ACCURACY - WHAT DOES IT MEAN?
It is generally accepted that if an image reaches the eye having no deviation greater than 1/4 wave at the nominal D line (sodium or helium light), the image is not seriously degraded (The Rayleigh limit). This superficially suggests that the entire telescope, not just the mirror (or objective element) should produce a wavefront accuracy of not less than 1/4 wave. But exactly what is meant by an accuracy of 1/4 wave as advertised by various makers of telescope mirrors? Frequently, this "wave accuracy" criterion has been poorly or incompletely defined. Is it 1/4 wave at the mirror surface? 1/4 wave at the image plane (wave front)? 1/4 wave entering the eye? For example, some makers advertise 1/4 wave surface accuracy. However, because of the law of reflection, this will result in a wavefront image accuracy of only 1/2 wave. Those mirrors with an advertised surface accuracy of 1/10 wave are really 1/5 wave at the wave front. And some just measure the half-wave amplitude - so it would really be 2/5 or .40 wave. One has to be careful.
And now with interferometery, there is RMS measurement - Root Mean Squared, yet another system you will see mentioned. RMS expresses a wavefront variance as the mean squared value of the wavefront over the pupil (diameter of mirror). And along with that is the Strehl Ratio, a measure of optical excellence in terms of theoretical performance results, rather than an expression of the physical surface or the shape of the wavefront. It is a complete statement, in terms of a single number, that describes probably the most significant measure of an optic's performance. (See A Better Method of Measuring Optical Performance.)
Still, the most common and generally accepted method of judging optics in the amateur world is looking at the total amplitude of the error over the pupil (diameter of mirror) in wavelengths of light. This known as the peak to valley criterion or OPD (optical path difference). It's simple, straightforward and easy to understand. There are other methods of measurement and other ways to interpret wave error, but when people speak of wavefront error they usually mean peak to valley. The wavefront error is usually expressed or assumed to be at the wavelength of helium light. (It used to be expressed in sodium light, which is very near the helium wavelength.) Just to help keep this all in perspective, one wavelength of helium light is 587.56 nanometers or 0.0005876 mm or 0.00002313 inch. That's 23.13 millionths of an inch - not very much. So, when someone is casually talking about 1/10 wave at the wavefront, or, roughly speaking, a .97 Strehl or a .031 RMS, they are talking about 1.15 millionths of an inch at the optical surface, over the entire surface.
The problem arises in that these various types of error measurement and quality ratings can be very confusing to the newcomer and advanced amateur as well. Broadly speaking, a 1/16 wave RMS is really only roughly 1/4 wave peak to valley, and if it's RMS surface accuracy, then the wavefront accuracy is 1/2 wave peak to valley - not very good. Unfortunately, many advertisements put out by makers of amateur optics make no attempt to clearly define the "accuracy" thing, or exactly what sort of "wave" we are talking about and where, not to mention that many are blatantly misleading - though fewer now than in years past.
And is the Rayleigh limit 1/4 wave peak to valley wavefront (.82 Strehl) accurate enough?
The Amateur Optical Market
Because amateurs do not purchase optics based upon a set of well defined specifications and tolerances, the quality of telescope optics have traditionally been described in broad descriptive terms only - terms which have no real meaning and can be interpreted in various (comfortable and convenient) ways. These terms include such impressive but meaningless things as: diffraction limited (not appropriate as used in this context), better than diffraction limited (impossible by definition) or whatever the next psychologically warm but unquantifiable term may emerge. Mirrors are also described as producing pinpointy or tack sharp images - well, I suppose thats better than fuzzy images. None of these terms, yes even diffraction limited, are true measures of the quality of an optical element that can be verified by any test method. They just sound good. Everyone wants tack sharp images, but what does that mean? - I'm not sure. Everyone wants diffraction limited images, I know what that means, but do the buyers of the optics? ... and can they tell? (Personally, I want to see an Airy disk, and that's not a pinpointy thing but a visible disk.)
Also, optics targeted to and sold within the amateur community have often been advertised as not only possessing high accuracy, but also as inexpensive; as if both were simultaneously achievable. The fact is, this is not, and really can not be, the case. In the world of optics, as in virtually everything else, you get what you pay for. The production of a high-quality optical component is a slow process, requiring a high level of skill and close attention to detail; anyone in the professional commercial optics business will tell you this. Good optics take time.
