Actual Aperture Opening and f Stop

[Attasit]

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I've not really thought about this much beore but a few days ago, I saw a cross section of Leica 75 Noctilux f/1.25 and get very curious about the location of its aperture blades within the lens. 

 

If you look closely at the design of the lens, you can see that the likely location of the aperture blade should be between lens element 4 and 5 (counting from the front of the lens). But if this is correct, then how can we get f/1.25 which imply that the opening diameter of the aperture blade should be 60mm at 75mm focal length.

 

I measure the 75mm length from the sensor plane and it coincide about the same aread (with guessing on my part since I don't physically have a dissect 75 Noctilux in hand) atthe location between lens element 4 and 5. Clearly from any picture you can see of cross section of 75 Noctilux, you can clearly see that the maximum openning between the element 4 and 5 cannot be more than, say 50mm.

 

Am I missing someyhing here? I was under an impression that the openning at the focal length should be exactly 60mm for f/1.25 75mm.

 

Thanks.

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Edited February 2, 2022 by Attasit

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[jankap]

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[UliWer]

You are right to assume that the aperture is in the lenses center between the fourth and fifth lens element.

Though your assumption that the maximum opening of the aperture should have a diameter of 60mm would mean that all light rays pass the lens in parallels. Yes, the sensor would like this, though I fear you would never be able to focus your lens. 

A lens for photography is always a combination of converging and diverging lenses. A converging lens in front of the aperture bends the light rays as if they would pass through a wasp's waist. Even the light which is collected by the most outward regions of the converging lens will need a much smaller diameter after it leaves this lens. So putting the aperture behind a converging lens - or an essembly of lenses which converge the light rays -  means that you need less diameter for the aperture even if all the light which hits the front lens with much larger diameter is transferred.  

btw: @jankapWhere did you find the graph for the 75mm Noctilux on the Leica site? I looked for it but could not find it - this site is a complete mess. 

[jankap]

The site is not user friendly at the moment. "User" seen as interested photographer here, not as potential customer. Perhaps they have a difficult time. I could not find the info again via the same way. 

New try via google (Nocti&75&Leica AG): https://leica-camera.com/en-int/photography/lenses/m/noctilux-m-75-f1-25-asph

A software engineer is patient; by definition.🙂

 

[adan]

4 hours ago, Attasit said:

But if this is correct, then how can we get f/1.25 which imply that the opening diameter of the aperture blade should be 60mm at 75mm focal length.

Your "naïve intuition" that the f/stop must be the physical focal length/physical aperture diameter would be correct - for a simple single-element lens. Like a magnifying glass on a focus mount. Or other fairly simple multi-element lenses.

Once a lens consists of many multiple elements, some bending the light even before it gets to the aperture (and thus able to focus the light, to some extent, at the aperture), there is a bit more leeway.

This diagram shows a "ray trace" of how the older 75 Summilux bends light, from Erwin Puts' .pdf-book M Lenses - Their Soul and Secrets. But the Noctilux will be generally similar.

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Another trick that lens designers have is to permit some vignetting of the outermost rays from the front element on their way to the film or sensor. Below is the vignetting chart for the f/1.25 Noctilux.

When set to f/1.25 - the center of the picture gets 100% of the "f/1.25" light. But the corners lose up to 70% of the light rays as they criss-cross through the lens and aperture  - effectively it becomes an "~f/2.2" lens in the corners, and other aperture values in between, across the picture (the slope of the red dotted curve). Which probably average out to around 75mm focal length divided by 50mm opening (f/1.5).

The lens design could eliminate that vignetting - but it would then be perhaps 20% larger in diameter, and 45% heavier.

Most photo lenses incur some vignetting when wide-open and at anything but the smallest f/stops.

Allowing some vignetting is useful not only in setting the overall lens dimensions, but in "fixing" other optical problems, such as curvature of field, or corner resolution, or aberrations like coma and astigmatism. Lens design is always a "juggling act" with the laws of optics and physics.

