It doesn't.

(Download)

It's pretty close but the crop factor and the CoC ratio are not exactly 2x and the M43 has a different aspect ratio.

Because of the difference in aspect ratio, the field of view has a 2x factor horizontally but 1.78 vertically.

Here is the list from the spreadsheet:

We can calculate until we are blue in the face but it all boils down to the classic definition of the circle of confusion (CoC), "The circle of confusion is a bunch of photographers arguing about the meaning of depth of field."

Aside from having to guess how good the viewer's eyesight is, the one thing we cannot control is how close they will get to view the image. And they will probably not even bother to get too close unless they run out of reasons to conclude that the image sucks.

Visual acuity factors

Here is some more information on the ratios of focal distance to HD and how they affect the distribution of DOF closer to and further from the focal distance. I have attached the spreadsheet if you want to explore how this works for your own camera.

The basic inputs are:
- the sensor's CoC (the spreadsheet includes a table with sensor sizes from a one inch sensor to 11x15" film.
- lens focal length
- aperture

That is used to calculate the hyperfocal distance.

The HD/FD ratio is 1 if you focus at HD, 2 at HD/2, 3 at HD/3, etc.

FD is calculated from the HD and the HD/FD ratio.

The near and far DOF limits and total DOF are then calculated.

Finally we see the ratios of the DOF beyond FD to DOF nearer to the camera than FD (Far/near ratio):

- Focused at HD, the ratio is infinite
- At 1/2 HD, the ratio is 3:1
- At 1/3 HD, the ratio is 2:1
- At 1/5 HD, the ratio is 1.5:1
- At 1/50 HD (close to macro), the ratio is 1:1

Those ratios are the same no matter what you enter for CoC, focal length or aperture.

If you focus beyond HD, the far/near ratio is always infinite. If you focus at infinity, the near limit for the DOF is always HD.

HD vs DOF spreadsheet
Attached file:
(Download)

That's not entirely correct. As you focus beyond HD, the DOF indeed remains infinite. But if you focus at infinity, the near limit of the DOF is at HD.

So the statement should read, "∞:(something greater than HD/2)". And the distance from HD to ∞ is ∞.

So it is not a mistake to focus at infinity if there is nothing of interest between the camera and HD.

The DOF preview never really worked because you can't judge the DOF on your camera's LCD or in the viewfinder of an SLR/DSLR. It's even difficult to see on the ground glass of a medium or large format film camera.

The 1/3-2/3 (1:2 ratio) "rule" only applies when your camera is focused at 1/3 of the hyperfocal distance. As you focus closer, the ratio approaches 1:1 and eventually gets there at true macro distances.

At the hyperfocal distance (HD) the ratio is ∞:HD/2 making the DOF infinite.

And once you pass HD, the ratio becomes ∞:(something less than HD/2) but the DOF remains infinite.

Some lenses can focus a little past infinity which might vary with temperature to avoid a hard stop.

Compare it to the one from Cambridge in Colour which has been thoroughly tested and documented before it was published.

But the numbers may not tell you anything useful if you are using a camera with a 1" sensor or smaller. That's so small that you can't see anything beyond the DOF (out of focus, OOF) unless your camera was very close to the subject and using a relatively long focal length and a very wide aperture.

A more extreme situation is when you use a smartphone which has an even smaller sensor. Despite the apparent wide fixed aperture, it's almost impossible to see the limits of the DOF. I showed this in https://www.uglyhedgehog.com/t-805958-11.html#14598145 along with a way to compare the iPhone to full frame camera.

Another factor with very small sensors is whether you are viewing the entire original (uncropped) image from a normal viewing distance (NVD) which is about the same as the image diagonal. You might only see OOF issues if you pixel peep, which artificially brings you much closer than the NVD, and there are a lot of MP in the original image (more than 8MP).

Anything posted online, especially when it's cropped or reduced in size, can be misleading - either out of ignorance or deliberate fraud.

Maybe a chicken and egg situation. Your success as an engineer may come from an aptitude for analytical thinking.

My engineering background gave me som credibility but I moved into mathematical modeling and financial analysis.

That scenario may be more common than we might think.

My father started as a civil engineer and so did my daughter. Both of them moved on to better jobs. My son skipped the engineering step, went straight to business and is earning more than either of us.

I guess the lesson is, if you want an interesting career, become an engineer. But if you want to get rich, don't.

How did Frank's statement prove that I was wrong about anything? All I did was to recommend the DOF calculator from Cambridge in Colour. I said nothing about the 1/3 assumption.

By the 1970s I had been working as a mechanical engineer for a decade and in the process of changing my career over to software engineering where I finally made some real money. I was never a clerk in a camera store.

As for doing the math, I have just proven that I can still do the math. You have proven nothing. You were not even able to catch the error that DOFMster made that doubled the hyperfocal distance.

One of us is a mathematician, engineer and programmer who can understand the issues clearly. The other is an amateur with a questionable memory and a bad attitude.

I will respond to anyone else who would like to discuss the subject, but I will no longer respond to you.

I did not suggest that you used a DOF calculator to guide you in taking the picture.

But if you relied on DOFMster to understand the subject, you could be incorrectly influenced by what you learned.

If you base your assumptions on information from a faulty DOF calculator, you are bound to make the wrong choices when it comes to deciding where to focus.

Below is another reason why Cambridge In Colour is a good source for information. It shows that your 20MP 1" sensor is diffraction limited at f/5.6. You would need to open the aperture to f/4 or drop down to a 12MP sensor to avoid this.

But I would not fret over whether the aperture is diffraction limited, especially with such a small sensor. It's not likely that it's going to show up with your built-in zoom lens.

But with a full frame 24MP sensor and a very good lens it might matter if you go beyond f/11. At 45.7MP, f/8 might be the limit.

The only reason I mention diffraction limit is because diffraction might make stuff near the DOF limits look like they are fuzzy.

Personally, I would not consider a compact camera since I can get perfectly fine snapshots from my iPhone or even my X100T. But when I want anything better than a snapshot, I will use a 24MP or 45.7MP camera and a good lens.

If you have been relying on DOFMaster, that would explain your confusion. I found several errors in their logic so I don’t trust them although the can probably do alright for full frame and APS-C.

The spreadsheet I just uploaded shows five different versions of COC based on visual acuity. For simplicity I just use image diagonal/1500.

Here is the equivalence between an iPhone and a full frame (24x36mm) camera.

I don't compare the iPhone directly to other formats but I have a way to compare full frame to a series of formats from APS-C (1.5) up to 8x10 including a couple of medium format digital sizes.

I also wrote a DOF calculator where I can vary the calculation of COC based on several popular assumptions.

For more on this topic, see Smartphone Depth of Field (DoF) With a Full Frame Camera

Sample results for one of the iPhone 15 cameras


And here is the download for the spreadsheet, updated for the iPhone 15
Attached file:
(Download)