Sensor Size Battles: Lenses as Equalizers

Camera makers used to fight using megapixels.  Then high ISO.  Now they tout the size of their sensor as a feature.  For example, among compacts, cameras with 1/1.7" sensors are deemed better than those with 1/2.5" sensors, and the RX100 and RX100 II are the kings of the hill among compacts, with their 1-inch sensors.  However, the available lenses for a camera can often make up for a smaller sensor.

The purpose of this post is to show how to calculate the equivalent full frame sensor size and depth of field that you can expect from a camera and lens combination.  Ultimately, I hope it helps you compare systems (including those with fixed lenses) and narrows your choice of ideal camera system.

CORRECTION: I made a mistake calculating the effective aperture of the RX100! Sorry!

BACKGROUND BLUR
The amount of background blur is based only on 3 factors: the distance between the camera and the subject, the distance between the subject and the background, and the actual (not relative) aperture size.  (Sensor size is not a factor per se, but is relevant insofar as larger sensors require longer focal lengths to achieve the same field of view.)

The first two factors are constant for lenses with the same field of view if you want to maintain the same composition.  So to determine the amount of blur, we would only need the actual aperture size, which is simply the actual (not 35mm equivalent) focal length divided by the maximum aperture at that focal length.  For example, the Sigma 35 1.4 has an actual aperture of 35/1.4 = 25mm.  The X100S' lens has an actual focal length of 23mm and an aperture of f/2 therefore its physical aperture is 23/2 = 11.5mm.  If we were to compare the X100S to a full frame 34.5mm focal length lens, the equivalent aperture would be 34.5/11.5 = f/3.


COMPARING SYSTEMS
(By system I mean a camera and available lenses.)  The easiest way for me to compare the effective aperture, taking into account the sensor size, is to multiply the aperture by the crop factor, just like you do for the focal length.  Let's say you have a Panasonic 25 f/1.4.  That's a Micro Four Thirds lens, so the crop factor is 2x.  Therefore the effective aperture is f/1.4 * 2 = f/2.8.  In other words the Panasonic 25 1.4 has the same DOF as full frame lens that is 50mm f/2.8.

What about compacts, with no standard crop factor?  Just look at the advertised equivalent focal length range and divide it by the actual focal length (usually printed on the lens).  For example, the Olympus XZ-2 has a focal length equivalent of 28mm - 112mm.  However, the actual focal length is 6mm - 24mm.  The crop factor is 28/6 or 112/24.  Either way it is 4.67x.  The aperture is f/1.8 - f/2.5.  In full frame terms it is like f/1.8 * 4.67 = f/8.4 at 28mm equivalent.  And f/2.5 * 4.67 = f/11.7 at 112mm equivalent.  That should also give you a pretty good idea of how much blur to expect realistically.

Note that we're only talking about DOF and blur here, not taking into account other benefits of larger sensors such as high ISO performance or dynamic range.

SOME SAMPLE EFFECTIVE APERTURES (DOF)
In approximate order of increasing size of aperture:

Among zooms:
Panasonic FZ200 = 25-600mm f/15.6
Panasonic Lumix LX5 = 24-90mm f/9.4-15.5
Olympus Stylus 1 =  28-300mm f/13.1
Sony RX100 or RX100 II =  28-100mm f/4.8*-8.8 13.2.  *Note however that the aperture rapidly shrinks at any focal length above 28mm.
Olympus XZ-2 or Pentax MX-1 =  28-112mm f/8.4-11.7
Fuji X10 or X20 = 28-112mm f/7.9-11
Panasonic Lumix LX7 = 24-90mm f/7.1-11.7
Olympus or Panasonic 14-42 kit lens for Micro Four Thirds = 28-84mm f/7-11.2
Canon G1X = 28-112mm f/5.2-f/10.8
Sony RX10 = 24-200mm f/7.6
Typical APS-C kit zoom (f/3.5-5.6), such as the Sony NEX 16-50 kit lens = 24-75mm f/5.25-8.4.

Among primes:
Sony 20 2.8 pancake = 30mm f/4.2
Panasonic 20 1.7 = 40 f/3.4
Fuji X100 or X100S. 34.5mm f/3
Sony 24 1.8 = 36mm f/2.7
Fuji 23 f/1.4 for X-system = 34.5mm f/2.1
Voigtlander 17 f/0.95 for Micro Four Thirds = 34mm f/1.9

Did any of the figures surprise you?  For example:

• The LX7 with its small 1/1.7 sensor but fast lens has about the same DOF as a Micro Four Thirds camera with kit lens or a Fuji X10 or X20 with 2/3 inch sensor, and is much more compact.
• The RX100 RX10 has almost the same DOF as an APS-C kit lens at longer focal lengths.

What about this: which has shallower DOF: a 2.8 zoom for APS-C or kit lens for full frame?
Sigma 17-50 f/2.8 = 25.5-75 f/4.2.  Which means that at longer focal lengths, the 2.8 APS-C zoom has about the same DOF as a Nikon 24-85 3.5-4.5 VR, and at shorter focal lengths, the difference is just about 1/3 of a stop, which is hardly noticeable.

My point is that you should look not only at the sensor size but the available lenses for the camera you're researching.  Sometimes, a small sensor with fast lens can offer comparable DOF as a camera with larger sensor, while having a smaller overall size.