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I have taken two photographs on a Canon crop sensor camera: 18mm f/9 with the following exiftool output (the focus was approximately at 3.5 meters):

Focus Distance Upper : 5.27 m
Focus Distance Lower : 1.82 m
Depth Of Field : inf (1.24 m - inf)

And 50mm f/1.8 with the following exiftool output:

Focus Distance Upper : 1.99 m
Focus Distance Lower : 1.41 m
Depth Of Field : 0.08 m (1.66 - 1.74 m)

Now, I assume I know what depth of field means. It's the same thing as the one that will be given by a depth of field calculator such as http://www.dofmaster.com/dofjs.html

But what are Focus Distance Upper and Focus Distance Lower?

Why in one of the pictures (shallow DoF) is the difference between focus distances higher than the DoF, and in the other picture (deep DoF) is the difference between focus distances lower than the DoF?

The Focus Distance Upper and Focus Distance Lower tags are in the Canon-proprietary "maker notes" and aren't part of standard EXIF, so documentation is scarce. However, it appears that these (together) represent the distance at which the lens's focus is set. That is, it's somewhere between the two bounds.

Why Canon does it this way rather than providing a single value (perhaps with second uncertainty or error value) is a mystery only Canon could resolve, and they don't seem to have publicly. Here's a forum post with some investigation: Re: Distance in EXIF.

Note also that Depth of Field is an exiftool composite tag. The information there is not set directly by the camera — instead, Exiftool generates this from other data, including whatever hint it gets as to focus distance. From the docs, it looks like it uses the Upper and Lower values, but also other info, which may explain the disparity you note.

In any case these values are approximate and should be taken as hints, rather than as gospel. Their original purpose is probably to hint at subject distance to aid the camera in making TTL flash power computations. They're not meant to be scientific measurements, or even photographic scene information (like GPS location tags or something).

As @mattdm found out, the FocusDistanceLower and FocusDistanceUpper, whatever they exactly mean, together denote the approximate focus distance. ExifTool then calculates depth of field based on these.

I took a look at the ExifTool source code, and the DoF calculation desires:

Desire => 
 3 => 'FocusDistance', # focus distance in metres (0 is infinity)
 4 => 'SubjectDistance',
 5 => 'ObjectDistance',
 6 => 'ApproximateFocusDistance ',
 7 => 'FocusDistanceLower',
 8 => 'FocusDistanceUpper',
,

And if focus distance is not defined (all of 3, 4, 5 and 6 are undefined), it is calculated as follows:

$d = ($val[7] + $val[8]) / 2;

So, ExifTool is simply using the arithmetic mean of the two focus distances. Not sure if that's correct or if it's just an educated guess.

Anyway, this probably doesn't matter as I don't trust in the accuracy of focus distance fields more than I would trust in the focus distance meter on a lens that happens to have one.

Imagine a train track with detectors every 2 miles that will detect the presence of a train. Also imagine that we have a transponder placed near the middle of the train that triggers the detectors when it passes.

If a very short express train less than a quarter mile in length has passed mile 6 but has not yet reached mile 8, the best that the system can tell anyone is that the train is somewhere between mile 6 and mile 8.

Now consider that we have a very long, heavy freight train that is three miles long. At times our three mile long train will be next to two detectors, with the transponder in between. At other times, when the transponder is within one-half mile of a detector, the train will only be next to one detector. When the transponder is between detectors, we still won't know exactly where the head end of the train is.

Basically, the sensors in the lens that report distance information to the camera are like the detectors every two miles along our train track. They tell the camera what positions the lens is focused between. The "Focus Distance Lower" is the closest position the lens might currently be focused at. The "Focus Distance Upper" is the furthest position the lens might currently be focused. The lens might actually be focussed anywhere within that range.

Why in one of the pictures (shallow DoF) is the difference between focus distances higher than the DoF, and in the other picture (deep DoF) is the difference between focus distances lower than the DoF?

The depth of field is like the length of our train. With a wide aperture, we have a short express train. With a narrow aperture, we have a long freight train. We only can sense when the focus distance in the middle of the DoF crosses from one detection zone to the next, just as we only have a transponder in the middle of our train. With a deeper DoF the edges of the DoF may or may not be past the "Upper" and "Lower" focus distance, but we can't know that since only the position of the actual focus distance can be measured as anywhere between two of the detectors at various positions between minimum focus distance and infinity.

The camera only reports the range of the actual focus distance, the focal length, and the aperture used. EXIF Info makes an educated guess at the DoF based on combining those three factors.

In the end, DoF calculations are only estimates. Since depth of field will change for different display sizes of the exact same image, any camera estimate of DoF is only a guess based upon an assumption of the intended display size. The long standing assumed "standard" is an 8x10 image viewed at a distance of 12 inches by a person with 20/20 vision. But in the digital age that goes out the window very quickly when pixel-peeping.