Relationship between image circle size and entrance pupil size?

quadrox

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As far as I understand, the size of the entrance pupil of a given lens is what determines the (maximum) f-stop for a given lens. For example, a lens designed for full-frame cameras with a focal length of 50mm and an entrance pupil of 25mm will give a (maximum) f-stop of 2 regardless of what camera/sensor size this lens is used on.

Mounted on an APSC camera the view will be cropped compared to a full-frame camera, which will mean that the final image will be different than for the FF camera according to the laws of equivalence, but it is clearly still a 50mm f/2 lens. Meaning that if the APSC camera could somehow magically capture the entire image circle instead of being limited by its physical sensor size, then the image should be entirely identical to what would be captured with a FF camera.

But here begins a train of thought that I want to make sure I have gotten right. If there were such a magical way of capturing the entire image circle on a crop camera, who is to say that the FF image circle is the limit? After all, couldn't the same logic be applied to the FF camera as well, make it magically capture the entire image circle? But then what would the size of that image circle be?


Since real world lenses do have finite image circles, I am assuming the image circle is limited by the parts that are not the entrance pupil. So I assume that obtaining a larger image circle would require all those other parts to be built larger, but the entrance pupil could still be limited to 25mm for our hypothetical lens. Is this understanding correct? Can someone point out in more detail exactly what parts of a lens could remain the same, and which parts would need to change to obtain a wider image circle? What impact would such changes typically have on image quality, if any?


And what about simple one element lenses, do they have an infinite image circle size? Something tells me that that wouldn't work, but then I am not sure how it would work. Can someone clarify this?
 
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As far as I understand, the size of the entrance pupil of a given lens is what determines the (maximum) f-stop for a given lens. For example, a lens designed for full-frame cameras with a focal length of 50mm and an entrance pupil of 25mm will give a (maximum) f-stop of 2 regardless of what camera/sensor size this lens is used on.

Mounted on an APSC camera the view will be cropped compared to a full-frame camera, which will mean that the final image will be different than for the FF camera according to the laws of equivalence, but it is clearly still a 50mm f/2 lens. Meaning that if the APSC camera could somehow magically capture the entire image circle instead of being limited by its physical sensor size, then the image should be entirely identical to what would be captured with a FF camera.

But here begins a train of thought that I want to make sure I have gotten right. If there were such a magical way of capturing the entire image circle on a crop camera, who is to say that the FF image circle is the limit? After all, couldn't the same logic be applied to the FF camera as well, make it magically capture the entire image circle? But then what would the size of that image circle be?

Since real world lenses do have finite image circles, I am assuming the image circle is limited by the parts that are not the entrance pupil. So I assume that obtaining a larger image circle would require all those other parts to be built larger, but the entrance pupil could still be limited to 25mm for our hypothetical lens. Is this understanding correct? Can someone point out in more detail exactly what parts of a lens could remain the same, and which parts would need to change to obtain a wider image circle? What impact would such changes typically have on image quality, if any?

And what about simple one element lenses, do they have an infinite image circle size? Something tells me that that wouldn't work, but then I am not sure how it would work. Can someone clarify this?
The 'size' of the image circle is determined by lens design and consequent vignetting in its various forms. Here is a good article on it.

Tokina AT-X Pro 11-16mm f/2.8 on Nikon Full Frame D610. Shot at 11mm, f/8.
Tokina AT-X Pro 11-16mm f/2.8 on Nikon Full Frame D610. Shot at 11mm, f/8.

Jack
 
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And what about simple one element lenses, do they have an infinite image circle size?
The simplest lens has no elements, i.e. a pinhole. It has a potentially infinite image circle, but the light falls off by an extreme amount at large angles to the optical axis and this will limit the useful image circle. At ninety degrees to the axis, the light in the image plane has dropped to zero, so the infinite image circle size is purely theoretical!
The problem with a simple one-element lens is that the aberrations increase rapidly as the angle to the axis increases, making the lens unusable at large angles. There would be no point in trying to use a large image circle.
 
Several of the images in the paper you refer to are upside down.

Fig 3 - enlarged field is above, not below per legend.

Fig 4 - Angle as defined as "b" in legend , is shown as "p" in image.

Fig 5 - text talks about angle "b", but image shows angle p".

Fig 6 - text in image is upside down
 
And what about simple one element lenses, do they have an infinite image circle size?
The simplest lens has no elements, i.e. a pinhole. It has a potentially infinite image circle, but the light falls off by an extreme amount at large angles to the optical axis and this will limit the useful image circle. At ninety degrees to the axis, the light in the image plane has dropped to zero, so the infinite image circle size is purely theoretical!

The problem with a simple one-element lens is that the aberrations increase rapidly as the angle to the axis increases, making the lens unusable at large angles. There would be no point in trying to use a large image circle.
Thank you, this part of my question at least is adressed well enough :)
 
The 'size' of the image circle is determined by lens design and consequent vignetting in its various forms. Here is a good article on it.

Jack
Thanks, the article looks interesting. I have not read it in its entirety yet, but it seems to address at least some of my questions :)
 

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