This page is for those of you who wish to learn more about what makes a good quality mirror. Optical quality is very important to me and all mirrors that I put into my telescopes are individually tested and come with their own optical test bulletin.
For primary mirrors, the test bulletin consists of:
- three Foucault tests (for the mirror rotated around its axis of symmetry by 0°, 45° et 90°) which certify the precision of the paraboloid figure
- a photo of the mirror as seen in the Foucault test, to show the surface uniformity
- a test against astigmatism (to prove good rotational symmetry) by examining the image of a point source under high magnification
For secondary mirrors, I supply the interferometric test report from the original manufacturer, certifying the surface flatness.
Importance of these measures
Precision of paraboloidal figure
A perfect primary mirror will concentrate all the light coming from a star in a single point, which requires a mirror of paraboloidal shape. The slightest deviation from this ideal shape will spread some light away from the ideal convergence point, which reduces contrast and the mirror’s ability to resolve fine detail. In practice, because of the light diffraction phenomenon, even a perfect mirror will not converge light exactly in an infinitely small point, but in a small bright spot (the Airy disk) surrounded by a few faint diffraction rings. A good mirror will focus a maximum amount of light inside the Airy disk and very little in the diffraction rings. A bad mirror will spread more light out into the diffraction rings, thereby greatly reducing contrast.
The necessary surface accuracy of a good telescope mirror is measured in nm (nanometers, one millionth of a millimeter)! A peak-to-valley (P-V) surface error of 65-70nm is considered to be the maximum acceptable, as long as this error has a slow variation along the mirror’s surface. I can achieve surfaces with a P-V surface error less than 28nm, thereby a P-V wavefront error less than one fifteenth of a wave (λ/15 on the wavefront)! The P-V wavefront error is one of the results seen in the Foucault test bulletin.
Note: for a primary mirror, the wavefront error is always equal to twice the surface error.
The P-V surface (or wavefront) error is not a complete measure of optical quality. Much more important is the root mean square error (Surface RMS error in the test bulletin), which describes the surface smoothness. To put it simple, the maximum deviation from the perfect paraboloid may be small, but if there are many, many such small deviations, the end result is a bad mirror.
For example, consider looking at a reflection on the surface of a lake. If the water is perfectly calm, the reflection is nice and sharp. If there are big waves, you won’t see much of a reflection. But even if the waves are very small, the reflection can still be destroyed if there are many, many such waves.
A direct consequence of the RMS error is the Strehl ratio, a measure of how well the light is concentrated towards the center of the Airy disk. A perfect optical system has a Strehl ratio=1. When the Strehl ratio is greater than 0,8, it is said that the optical system is “diffraction limited”; this doesn’t mean that it is indistinguishable from a perfect system! I fact, Strehl=0,8 is just the minimum acceptable limit for astronomical telescopes. I strive for a Strehl ratio of at least 0,95 so you will benefit from improved contrast when observing deep-sky objects, the planets or the Moon. In 200mm optics, I guarantee at least Strehl=0,95 but I can generally achieve 0,98.
Qualitatively, surface smoothness can be evaluated in the Foucault test by noticing whether or not the mirror looks creamy-smooth, with progressive transitions between light and dark areas and without a blotchy appearance (what mirror makers call “dog biscuit”).
Absence of astigmatism
In the context of telescope mirrors, astigmatism is a fabrication error which translates in an imperfect rotational symmetry of the paraboloidal shape. The focal length of the mirror varies slightly depending on which section you consider through the optical system. The consequence is the inability to focus light from a star in a nice, perfectly round and small Airy disk.
I test all my mirrors against astigmatism by examining the image of a point source at high magnification. The image must be perfectly round, symmetrical and as small as possible.
In addition to the measures mentioned above and summarized in the optical test bulletins, I also guarantee an excellent optical polish of my mirrors. A good polish means obtaining a smooth surface at an even smaller scale than examined above, at a sub-nanometer level. This is another factor that ensures good contrast, especially in the case of faint targets such as nebulae.
A poorly polished mirror disperses light in a wide angle, throughout the telescope’s entire field of view. The sky background is no longer perfectly dark, therefore faint nebulae won’t stand out as much. Contrast will suffer especially if the nebula shares the field of view with a bright star, because stray light from the star will flood the background.
Polish quality should be checked even before starting the parabolization (and long before aluminizing the mirror). A laser beam directed at the mirror will quickly indicate polish quality: the laser should not be visible on the useful surface of the mirror.
In the attached photo, a red laser beam comes from the upper-right and hits the front (useful) surface of a mirror (not yet aluminized). Afterwards, the laser beam can be seen traversing the glass, then hitting the back surface of the mirror. The back surface has a regular, non-optical polish (notice the intensity difference of the laser spot compared to the front surface). After exiting the mirror through the back, the laser finally touches the black surface of the table (the brightest spot). With the naked eye, the laser spot on the front (useful) surface and the beam inside the glass are invisible even in a darkened room. A long exposure photograph was necessary to capture them. Such an excellent polish, on the entire front surface of the mirror, guarantees the best possible contrast!