(BTW these charts and diagrams can be found in the Technical Data .pdf files for each individual design, available both on that lens's "downloads" page at Leica's site, and in our own Leica Wiki of M lenses. Which includes the Puts e-book, for some lenses. Except for very old lenses (~ pre-1970-80)).

https://www.l-camera-forum.com/leica-wiki.en/index.php/M_Lenses_x_Focal_Length

Edited February 2, 2022 by adan

[Attasit]

Thanks everyone. This becomes much clearer to me. I assume similarly to the concept of multiple elements converging lights as in your explanation. Which mean that for subsequent smaller aperture setting (for example f/2 from f/1.4 for 75mm Noctilux), Leica simple close down the aperture to the point that the area of aperture openning is 50% at f/2 compared to at f/1.4.

 

But when I think about the converging light with maximum openning at the location of aperture openning to be the maximjm f/stop, it opens other questions to me. Such as, if this concept is correct (which I believe and agree with you that it is), then it would dictate that a very fast lens can be designed to be much smaller in diameter assuming we sacrify some other qualities such as vignetting, perhaps less sharpness, etc.

 

And effectively the aperture blades does not need to be fully opened at the maximjm aperture but rather just open enough to allow for the sufficient light to pass through to form the maximum f/stop. So Leica, for example, test the amount of light passing through each aperture setting to confirm the f/stop per each aperture setting.

 

It would be interesting if a very fast lens, say 35mm f/1.0 can be designed so that the front element bend the light more but keep the overall diameter except the front couple of elements similar size to 35mm Summilux.

 

Thanks.

[laowai_]

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On 2/2/2022 at 9:55 AM, Attasit said:

I've not really thought about this much beore but a few days ago, I saw a cross section of Leica 75 Noctilux f/1.25 and get very curious about the location of its aperture blades within the lens. 

 

If you look closely at the design of the lens, you can see that the likely location of the aperture blade should be between lens element 4 and 5 (counting from the front of the lens). But if this is correct, then how can we get f/1.25 which imply that the opening diameter of the aperture blade should be 60mm at 75mm focal length.

 

Hi Attasit,

you need to measure the apparent opening, i.e. how large the opening looks like when looking into the lens, not the opening you measure in the cross section. The apparent opening is called the entrance pupil.

 

The aperture of a photographic lens is defined as the focal length divided by the diameter of the "entrance pupil". 

The entrance pupil measures how large the clear opening of the lens is when looking into the lens. 

If a lens does not have any lens element in front of our aperture blades, then you can simply measure the size of your aperture and use that value as the size of the entrance pupil. Lens elements in front of your aperture blades usually enlarge how large the opening of the aperture appears to be. You need to multiply the size of the aperture that you measure by the magnification  of the lens group in front of the aperture. 

For the 75 mm Noctilux, what is the magnification of the lens group in front of the aperture? You'd have to ask the lens designers I suppose. If you know the exact geometry of the lens elements and the refractive indices of the glass used, you could reverse engineer this lens, too. 

 

 

[laowai_]

On 2/2/2022 at 7:37 PM, Attasit said:

 

It would be interesting if a very fast lens, say 35mm f/1.0 can be designed so that the front element bend the light more but keep the overall diameter except the front couple of elements similar size to 35mm Summilux.

 

I am sure this could be done. But as my friend Ed always said: "Because it could be done doesn't mean it should should be done". 

Rudolf Kingslake's book "Lens Design Fundamentals" is the classic textbook to answer these kind of questions.

https://www.amazon.com/Lens-Design-Fundamentals-Rudolf-Kingslake/dp/012374301X/ref=sr_1_2?qid=1644169713&refinements=p_27%3ARudolf+Kingslake&s=books&sr=1-2

And you can try it out yourself!

Go to a place like Edmund Optics where you can buy pretty much any lens you can think of (concave, convex, achromatic, aspherical, etc.), get yourself a 3D printer to build yourself some lens mounts. With a bit of practice and research I bet you'll be able to build yourself a few Lomography-style lenses for very little money.

For example, you'll get a coated precision polished aspherical lens with f/0.75 and 37.5 mm focal length for $509, shipped from stock...

https://www.edmundoptics.com/f/precision-aspheric-lenses/13139/

 

 

 

prnt_66325.pdf

Edited February 6, 2022 by laowai_