Sensor Size and Bokeh

Photographers like to call the blurred quality of a background in a portrait "bokeh."  You can get a numerical value for the size of the blur circle (circle of confusion) from an out of focus point of light at infinity starting with the thin lens formula:

1/f = 1/u + 1/v

f is the focal length of the lens, u is the distance from the lens to the object and v is the distance from the lens to the image.  When u is infinite 1/f = 1/v.  The distance from the lens to the image is equal to the focal lens of the lens.  You could express 1/v as 1/(f+e), with e being the distance the image moves as you focus on objects closer than infinity.  With a little algebra you can derive a formula for e as

e = f^2 / (u - f)

The amount of blur you get for an out of focus distant object is 

b = e / N

where N is the focal ratio of the lens.

Finally, the blurriness of the image on the final print depends on how much the image is enlarged. A Micro 4/3rds image has to be enlarged twice as much as a full frame image to make the same size print.

Let's aim our cameras at a subject 3m (10 ft) away.  We'll use a full frame digital camera with a 50mm lens set at f/2.8 and a Micro 4/3rds camera with a 25mm lens set at f/1.4.  The 50mm lens on a full frame camera has the same field of view as a 25mm lens on a Micro 4/3rds camera.  Both cameras see the same perspective because both are at the same distance from the subject.

Full Frame (36mm x 24mm)

f = 50mm

u = 3,000mm

N = 2.8

b = 50^2 / ((3,000 - 50) * 2.8)

b = 0.30

Enlarge the image 8 times to make an 8x10 print and you get a 2.4 mm blur circle.

Micro 4/3rds (17.3mm x 13mm)

f = 25mm

u = 3,000mm

N = 1.4

b = 25^2 / ((3,000 - 25) * 1.4) 

b = 0.15

Enlarge the image 16 times to make an 8x10 print and you get the same 2.4mm blur circle.

When you set up for the same perspective and field of view, to get the same background blur you need to open the aperture twice as much on the Micro 4/3rds camera as on the full frame camera.