Diffraction, Aperture Size and Focal Length

Started 11 months ago | Questions thread
alanr0 Senior Member • Posts: 2,073
Re: Diffraction, Aperture Size and Focal Length
8

Rod McD wrote:

Hi,

I have a question about diffraction to ask of those more knowledgeable than myself. What is the relationship is between diffraction as we observe it in photography and the physical size of the diaphragm hole, which in turns depends on focal length?

In my high school and early uni physics days (where I left it behind decades ago), diffraction was described to be the effect on light rays passing an edge and ascribed, at least in the wave theory of light, to be the product of interference.

Diffraction and interference are related effects which arise from the wave nature of light.

Don't get too hung up on the "edge effect" argument. Diffraction occurs wherever the transverse extent of a wave is restricted. You still get diffraction with a graded filter with no obvious edge.

In the many DPR forums I have inhabited, there is a conventional wisdom often adopted that diffraction will start to take effect at particular apertures on particular sensors. For example, people usually talk about it as being around f8 on MFT, f11 on APSC and f16 on FF. But put aside sensor size for a moment - the physical size of the aperture also varies massively according to FL. If I use a 20mm lens, an aperture of (say) f10 would have a diameter of 2mm. If I use a 400mm lens, an aperture of f10 will have a diameter of 40mm. The proportion of light transmitted proximal to the circular edge formed by the diaphragm blades must be very different too - the diaphragm edge diameter is proportional in length to the hole's radius; the area of the hole to its square.

So what is the relationship? And why is it that despite the massive increase in aperture hole size with FL, the conventional wisdom that resolution will start to soften after f11 on APSC, (the sensor size I use) seems to hold true? Why is it that we can't or don't relate diffraction to FL?

Analysis of diffraction often starts with an extended parallel beam of light (from a distant point source, or a collimated laser beam) incident on a circular aperture. Wave theory predicts that the transmitted light is no longer strictly parallel. If the divergent beam is projected onto a distant screen, we see an Airy Disk pattern, with a bright central spot, with fainter concentric rings.

The angular radius of the first dark band is 1.22 x wavelength / Aperture_diameter (measured in radians). For a 2 mm diameter aperture, this is roughly 1 arc minute, which is not far from the angular resolution of a healthy young human eye.

The resolution of a telescope is determined by the physical diameter of the aperture, so powerful telescopes need large apertures to achieve good resolution (apart from collecting more light). For photography, we are more interested in what is focussed onto the sensor. Here the size of the diffraction spot is proportional to the focal length of the lens.

Radius of Airy disk at sensor = 1.22 x wavelength x focal_length / Aperture_diameter

Focal length divided by aperture is just the F-number of the lens. In the absence of lens aberrations, the size of the diffraction spot depends only on the F-number and the wavelength.

The eye is most sensitive to green light with wavelength 555 nm, so r ~ 0.68 F# μm.

The spot is rather fuzzy, so a conveniently remembered approximation is simply:

Diameter of diffraction-limited spot at sensor (measured in microns) = F-number

Typical DSLR sensors have pixel pitch in the range 4-8 μm, so the effects of diffraction from well-corrected lenses become apparent for F-numbers larger than f/4 to f/8.

HTH.

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Alan Robinson

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