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Stranger than Fiction!
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Stranger than Fiction!
By Neil English
When I was a child, I spoke as a child, I understood as a child, I thought as a child: but when I became a man, I put away childish things.
1 Corinthians 13:11
This paper has compared and contrasted the optical properties of two refractors; a 4” F/6.3 doublet apochromat and a 4” F/15 Fraunhofer achromat, of classical design. The remit of the study was initially broader, including triplet apochromats, but this class of telescope was omitted from consideration, as the findings were broadly similar to those of doublets.
The study was particularly focussed on examining the veracity of claims that long focus refractors provide steadier/more stable views than their lower F ratio counterparts. Specifically, I have identified the following factors as being significant;
- The optical quality of the instrument; specifically how much spherical aberration/spherochromatism it is likely to have, and its impact on the telescopic image.
- The fundamental differences between the achromat and the apochromat; in particular, the inherent property of the achromat to scatter a given amount of energy lost to the rings farther away from the central diffraction maxima than the apochromat.
- The importance of depth of focus as an attribute in reducing focussing errors during a typical observing program.
- The importance of elevation of telescope objective above the ground, away from heat sources.
Finally, on a slightly tangential matter, the article will compare and contrast achromats and apochromats in relation to observing both bright and faint, low-contrast objects in photopic and mesopic mode.
I’m a double star guy. Don’t get me wrong, I love eyeballing Jove, Luna and the Red Planet like the rest of you, but only when they decide to turn on a show. My staple comes from splitting binaries. They’re fairly easy to track down, even in light polluted skies, and I’ve followed a good few stellar duos right through from my pre-teen years to the present day. I’ve had the pleasure of looking through all kinds of instruments, owned, borrowed and reviewed. I’ve had great experiences with Newtonians, Maksutov and Schmidt Cassegrains. But for me at least (and I know I’m not alone), only the refractor, with its unobstructed optics and the technology invested in it, exudes an allure and charm that inches it above the others.
My bias is well founded. My first telescope, a brazen red 60mm F/13 Tasco was a scope with an attitude problem. I could bring it outside from a warm room to the cool of the winter air and within a quarter of an hour or so, I was observing Albireo, Mizar & Alcor and even fairly close colour contrast doubles like Gamma Delphini and Almaak, jewel of the Chained Lady.
Through much of my adult life, my instrument of choice was a good 4” refractor. I have, and still regularly use a fine 4” F/10 Russian instrument. It is well corrected for spherical aberration and has very modest amounts of false colour. Indeed, when I used a variety of doublet apochromats of the same aperture and F ratio (or lower), I found little or no advantage in their use over the considerably less expensive achromats. Events got even more interesting when I started using a 4” F/15 Fraunhofer refractor. My story is recounted in more detail here: http://www.cloudynights.com/item.php?item_id=2473.
This classical achromat seemed to resolve some tough binaries more quickly after being taken outside, and with greater efficacy than the lower F ratio apochromatic doublets I had used. It also seemed to yield up images that were less prone to degrading even in conditions that proved just too much for my shorter scopes. Puzzled, I began a detailed study of why it seemed to do so well in this regard. Was it fine optics or long focal length that provided the killer views?
Optical theory informs us that they are actually interconnected. For refractors at least, lower F ratio scopes are much more difficult to figure well in comparison to their higher focal ratio (F-ratio) counterparts. And while the only aberrations that unavoidably increase with relative aperture are field curvature and chromatism, other aberrations increase mainly because of the practical difficulty of adhering to requirements set by extremely tight tolerances. This gives higher F-ratio scopes a number of advantages in regard to image quality.
For example, they enjoy greater areas of the field of view that are diffraction limited, many eyepieces work better, especially in regard to their ability to reduce astigmatism. Further more, high F ratio scopes are easier to collimate and less sensitive to misalignment. In addition, the greater depth of focus of high F ratio telescopes renders them much easier to focus accurately. That’s the reason short F ratio (fast) scopes require, almost by necessity, micro-focusers to facilitate accurate focussing. Finally, it can be very difficult to place your eye in the right position when using short eye relief oculars in low F ratio scopes, (which is more common as shorter focal length eyepieces are usually needed as the telescope’s F ratio is lower). This rapidly causes eye strain and so could adversely affect perceived image stability. Glass wearers may also have that problem while using medium eye relief eyepieces.
