Optics

For this (long) blog entry, I want to explore a little bit about optics and how it affects us photographers. It will be part of a series of blog entries about optics. With the more high resolution sensors and high density sensors being brought into the market, I was curious to see how the laws of physics will limit high resolution photography.

The first concept that is required to be covered is that of the Airy Disk. Now, Wikipedia covers this topic quite well, and I will try not too verbose. But very simply, the airy disk is an optical phenomena. It is the result of an optical system unable to reproduce a point source as a true point. Instead, it appears as an airy disk. That is, a point source, technically having no linear dimensions, becomes a circular disk of a finite and definable size. The size of disk is depend on a few basic parameters of the optical system - aperture and wavelength.

But for photographers the most important aspect is that the size of this disk is proportional to the f-number. The larger the f number (i.e., smaller the physical size of the aperture), the larger this disk becomes. The table below shows the airy disk size for different wavelengths of light as it changes with the f-stop. The units of the airy disk is μm, and for the keen reader, you will also note that most sensor pixel pitch is given in μm. 

Aperture	350 nm	450 nm	500 nm	750 nm
f/32	13.7 μm	17.6 μm	23.4 μm	29.3 μm
f/22	9.4 μm	12.1 μm	16.1 μm	20.1 μm
f/16	6.8 μm	8.8 μm	11.7 μm	14.6 μm
f/11	4.7 μm	6.0 μm	8.1 μm	10.1 μm
f/8.0	3.4 μm	4.4 μm	5.9 μm	7.3 μm
f/5.6	2.4 μm	3.1 μm	4.1 μm	5.1 μm
f/4.0	1.7 μm	2.2 μm	2.9 μm	3.7 μm
f/2.8	1.2 μm	1.5 μm	2.0 μm	2.6 μm
f/2.0	0.9 μm	1.1 μm	1.5 μm	1.8 μm
f/1.4	0.6 μm	0.8 μm	1.0 μm	1.3 μm
f/1.0	0.4 μm	0.5 μm	0.7 μm	0.9 μm

For the purposes of comparison, we shall use the longest wavelength in the visible spectrum (which ranges from about 350nm to 750nm) which is around 750 nm - red light. The assumption is that we are working with colour images in the full visible spectrum (no UV or IR photography, but the formula and concept apply equally). We want the take the most stringent criteria - that is the airy disk being the largest in the visible spectrum. Form this point onwards, all the various commentary and tables will be based on the airy disk at 750 nm wavelength of light.

What this airy disk describes is that no matter how good or perfect the lens, the highest resolution possible if limited to the size of the airy disk. This is where diffraction limit comes in. Any optical system in which the ability to render a point souce is only limited by the airy disk, is said to be diffraction limited.

To make another conclusion, if the airy disk size for a given aperture is less than double the pixel or sensor size (i.e., to capturean airy disk requires four pixels, two in each direction), it too is said to be diffraction limited.