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Coating, anti-reflection and dispersion

The dispersion (II)

Generally speaking all aberrations depend on the refraction index of glasses used. But if we want to be accurate, when a master optician has to design an optical glass he takes attention to at least four parameters :

- The index of refraction

- The Abbe number

- The density

- The coefficient of expansion

With these values the manufacturer can define the "degrees of freedom" at his disposal to design the lens.

The index of refraction refers as the ratio between the speed of light in the vacuum and its speed in a given material at a specific wavelength. Abbe number define the variation of index or the amount of dispersion in the given material for a specific spectral range.

Higher indexes bend strongly the light and avoid to design lenses with strong curvature. Knowing such high curvatures are the most complex to design, optician take advantage of high index glasses when designing fast refractors (f/8 and below). Using high index, spherical aberrations are also reduced in lenses.

The second parameter, Abbe number, defines the color dispersion; a high Abbe number reduces color aberration.

Like certain eyeglasses, sophisticated glasses can also have different transmission wavelength regions due to density variations. When the lens becomes large this third parameter also influences the weight of the optical assembly and becomes critical for sensitive applications (military, microscopy). At last when extreme temperatures or quick variations occur the coefficient of expansion of glasses becomes a key factor, mainly using mirrors.

As we explained previously the objective of a refractor, an eyepiece or a photographic lens is made of various glasses combining very poor to high grades lenses ensuring a certain level of color control to correct the chromatic aberration so that all visible wavelenght focus at the same point, from the ultraviolet to the deep red.

At left Nikon ED glass minimizes chromatic aberration like a Fraunhofer air-spaced doublet. At right an optical designer examining a multicoated objective at Nikon. Document Nikon.

Roughly 2000 glasses are available for making lenses. 99 % of them are used to correct the chromatic aberration. Of these 99 %, some are very expensive, others cheaper but in all cases the cost has no bearing on whether a glass can correct secondary spectrum (colors) or not. In fact, some of the most expensive glasses will result in slightly higher chromatic aberration.

In order to correct secondary spectrum, a designer like Roland Christen from Astro-Physics or Al Nagler from Tele Vue must choose two glasses that lie considerably off the normal Abbe line, which means that at least one of them will have abnormal dispersion and totally different chemistry than an ordinary glass made of FK5 Crown or Flint (lead crystal).

These "abnormal" glasses tend to be physically fragile because they typically use Fluorite cystals (CaF2) instead of oxides in their chemical makeup. There also more sensitive to variations of temperature. A sudden drop in temperature on the surface will fracture ED and especially Fluorite.

TEC 140 mm f/7 aplanatic oiled triplet made of one ED glass and two other ones. This apochromatic objective is cut at l/20 (P-V), optimized for the e-line at 546 nm.

Very few of them are also suitable for making lenses and they are available from only a couple of manufacturers. All these factors are well known to the optical manufacturers who make astronomical lenses. There are no hidden designs or secrets because they are so many new glasses that remain to be discovered.

Optical designers can then choose the shape of each lens constituing an objective between a double convex lens, a planoconvex lens, or a meniscus lens. This physical bending is an important method to control the spherical aberration, coma, and the other three Seidel aberrations, astigmatism, field curvature and distortion. Another method is to determine how to abolish both kinds of chromatic aberration (axial and lateral) at once by using two lenses in close contact made from two different kinds of glass, so that their total power is the same, at least for two wavelengths of light. The lens formed by two elements of this sort is called an achromatic doublet.

Newer glasses function like crown glass, but with considerably less dispersion to cancel out. Such lenses are often made with glass including oxides of Barium or Lanthanum. Achromats using such glass can have a level of chromatic aberration comparable to that of apochromatic lenses, but they continue to display a small amount of spherical aberration.

Remind you that an apochromatic objective lacks both spherical and chromatic aberration.