All of the above, of course, are well established attributes of high F ratio scopes. But this impressive list, in and of itself, could not explain why images appeared less prone to degrading in long scopes compared with their lower F ratio counterparts. Considering all the aberrations in turn, there was only one notable feature I could think of that distinguishes high F ratio scopes from their low F ratio counterparts - depth of focus and its reciprocal, defocus aberration. High F ratio scopes enjoy greater depth of focus (proportionally as the square of focal ratio) than their lower F ratio counterparts.
That led me to explore the possibility that the greater depth of focus of the F/15 scope helps maintain good image quality or even help steady the images in a way that did not violate the tried and trusted principles of optics. My strategy was to investigate the environmental and optical sources that could destabilise or defocus an image but I couldn’t do it alone. With the assistance of the learned author and creator of www.telescopeoptics.net, Vladimir Sacek, we fleshed out some very interesting findings.
The heat is on
One of the first things you’ll notice about long focus refractors are that their objectives are perched high off the ground and well away from heat sources. In contrast, because short tube scopes can be very close to body heat, it is not unreasonable to think that they might perturb the air immediately in front of the objective causing the ‘seeing’ to be poorer. Some astronomers of historical repute seemed to think so. The English astronomer Webb (1807-1895) for example, even went so far as to insulate his tube with asbestos (I hope he didn’t inhale!) to prevent any interference from body heat. Was he justified in doing so?
It is the convective movement of air – caused by temperature differentials between a surface and the surrounding air - that makes it an optically non-homogenous medium, deforming the incoming wavefront and causing image deterioration. As you might expect, attempting to quantify this is fraught with difficulty, as it varies both geographically (some places radiate more heat than others) and temporally (ground heat dissipation varies with time after sunset). Anthropogenic heat has also been invoked as a source of turbulence for those who use very short telescopes. Even in the absence of wind, convection is an important mechanism in cooling the human body. Under such conditions, convection accounts for about one third of the thermal loss of the human body in cool, still air. Owners of reflecting telescopes will doubtless be aware of thermally induced turbulence from body heat creating turbulent flows near the secondary mirror. But how does heat affect refractors?
Before making any assessment of this issue, it pays to know what you’re fighting against. Take a look at the left hand side of Fig 1 which features work carried out by Herb et al at the University of Minnesota (St.Paul) http://home.safl.umn.edu/bmackay/pub/pr/pr478.pdf. It shows some diurnal temperature variations of different surfaces over five consecutive summer days at a few locations in Minnesota. Most significantly, the data show the majority of surfaces maintain a significantly higher temperature than the surrounding air for much, if not all of the night.
Fig 1. Illustrating diurnal temperature (left) variations for different surface materials at various sites in Minnesota and Illinois.
I observe on grass and by the looks of the data presented in Fig 1, I’m very glad I do. Its fairly high specific heat capacity means that it soaks up heat well without registering much in the way of a temperature rise, and its rate of cooling (measured by the shallow gradient of the curve) is fairly low at night, compared with other surfaces such as concrete or even bare soil. Oh, and did I mention ROOFS?
The right hand side of Fig 1 shows some kinematic aspects of heat convection. On the graph, it can be seen that the strength of ground turbulence, for a given ground/air thermal gradient has three components:
1. A convective cell density gradient (proportional to the thermal gradient), which determines the extent of deformation of the wavefront
2. The size of convective cells (which may influence to the coherence length at your site)
3. The velocity of convective cells (normally upward, but simultaneous sideways movement caused by wind is also common).
Since the density and velocity diminish with the height above ground, and since the size of the convective cells increases with elevation too, all three factors favour placing the objective at as high an elevation as possible. There’s yet another twist to all of this. On the occasional night, something called "inversion" occurs, when the air actually gets warmer than ground below it. This phenomenon can vary widely with the locality and weather conditions, but, on the average, ground turbulence is more likely than not to be the dominating mechanism for generating convective turbulence for ground-based amateur astronomers. All things considered, it’s always a good idea to have the entrance pupil of the objective raised as far off the ground and as far away from you (and other folk) as possible
Let us now turn our attention to the fascinating playground of thought that is telescope optics, and explore other, less obvious factors that could potentially destabilise an image. I discovered that some aberrations, particularly spherical aberration, can significantly affect the acceptable (or diffraction limited) defocus range. In the presence of spherical aberration - a rather common scenario that usually afflicts low F ratio scopes more than high F ratio scopes – the allowed defocus is significantly smaller. That’s because a spherically aberrated lens has no well-defined focus; some rays converge ahead or behind the locus of ‘best’ focus (as defined by a theoretically perfect objective, which geometrically has a best focus position), thereby creating a larger circle of confusion. The greater the spherical aberration, the harder it is to judge where the position of best focus is.
