You will find mirror surface quality measured by a variety of units.
The common examples are Peak to Valley (PV), on the surface; Peak to Valley (PV), on the Wavefront, (Or at the focus); RMS smoothness or Strehl ratio.
This page cannot explain the units in depth in the space we have available, as to do so would need a thick text book on Optics - but it does try in practical terms to give a idea as to what the measurements mean and to give a idea of what might be "good" values to aim for.
You will have noticed from the above that if PV or RMS is quoted then the first thing you have to know if it is the surface or the wavefront that is being measured, since PV of one is twice the other.
You will see it stated in lots of astronomical texts that a good standard to aim for on a mirror is PV 1/8λ error measured on the surface of the mirror, which is also the same thing as PV 1/4λ error measured on the wavefront.
This standard was originally proposed by Lord Rayleigh, and it is now known as the "Rayleigh Tolerance" The matching RMS wavefront error for these PV figures is about 1/15λ and the matching Strehl value is about 0.82.
All these different values are probably already confusing! - So what does PV 1/4λ wavefront error and the other values mean in practice? Is 1/4λ really a good criteria to aim for?
In the real world it is impossible to make an absolutely perfect mirror. Any real mirror always has defects of some sort or description.
However let's suppose a mirror maker could produce an absolutely perfect mirror. It would have exactly the right parabolic curve and it would have no defects or roughness of any kind on the surface, then you would probably expect it to focus all the light from a star to a single infinitesimally small point at the focus?
Sorry! - You would be wrong!
The very simple explanation of what happens is that because of the wave nature of light, the mirror focuses the light into a finite sized disk rather than the infinitesimally small point that you expected.
There are also some faint rings outside the central disk but the combined pattern of the disk and
rings is just called the "Airy Disc" after the person who first analysed it mathematically. For any mirror, - perfect or otherwise, - it is impossible to focus the light to a spot smaller than this disc. Any defects in the mirror only make the disc bigger. The size of the Airy Disc is directly related to the wavelength of the light and the Focal Ratio of the mirror. The formula is in the table below.
Airy Disc Size (mm)
D = 2.43932 x λ x Focal Ratio
D = Diameter of Airy Disc in mm
λ = Wavelength in mm (e.g. 546nM = 0.000546mm)
Adjacent table gives figures for 546nM
So even if a mirror maker could produce a perfect mirror, - it still would not focus perfectly.
For more about the Airy Disc - and why it can't be avoided see this page of our website.
Any defect or departure from the perfect parabolic shape or any roughness in the mirror surface will cause additional blurring on top of that due to the Airy Disc.
However, if the defect is minor and the resulting blur caused by the defect is less than the Airy Disc diameter, then in practice the defect has only a very marginal effect.
Mirrors where the defects are so minor that they cause less blur than the Airy Disc are said to be "Diffraction Limited"
There is a slight proviso about viewing the moon or planets which is discussed later, but if you are using your telescope to view point sources like stars, then once your mirror is diffraction limited, it will perform just as well as a perfect mirror.
So an obvious high specification target for any amateur or professional mirror maker to aim at would be to produce a "Diffraction Limited Mirror"
It is possible to make a mirror better than diffraction limited, but once beyond this point, there are rapidly diminishing returns in performance for the extra work as the Airy Disc remains as the dominant "error" that cannot be removed.
Diffraction Limited "Values"
There is considerable debate as to at what point a mirror becomes diffraction limited and no consistent agreement.
Various limits have been proposed and the "Rayleigh Tolerance" is one of them.
Oldham Optical puts forward here its interpretation of "Diffraction Limited" and follows up with what you will get if you buy a "Diffraction Limited" mirror from us.
Using a professional optical programme, it is possible to model various defects on different sized mirrors, and find the limits where the blur caused by the error is the same size as the Airy Disc.
Diffraction Limits of Various Sized Mirrors Measured in Different Units
Airy Disc (mm)
Peak to Valley on Wavefront λ
RMS Surface Smoothness λ
A Perfect Mirror
See Values Below
The adjacent table was compiled using "ZEMAX", a professional optical ray tracing programme and gives figures in the common measurements where an error on a mirror causes the same diameter blur as the Airy Disc.
A perfect mirror is included as reference at the top of the table, to show what the measurements would be if it was possible to make one.
For the experts with access to ZEMAX, - the figures were obtained by starting with a perfect parabolic mirror of the noted diameter and focal ratio, then deforming by altering the conic constant while optimising for best spot until the resulting spot is just contained within the boundary of the Airy Disc. Once this condition is reached, - the Wavefront error and Strehl are found by re-optimising for minimum Wavefront error.
This method does assume that the mirror surface is perfectly smooth. Finally the wavelength of light used is 546nM.