The thread Will full frame sensors survive?
over in the Off-topic
section got me thinking about Depth of Field and, of course, that got me confused! What follows was written in an attempt to unconfuse
This is a long post so I'll set out my conclusions, so far.
- Full-frame sensors have better dynamic range: .......... True
- Full-frame sensors give better image quality: ............. True
- Full-frame sensors can work at higher ISO numbers: .. True
- Full-frame sensors give a shallower Depth of Field: ..... True, but they don't have to
Nothing too controversial, I hope, but the DoF question is complicated. I'll explain my reasoning next. Skip to the final paragraph, if you would rather, to see my invitation to continue the conversation.
To set the scene, I will compare two sensors, both
with 12 megapixels and assume that the anti-aliasing filters have similar effects. To keep the sums simple one sensor will be full-frame (same as 35mm film) and the other will have a 1.5x crop factor. I will use the terms "detector" to refer to the electronics at each pixel and "sensor" to refer to the whole chip.
For simplicity I will assume that each pixel (cropped-or full-frame sensor) captures all the light arriving in its bit of the sensor (in other words the microlenses are 100% efficient). The detector at each pixel is just a device for detecting incoming photons and adding the liberated electrons into temporary storage (the "well") as they arrive. The process isn't 100% efficient by any means but the number of electrons stored will be proportional to the number of photons that have arrived provided the well hasn't been totally filled (blown highlights). After the exposure is complete the number of electrons in each well is measured (or read out). I will assume that differences in thermal and readout noise between the full-frame and cropped sensors are not major factors compromising what follows. EDIT: In the light of subsequent posts in this thread such differences cannot be ignored but would appear to be only second order effects.
Full-frame sensors have better dynamic rangeNo argument here, I believe, as the larger geometry of each pixel's detector in a full-frame sensor typically allows a greater full-well capacity (number of photons "converted" into electrons). Note that I am defining dynamic range here as the ratio between the largest number of electrons from each pixel and the smallest number of electrons which is above the noise level. Of course you can have all the dynamic range in the world but if the A/D (analog to digital) converters don't have sufficient precision that dynamic range is wasted. Hence the recent move from 12 to 14 bit A/D.
Full-frame sensors give better image qualityNow it gets trickier! The answer is, of course, that they do but the reason is interesting. It's to do with the dynamic range advantage discussed above but greater dynamic range is only useful if the camera can supply enough photons to each pixel. Let's assume that a scene is captured by the cropped sensor using a 40mm focal length lens at f/4. To capture the same amount of the scene on a full-frame sensor we would use a 60mm lens (applying that 1.5x factor) and, being simple souls, we might opt to continue to use f/4 so, given both cameras are working at the same ISO, achieving similar shutter speeds. But remember that both full-frame and cropped sensors have 12 MP and that each microlens is assumed to feed all of the light falling on it to its detector. Of course the 60mm f/4 lens is collecting 2.25 times as much light as the 40mm f/4 lens (1.5 squared) so the full-well capacity of each detector on a full-frame sensor has to be bigger than that of a cropped sensor. So the better image quality of the full-frame sensor is simply down to the fact that it typically gets more photons when capturing the same scene using the same f-number, ISO and shutter speed.
Full-frame sensors can work at higher ISO numbersExactly the same reasoning applies as in the case above. In fact it's the other side of the same coin but I thought it worth giving a separate heading and now I understand why higher ISO numbers are usable.
Full-frame sensors give a shallower Depth of FieldOK, here's the "biggie"! At a simplistic level this is true but if you are seeking to maximise the depth of field (e.g. in a landscape) then the diffraction limited depth of field is pretty much the same - hence my "True, but they don't have to" answer in the summary. Two things are going on here so to start with let's take the example above with a 40mm lens at f/4 on our cropped sensor camera. Using the DOFMaster Depth of Field Calculator we can see that focussing at 20 metres gives acceptable sharpness from 10m to infinity. However on the full-frame 60mm lens at f/4 the best we can do, while retaining acceptable sharpness at infinity, is to focus at 30m giving a closest distance of acceptable focus of 15m. Not nearly so good as the 10m with the 40mm lens on the cropped sensor.
So from that analysis full-frame sensors give shallower Depth of Field. Yes, but they don't have to! To understand why we need to consider diffraction. Far too big a subject to cover here but a good introduction is the CambridgeInColour article Diffraction & Photography. Towards the bottom of that page there is a Diffraction Limit Calculator. Accept the defaults for print size, viewing distance and eyesight (for why these are relevant see this DoF tutorial) and plug in our 12 MP sensor and click the "Set Circle of Confusion = Twice Pixel Size?" checkbox. With a little experimentation we see that on the 1.5x crop sensor f/8 is the smallest f-number before diffraction becomes an issue while on a full-frame sensor we can go to just under f/13. By the way, this relationship between diffraction limiting f-number and frame size explains why large format (film) landscape photographers can use ridiculously large f-numbers compared to the digital world.
So, returning to the Depth of Field calculator and focussing at the hyperfocal distance, then taking the 1.5x cropped sensor 40mm lens at f/8 we get sharp focus from 5.1m to infinity and with the 60mm lens at f/12.7 (full-frame) we get sharp focus from 4.8m to infinity, which is near enough exactly the same total DoF. This result is also confirmed by using the Depth of Field Equivalents calculator nearly halfway down the CambridgeInColour article Digital Camera Sensor Sizes. That shows that f/8 on a 40mm lens in front of a 1.5x cropped sensor has an equivalent DoF to a 60mm lens at f/12 in front of a full-frame sensor. No real surprise there (the 1.5x factor applied to f/8 to give f/12).
In case you think this still gives the advantage to the cropped sensor because it can work at smaller f-numbers and so faster shutter speeds, in my opinion it doesn't. When maximum depth of field is needed, the two sensor sizes are equivalent because for the same image quality you can crank up the full-frame ISO number higher before you get the same levels of sensor noise that you would see from a cropped sensor. And, as discussed, the full-frame sensor can more easily achieve a shallower depth of field than the cropped sensor.
Phew! I hope that made some sort of sense. Please feel free to shoot the arguments above down in flames if they are in error. The purpose of this thread is, hopefully, to explore the pros and cons of full-frame and cropped sensors to help future buying decisions. Please also feel free to add posts discussing other full-frame versus cropped sensor trade-offs which I haven't covered.