Optical Design

About the focal ratio of apochromatic lenses

Over the past years several customers asked me why we “force” the making of lenses with rather fast focal ratios. Most of them were afraid that the optical correction of such lenses would not be satisfactory for night-time observations.

Reality is more complex than a single number that specifies the focal ratio of the lens. Several factors have to be taken into account to design a lens that will satisfy observers:

– aperture v.s. focal ratio (the larger the lens, the longer focal length is needed to maintain optical quality)
– the physical size of the telescope tube (the longer/heavier the tube is, the less chance it has to get under the night sky, especially if the owner has had an exhausting workday)
– maximal possible field of view for photography (for this parameter, shorter focal length is preferable)
– maximal focal length for planetary observations (so we can achieve a large magnification with reasonable focal length eyepieces)
– mounting (a longer/heavier tube requires a more robust mount)
– transportability (into which equation we must keep in mind the mass/size of the mount)

There are other important parameters, but the above list is enough to help one realise that the requirements contradict each other. Planetary enthusiasts urge us to increase the focal length, photographers urge us to decrease it. There is no single solution for this dispute.

From the point of view of an optical designer, there are strict guidelines to follow. If we want to market a telescope under the “APO” name, then it should meet the practical definition of apochromatism. In practice, it should be diffraction-limited (a Strehl ratio of above 80%) at every single wavelength from 486 nm blue to 656 nm red, should have an excellent Strehl ratio around the wavelength of green color (better than 96%) and even in the violet wavelength range (around 435 nm) it should be better than 1/2 lambda PV error. Off-axis coma should be perfectly corrected. These requirements, if met concomitantly, guarantee a color free, highly enjoyable image in the eyepiece, with sharp contrast and excellent performance even at the edge of the field.
The natural choice of focal ratio (at least for me) is to use the shortest focal length that makes it possible to guarantee all the above criteria.

The choice of glasses also plays an important role in this discussion. Today’s optical materials make it possible to satisfy the above requirements between about F/5.8-F/7 focal ratio, depending on the aperture of the lens. These numbers are true for oil spaced triplet APO lenses of 80-200 mm in size. This is why our “mainstream” APO telescopes use this focal ratio: the lowest possible that still delivers optical parameters which satisfy the requirements of real apochromatic performance. Using this focal ratio, the scopes are as short as possible, have maximal photographic field and are as easy as possible to transport and mount. My personal opinion is that they are optimal in terms of optical performance vs size.

In some cases our customers don’t require an optimal size/performance ratio, but maximal optical performance. Building telescopes based on this baseline requires a different approach. For these scopes “diffraction-limited” performance is not enough, as the Strehl ratio must be kept above 97-98% over the whole visual wavelength range. A lens designed with this in mind will behave under the night sky very similarly to a mirror. Even defocusing will show pure white color on every object in the sky (or Earth, if the scope is also used for terrestrial observations). The key of this performance is reducing spherochromatism (i.e. the variation of spherical correction with wavelength) as much as possible.

As a side note: based on the experiences with refractors in the past decades, most amateur astronomers still believe that the main problem of apochromatic lenses is the variation of focal length with wavelength (i.e. longitudinal color aberration). But this is not true. This was true when achromats were in general use, and even some of the “ED APO” lenses did show some significant longitudinal false color, causing a serious defocusing of red and/or blue colors. But this problem was practically completely solved in the meantime. Using modern optical materials, the focal length is constant over the whole visual range (and even after). But another problem took on the “main problem” status in the meantime: spherochromatism. This causes red color to show spherical under-correction and blue becomes over-corrected. This decreases the Strehl ratio of these colors and slightly decreases the perceived sharpness of the image.

