optical quality

Telescope output mainly depends on the Optical Quality of its items.
In reflecting telescopes, based on Newton’s optical scheme, it is a parabolic mirror that acts as objective to gather flat light wave coming from a point source (for instance a star) located at a distance reasonably infinite. That wave, when reflected by the primary mirror, changes its shape to spherical and is sent towards the parabola’s focal point or, when intercepted by the secondary mirror, towards the telescope’s focus.
The resulting image in the focus is not a bright dot but a small disc (known as Airy’s disc or Diffraction Smear, that gathers 83.8% of the light energy) surrounded by a set of rings getting fainter as the distance form the central disc increases. The entire, disc and rigs, is called also “the Centric” and distinguishes each mirror as depends on its focal length and diameter. It is an evidence of the waving nature of light as well.
Every optical flaw warps the figure, changing its pattern or moving some brightness from the central disc to the external rings. As a consequence: the image contrast decreases, the resolving power is affected, and the observer feels more uneasiness.
Considering that perfection is impossible within the human sphere, anyway there is a clear boundary between good optics and lacking ones, defined by some allowed tolerances.
The generally accepted rule to state optics quality is the Rayleigh criterion: the maximum acceptable defect on the spherical reflected wavefront mustn’t exceed 140 nanometers or a quarter of the human eye more perceived wavelength (560 nanometers).
But this criterion is not sufficient to fully qualify an optic instrument. There are some other important elements: the residual transversal aberration must be less of the radius of the diffraction disc, moreover the number of defects existing on the whole reflecting surface, even if less than 1/4 wavelength in size, is a disadvantage (the more are the errors and the more are the surface slopes); mirror’s astigmatism notably penalizes as well.
So optical quality must be regarded studying the whole wavefront.
The above evaluations entrust to the maker’s experience when using the appropriate testing tools (Focault‘s tester, Ronchi’s grating, etc.) but the user himself should be able to perform his own via the so called Star Test. Anyway these all are subjective measurements because they have discretional limits.
An objective test case that is gaining success is the Interferometric way. Accordingly this method the wavefont generated by the optical under test is analyzed against another accurate reference system. It produces interference fringes that once evaluated by a specific software program provide a lot of information on optical quality.
The most important are:
Peak-to-Valley (P-V) = maximum detected error on the wavefront,
RMS (Root Mean Square) = a statistical value, calculated considering the entire area of the wavefront, hence more significant than P-to-V,
Strehl ratio = corresponding to the bright intensity of the false stellar disc, expressed as percentage of that from a perfect system, conventionally set to 1.
The information frame is fulfilled with: MTF, PSF, Wavefront coding and the Astigmatism level. A good example of handling these tests can be found on the Caelum magazine, within the column edited by Plinio Camaiti, treating instrument measurements, in the section reserved to M. Riccardi’s tests.
M.Riccardi is the creator of the ATMOS software, a program designed for projecting and testing optical astronomic instruments (see at: http://www.atmos-software.it/ ). Here you find a simple table and brief comments to qualify optical goodness accordingly the parameters I mentioned above.

P-V (ratio)	P-V (decimal)	RMS (ratio)	Marechal RMS	Strehl Ratio	Commento
1/3	.333	1/10	.094	.71
1/4	.250	1/14	.071	.82	Rayleigh's limit
1/5	.200	1/17	.057	.88
1/6	.167	1/21	.047	.92	Good Optic
1/7	.143	1/24	.041	.94	Very good Optic
1/8	.125	1/28	.036	.95	Premium Optic
1/9	.111	1/31	.032	.960	Premium Optic
1/10	.100	1/36	.028	.969	Premium Optic
1/11	.091	1/38	.026	.974
1/12	.083	1/41	.024	.978