There’s a neat little equation which sums it up when light of a single (monochromatic) wavelength is considered. Quantitatively, the allowed defocus range remaining at the conventional "diffraction-limited" level, or better, is given precisely by the expression 4.13λ(1-16W2)0.5F2 (TelescopeOptics.net), where W is the P-V wavefront error of primary spherical aberration present. As more spherical aberration is introduced, the allowed defocus range rapidly diminishes and actually becomes zero when W = ¼. Thus, any additional seeing perturbation introduced to the system could adversely affect the image, impelling the observer to refocus frequently in moments of poor seeing.
It must be stressed that this equation only applies to light of a single wavelength and that the situation is much more complex and, dare I say, interesting, when one considers how differently achromats and apochromats distribute their energy both within and outside the Airy disk. Still, the implication is that, all else being equal, well figured optics always do better in less than perfect seeing and this applies equally for high quality, classical achromats as well as apochromats.
I have commented elsewhere that a very well corrected achromatic objective can deliver high quality views despite its display of obvious secondary spectrum. This, I suggested, imparts a more precise meaning to rather loose statements made in amateur circles such as “the colour is well controlled.” I have star tested a variety of ED doublet apochromats and my impression is that they all, to some degree or other, exhibit significant amounts of spherochromatism, that is, the variation in spherical aberration with wavelength. Ordinary spherical aberration is fairly easy to spot as an asymmetry in the definition of the rings either side of focus. On one side of focus, the rings are very well defined, whereas on the other side, they appear ‘softer’. Spherochromatism, on the other hand, which is an inherent problem in low F ratio apochromats (doublets and triplets alike) is much more difficult to pin down and is more a reflection of the limitations of the design and not the optician's skill per se.
You can do some simple tests yourself by isolating green wavelengths (by attaching a narrow band pass green filter) during the star test. This procedure almost invariably improves the intra-focal and extra-focal patterns of most, if not all, apochromatic doublets. Conducting the same tests on a number of quality long focus achromats, including my high specification 4” F/15 Fraunhofer, a 63mm F/14 Zeiss Telementor and an Japanese-made Swift 3” F/ 13 refractor, I found that they displayed better symmetry in the diffraction rings either side of focus – even in the absence of a green filter. See this article for more details: http://www.freewebs.com/skylight/Going%20retro%20May08.pdf
After experiencing the views in these fine, classically designed instruments, I have come to prefer the images rendered by refractors with very low spherical aberration but with a little secondary spectrum, to a better colour corrected instrument with more spherical aberration. The optical resilience of the classical achromat is also reflected in its tolerance to design deviations. Table 1 below clearly demonstrates that these instruments are very forgiving to design/manufacturing errors in comparison to the much more exacting requirements of the apochromatic doublet.
Table 1 showing how a long focus achromat and short focus apochromat respond to deviations from design specifications.
As reported elsewhere, I estimated – by careful star testing – the figure on my 4” F/15 Fraunhofer to be ~ 0.037 RMS (if you prefer units of wavelength, simply multiply by 3.354, so 1/8 wave P-V in this case). I reported that it could be even better than this but my eyes weren’t good enough to make a reliable judgement in this regard. Considering the data presented in Table 1, it actually doesn't seem realistic comparing an F/15 achromat with 0.037 RMS and an apochromat with 0.05 RMS spherical error. To see why, consider this. In order to generate the 0.037 RMS error in the achromat, you’d need to increase the lens separation by more than 8mm (extremely unlikely to happen either in assembly or use), or, alternately, to change the inner radius by over 11mm (2.1% relatively). In comparison, generating 0.050 wave RMS (equivalent of 1/6 wave p-v lower order spherical aberration) in the apochromat only takes a 0.16mm change in lens spacing or, alternately, a 0.16mm change in the inner radius (less than 0.1% relatively).