The reality is that inexpensively produced optics can not be depended upon to have the quality desired by a discriminating user who wants to resolve close doubles and observe fine planetary detail. It may also come a surprise to those who love "light buckets" that smaller mirrors of high quality will out-perform larger thin mirror scopes because nearly all the light is being focused rather than just most of the light. The recent success of small refractors is a case in point, but then again, these are instruments with 3 inch apertures, not 8 or 10 inches.
Badly focused images from poor optics not only causes light to be lost from the actual image but the lost light is scattered about and around the image and results in lost contrast; something which has a deleterious effect on not only planetary images but star clusters and faint galaxies as well. To a certain extent, many of us have come to accept poor images as the norm.
And if that is not bad enough, few amateurs realize that Newtonian telescopes using very short ratio mirrors (anything below f/5 and really below f/6) create a set of problems all their own. Testing these mirrors to the high degree of accuracy required is extremely difficult, and certainly not possible in a production environment where time is of the essence. And even if optically perfect and perfectly collimated (aligned), short ratio mirrors produce wild aberrations even when objects are viewed even slightly off axis. All of this results in images of less than diffraction limited potential. Short ratio mirrors are simply extremely difficult to align and keep aligned and are under most normal circumstances unlikely to produce an image approaching the diffraction limit. These short tube large aperture scopes are convenient to get into the car or van, but the advantages end there.
Production methods are also suspect in inexpensive, rapidly produced optics. I have seen many mirrors with large pits in the surface and unpolished edges are quite common. Surface ripple can also be a problem if the mirror has been "screech" polished at high speed to "burn in" a quick polish. Surface ripple can cause scattering of light and a serious loss in contrast. But we the purchasers frequently have no way of knowing how these mirror were made.
The term diffraction limit has been tossed around a lot, but is really not a good way to advertise the quality of an optical component. Strictly speaking, it describes the ability of an optical train to focus a distant infinitely small light source into the theoretical spurious disk; literally, a small spot of light, the Airy disk. It is also applied when discussing the resolution of complex images. Diffraction limit relates to a statement regarding end performance and can be vague, determining the quality of an optical component by measuring and quantifying the performance of the optic at the wave front in terms of wavelengths of light and scatter at a specific point in the spectrum is not so vague. Also, as a maker of objective mirrors, I can not be responsible for the performance of the entire telescope, only the objective as a separate element.
Why Go Beyond the Rayleigh Limit? Why Bother?
The eye and how it sees is a complex subject and the eye (really, the brain), by virtue of its remarkable image processing capacity, can actually occasionally see things even smaller than diffraction limit might indicate; faint planetary markings are a good example. The use of CCDs and image processing software (which imitates the work of the human brain) has extended this effect to the world of "photography". For this reason, we argue that the Rayleigh limit may not be sufficient for the finest work and higher tolerances may be more desirable. Other factors influence this opinion as well, such as the fact that other optical elements, such as secondary mirrors, are in the optical train and are not likely to be perfect. Atmospheric turbulence in the form of tube currents further deteriorate the image. The eyepiece makes its own contributions. Making a mirror only at the Rayleigh limit strongly suggests that the final image will be something less than optimal.
Tests conducted by Peter Ceravolo and published in Sky and Telescope, March 1992 convincingly indicate that telescopes with final images of less than 1/4 wave P-V wavefront were not as revealing of fine planetary detail as those which were working at 1/8 wave or better.
The Star Test
Reference is made here to a newly popularized test for telescopes. The star test has been around for a long time. It was first published in detail by the English optician Harold Dennis Taylor in 1891. A recent excellent book by Harold Richard Suiter, Star Testing Astronomical Telescopes, Willmann-Bell, has popularized and brought the test into the current world of amateur astronomy. Let me emphasize, however, that while this test is potentially a simple one (all you need is your eye and a telescope), interpretation of the expanded stellar image as a method of testing telescopes is filled with subtleties and requires careful study. I encourage everyone to get a copy of Suitor's book and read it carefully before tearing around star parties and "testing" everyone's mirror.
I guarantee that my mirrors will pass a star test but the interpretation of the test must be reasonable and performed by a knowledgeable person. For example, the star test is particularly valuable in three areas of examination: overall correction, surface ripple and the turned edge. With regard to all of these, the mirror should pass easily. However, one should understand that while the expanded Fresnel rings should be exactly the same intensity and clarity both inside and outside of focus, the rings inside of focus on a Newtonian reflector will invariably be a little softer than those outside of focus. Refractor rings will be a trifle softer outside of focus. You will be amazed at how many telescopes can not produce rings on both sides of focus. Some can not produce any rings at all.