How to calculate the Image Circle

[Wurstman]

Hello there...

I've found out about this messgae board through a google search on the "image circle" but didn't find a statisfying answer yet... Maybe on of you can help me out though

All I could find was the derivation of the angle of view if the sensor size is known...
But what happens if you dont know both of them?

I'm trying to calculate the image circle of a camera lense to prove that I could possibly use it with a sensor that differs in size. I got this lens. The data sheet says that the lens got an image circle of 30mm.

My understanding is that one could calculate the image circle by "sending" a beam of light which starts at the center of the principal plane H' on the image side and crosses the edge of the exit pupil X and finally crosses the image plane. Then one should be able to derive the radius of the image circle since the size of the exit pupil and the distance of the principal plane H' to the exit pupil X.

Is there anything wrong with my thoughts?

[Colin Southern]

This may seem too obvious, but if one didn't believe the datasheet then surely all you'd need to do would be to measure it with a ruler (in essence it's just the diameter of the lens element at the back)?

I'm not sure what camera it's designed for, but I would have thought that so long as it mounts - is the right distance from the sensor - and the diagonal distance across the sensor isn't more than 30mm then you should be good to go (assuming no issues with aperture selections etc).

[Saorsa]

The leica mount is a 39mm thread with a flange to sensor distance of 28.8mm. It has a fine pitched whitworth thread.

This would mean that the lens would project a 30mm circle at a distance of 28.8mm when focused at infinity. For closeup applications, it will project a larger circle as magnification increases.

[Manfred M]

I would have assumed that the image circle is the same dimension as the diagonal of the the sensor.

[Saorsa]

The image circle is a characteristic of the lens. you can have equal FL lenses with different sized image circles. An 85mm designed for a 35mm camera has a smaller image circle than an 80mm designed for a 6x6.

[Colin Southern]

The image circle is a characteristic of the lens. you can have equal FL lenses with different sized image circles. An 85mm designed for a 35mm camera has a smaller image circle than an 80mm designed for a 6x6.

I agree, of course, but to me it almost seems like people are missing the forest for the trees on this one. Because image projections out the back of the camera are round - and because sensors are rectangular - then providing that the diameter of the (projected) circle is equal to or greater than the diagonal (the "diameter" of the sensor if you will) then "no problem".

As to how much the projected image circle diameter varies from the diameter of the last optical element I have no idea, although I suspect that the answer would be "virtually nothing" considering the short distance involved.

In summary, "the bigger the sensor the bigger the hole at the back of the lens that's needed to cover it", but the actual maths seem trivial, unless I'm missing something here?

[Saorsa]

I agree, of course, but to me it almost seems like people are missing the forest for the trees on this one. Because image projections out the back of the camera are round - and because sensors are rectangular - then providing that the diameter of the (projected) circle is equal to or greater than the diagonal (the "diameter" of the sensor if you will) then "no problem".

As to how much the projected image circle diameter varies from the diameter of the last optical element I have no idea, although I suspect that the answer would be "virtually nothing" considering the short distance involved.

In summary, "the bigger the sensor the bigger the hole at the back of the lens that's needed to cover it", but the actual maths seem trivial, unless I'm missing something here?

It's not so much the diameter as the actual optical design of the lens. An extremely complex subject in it's own right.

I am really surprised at the small size of some rear elements like that of the kit lenses.

[ajohnw]

If the OP wants to capture all of the 30mm image circle the sensor diagonal will need to be under 30mm if not all that will happen is that only the 30mm will be recorded. Not a problem really but it will need the rounded bits cropping off.

The diagonals of the various sensore sizes can be calculated from this.



It isn't really possible to relate the diameter of the last element in a lens to it's image circle. It will generally be smaller. Sometimes a lot smaller. In that case on M 4/3 for instance the last element would be recessed into the back of the lens. They often are in practice - on my lenses anyway.


As an aside the sensor sizes show just how much of an improvement a Nikon 1 should be over typical bridges etc.

John
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[ajohnw]

Another attempt if the OP has some unknown lens. Point it at some distance object and focus the image onto a card and measure it. Best done through a gap between drawn curtains.

I think the OP has the term principle plain mixed up. They relate to the points in a lens where all of the refractive action can be considered to take place. A google should clear that up quickly.

It might be possible to determine the image circle of a lens optical bench style by projecting a narrow beam and rotating the lens about it's nodal point but considering that the that a lens flange to sensor distance should be controlled to better than 0.05mm locating the nodal point will not be easy. It's best found by using a collimator to generate a plane wave that the lens should then focus to a point.

Google can clear up the gobble de guk.

John
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[tao2]

Hello there...

I've found out about this messgae board through a google search on the "image circle" but didn't find a statisfying answer yet... Maybe on of you can help me out though

All I could find was the derivation of the angle of view if the sensor size is known...
But what happens if you dont know both of them?

I'm trying to calculate the image circle of a camera lense to prove that I could possibly use it with a sensor that differs in size. I got this lens. The data sheet says that the lens got an image circle of 30mm.

My understanding is that one could calculate the image circle by "sending" a beam of light which starts at the center of the principal plane H' on the image side and crosses the edge of the exit pupil X and finally crosses the image plane. Then one should be able to derive the radius of the image circle since the size of the exit pupil and the distance of the principal plane H' to the exit pupil X.

Is there anything wrong with my thoughts?

Ah'd believe the original spec. If they claim 30mm, then, within a tiny fraction, it will be. Schneider is an old, well-respected lens+optic manufacturer. Ah found that the limitations of using an enlarger lens (without a helical focus ring) is more constricting than the useable sensor size, from experience.