Diffraction Limit

Started 11 months ago | Discussions thread
Krich13
Regular MemberPosts: 381
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Re: Diffraction Limit
In reply to LTZ470, 11 months ago

LTZ470 wrote:

From a very credible source:

"Diffraction thus sets a fundamental resolution limit that is independent of the number of megapixels, or the size of the film format. It depends only on the f-number of your lens, and on the wavelength of light being imaged. "

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Sorry, I didn't read the thread, may be someone already said it.

Anyway, there are different types of resolution and different criteria for its measurement.

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One criterion is the size of the focused spot (e.g. the minimum spot size on the sensor). That one indeed depends only on the f-number (more precisely on numerical aperture (NA) of the lens) and the wavelength lambda of light used. NA is defined as sine of half-angle of converging light cone (in media other than air multiplied by index of refraction of said media). For not-too-fast lenses (in air), NA~1/(2*f-number)

Different criteria exist:

Rayleigh: spot size=0.61 lambda/NA (spot maximum positioned over the neighboring spot minimum)

Abbe: spot size=0.51 lambda/NA (width of the spot at half-height)

Sparrow: spot size=0.47 lambda/NA (neighboring spots of equal intensity stop being resolvable).

Obviously, if the diffraction limited spot is smaller than a pixel, diffraction limit of resolution can not be reached. Megapixels still matter.

For instance, for yellow-green light (lambda=550 nm), diffraction limited spot (Rayleigh) for and f/4 lens (NA=1/8) is ~2.7 microns (2.1 microns for Sparrow criterion), smaller than a single photosite of current m43 sensors. Pixels (as in "full-color picture elements") are bigger still.

Obviously, the same diffraction-limited spot would occupy larger portion of the smaller sensor than of a larger sensor.

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Another way to look at resolution is angular resolution (this is tha one relevant for photography. Minimum resolvable angle depends only on the wavelength and the lens diameter (or absolute aperture).

The minimum angle resolvable (in radians, multply by 57 for degrees)

is 1.22/1.02/0.98 D/lambda (Rayleigh/Abbe/Sparrow) where D is the diameter of the lens/aperture.

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