[defaultname]

"You have a 4mm lens at f/2. To get the same depth of field you'd need a 50mm lens at f/25, not f/512."

Humorously years back I had authored a giant depth of field essay with online calculators specifically because so many people just couldn't understand why their iPhone couldn't get bokeh. Yes, f/512 would be the impossible equivalent. This is easily calculated.

Regardless, the lens Apple uses for macro mode has a 1.54mm focal length. The 4mm example was just demonstrating how fundamentally small cameras win on depth of field, at least if you want maximal depth of field. Conversely they lose when you want to limit depth of field, which is why we have computational bokeh.

"Macro lenses are typically 24mm or so."

The smallest from most makers is 35mm, but the majority are 50mm+.

This conversation has turned weird. As someone who has had many SLRs, and many lenses, and has taken thousands of macro photos, I know that in the real world macro photography is a massive pain. That DoF is by far the number one obstacle (which is why focus stacking is simply necessary, often with ten or more varied focuses). Physics benefits small camera systems for that specific scenario.

[sudosysgen]

That's just not how lenses work, fundamentally. Bokeh is determined by two things, and two things only - the diameter of the aperture and the distance to the object. That's it.

Also yes, the wide angle of the iPhone 13 is much smaller. Just stop down even further then.

Cheap macro lenses in 2021 are typically around 24mm. I'm talking about the Mitakons and the Laowas of the world.

Focus stacking is needed when you're trying to take very high detail pictures with 60, 70, 90mm lenses on high resolution sensors. You don't need anywhere near as much to take an image with the same magnification as a 13mm equiv. 2cm away.

[defaultname]

"That's just not how lenses work, fundamentally."

Go to the wikipedia page on depth of field and see how it is calculated.

"Cheap macro lenses in 2021 are typically around 24mm"

You claimed they were the norm. Now it's that they simply exist.

"Focus stacking is needed"

Focus stacking is needed when the depth of field is so small that the resulting photo would be unpleasant. This is the case for almost all macro photographs shot on SLRs. It's interesting that someone else claimed this is a fixed issue and posted a photo that looks like it was taken with one of those terrible lens adapter kits. If that is one's standard for "fixed", then sure, but most of us have higher standards.

[sudosysgen]

24mm is a normal focal length for entry level macro lenses nowadays, yes. They don't just exist, they are very common in the entry level market. If you want to get those kinds of macro shots that's what you'll get.

If your goal for macro photography is to take a picture that is reasonably sharp at 12MP 2cm away with a magnification of less than 2, then yes, getting acceptable depth of field is a solved problem. Set your wide angle macro lens to F/22 and there you go.

If you have higher standards, then the problem is not fixed on DSLRs. But the iPhone doesn't do it either.

If you don't understand why using the CoC criteria for depth of field is incorrect on two cameras with vastly different sensor sizes, I can't help you. The only measure for depth of field that works across cameras with two different sensor sizes is the ratio of distance and aperture diameter, which determines the solid angle of light capture. You're the one that brought up physics, so actually look at the physics instead of using photographer's ready-made formulas without actually understanding them and where they break down.

As for the image that you replied to, it doesn't look any worse at all to the images in the post technically. If you look at the image of the lightning connector, it doesn't even have 2mm of depth of field at a pretty low actual resolution. You can say whatever you want as for the composition and artistic value, that's not what we're talking about.

[defaultname]

"I can't help you"

No, you can't, because you are painfully ignorant on this topic.

Literally, spend 30 minutes with an iPhone and an SLR and you'd be illuminated. Instead you seriously argue that I need to look at the "physics" (which is farcical when you ignore the most important part of a camera, which is the focusing from the lens to the sensor. Dismissing that betrays a complete misunderstanding of optics).

This conversation is clearly futile, but again - spend 30 minutes and actually test your theories. Or, you know, read any single article on the tubes.

