Mirror Cells for Amateurs: RMS and Strehl Calculator: Notes

Notes for RMS and Strehl Calculator

PrimaryRMS
From Sixtests or another mirror test analysis program. Sixtests reports this value in nanometers (nM). This is a surface RMS value, not a wavefront value.

SecondaryRMS
Not yet written.

Secondary Angle
For a Newtonian, this is 45 degrees. For a Cassegrainian, it is 0 degrees.

Secondary Illuminated Fraction
How much of the secondary mirror is illuminated when viewing an isolated point source at the center of the field. This is given as a decimal fraction. Default is 0.66, which is a typical value for Newtonians.

Cell RMS
From Plop. Plop reports this value in millimeters. Plop reports a surface RMS value, not wavefront. Surface is needed here.

Combined RMS
= SQRT(Primary RMS² + (Secondary RMS * Illuminated Fraction / Cos(Secondary Angle * Pi / 180))² + Cell RMS²)

The combined RMS value is a surface value even though it refers to two surfaces. Multiply by 2 to get the wavefront RMS value.

Reference Wavelength
Visible light wavelengths run from about 400nM (violet) to about 700 nM (deep red). In millimeters, this is 0.0004mm to 0.0007mm.

Common reference wavelengths for Strehl ratio and wavelength ratings are 500nM (peak sensitivity of dark adapted vision), 550nM (peak sensitivity of color vision), 589nM (sodium D lines) and 633nM (helium-neon laser).

Sometimes wavelengths are listed in Ångstrom units. One Ångstrom is 0.1 nM. 5000Å = 500nM.

RMS (Waves)
= Reference Wavelength / Combined RMS
This is the surface RMS "wave rating" of the combined system. It is given as a fraction. Example: 1/100 wave RMS. If the number in the box is a decimal fraction, then the rating is the reciprocal. e.g. If the box says 0.5, the wave rating is 1/0.5 = 2 waves.

Strehl Ratio Estimates
Strehl estimates 1 and 2 use formulas from Jim Burrows web page ATM Mirror Mathematics. Estimate 1 is good only for small RMS values. Estimate 2 can overestimate the true Strehl ratio slightly.

Strehl Estimate 1 = 1 - (4 * Pi * Combined RMS / Reference Wavelength)²

Estimate 1 can go negative for some input values. My program eliminates negative results, reporting them as zero.

Strehl Estimate 2 = 1 / e^{(4 * Pi * Combined RMS / Reference
Wavelength)²}

The true Strehl ratio value is probably between these two estimates in most cases.

You may notice that the Strehl estimate formulas on Jim Burrows' web site have 2's where mine have 4's. The versions with 2 are correct when the RMS value is for the wavefront. In this calculator, I am feeding them a surface RMS value that needs to be multiplied by 2 to turn it into a wavefront value.