Introduction  Some Numbers  Test Photos: f/5.6  f/8  f/11  Diffraction Comparison  Conclusions  References
On this page, I present comparisons for the Sony RX100 M1 between shots taken at the hyperfocal distance (HFD) and at infinity with various aperture values (f/5.6, f/8, f/11). f/11 is already beyond the diffraction limit and the smallest fnumber for the camera. I use these conditions to compare the traditional depth of field (DOF) approach with the approach proposed by Merklinger.
I did these tests with two other cameras, the Leica X Vario, and the Leica M. All three cameras used the same equivalent focal length of 28 mm, which result in the actual focal lengths of 10.4, 18, and 28 mm. Note that, according to the formula for the HFD (and DOF), only the real focal length is of interest. Sensor differences are not reflected in the formula (only via the crop factor for the focal length). Therefore, you may want to take a look at the pages for the Leica X Vario (18 mm) and the Leica M (Typ 240) (28 mm) to see how the results would look like (with the aperture range of the Sony RX 100 M1).
I placed two test objects (mugs) at the hyperfocal and half the hyperfocal distance. I also took care that in the background some far away objects were visible.
I took the photos at three different apertures: f/5.6, f/8, and f/11. The fnumber f/11 is the smallest aperture available for the RX100 M1 and already beyond the diffraction limit (the recommendation is not to go beyond f/8 with this camera  see details). Depending on the aperture, the HFD is different: the larger the fnumber, the smaller it is. This means that the objects get closer and larger (and thus, more detailed), the larger the fnumber is. Only the background objects should always be about the same size.
The photos were taken with a focal length of 10.4 mm, that is an equivalent focal length of 28 mm (as in my other tests of this subject). The HDF values were taken from my HDF tables for the Sony RX100 M1. Distance was set using the spot autofocus on the mug at HFD/2, the mug at HFD and at infinity.
For each condition and aperture, I present below 100% crops of the mug at HFD/2, the mug at HFD, and a section of the background. The original photos can be downloaded by rightclicking the small versions of the photos or by clicking the "original" link.
The following table lists the circles of confusion (CoC) and disks of confusion (DoC, see Merklinger method) for the conditions specified above and demonstrated in the photos below (objects at HFD/2, HFD, and infinity; fnumbers f/5.6, f/8, and f/11):
Focused at HFD (H) 
Focused at Infinity 

fNumber  H (m) 
CoC (mm) 
DoC (mm) 
CoC (mm) 
DoC (mm) 
Comment  
N  H/2 
H 
inf 
H/2 
H 
10 m* 
inf 
H/2 
H 
inf 
H/2 
H 
inf 
10 m as "typical" distance  
f/5.6  1.75 
0.011 
0** 
0.011 
0.92 
0** 
8.7 
inf 
0.022 
0.011 
0** 
1.84 
1.84 
1.84 
DoC = d = f/N = 1.84 mm  
f/8  1.24 
0.011 
0** 
0.011 
0.65 
0** 
9.2 
inf 
0.022 
0.011 
0** 
1.30 
1.30 
1.30 
DoC = d = f/N = 1.30 mm  
f/11  0.88 
0.011 
0** 
0.011 
0.46 
0** 
9.5 
inf 
0.022 
0.011 
0** 
0.95 
0.95 
0.95 
DoC = d = f/N = 0.92 mm 
*) 10 m distance, for details see below ; **) "0" means optimal sharpness, resolution is limited by other factors (diffraction, resolving power of lens and sensor, ...)
Legend: f = focal length = 10.4 mm (real); N = f number (exact value used in calculations); H = hyperfocal distance (HFD); CoC = circle of confusion (image field); DoC = disk of confusion (object field)
H was determined using the table for hyperfocal distances for the Sony RX100 M1. The CoC of 0.011 mm is given by the manufacturer Sony (for an 1" sensor).
According to Merklinger's formula for the DoC and its relationship with the HFD (H), the DoC is d/2 at HFD/2, when the lens is focused at HFD (H). It is zero at HFD (H), d again at twice HFD (2H), and goes beyond every limit far beyond HFD. I therefore also calculated the DoC for a distance of 10 m (see below) to get an impression of how large it is at a closer distance.
I also used the Merklinger method to find out that the CoC is double the "nominal" CoC at H/2 and the same at HFD (H) when the lens is focused at infinity (every DOF scale on a lens will tell you this).
I calculated the DOC diameter Sy for a distance of Y being a multiple y of H, the HFD, according to Merklinger's formula Sy = (Y  D) / D * d and got:
For Y = 10 m, based on it's being a multiple of H, the results are as follows (using the exact fnumbers, not the "nominal" ones):
Thus, we get the (for me) surprising result that the DoC is about 1 cm for objects at 10 m distance for all the apertures (f/5.6, f/8, f/11)  it grows only by a Millimeter with increasing fnumbers.
The letters on the mugs are about 3 mm high (there are also black letters that are about 2 mm in height). The patterned double lines on the "Darjeeling" mug are about 1 mm high (or thick). I list the DoC for each image so that you can compare it with these objects easily.
For these comaprisons, it is useful to remember, what Merklinger (p. 34 writes about the readability of letters:
Note: You can download the original photos to view them on your monitor(s), or print them in the sizes you are interested in.
Aperture f/5.6 