Acronyms like SD or HD are in fact marketing terms. A glass with a dispersion number above 80 and a partial dispersion far from Abbe line is ED glass, and this includes the Fluorite. SD or HD are trading terms used to underline the quality of a so-called new glass rather than a true technology discovery. A soon as you create a new lens, e.g. a 100 mm f/7.345, you can qualify it as a high definition, HD. Nothing prevent it but that creates confusion in the mind of buyers who think that the new lens is better than the one sold by his competitor... and the goal is reached. Therefore you must well known the specifications of the lens you want to buy to not fall in these marketing traps.

Financial side, it must be known that it is also actually cheaper to make a well corrected ED lens with four times better color correction than a normal achromat, than it is to make a "semi-apo" with only twice better correction. The Meade ED design and the Orion ST-80 ED are two examples of that.

So, when designers build objective lenses and want to be sure to get images of the best quality, glasses must yield different dispersions, both very low and very wide in order to be left free to correct all aberrations.

At left the field flatness at focal point of a achromatic and an apochromatic refractor vs. the field of view and the depth of focus. At right the chromatic aberration of the three main type of lenses. Documents Diagnostic Instruments, Inc.

Most used glasses in two elements objectives are constituted of ED glass (Extra-low Dispersion). We find it in Orion ST-80 ED, Vixen GP ED 80S or Tele Vue Pronto 70. It is also used in camera lenses (Zeiss, Nikon, Canon) and binoculars (Fujinon).

The ED or Fluorite element (n=1.620) can be placed anywhere in the objective. Placing it at the rear of the group of lenses has two advantages :  it is less sensitive to decentering and it protects the relatively soft glass from scratching (even if fully multicoated). Placing the Fluorite element in front allows slightly smaller and thinner blank to be used, thus saving a small amount of money in glass cost (Orion ST-80 ED, Megrez II 80, Takahashi FS-78,...). In both cases the aberrations will be identical.

The place of a Fluorite has no effect either on the spherical aberration. You can take the same design with Fluorite placed in front or at rear of the objective, and with proper curves have the same color and spherical correction.

SD glasses (Super-wide Dispersion) are less common and more expensive. They are often assembled with a Fluorite crystal element in 3 to 4-lenses-element scopes (Megrez 80 APO, Tele Vue 101, Pentax 105 SDHF,...). 

Some low power binoculars but of very good quality use UD glasses (Ultra-wide Dispersion).

These glasses are usually coated with magnesium fluoride (n=1.38) (Vixe, Tele Vue), zirkonium oxide (Fujinon) or SMC (Pentax), all ensuring 99.9 % of light transmission. An uncoated Fluorite is sensitive to moisture and this is for this reason that some manufacturers offer a 30-year warranty on their lenses.

Coater device at Navitar (left) and Zeiss (right). During the coating process the pressure is dropped to 2x10-5 Torr at a temperature between 200-300°C. The process last over 3 hours.

No third choice

Some advertisments qualify their refractor of "semi-apochromat". What does it means ? In the mind of a master-optician a lens displays or not chromatic aberrations (among others). It is either an achromat or an apochromat but there is not a third choice or that hides a residual optical problem that he was not able to remove for the proposed price. Up to now and until proof of the contrary, a doublet cannot compete vs. a triplet, or that would be know !

Trying to sell a refractor as a "semi-apochromat" is thus a diverted mean to say that an objective does not offer the quality of an apochromat. In other words, for some dark marketing reasons, this is at best an improved Fraunhofer achromat but that continues to display a chromatic aberration at more of less high magnifications on bright objects.

Unfortunately the better the glasses the higher is the price of the scope. So if you discover a strange word qualifying a refractor, look first at its design and residual aberrations before reading the marketing and quality arguments of the saleman, and to loose your money for little.

I thank Roland Christen from Astro-Physics for his comments and corrections.

For more information

Anti-Reflection Coatings, Edmund Optics

Celestron StarBright XLT Coatings vs. Meade UHTC Coating, Celestron

Optical Thin Film Software, Film Star

The Crizal Avancé™ with Scotchgard™ Protector (coating for eyglasses).

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