But there is a significant mathematical difference between the longitudinal false color of achromatic/”ED APO” lenses and the spherochromatism of modern lenses: longitudinal false color decreased linearly with focal length, while spherochromatism is non-linear. This is why there aren’t many (triplet) APO lenses with a focal ratio faster than about F/6: spherochromatism would be really horrible. Using air spaces, faster lenses can be built, but the difference is negligible. So, what was easily possible in the age of achromats (F/5 lenses with doublet configuration) cannot be done today even with a triplet lens, if we want to make a real apochromat.

The non-linearity of spherochromatism (i.e. today’s main problem of APOs) has a real advantage: to significantly decrease spherochromatism, we only have to add a moderate focal length to the lenses. Achromats were in many cases F/15 or even F/20 focal ratio lenses, but even these lenses had visible color on the Moon, Vega, Venus, etc. In the case of triplet APO lenses, we need only a much more moderate focal ratio to make the lens practically corrected entirely in every respect. Practical simulations show that based on FPL53 glass, an F/10 lens is already perfect in every respect.

At around F/10 focal ratio, the spherochromatism of an oil spaced triplet lens becomes so small, that the slightly changing parameters of optical glasses (i.e. slightly different partial dispersion from melt to melt) become the primary issue. But using the tri-color interferometer we can measure the focal length differences caused by the changing glass parameters with around lambda/100 precision and based on this measurement we can compensate the problem in the final phase of manufacturing. Subsequently, a lens can have a (nearly) 1 Strehl ratio uniformly over the whole visual (and photographic) spectral range. If an amateur astronomer is ready to accept the physical length of an F/10 focal ratio refractor, then she can have a refractor that is essentially free of any color aberrations.

Having a longer focal length lens free of color-related problems includes several advantages: using simple eyepieces and still getting high magnification makes it possible to see the stellar objects in previously impossible “purity”. Mostly everybody agrees that after removing color aberrations, the remaining limit of the image quality (of an actual telescope, in the middle of the FOV) depends on the total number of air-to-glass surfaces in the system. The less/fewer glasses (and surfaces) are in the path of light, the fewer problems they cause. For this reason, planetary enthusiasts tend to use simple eyepieces and accept the compromise of having a smaller FOV. More complicated eyepieces have a larger field, but every actual glass surface has some microscopic polishing errors, and sooner or later dust particles settle on the optical surfaces, without mentioning dew condensation. To improve contrast, we have to decrease the number of air-to-glass surfaces. For an eyepiece, the absolute limit seems to be 2 such surfaces. These eyepieces are usually based on some monocentric design and they are commercially available (in the worst case on the used market), so we can conclude that the “eyepiece side” of the telescope can be rendered optimal using one of these eyepieces.

In the case of oil spaced lenses, the internal surfaces are mostly nullified (regarding optical problems) by the thin layer of oil applied between the facing glass surfaces. These surfaces give practically zero optical errors to the system, so that the remaining two air-to-glass surfaces are also optimal on the “front side” of the telescope.

For further optical purity (i.e. to further decrease the number of optical surfaces) we should possibly fill the whole telescope with oil. Only two surfaces would remain, one on the front surface of the objective lens, and the other on the eye lens of the eyepiece. But I believe the practical problems associated with this solution would make the resulting telescope mostly unusable. I believe that solving these practical problems will be the task of the next generations of optical designers.

Our new, “super planetary” series of apochromatic lenses is based on the above ideas. The color errors of these lenses are practically non-existent and every lens is guaranteed to give very high Strehl values all over the visual spectrum.

The above thinking might seem to be a little different from the thinking of some other manufacturers, but there are some historical examples of very similar telescopes already successfully produced. For example the legendary Zeiss APQ 100/1000 was designed along the very same ideas.

Personally I do NOT recommend to every amateur astronomer the purchase one of our Super Planetary APOs, because in some cases they (e.g. photographers) gain much more by the larger field of our shorter focal length lenses then they would by the additional color correction of the Super Planetaries. But I encourage everybody to try them out if given the chance. I am sure it will be a memorable experience.

Pal Gyulai
Optical Designer of refractive optics
CFF Telescopes