Indeed, if you take a look at some star test patterns carried out by Markus Ludes (APM-Telescopes) on Cor Berrevoet’s website http://aberrator.astronomy.net/scopetest/ it reveals that even the better designed ED doublets (with F ratios up to 9) have optical aberrations of the order of 0.050 wave RMS. Not that these instruments are slouches in any way, shape or form. After all, they would still be well above the diffraction limit (actually 0.91 Strehl).
In contrast, consider the versatile little 63mm F/14 Zeiss Telementor, These instruments were made fairly inexpensively and were issued in their hundreds and thousands to East German schools. Star tests on some of these units seem to converge on figures of between 0.03-0.02 wave RMS (1/10th-1/15th wave P-V) of ordinary spherical aberration, explaining why, amongst other things, they are so highly thought of in the amateur community.
Here’s another test on a ‘no name’ 80mm F/11 instrument;
These things considered, it is entirely reasonable to assume that, for well figured long focus achromats, both spherical aberration and spherochromatism are likely to be entirely negligible in comparison to the ubiquitous short focus apochromat.
So, the present study concentrated on comparing the optical properties of a 4” F/15 classical achromat and a F/6.3 FPL53 doublet apochromat of the same aperture. The graphs drawn in Fig 2 show how Strehl ratio varies as a function of wavelength for these telescopes.
Fig 2. Strehl ratio versus wavelength for a 4” (100mm) F/15 achromat and a 4” F/6.3 doublet apochromat with either perfect and 0.050 wave RMS e-line error (both over- and under-correction).
You will note that the 4” F/15 instrument has better e-line correction (at 547nm) than the shorter focus apochromat, even if perfectly executed. Note however, that if one considers a more realistic scenario where 0.050 RMS over- or under-corrected spherical aberration is introduced, it significantly reduces the peak Strehl and dramatically alters the colour correction of the apochromat.
That would have been the end of the story, were we not to consider how the imperfect colour correction of the achromat plays out in the scheme of things. A very important development came after comments were made in passing by Chris Lord of Brayebrook Observatory, England, on the progress of an earlier draft of this work. Chris alerted us to the simple fact that the achromat suffers from chromatic aberration, which inevitably reduces its diffraction limited defocus range in comparison to an aberration free system of the same focal ratio. At that time, we were only considering a simple, monochromatic situation. I remember the email I got from Vladimir: “How could we be so dumb as to overlook something as fundamental as that?”
Curiouser & Curiouser
Thus, to gain further insight into the differences between classical achromats and apochromats, it is necessary to assess their performance over all visible wavelengths. This is achieved by measuring how their polychromatic Strehls (found by integrating all the Strehl values over the visible spectrum) change as a function of linear defocus. So, Vladimir took the problem to OSLO. And boy, were we in for a surprise! It was one of those ‘Eureka’ moments!
Fig 3. showing linear defocus as a function of polychromatic Strehl (photopic) for a 4" F/15 achromat (red - solid based on the peak diffraction intensity, dashed based on encircled energy within central maxima) and 4" F/6.3 doublet apochromat (gray - solid for near-perfect system, dotted for system with 0.050 RMS spherical aberration).
Take a look at Fig 3 which shows how polychromatic Strehl changes as a function of linear defocus for a near perfect 4” F/15 achromat and a F/6.3 doublet apochromat of the same aperture with a 0.050 wave RMS spherical aberration error. For the record, the data is weighed by photopic eye sensitivity for 25 wavelengths between 440nm and 670nm (using 10nm intervals, except the e-line).
The grey plots are those for the apochromat. The red plots are for a high F ratio (F/15) achromat. Of course, these graphs demonstrate some points already mentioned, namely, that the greater the F ratio and lower the spherical error, the greater the diffraction limited defocus range (0.8 Strehl on Fig 3.). But they also reveal that the high F ratio achromat has some remarkable properties! First, let’s get acquainted with the curves. As expected, the F/15 achromat has a better polychromatic Strehl than the apochromat with 0.050 wave RMS level of e-line correction error. The steepness (gradient) of the parabola indicates the defocus sensitivity of the instrument and you can clearly see how the ‘slow’ achromat enjoys a diffraction limited defocus range much larger than the ‘fast’ apochromat. In general, this best focus shift in the achromat greatly extends its diffraction limited defocus range whenever the e-line Strehl is over 0.80. In this case, the graph shows that the F/15 achromat’s diffraction limited defocus range (solid red line) is over four times greater than the apochromat with near-perfect e-line correction, and more than nine times grater than the same apochromat with 0.050 wave RMS e-line error.
