[defaultname]

"I think it makes sense to assume the same target resolution for the iPhone and the DSLR, even though this isn’t true in practice"

It yields a practically perfect comparison of focus. This isn't a trick or handicapping, and the degree of focus/defocus is identical whether that SLR had 10x the resolution. There is utterly nothing arbitrary chosen here, and the amount a tree 10 feet outside the focus is out of focus will be identical on a 12MP SLR or a 24, 48, or 96MP version with the same focal length / f / sensor size.

[foldr]

My point was that it doesn’t matter what resolution we choose as long as we do the calculations based on the same resolution for both the iPhone and the DSLR (and hence with different values for the CoC in each case, given the different sensor sizes). Thus your value for the iPhone’s CoC derived from its pixel size is irrelevant. We can choose any target resolution we like to make the comparison and get the same result (comparatively speaking).

By resolution here I’m talking about what we could crudely measure in megapixels. Say for example that we have a target resolution of 5MP. We then calculate the corresponding CoC for both cameras based on their respective sensor sizes. You’ll find that the CoC for the iPhone will be smaller in proportion to the difference in focal lengths between the iPhone and DSLR. That cancels out one of the factors of f.

Sudosysgen is saying the same thing, but without going indirectly via the DoF formula that you’ve been using.

[defaultname]

The CoC for the iPhone is smaller than the ASP-C given the smaller sensor. By choosing the same resolution of an ASP-C sensor, we are calculating for a given level of "good enough for that resolution". It is perfectly comparable level of focus. I have no idea why you are so caught up in distractions.

I calculated the hyperfocal length for an iPhone and an equivalent zoom SLR, at the same aperture. These yield effectively identical degrees of focus from 1/2 the HF to infinity. The iPhone is from 3.2ft to infinity, the SLR is from 27 feet to infinity.

Nothing else matters if you can't tell me why that's wrong. Because it isn't wrong. It's absolutely right. The same zoom level and cropping. MASSIVELY larger focus zone.

If we doubled both dimensions of the sensor, thus doubling the CoC, it would halve the HF. If we instead doubled the focal length it QUADRUPLES the HF. The focal length is a squared factor and outweighs any other component. For a reason.

[foldr]

If you double the focal length you also have to double the sensor dimensions (to get the same angle of view) and hence double the size of the CoC - so you end up with f^2/f = f. That is, you double the numerator in the DoF formula because the CoC has doubled, and quadruple the denominator because the focal length has doubled, with the end result that the DoF halves.

Your mistake is one that’s easy to make and one that I’ve made myself before. We’re not trolling you. You’re just losing track of a factor of f and thereby getting the wrong result.

By the way, I also agree with your overall point about smaller sensor cameras being better suited to macro photography. It’s just that your f512 claim is based on a mistaken calculation.

[defaultname]

"Your mistake"

There is no mistake. Your first paragraph is unfortunately founded on some misunderstandings of optics, however I calculated the hyperfocal length for an equivalent ASP-C 35mm system and an iPhone at the same crop (which anyone with an SLR and an iPhone can replicate in moments). The iPhone has a dramatically higher DoF. There are no mistakes in that calculation. This is the reason why you need computational bokeh. It's why it's so easy for everything to always be in focus. Could someone contrive ridiculous focal length / f-ratio / CoC parameters? Of course they can -- it's just a function with parameters that you punch in, and they can offset. In actual reality, however, short focal length is the primary input into why small cameras feature larger depths of field. Why we talk about the equivalent aperture in the way that we talk about equivalent focal length.

sudosysgen's argument in the end seems to distill down to "yes, but compare it via the equivalent DoF f-stop on the larger camera" which is a short circuit of the entire argument. It is basically saying that AMC is worth the same as Apple if AMC shares were each worth $4636.

Okay.

[sudosysgen]

That's not how it works. If I take a picture with 2x crop sensor at 100mm f/2 it is going to be exactly the same picture as at 50mm f/4 on a FF camera. Its just how it works. They have proven it using the DOF equation by showing that scaling the CoC factor down with the focal length and scaling the focal length down means you have the same DoF as long as the actual aperture diameter is the same, algebraically. I gave you an explanation of why it is the same because the solid angle is preserved. In the end you're making the typical photographer mistake of misunderstanding crop factor.

[sudosysgen]

You can't use the same aperture. The SLR has to be at a smaller aperture so the diameter of the lens is the same. That way both will gather the same amount of light and have the same amount of bokeh.

That's your issue - you need to use equivalent apertures.

[defaultname]

At this point I'm sure you must be joking.

[sudosysgen]

I really am not. If you don't believe me, calculate the depth of field on this website: https://www.pointsinfocus.com/tools/depth-of-field-and-equiv...

Set sensor size to "custom (NaNx)". Set Custom Sensor to "1". Set focal length to "25mm". Set aperture to "f/2". Set distance to 2m You will find a DoF of 759mm.

Then set Custom Sensor to "0.5". Set focal length to "50mm". Set aperture to "f/4". You will find a DoF of 748mm due to rounding errors in the calculator.

Then if you set custom sensor to 2, focal length to 12.5, and aperture to f/1, you'll find a DoF of 739, again not quite equal due to rounding errors.

As you see, if you double the sensor size, double the focal length, and use an equivalent aperture, you have the same DoF.

[sudosysgen]

The CoC refers to the circle in the pixel that a point will be focused to. The pixels on an iPhone are much smaller than the pixels on a camera. If you use the same CoC for the iPhone, you are referring to many more pixels than on a DSLR.

Therefore, when you use the same CoC, you are asking the DSLR to be dozens of times closer to perfect focus, in pixel terms, than the iPhone, which is why you are calculating outlandish f stop values.

If instead, you have a target that the object must resolve to a pixel with the same resolution on both, you will arrive to an f stop linearly proportional to the sensor size, instead of proportional to the square of the sensor size.

[defaultname]

I clearly used completely different CoCs, factoring in the different sensor sizes.

At this point I feel like you are just posting things hoping some future visitor will think that your commitment must demonstrate that you are right. I guess.

[sudosysgen]

You clearly did not. If you scaled the CoC exactly with the crop factor, we would find exactly the same numbers.