Hyperfocal Distance (1.75) 
Infinity 

Sony RX100 M1 at ISO 800  overview (original) 
Sony RX100 M1 at ISO 800  overview (original) 

Sony RX100 M1  detail at HFD/2 (100% crop), DoC = 0.92 mm, f/5.6 
Sony RX100 M1  detail at HFD/2 (100% crop), DoC = 1.84 mm, f/5.6 

Sony RX100 M1  detail at HFD (100% crop), DoC = 0.92 mm, f/5.6 
Sony RX100 M1  detail at HFD (100% crop), DoC = 1.84 mm, f/5.6 

Sony RX100 M1  detail at infinity (100% crop), DoC = 0.92 mm, f/5.6 
Sony RX100 M1  detail at infinity (100% crop), DoC = 1.84 mm, f/5.6 

Aperture f/8 

Hyperfocal Distance (1.24 m) 
Infinity 

Sony RX100 M1 at ISO 800  overview (original) 
Sony RX100 M1 at ISO 800  overview (original) 

Sony RX100 M1  detail at HFD/2 (100% crop), DoC = 0.65 mm, f/8 
Sony RX100 M1  detail at HFD/2 (100% crop), DoC = 1.30 mm, f/8 

Sony RX100 M1  detail at HFD (100% crop), DoC = 0.65 mm, f/8 
Sony RX100 M1  detail at HFD (100% crop), DoC = 1.30 mm, f/8 

Sony RX100 M1  detail at infinity (100% crop), DoC = 0.65 mm, f/8 
Sony RX100 M1  detail at infinity (100% crop), DoC = 1.30 mm, f/8 

Aperture f/11 

Hyperfocal Distance (0.88 m) 
Infinity 

Sony RX100 M1 at ISO 800  overview (original) 
Sony RX100 M1 at ISO 800  overview (original) 

Sony RX100 M1  detail at HFD/2 (100% crop), DoC = 0.46 mm, f/11 
Sony RX100 M1  detail at HFD/2 (100% crop), DoC = 0.92 mm, f/11 

Sony RX100 M1  detail at HFD (100% crop), DoC = 0.46 mm, f/11 
Sony RX100 M1  detail at HFD (100% crop), DoC = 0.92 mm, f/11 

Sony RX100 M1  detail at infinity (100% crop), DoC = 0.46 mm, f/11 
Sony RX100 M1  detail at infinity (100% crop), DoC = 0.92 mm, f/11 
The distant crops at f/5.6 and f/8 are compared with the crop at f/11:
Sony RX100 M1 at ISO 800  detail at infinity (100% crop)  f/5.6 
Sony RX100 M1 at ISO 800  detail at infinity (100% crop)  f/8 

Sony RX100 M1 at ISO 800  detail at infinity (100% crop)  f/11 
Sony RX100 M1 at ISO 800  detail at infinity (100% crop)  f/11 
Just a few observations from viewing the photos on a computer screen at 100% (or 200% for a Retina display):
Just a few observations from viewing the photos on a computer screen in fullscreen mode (Retina display, 5 MP):
And here a few observations from prints in postcard size (6" x 4" or 15 cm x 10 cm):
Finally, a few general conclusions:
One more important note:
14.02.2016 