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Optics quality

Leica Kinoptik 100

Close-up on the mirror and lens surface

We often read in technical papers that the quality of an objective is measured in fractions of wavelength, in P-V or RMS error. What all that means ?

Brian Tung recall us that by nature, light coming from a distant object arrives at a mirror surface in parallel rays. If the objective was perfectly designed all the incident light would focus to one and only point. 

But we all know that such perfection is impossible to reach. Invariably, some light rays overshoot the focal point while other undershoot it. One measure of the quality of an optics is how far the light ray miss the mark.

The precision of polishing is measured in fractions of the working wavelength as errors in such a field are astonishing small : an error of 0.000025 mm is about 1/2-wave if we take the blue-green light as reference (500 nm).

The P-V error (peak-to-valley) 

Ordinary, the error is measured at the wavefront, once the light has passed through (or was reflected by) the objective. Now a slim but perverse publicist can use the red light of 700 nm as yardstick. An error of 0.000025 mm in the mirror drops to 1/3-wave, simply because he used a longer wavelength... This optics seems better polished ! Indeed, but that depends on the wavelength used too... !

Suppose now that we measure the error at the surface of the mirror objective. How to do ? Imagine that we have a pit of depth "x" in the mirror, then light hitting that pit is delayed by (2x) on the way, one x on the way in and one x on the way out. In other words, the surface error is half of the wavefront error. Now our 1/3-wave error drops to just 1/6-wave ! Our mirror is getting better without having repolished it !...

Note that for a lens, an error of "x" in the surface gives a smaller wavefront error equals to "x.(n-1)", where n is about 1.5. Indeed, as the wavefront travels slower into the lens (n-1 time or about 0.5c), the importance of the defect is divided per two instead of being multiplied by two for a mirror showing the same surface accident. An optical defect that occurs 4 times into a lens gives thus the same effect than only one defect on a mirror ! Therefore there is a factor of about 4 between an error per reflection and an error per transmission.

Astronomical standards

At left, contour and isometric of phase maps. RMS = 0.0092l or l/108 or 6 nm. This mirror respect the astronomical standards. At right, the interferogram with a contrast transfert map. RMS = 0.003l or l/333, Strehl ratio = 1, this plane mirror is almost perfect.

The RMS error (Root Mean Square)

How to know how smooth is a wavefront, not in the worst cases, but just on average ? You have to measure the error in terms of "RMS" (standing for Root Mean Square, a statistical value). Because of the way the RMS error is derived, it is impossible to make a hard rule about the relation between it and P-V error, but we might reasonably see that a P-V of 1/6-wave might become a 1/8-wave RMS.

So if you want to be hard on an objective, you measure its P-V error, at the wavefront, in a short wavelength like blue-green. If you want to be kind to the objective, you measure its RMS, at the surface, in a long wavelength like red. The difference can be something like an entire order of magnitude, and you need to be sure how your particular error is being measured. Measuring errors RMS without mentioning the wavelength used is pretty slimy and nobody doesn't think anyone big does that, but measuring at the surface in a long wavelength is probably at least somewhat extant.

The optical quality

From all this you understand that 1/2-wave and higher errors are considered as being of poor quality. A 1/3-wave error could be considered OK though you would hardly get anyone to cop to *that*. 1/4-wave error is considered minimally good, and 1/8-wave error or better, is usually consider by all amateurs and manufacturers brilliant. These are all wavefront errors, measured P-V with a reasonable wavelength, typically something like 550 nm or so, in green light.

The quality of the image is also affected by other factors. Some authors would have you believe that the central obstruction on certain catadioptics reflectors like Schmidt-Cassegrain's and Maksutov's is the all-important, overriding factor, but it is not; it is just one factor among others. It just happens to be very easily measurable, and there is plenty of theory to back up the impact. But all in all, optical quality (smoothness and precision of the figure) stays the most important.

Visual and photographical impact

These differences of quality have an impact, at least visually. Low-contrast and high-spatial-frequency detail will be washed out in a telescope with substantial error. On most nights, the difference between, say, an 1/4-wave scope and a 1/8-wave scope will be noticeable but hardly objectionable to most observers, but the 1/2-wave scope's image will be rather degraded. The degree to which such detail is degraded can be expressed in terms of an MTF (Modulation Transfer Function) able to display a contrast curve.

Isometric of phase map of a 125mm f/6.4 Pentax aprochromatric lens.

Photographically the impact is less pronounced as many other factors, as turbulence and obstruction will reduce the overall performance of the scope, mainly on wide-angle shots. The impact also depends on the focusing. With a focus shift of 1/2-wave, over 50% off-axis the contrast drops of 50% without take in account the mirror quality.

If you add to a l/30 polish, an excellent curve and aberrations corrections to 3th order, a multicoating on lenses and dielectric on mirrors, an excellent finish, the all set supported by a sturdy and accurate mount with high-ends accessories, now you know why some instruments are so expensives (for your information, the apochromatic refractor Astro-Physics Starfire 155 mm (6.1") f/7 EDF, considered as one of the best on the place, costs, mount included, about $10000, plus charges).

Further readings

All you need to know about optical aberrations (on this site)

Amateur websites : Thierry Legault, Brian Tung, Astrosurf (Tests optique), Astrosurf (Tests optique)

Software : ATMOS, Quick Fringe, Aberrator

Advanced Telescope Making Techniques, Mackintosh, Willmann-Bell, 1986

Amateur Telescope Making (3 vol.), A.Ingals, Willmann-Bell

Telescope Optics, H.Rutten/M.van Venrooij, Willmann-Bell, 1992

Optique, Ed.CNRS, 1985

Calcul des combinaisons optiques, Chrétien.

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