sorry late reply

how does it make a difference; 30 x40 or 30 x 30"

are we not dealing with a circle?

also isnt twice the focal length of 24 48?

so if 762mm or 30" is the film plane 48 is enough to spare?

i am clearly missing some thing.

cheers

[Dan Fromm]

thanks dan sorry late reply

how does it make a difference; 30 x40 or 30 x 30"

The diagonal of a 30 x 40 rectangle is 50. The diagonal of 30 x 30 is 42 (rounded, Leigh, don't you dare jump on me for rounding). A rectangle's diagonal (a square is a rectangle too) is the diameter of the smallest circle that will cover it.


are we not dealing with a circle?

Yes, see above.


also isnt twice the focal length of 24 48?

Yes, again. So what?

I ask because for a given prescription the angle covered declines a bit as focal length increases. This because increasing focal length increases the size of the blur circle due to aberrations and some aberrations -- look here http://toothwalker.org/optics.html for a concise explanation of which ones -- get larger as the distance off-axis increases.

Apo Ronars have come up a lot in this thread. Note that there's more than one Apo Ronar prescription.


so if 762mm or 30" is the film plane 48 is enough to spare?


Sorry, I don't understand what you're getting at.

i am clearly missing some thing.

Sorry, you seem to be. Please think a little about what you're trying to do and ask again.

Cheers,

Dan

[Leigh]

The diagonal of 30 x 30 is 42 (rounded, Leigh, don't you dare jump on me for rounding).
42.4264, but who's counting? :p

We'll let it slide this time. :D

- Leigh