Originally posted by audiobomber So your dismissal of equivalence is that it isn't accurate to three decimal places? Has it occurred to you that the FA 50mm f1.4 has a focal length of 53mm? That the DA 60-250mm is only about 135mm at close focus and maximum range? That an f2.8 lens can have a T-stop of f3.3? Or that f8 is not precisely f8 (f5.6 x 1.4 = 7.84)? That f/1.2 may be used in either a half-stop or a one-third-stop system? You can't see a difference of 400 pixels in 12 million. Your eye can't tell the difference between 1.5x crop or 1.53X crop. Photography is nowhere near as precise as mathematics because it is also subjective.

Have a play with a DOF calculator. It will show that you can equalize DOF between formats, but DOF is not a precise measure, so don't be expecting mathematical precision.

A Flexible Depth of Field Calculator Originally posted by osv it's not that precise.

there is no such thing as a universal calibration standard for lens measurements, so a nikon 50mm lens could easily be a couple of mm longer than a canon 50mm lens... same thing with aperture, it's only whatever arbitrary measurement the manufacturer assigns the lens... it'll generally be pretty close with modern lenses, but nowhere near as precise as you are calculating.

take for example the batis 25mm prime, it's actually a ~22-23mm prime... some people speculate that modern lenses might be wider in order to leave elbow room for in-camera distortion correction.

another example would be the olympus 24/2.8 legacy prime, it's the widest 24mm prime that i've ever put on the a7r, probably by ~2mm or so.

Originally posted by BrianR You might want to state the assumptions you've used in your DoF calculations (specifically, what's happening to your circle of confusion as you vary formats and the implications this has in a real world print comparison).

Anyway, the 'derivations' that show you'll get the same DoF under some equivalence conditions use simplified equations for DoF. Ones that are *pretty true* when the subject distance is *large enough* compared to the focal length. In other words, it's close enough for most people at everyday distances, but not a mathematical gospel.

I think we can ALL agree that it is near impossible to practically compare different camera systems, not to mention prohibitively expensive. They just aren't made to allow us to compare them fairly. We can only do it theoretically.

I have a spreadsheet that performs photography related calculations for me. It also allows me to see some results side-by-side for easy comparison. Originally, it did not include a depth of field calculator, but I eventually added one when I stopped believing that 1. 'A 50mm lens is a 50mm lens', and, 2. 'You get better Bokeh on a 'Full Frame' camera', could both be true at the same time.

Since bokeh is, very simply, the defocused areas, usually in the background, in a photograph, I reasoned that a good way to visualise how defocused the defocused areas are was to know where the focused areas are, and, their depth. All things being equal, the more out of focus something is the more pleasing the bokeh it will create in the picture. So I started looking for Depth of Field calculators.

Everywhere I looked, including the DoF calculator linked above, seems to be trying to give me a subjective answer. I was looking for the truth, not opinions. I looked for the mathematical formulae to create my own calculators in MS Excel, I found many of them on Wikipedia.

For interest, I plugged a few figures into the DoF calculator above, to match my earlier post, 32.753mm lens f1.4 and 4.72m from the subject.

APS-c (1.5 crop) - focus is from 4.18m to 5.43m giving a depth of 1.25m

35mm - focus is from 3.94m to 5.88m giving a depth of 1.95m

These results are saying that DoF is shallower on an APS-c than the 35mm. This would hint at bokeh being better on APS-c than on larger formats, contradicting what we all know to be true. Using the same distance and aperture, for a 50mm lens, the APS-c has narrower DoF. ???

For me rounding to three decimal places seemed to be the natural thing to do to keep things under control. Applying a 1.5 Crop Factor to a FF/50mm lens combo to find the 'Crop Appropriate' lens for an APS-c would leave me in a recurring nightmare.

In metres, three places is rounding to the nearest millimetre.

When I started my depth of field calculations I could not get anything to line up, there were significant errors. I was beginning to think that a 50mm lens was not a 50mm lens. It then dawned on me to use an 'Actual Crop Factor' calculated from the dimensions of the sensor. That changed everything. Suddenly, a 50mm lens was a 50mm lens.

I chose to use a 50mm lens as a standard on a 35mm sensor because that is what it is. All of us who have used 35mm, and, many who haven't, can relate to that combination. The fact that there might be slight differences between lenses, or a lens may not quite match up to its stated focal length, is not important to my calculations. The calculations ignore other factors too like lens design and engineering prowess because these are factors that add to the subjectivity.

I also had to use a standard Circle of Confusion, I used 0.018mm (Typical APS-c value) I could have chosen any value. My reasoning for this was because 1. Circles of Confusion tend to be more lenient towards larger format cameras, 2. Using a different value for different formats would somehow suggest that the lens knows what camera it has been attached to and starts behaving differently, 3. Circle of Confusion relates to how those images are projected to the viewing medium, and then viewed by the viewer, and, is another area that introduces subjectivity.

My DoF calculations were an attempt to find a way to make accurate comparisons without needing to resort to subjective answers.

My example showing the difference in size (px) of the same subject shot from the same distance using different format cameras does not result in a loss of 400px in 12Mp. It is 400px (height) lost from the short side of the picture, roughly the same number of pixels difference between the K-x (12mp) and the K-5 IIs (16Mp), and is approximately 4Mp. I would say that is a large chunk of detail to lose.