Tim Griffith
Member
I’ve noticed recently there has been a bit of discussion on depth of field, focal length and format size and how they all affect each other. My background is large format photography, and while photography has never been my bread and butter, I do have a deep interest in how all these above factors work and effect the final image.
The one element that all of these factors have in common (except focal length) is the concept of circle of confusion or simply written as CoC. So I’m hoping that my understanding of CoC will help others understand these concepts (I am not saying my understanding is correct in fact they are more than likely incorrect but they have got me by over the years, DoF and CoC are extremely complicated, this is just my interpretation of these complexities).
So, to CoC:
Essentially, at the plane of focus, say 10m, all points in this plane are rendered as points, all points that fall behind or in front of this plane are rendered as discs, so at the near and far of DoF the CoC determines the size of these discs. So reducing the CoC will give the impression of increasing depth of field by reducing the disc size.
Now, to put CoC into practice, lets take three different sized sensors, say a 2/3” (10.1mm wide), S35 (30mm wide), and 645 (56mm wide) (I’m only using widths to eliminate format ratio differences), now lets assume all the images captured with these sensors are destined for the same size big screen.
Lets start with the 645 sensor, the acceptable CoC for this sensor is say 0.1mm, now take the S35 sensor, to get the same enlargement properties (relative sharpness, visual acuity, etc.) as the 645 on the big screen you will need to change the CoC, this can be done simply by dividing 30 by 56 (widths) = 0.54 then multiplying by 0.1mm = a CoC for S35 of 0.054. Now lets take the 2/3” sensor, to get the same enlargement properties as 645, divide 10.1 by 56 = 0.18 and multiply again by 0.1mm = a CoC for 2/3” of 0.018.
So the question must be asked, how do we actually change the CoC? By changing the f-stop, that’s how!
Lets take a look at this formula shall we:
Now the only important bits in this formula are: f-number and CoC, and what can be seen is that the two are inversely proportional by the same ratio, or as the CoC is reduced by one unit, the f-number must go up by one unit.
So putting all these bits together we start to see a bigger picture, if we decrease that CoC to compensate for the smaller sensor, we need to proportionately increase the f-number which therefore increases ISO, exposure time or subject luminosity to compensate.
So, the only thing left is how much is the f-stop affected by the CoC? Well this can be worked out with another formula and a simple example.
Take this formula for instance, it’s the formula for working out hyperfocal distance (HFD) but includes all the necessary variables, now if we assume the HFD to be fixed at say 5800cm we can effectively eliminate it from the equation... it has no effect on the final result.
Which when rearranged to suit our needs gives us:
Now if we take that70mm lens off the shelf we can work out some examples:
So as we can see there is a huge difference in f-number, to get the same enlargement properties as 645 on 2/3” you need to stop down ALOT!
But this example is not being all together fair to 2/3” and I feel is where most confusion stems from, 70mm for 645 is in the ‘normal’ range whereas 70mm for 2/3” is on the long end of telephoto, so if we rearrange the formula to compensate for this and put a 12mm lens on the 2/3” camera we get a completely different story:
So what this means is that for a 2/3” image to have the same enlargement properties as a 645 image where focal length is maintained (70mm vs 12mm) then you will have to open up the aperture, or the other way around, if you are using 645 and require the same enlargement properties as S35, you will be required to stop down.
Now in explaining this concept I think I may have inadvertently raised more questions; does focal length have that much of an effect on depth of field? Large format lenses are symmetrical in their design, most of the cinema and general photography lenses are asymmetrical in their design (AFAIK), so is this a fair comparison, comparing symmetrical to asymmetrical?
Perhaps one day soon I will try to answer these... Or somebody else might like to step in and answer these questions or disprove everything I have just written.
Either way... thanks for reading and I hope this clarifies some issues.
For further reading visit:
Introduction to depth of field: http://www.largeformatphotography.info/articles/IntroToDoF.pdf
Depth of field in depth: http://www.largeformatphotography.info/articles/DoFinDepth.pdf
These articles are for large format photography and what I have used to gain my knowledge, but they cover the subject in so much depth they can easily be used for other formats.
The one element that all of these factors have in common (except focal length) is the concept of circle of confusion or simply written as CoC. So I’m hoping that my understanding of CoC will help others understand these concepts (I am not saying my understanding is correct in fact they are more than likely incorrect but they have got me by over the years, DoF and CoC are extremely complicated, this is just my interpretation of these complexities).
