Depth of Field

What it is

A photographic image is only sharp in the focus plane. The farther an object is located in front of or behind the focus plane, the more it is blurred.

However, this blur is not recognizable if it stays below a certain amount. In classical photography which has a printed image as a goal (no matter whether digital or analog) the perception of the human eye is the limiting factor.

The human eye commonly accepts an edge as sharp, if the angle of view of the blur is smaller than 1 arc minute. Hence a point blurred to that amount has the diameter of 2 arc minutes, which is the same as 1/1700 of the viewing distance.

This is the allowed diameter of the so called Circle of Confusion. The normal viewing distance in classical photography is assumed to be equivalent to the printed image diagonal. The circle of confusion is the basis for most Depth of Field calculators or tables.

Considerations for VR panoramas

For VR panorama creation where one can zoom into the image, the limit must be the pixel distance in the viewable panorama - unless you don't allow to zoom in until 100% pixel view.

Since a pixel in an equirectangular panorama corresponds to a certain angle of view in reality, we can directly calculate the allowed angle of confusion in the shot image. It is 360� divided by the width of the equirectangular image.

For a standard angle of confusion of 2 arc minutes this would result in an equirect image with 10800*5400 pixel. Hence the Depth of Field for most VR panoramas is far bigger than for classical photography and standard depth of field calculators are of no big use. Read on to see how to circumvent this.

Hyperfocal distance

In most cases a panorama should be sharp from the horizon to the nearest objects. Since the Depth of Field region is partly in front of and partly behind the focus plane, you sacrifice a fair amount of Depth of Field if you focus to infinity.

However, there is a distance you can focus on, that extends the Depth of Field exactly from infinity to a nearer limit. This is the hyperfocal distance. It can be calculated, if the allowed circle of confusion (see above) on the sensor is known.

Following the considerations on Depth of Field for VR panoramas we can calculate a small table with

• Width - image width in pixels
• AoC - angle of confusion in arc minutes
• CoC - Circle of Confusion on full format DSLR or analog film in mm
• CoC1.6 - Circle of Confusion on crop factor 1.6 DSLR in mm

Width  AoC  CoC    C0C1.6
8000   2.7  0.034  0.021
6000   3.6  0.045  0.028
4000   5.4  0.068  0.042

The formula for this calculation is

CoC = sin(AoC) * sensor diagonal
AoC = 360 / Width

With this values you can go into any depth of field calculator where you can enter the circle of confusion like for example http://www.tawbaware.com/maxlyons/calc.htm and calculate the hyperfocal distance (and the Depth of Field if required).

In any case the near limit of the Depth of Field is half the hyperfocal distance.

Please note, that all these values for fisheye lenses are only approximations, since their focal length changes from the center to the edges as well as the effective aperture changes.

Erik Krause 16:50, 6 Jun 2005 (EDT)