Which cameraphone is king of natural bokeh?

Trying to put a number on bokeh

We started with the theory and our refresher in the physics of it all, illuminating our lack of depth in that field, so to speak. In addition to the 'trivial' focal length and f-stop number, there were also entrance and exit pupils, hyperfocal distance, circle of confusion (that last one neatly describes us during the process of researching this), and formulas tying everything together.

Since 'bokeh' or 'blur' isn't something that we can measure, strictly speaking, we went out to quantify the depth of field - the idea being that there should be a correlation between DoF and level of background blur. Depth of field is the distance between the nearest and the furthest objects that are in acceptably sharp focus and it's in there that you already start to see a problem - what is 'acceptably' sharp focus?

Explaining the intangible through numbers comes with the necessary evils of simplification and assumption. We used the simplified formula for DoF found on Wikipedia, which calculates a value based on a relatively simple relationship between the subject distance, f-number, circle of confusion and focal length.

Most of these are straightforward - the subject distance is the easiest and the f-number and focal length we got from the EXIF data. We used the actual focal length, not the 35mm equivalent one, and that indirectly accounts for sensor size as well. That leaves the circle of confusion.

It's this circle of confusion that is the assumption used to address the concept of 'acceptably sharp focus'. The CoC is the maximum acceptable diameter of a point in the image before it starts being perceived as a blurry spot. It will inevitably differ depending on how the final image will be examined - on a computer monitor or in print, but also from what distance you will be viewing the image and at what magnification.

We thought long and hard what is the correct approach for figuring out our CoC for all those different cameras with different sensors. With all other things being equal (framing and subject size, but also viewing distance and the medium for the examination), the circle of confusion in our case was mainly dependent on the resolution of the images captured by each camera sensor.

We didn't have the means to calculate the exact CoC but we didn't have to. We just needed to get how its size on Camera A related to its size on Camera B with framing and subject size being equal. So we ultimately settled on using the single pixel size on each of these cameras as a measurement of the CoC. And by one pixel on these sensors, we mean the resulting pixel size after any pixel binning has taken place - so, for example, 2.8µm on the Mi 11 Ultra, and 2.4µm on the Galaxy S22 Ultra.

So with the circle of confusion all sorted out, we attempted calculating the DoF the cameras in this comparison will produce. The numbers we got are the physical depth of the field that is in focus. So the smaller the number, the shallower the focus and the greater the background defocusing would be.

Below, you will find two columns with calculated DoF - one's for a fixed subject distance (the values shown are for a 50cm distance), and the other is for a fixed subject size within the frame.

Our ultimate goal in this test was to compare background blur with normalized framing (same size of the model's head within the frame), so it's the second column that is more important for us. We are hoping the numbers there would correlate to the background blur we will witness in the camera samples on the next page.

The figures we arrived at using this method showed a clear gap between the 'main', wide cameras and the telephoto cameras in terms of depth of field. The numbers made sense - telephoto cameras will have a shallower depth of field at a fixed subject distance, but normalizing the subject size puts them way further from the subject, thus increasing the DoF.

	Type	EQ focal length [mm]	F-number	Distance ratio	DOF at fixed subject DISTANCE [mm]	DOF at fixed subject SIZE [mm]
Xiaomi Mi 11 Ultra	Main	24	1.95	1.04	47	52
Galaxy S22 Ultra	Main	23	1.8	1.00	53	53
ZTE Axon 40 Ultra	Main	35	1.6	1.52	23	54
Honor Magic4 Pro	Main	23	1.8	1.00	59	59
Galaxy S22	Main	23	1.8	1.00	63	63
Sony Xperia 1 IV	Main	24	1.7	1.04	59	64
Honor Magic4 Pro 3.5x	Tele	90	3.5	3.91	9	132
ZTE Axon 40 Ultra 3.5x	Tele	91	3.5	3.96	9	136
Sony Xperia 1 IV 3.5x	Tele	85	2.3	3.70	11	150
Galaxy S22 Ultra 3x	Tele	70	2.4	3.04	20	182
Xiaomi Mi 11 Ultra 5x	Tele	120	4.1	5.22	7	184
Sony Xperia 1 IV 5.2x	Tele	125	2.8	5.43	7	198
Galaxy S22 3x	Tele	70	2.4	3.04	22	207
Galaxy S22 Ultra 10x	Tele	230	4.9	10.00	3	338

Now, it's worth stressing that these are DoF values obtained under certain assumptions and are just theoretical. While we expect to see them materialize as some kind of a relationship between the level of background blur we'd get in actual photos, we're not saying there won't be outliers and there aren't any other variables that could affect things in a manner that a simple DoF formula can't capture.

But surprisingly, the numbers all matched our observations in the camera samples you will find on the next page.