Why does focus distance affects depth of field

[Shai]

Hi,

I've been a long time reader but this is my first post, hope I'm using the right forum.

One of my students asked my WHY does the focus distance affect DOF. I just couldn't clearly explain it to him. I know I must have learned it way back in photography collage but I just can't seem to remember.

It's common knowledge that subject distance affects DOF, but why? does it have to do with magnification? I know the formulas, but I'm more interested in the logic behind them than the actual calculation.

Thanks!
Shai

[Andrew1]

If you google "how does depth of field work" you'll get a few million hits and some will show you the math.

[NorthernFocus]

It's basically geometry. You can check out the on line DOF calculator which has some nifty tools and does a good job of explaining with both math and pictures.

[ajohnw]

It's a very woolly subject. In real terms a lens doesn't have any depth of field at all. Best illustrated with diffraction limited optics. The lens will give this resolution with objects a certain distance from it causing an image which is also a set distance behind it. If the distance to the object is changed so does the distance to the image behind the lens and the lens will become less and less diffraction limited. Camera lenses are a little different. They can be focused and aren't diffraction limited. They produce circles of confusion rather than diffraction spots. When focused the minimum circles of confusion are focused onto the sensor.

For some final reproduction size there is a certain sized circle of confusion that is not obvious to the human eye at a certain distance. There are some calculators about that do this correctly for prints by allowing the viewing distance to be specified. It cam come as a bit of a shock.

Now the crunch remembering that the circles of confusion increase in size each side of the best focus. Lenses have 2 types of magnification. Opticians call them transverse magnification and longitudinal magnification. The transverse one is what fits an image onto the sensor in a camera and simply relates to the distance from the subject over the focal length of the lens. The longitudinal one relates to 1/focal length + 1/distance to the subject. In other words the longitudinal spread the length of the object causes each side of the the best focus. So taking an object 25mm long and 100mm away the 25mm is a bigger proportion of the distance than it would be if the object was 100m away so the magnification is greater = more spread each side of the minimum circle of confusion / best focal plain.

Not easy to explain. A search for the terms will bring up formulae and probably example calculations that might be done in several ways. As it will be for optical people it's best to remember that magnification can be more or less than 1. They also sometime view things the other way round ie from the sensor end in respect to a camera - that gives a magnification of greater than 1. They swap images and objects around to suit as calculation wise it makes no difference. You might find I have used the term focal length when I should have used the power of a lens which is 1/f too. Don't think so but it's mostly from memory.

John
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[Mike Buckley]

This is a fascinating topic. I would actually make a point of following this thread if I believed for as little as a nanosecond that I would be able to understand the details. My hat is off to all of you who do.

[jcuknz]

Forget the maths and make a drawing ... as Dan Northern Focus wrote it is simple geometry. Working with these drawings adjust the focus points while maintaining the refraction angle.

and


You will need a larger sheet of paper

[ajohnw]

It's hardly surprising lots of people don't really understand depth of field. I searched the web for longitudinal magnification and nothing of any use came up. Plenty on magnification without mentioning transverse and even more on aberrations.

If some one understands that focus varies with distance and that a lens can only be focused to one specific exact distance it's easy to visualise that the nearest point of the object will focus to one distance back towards the sensor and the furthest point to another distance. That's where the 1/distance to furthest point of an object and 1/distance to nearest point of an object comes in. They are each side of the exact point the lens is focused too and clearly as the distance increases the depth of the object can be greater for the same sized circle of confusion. The circle of confusion is simply the smallest circle a lens can produce from a "zero sized" point that it's focused on. In quotes as diffraction effects mean that it needn't be a zero sized point. Best disregarded as it just complicates things and doesn't really change the result. The 1/whatevers are also simple lens approximations but all lenses have the same characteristics.

Fortunately longitudinal magnification is usually a lot less than transverse. It gets problematic as the macro region is reached and even more so on microscopes where an 100x objective might only have a depth of field of a few 0.001mm.

John
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[jcuknz]

A picture is worth a thousand words

EDIT So I thought I had better organise a picture and here not to scale we have the lens left coming to focus at the sensor with a very large circle of confusion 'gate'.
On the right the lens has moved forward but the bending [refraction ?] remains constant and the result is the focus is diverging behind the focus point to give a blurred result on the sensor.

So to maintain reasonable sharpness we need to have a larger angle from a smaller f/stop as my drawing earlier.

I hope your students will follow that Shai

[ajohnw]

The angles that refraction forms at the sensor get smaller and smaller as the aperture is reduced. In other words rays on axis go straight through. Rays have to be bent more and more as they move away from the centre so that they still focus on the same point.

John
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[jcuknz]

I am afraid that is not answering the question originally asked ...which is heading all our contributions ... basically it is the amount of lens movement before one looses acceptable focus, the size of the CoC produced ... movement which is less at close distances than at far distance. In my first drawing if red was the focus then there would be another line meeting at about twice the blue-red distance drawn ... assuming the 33/66% balance. So the reverse is true that the angle is so small at far distances it takes a greater change to go beyond the acceptable CoC than at closer distances. Hence we have greater DoF at distance than when close and I think the angles involved are the 'why' of what is the 'what'. The refraction remains the same but it requires greater differences in distance to go out of focus way out than close in.

As the subject moves away the angle to the circumfrance of the lens is smaller so the complimentary angle behind the lens is greater helping to keep it is focus ... a different way of saying the same thing

As Dan said it is basically geometry.

[ajohnw]

I just read one of your posts and assumed that it related to F stops.

John
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[Shai]

Thanks a lot all of you!
I think that jcuknz in his last reply really helped me understand.
I think it might be described as a matter of relative distance.
I'll let these sink in!
(wish I had paid more attention on those geometry classes back in highschool *sigh*)

Shai

I am afraid that is not answering the question originally asked ...which is heading all our contributions ... basically it is the amount of lens movement before one looses acceptable focus, the size of the CoC produced ... movement which is less at close distances than at far distance. In my first drawing if red was the focus then there would be another line meeting at about twice the blue-red distance drawn ... assuming the 33/66% balance. So the reverse is true that the angle is so small at far distances it takes a greater change to go beyond the acceptable CoC than at closer distances. Hence we have greater DoF at distance than when close and I think the angles involved are the 'why' of what is the 'what'. The refraction remains the same but it requires greater differences in distance to go out of focus way out than close in.

As the subject moves away the angle to the circumfrance of the lens is smaller so the complimentary angle behind the lens is greater helping to keep it is focus ... a different way of saying the same thing

As Dan said it is basically geometry.