Bokeh

Long time between posts. But this is a short one about bokeh. For me it has two qualities - the aesthetic look and the degree of blurring. The former can only be decided on a per lens basis and is highly subjective. The second factor, which is degree of blurring, is primarily based on the objective size. That is, the true aperture size. The larger the physical size of the diameter, the more the blur. For example, a 50mm f/2.0 has an aperture size of 25mm. A 200mm f/2.0 lens has an aperture size of 100mm. In most circumstances (i.e., same image size) the blur on the 200mm at f/2.0 will be far more than the 50mm f/2.0.

Given this, and the fact that I love blurred out background, I can make an informed choice between lenses as to which one will give me the most blur - but not necessarily the most beautiful blur. Some interesting conclusions is that the smaller the format, the larger the aperture needs to be to have good background blur.

In principle, my choices of lens for bokeh (for full frame D700) ranges between 50mm to 300mm. In this example, the following is a measure of the theoretical aperture size for various lenses. Noting that the large the aperture, the more blur.

50mm f/1.0 = 50mm (e.g., Leica Noctilux)

50mm f/1.4 = 35mm

85mm f/1.4 = 60mm

85mm f/1.8 = 47mm

100mm f/2.0 = 50mm (e.g., Zeiss ZF2 Planar)

135mm f/2.0 = 67mm (e.g., Zeiss ZF2)

200mm f/2.0 = 100mm (e.g., Nikon 200mm f/2.0 )

200mm f/2.8 = 71mm (e.g., f/2.8 70-200 zooms)

300mm f/4.0 = 75mm (e.g., Nikon 300mm f/4.0)

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.