Mirror Zone Calculator
for Couder Masks & Everest Pin Sticks
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 Many Zones?
How many zones should you use? There is no set answer. We strongly prefer to use an odd number of zones - this puts the critical 70.7% zone of a parabolic mirror in the middle zone, and not split between two adjacent zones when an even number of zones is used.
More zones means more data points and should result in a more accurate test result – but also means longer testing times. It is typical to use fewer zones for typical work session testing, and then increase the number of zones for final testing to be sure you have it 'right'. For typical sized mirrors, we would suggest:
- 6-inch: 3 zones for working, 5 zones for final test.
- 8-inch: 5 zones for working, 7 zones for final test.
- 10-inch: 5 or 7 zones for working, 9 zones for final test.
- 12-inch: 7 zones for working, 11 for final test.
Another way to estimate the number of zones to use is to use somewhat less than 1 zone per inch of mirror diameter for final testing, and then back off on this number to reduce it for working testing while figuring. Since we desire to use an odd number of zones, and the most common mirrors come in standard sizes of even inches, you can just subtract one from your mirror diameter,
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) 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).