Portraits: Biggest Blur for the Buck

Nikon D600 + Nikon 85 1.8G.  f/1.8, 1/800, ISO 100

This question was posted on DPReview and I thought it is a useful question: "What is the greatest amount of blur you can get in the most compact package for portraits?"

Update: thanks to readers' suggestions, I added Fuji 56 1.2, Samsung 85 1.4, and Nikon 135 f/2.

Answer:  First, we need to note the distinction between depth of field and background blur. Depth of field is the range of the photo that appears to be in focus.  Background blur is exactly what its name implies. 

For portraits, what most people actually care about is background blur. Background blur depends on the actual aperture size. You can determine this from the actual focal length usually printed on the front of the lens, divided by the maximum aperture at that focal length.  So, for example, the Sony RX1 has a 35mm actual focal length and f/2 maximum aperture, therefore its actual aperture size is 35/2 = 17.5mm. You can compare cameras based on their maximum physical aperture size and focal length.

The other thing you may want to consider is the field of view, because portraits are more flattering at certain distances from the subject.  Traditionally, portrait lenses are around 85-135mm. Shorter than that, you'll probably need to be closer to the subject (unless it's an environmental portrait) which will tend to make noses look larger. Longer than that, you'll probably need to be farther from the subject, which will tend to make faces look flatter.

Sony a6000 + 50 1.8, f/2.8, 1/250, ISO 100.

Here are some candidates (depending on your definition of compact), with larger apertures showing greater background blur:

Camera and Lens	Actual FL; aperture	Actual aperture size and field of view	Notes
Sony RX1	35 / 2	17.5mm (fov equiv to 35mm)	Reviewed here.
Sigma dp3 Quattro or Merrill	50 / 2.8	17.9mm (fov equiv to ~75mm)
Olympus Stylus 1	64.3 / 2.8	23mm (fov equiv to 300mm)	Reviewed here.
Samsung NX500 + 45 1.8	45 / 1.8	25mm (fov equiv to 69.3mm)	Reviewed here.
Sony RX10	73.3 / 2.8	26.2 mm (fov equiv to 200mm)
Sony a6000 + 18-105 f4	105 / 4	26.25 (fov equiv to 157.5mm)	18-105 reviewed here.  Sony a6000 first impressions.
Sony a6000 + 50 1.8	50 / 1.8	27.8 (fov equiv to 75mm).
Sony a7 series + 55 1.8	55 / 1.8	30.6 (fov equiv to 55mm)	Samples here.
Fuji X-T1 + 56 1.2	56 / 1.2	46.7 (fov equiv to 84mm)
Nikon D600 or D610 + 85 1.8	85 / 1.8	47.2 (fov equiv to 85mm)	Nikon D600 reviewed here.  Nikon 85 1.8G reviewed here.  Canon 85 1.8 reviewed here.
Samsung NX500 + 85 1.4	85 / 1.4	60.7 (fov equiv to 131mm)
Nikon D600 or D610 + 85 1.4	85 / 1.4	60.7 (fov equiv to 85mm)
Nikon D600 or D610 + 135 f/2	135 / 2.0	67.5 (fov equiv to 135mm)

What about the sensor size or crop factor?

Background blur does not depend on crop factor. It only depends on physical aperture size, which is a function of the actual focal length and the aperture.  Sensor size is relevant only insofar as larger sensors have longer focal lengths for the same field of view.  Real life example:

• The Sony RX1 has an actual focal length of 35mm, a max aperture of f/2, and a crop factor of 1.0.
• The Sony a6000 with 35 1.8 has an actual focal length of 35mm, a maximum aperture of f/1.8, and a crop factor of 1.5. 

Notwithstanding the crop factor, the Sony a6000 + 35 1.8 has a greater amount of background blur compared to the Sony RX1.

RELATED RESOURCES [Added 6/23/15]
Background blur and its relationship to sensor size.  TLDR: "As shown above, estimating the maximum strength of background blur is very easy. Just take the maximum zoom (the real value, not the 35mm equivalent), divide it by the maximum aperture at maximum zoom and then divide this by a typical size of the subject you want to take photo of (as said above 0.6m - 0.7m are good reference points for portraits)."  Comment: since the size of the subject is constant when comparing cameras, you don't even need to include subject size in the equation.  Therefore, if I may paraphrase: "Just take the maximum zoom (the real value, not the 35mm equivalent), divide it by the maximum aperture at maximum zoom and then divide this by a typical size of the subject you want to take photo of."  Which is exactly the same formula I provided above. :)