Or how about simply ask yourself "why does the iPhone need to do computational bokeh"? 65mm equivalent lens, f/2.2...should be the easiest thing in the world. In SLR world that is bokeh gold.

[sudosysgen]

I have a phone with a macro lens. I have a mirrorless camera. As I told you, what matters for bokeh is the distance to the object and the diameter of the aperture. The iPhone needs computational bokeh because the aperture is 2.4mm wide, whereas one of my lenses has a 40mm aperture. That's why my camera produces more bokeh - the aperture has a wider diameter while the distance to the object is the same.

That is literally the one and only thing that matters. The diameter of the lens, and the distance from the object. Take a piece of paper, draw the lens as a slit, draw the object as a point, and make a line from the two edges of the slit to the point, that continues furhter back. You'll get two triangles. Everything that is contained in those two triangles will be focused to the same point on the sensor. That's why the ratio between the two is what matters. That's why closer objects produce a more out of focus background than objects farther appart. That's what I'm trying to explain to you.

The DoF formula that photographers use does not work for comparisons across two different film sizes.

[defaultname]

You understand that cameras don't use a slit, right? Do you understand the optics in a modern camera?

Further my 70mm lens has a smaller aperture than my 35mm f1.4 lens. Yet it has a much smaller depth of field for a given distance. Weird! Lens makers must not know your remarkable "slit lens" trick.

At this point I'm convinced you are either trolling, or have dug so far into the depths of wrongness that you're dedicated to sticking with it. So good luck with that. I'm out of this conversation.

[foldr]

I think you are right if you hold constant the CoC. In that case the DoF is proportional to the f number but inversely proportional to the square of the focal length (http://graphics.stanford.edu/courses/cs178/applets/dof.html).

However, for a smaller format, we arguably ought to reduce the CoC proportionally. And I think that reduction will end up canceling out one factor of f, bringing us back to the ratio of the focal length to the f stop (i.e. the absolute diameter of the aperture).

[defaultname]

The focal length input is squared, but the CoC impact is linear. The iPhone has a small CoC compared to SLRs, but its input on the calculation is undersized relative to focal length.

The iPhone is widely assumed to have a CoC of 0.004mm (this actually increases on the most recent iPhone, though it's tough to get precise numbers). A Nikon D5000 (going with an equivalent resolution -- larger pixels -- on an ASP-C camera) has a CoC of 0.020.

So let's calculate hyperfocal distance of the two systems for the same effective focal length (but obviously very different real focal lengths)-

iPhone 12 telephoto lens - 65mm (7.5mm real) equivalent, f2.2.

Nikon D5000 equivalent lens - 65mm (43mm real) equivalent, f2.2.

For the iPhone, the HF is 6.4m. For the Nikon, it is 54.3m. For those who don't know, hyperfocus is the point where everything from 1/2 of that distance to infinity is in focus if you set the focus to that magical point. It's a proxy for the other depth of field calculations, and is the simplest to demonstrate.

Anyone who owns an iPhone w a "telephoto" and an ASP-C SLR w/ a 50mm lens needs to try to replicate bokeh at various distances without the computational bokeh. Focus on a subject at 1m, 2m, 4m, etc at the same aperture. Close down the aperture on the SLR even.

[foldr]

Holding constant the target resolution, you need a smaller CoC in proportion to the difference in focal lengths (assuming the viewing angle is also held constant). That removes one of the factors of f.

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. The DSLR user is obviously free to downsample their photo to a lower resolution and thereby (in a rather uninteresting way) gain more depth of field. We shouldn’t be giving the iPhone extra DoF points just because it happens to have a lower resolution.

So we are not talking about any empirically derived value for the iPhone’s CoC. The CoC here is a value derived for each format from an arbitrarily chosen target resolution.

[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.

[sib]

If you are going to try to get persnickety, that's not "bokeh" at all. It's depth of field.

Bokeh is the quality of rendering of out-of-focus highlights.