olyflyer wrote:

myzel wrote:

…

First, i don't like the concept of equivalency because it's futile. It tries to make something equivalent that isn't and while doing so makes so much assumptions that it is reduced to a nice feeling.

"Futile"? Why? Because you can't understand it or because you don't WANT to understand it?

You are aware that I answered the "Why?" question?

If equivalency isn't used to just get equivalent DoF and FoV, then there are to many assumptions needed to make it work to be useful in the real world. Sensor are different, lenses aren't available that have the exact focal length or aperture. Different format systems are simply that, different.

Why try to make something "equivalent" that isn't equivalent, that is used differently? Why try to make a CX camera work like a FX camera? Why not just use a FX camera?

We use single element lenses and assume that they are optical perfect.

That's too much simplification... real lenses are better than fictional single element lenses.

Sure, real lenses are used to make real photographs, but fictional single lenses are a good way to explain a concept.

We use cameras without lens mount and no flange distance.

Wow... OK, I believe in Santa also...

OK, nice to know.

We take a 135 format sensor ("full frame") and a 1" sensor, booth with identical sensor technology and the same amount of pixels.

Same amount of pixels? Why?

To get similar pictures.

If something should be assumed same then it is the pixel density, not the number of pixels.

That's an other valid way to look at it, but I preferred to look at the whole picture since most viewers will look at the whole picture.

Lets see what we need to get equivalency.

The FoV has to be the same, the DoF has to be the same, the image noise has to be the same and the shutter speed has to be the same. (I guess that's enough for the beginning).

OK. But what about ISO noise?

That's why I mentioned image noise.

Now lets look at a 50mm 135-format lens. To get the same FoV with CX we need a 18.5mm lens. Last time I checked 50 mm is much bigger than 18.5 mm. No magic involved, smaller format = shorter focal length = shorter lens barrel.

No magic, a 50mm real lens …

As I wrote in the beginning - a ideal single lens element construction. The length of a real lens will be different depending on flange distance and lens design.

OK, now lets look at the DoF. We want a f/2.8 135-format lens, so we need a f/1.0 CX lens (yea, not exactly but close enough). That would result in a 17.9 mm diameter entrance pupil and just lets assume that the front lens element has the same size (yea, simplification).

Actually... the 18.5mm lens would demand a front element of minimum 18.5mm in diameter. Not a lot of difference, but if you are typing decimals lets use the right approximation.

I wanted the DoF to be the same and therefore the entrance pupil has to be the same. In this case the entrance pupil is 17.9mm. The CX lens would have to be f/1.033. (d=f/# => #=f/d => 18.5/17.9 = 1.033). I think 1.0 is close enough to 1.033.

Now we have a 50x17.9mm lens and a 18.5x17.9mm lens. Don't know about you, but that CX lens is still smaller in my opinion.

This is totally wacko to me. Where did you get the 50x17.9 from?

Length x diameter. Thought it would be clear if I wrote all the time about a 50mm lens and a 17.9 mm entrance pupil.

A 50mm lens would NOT be 50mm thick, …

No, but it's 50 mm long (you know focal length and single lens element - I know, you think it's over simplified, but I made the simplification exactly because of this. Focal length is equal to lens length in that scenario).

Lets take a look at the other things. To get the same DoF we need to use that "equivalent" aperture, this results in a higher shutter speed on CX. Faster shutter speed results in a different image - so no equivalency unless we change the ISO accordingly.

Wrong. It will result in higher ISO

You know, that's why I wrote "unless we change the ISO accordingly".

… You must let the camera select the ISO because that way you actually make the image equivalent.

And that's why I wrote we have to change the ISO. Strange isn't it?

Changing the ISO only works if we assume that that change of ISO is linear to the crop factor - that is that a CX sensor has 3 times more noise than a 135-format sensor.

… So why would you like to ignore this assumption?

I didn't ignore that assumption.

This obviously only works if we use the 135-format not at it's base ISO, if we use it at base ISO we can't get "equivalency".

For the sake of discussion, this is totally irrelevant.

OK, this is where I took a short look at real world cameras. IF one of the cameras is at base ISO - lets say ISO 100 and the other, smaller sensor camera, has a base ISO of 100, then I can't use a lower ISO on the smaller camera. Not so irrelevant since in this case I can't get "equivalence" because I can't change the ISO of the small camera since it is already at the lowest ISO possible.

OK, so we use the CX camera at ISO 100 and the 135-format camera at ISO 800. Both have the same DoF and the same FoV, both have the same lens barrel diameter and the CX lens is shorter.

Wrong again. The ISO difference is not 3 stops, but 2.7x, i.e. multiply the ISO100 and you get ISO270. Quite a bit of difference from ISO800.

I want to use the same size of the entrance pupil. In my example this is 17.9mm and on FX that would be f/2.8 and on CX f/1.033. That's roughly 3 stops if I want to get the same shutter speed.

…

Cameras have a flange distance and interestingly the flange distance of the F-mount and the Nikon 1 mount are scaled versions of each other. This results in similar lens constructions at equivalent focal lengths. I guess it's save to assume that the lens lengths simply scale.

The flange distance is constant so the lens length differences will be: Lens length - FT1, regardless of focal length, meaning that the gain is largest at shorter focal lengths.

The flange distance of the F-mount is 46.5mm, the flange distance of the Nikon 1 system is roughly 17mm. So the flange distance of CX is roughly 2.7 times shorter than the flange distance of F-mount.

This results in Nikon being able to use roughly the same lens designs for FoV equivalent lenses. A wide angle lens for CX will require a very similar retrofocus design like a similar lens for FX. As I wrote I think it's save to assume that the CX lenses can be simply scaled versions of the FX lenses. In short, shorter versions of the FX lens (front lens elements will have to be the same size to get the same entrance pupil).

tl;dr:

Equivalent lenses can be/are shorter and will have the same sized entrance pupil and therefore the same sized front elements (diameter).