So, to CoC:
Essentially, at the plane of focus, say 10m, all points in this plane are rendered as points, all points that fall behind or in front of this plane are rendered as discs, so at the near and far of DoF the CoC determines the size of these discs. So reducing the CoC will give the impression of increasing depth of field by reducing the disc size.
Now, to put CoC into practice, lets take three different sized sensors, say a 2/3” (10.1mm wide), S35 (30mm wide), and 645 (56mm wide) (I’m only using widths to eliminate format ratio differences), now lets assume all the images captured with these sensors are destined for the same size big screen.
Lets start with the 645 sensor, the acceptable CoC for this sensor is say 0.1mm, now take the S35 sensor, to get the same enlargement properties (relative sharpness, visual acuity, etc.) as the 645 on the big screen you will need to change the CoC, this can be done simply by dividing 30 by 56 (widths) = 0.54 then multiplying by 0.1mm = a CoC for S35 of 0.054. Now lets take the 2/3” sensor, to get the same enlargement properties as 645, divide 10.1 by 56 = 0.18 and multiply again by 0.1mm = a CoC for 2/3” of 0.018.
So the question must be asked, how do we actually change the CoC? By changing the f-stop, that’s how!
Lets take a look at this formula shall we:
f-number≈((focal length)^2×(far distance-near distance))/(CoC×far distance×near distance)
Now the only important bits in this formula are: f-number and CoC, and what can be seen is that the two are inversely proportional by the same ratio, or as the CoC is reduced by one unit, the f-number must go up by one unit.
So putting all these bits together we start to see a bigger picture, if we decrease that CoC to compensate for the smaller sensor, we need to proportionately increase the f-number which therefore increases ISO, exposure time or subject luminosity to compensate.
So, the only thing left is how much is the f-stop affected by the CoC? Well this can be worked out with another formula and a simple example.
Take this formula for instance, it’s the formula for working out hyperfocal distance (HFD) but includes all the necessary variables, now if we assume the HFD to be fixed at say 5800cm we can effectively eliminate it from the equation... it has no effect on the final result.
HFD=focal length^2/(f-number×CoC)
Which when rearranged to suit our needs gives us:
f-number=focal length^2/(HFD×CoC)
Now if we take that70mm lens off the shelf we can work out some examples:
f-number (645)=70mm^2/(5800cm×0.1mm)≈f/4.5
f-number(2/3")=70mm^2/(5800cm×0.018mm)≈f/45
f-number(2/3")=70mm^2/(5800cm×0.018mm)≈f/45
So as we can see there is a huge difference in f-number, to get the same enlargement properties as 645 on 2/3” you need to stop down ALOT!
But this example is not being all together fair to 2/3” and I feel is where most confusion stems from, 70mm for 645 is in the ‘normal’ range whereas 70mm for 2/3” is on the long end of telephoto, so if we rearrange the formula to compensate for this and put a 12mm lens on the 2/3” camera we get a completely different story:
f-number (2/3")= 12mm^2/(5800cm×0.018mm)≈f/1.2
So what this means is that for a 2/3” image to have the same enlargement properties as a 645 image where focal length is maintained (70mm vs 12mm) then you will have to open up the aperture, or the other way around, if you are using 645 and require the same enlargement properties as S35, you will be required to stop down.
Now in explaining this concept I think I may have inadvertently raised more questions; does focal length have that much of an effect on depth of field? Large format lenses are symmetrical in their design, most of the cinema and general photography lenses are asymmetrical in their design (AFAIK), so is this a fair comparison, comparing symmetrical to asymmetrical?
Perhaps one day soon I will try to answer these... Or somebody else might like to step in and answer these questions or disprove everything I have just written.
Either way... thanks for reading and I hope this clarifies some issues.
For further reading visit:
Introduction to depth of field: http://www.largeformatphotography.info/articles/IntroToDoF.pdf
Depth of field in depth: http://www.largeformatphotography.info/articles/DoFinDepth.pdf
These articles are for large format photography and what I have used to gain my knowledge, but they cover the subject in so much depth they can easily be used for other formats.
rrr: I will try to explain as best and, at the same time, as short I can: