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Sharpness - Bokeh
Foto tutorial (English)
Foto tutorial (Espaņol)
Equipment recommendations US-ES
Flaat for Canon
Flaat for Nikon
Flaat for the BMC
Flaat for NEX-5N
Old Picture Style Tests
APS-C vs Full Frame
Badly assembled lenses and image quality
Lens mount compatibility chart
ISO on different cameras
High ISO on the 5D3
DIY: DR test chart
RGBWK Bayer sensors
Notes on DoF-FoV
Notes on crop-DoF-FoV
Custom Cropmarks for Magic Lantern on the Canon 550D
How many megapixels do I want?
How many megapixels can I see?
Quick Monitor Calibration Chart
Given a sensor size, the wider the aperture in the lens, the shallower the depth of field. And, given an aperture, the bigger the sensor, the shallower the depth of field. So, if we want a shallow depth of field, we want fast lenses with wide maximum aperture (expensive) and cameras with big sensors (expensive).
The relation between aperture and sensor size in terms of depth of field is the same one as in terms of focal length: you have to multiply the aperture by the crop factor. For example, if we put a tripod in a set place and change cameras and lenses, we'll get exactly the same image with each of the following combinations:
My 35mm f/2.8 on my Canon APS-C (1.6x) is equivalent in terms of field of view and light intake to a 56mm f/2.8 on a full frame camera, but is equivalent in terms of field of view and depth of field to a 56mm f/4.5 in a full frame camera.
And in that table you can see one of the biggest problems of pint-and-shoot cameras: having a small sensor, it is not easy to get shallow depth of field (a problem that is even bigger if the built-in lens is a slow zoom). If we want a deep DoF (for example, for a landscape) this won't be a problem; but if we want to have selective focus (for example, for a portrait) it will be very difficult (or impossible) to get the desired effect (there are no f/0.5 lenses, which would deliver the same DoF of a f/4 lens on fullframe; with a fast lens, like f/1.4, we get the same DoF that a fullframe camera would get at f/11; with a slower lens, like f/2.8, everything will always be in focus).
This is the most important reason for wanting a camera with a big sensor (other reasons: they usually deliver images with less noise at high ISO, have more dynamic range, etc), and one of the two reasons for wanting fast lenses (the other one being that they are useful in low light situations, although in this case we'll have to be careful because depth of field may be reduced more than we initially intended).
You can calculate the depth of field for your camera and your lenses, at different setting, with my field of view and depth of field calculator, here.