This program is unit less - it works with any length measurement you care to use;
The units you use for Mirror Diameter are the units you get back as Radii.

In the table below are the calculated radii for the center and edges of each zone.
Zones and zone centers are calculated to be of equal mirror area.

What the calculations are used for:

They are used to create devices to mark mirror test zones: Couder Masks or Everest Pin Sticks.

How it works:

The zone calculator uses an equal area formula, so that each zone contributes the same amount of light to the resulting image (this is not strictly true, since we don't allow for the shadow of the diagonal on the inner zones). Also, the zone "centers" are calculated with the same equal area formula, so they are, in fact, biased towards the outer edge of the zone. The is the strategy used in [Berry94].

The formulas are:

N = Number of Zones        X = Current Zone

InnerEdge( Zone 1 ) = 0    (Zone 1 has no inner edge)

OuterEdge( X ) = SquareRoot( X ) / SquareRoot( N)
OuterEdge( X ) = InnerEdge( X + 1 ) 

Center( X ) = SquareRoot( X+0.5 ) / SquareRoot( N )

These formulas yield normalized zone radii (i.e. radii for a mirror of radius 1). Multiply by your mirror radius to get actual zone radii for your mirror (or multiply by 100 to get zone percentages).

Page last edited 2007-Sep-23