Intriguingly, Fig 3 also shows that the location of best polychromatic Strehl in the F/15 achromat is significantly higher than that exhibited at the e-line focus. Notice especially that the peak is offset toward the yellow580nm/green520nm focus. This is caused by all the other visible wavelengths –including those to which the eye is very sensitive – focussing behind the optimal visual wavelength.
See: http://www.telescope-optics.net/eye_spectral_response.htm for further details
It is the defocused nature of chromatic error in the achromat (which increases exponentially towards the ends of the visible spectrum) that places more energy in the central maxima for a given Strehl value and less in the rings area, especially the first bright ring. Another peculiar property of the achromat resulting from the nature of its chromatic error (defocus which increases exponentially towards the ends of the visible spectrum) is slightly enlarged central maxima. It has the curious effect of encircling more energy for a given Strehl value, leaving less in the rings area, especially the first bright ring. Fig 4 illustrates the idea nicely.
Fig 4. Showing polychromatic encircled energy in a F/15 achromat and F/6.3 apochromat
Moreover, these slightly enlarged central maxima actually result in greater encircled energy (dotted red line in Fig 3.) than what the nominal diffraction peak (depicted by the solid the red line of Fig 3.) implies. This, in turn, results in higher contrast transfer efficiency over most of Modulation Transfer Function (MTF) range. Consequently, the effective Strehl of the achromat is correspondingly higher. What is more, if one takes into consideration this extra encircled energy within the first minima (dashed plot in Fig 3), the achromat’s defocus range would be significantly greater still!
See http://www.telescopeoptics.net/polychromatic_psf.htm for more details on this phenomenon.
The finding that achromats have a greater amount of encircled energy for a given Strehl, to my knowledge, has not been reported in the literature before. Certainly, the time-honoured authorities such as Conrady and Sidwick, make no mention of it. Nor is there any relevant discussion of this subject matter in any of the contemporary optics texts. I ask, in all humility, just who would explore such a novel and obscure avenue as this? For these reasons, I propose that this significant discovery be credited to Vladimir Sacek, and henceforth I suggest we refer to the phenomenon as the “Sacek Effect”
Beating the Seeing
I have reported elsewhere that since I started using my 4” F/15 achromat, I could split difficult binary pairs more frequently and in less than ideal conditions than with the shorter focus apochromats of comparable aperture. Put another way, the long scope was giving me more observational ‘mileage’. Could there be an optical explanation for this? One likely factor pertains to the different responses of both telescopes to a focussing inaccuracy induced by seeing.
At first, I entertained the idea that the atmosphere was inducing defocus and that instruments of different F ratio were responding differently to this. That simply isn’t true. Telescopes of equal aperture are affected the same by atmospheric turbulence, irrespective of their F ratios. To quote Bryan Greer, who conducted an OSLO analysis of this scenario over a decade ago, “While the high F ratio telescope does enjoy a greater depth of focus, unfortunately the shift in best focus caused by turbulence is also greater. In fact, the two are locked together; the instrument with four times greater depth of focus also has a four times greater linear shift of the best focus position.”
If it’s any consolation, I discovered, to my horror, that a few big names (if I disclosed them to you, I’d have to shoot you!) on both sides of the pond appear to have ‘sleep walked’ their way into believing the atmosphere causes appreciable defocus. Mea non culpa!
So, let’s all sing from the same hymn sheet: SEEING DOES NOT INDUCE DEFOCUS TO ANY SIGNIFICANT DEGREE.
But that’s not to say that the large depth of focus associated with high F ratio refractors isn’t an important tool in grappling with the seeing. Here’s an altogether better idea; compromised seeing induces focusing inaccuracy and it affects lower F ratio instruments more. Because any deviation from perfect focus will have a more pronounced effect in the low F ratio instrument, the long focus scope could be said to enjoy more moments of good seeing. During bouts of bad seeing, the F/6.3 apochromat will suffer significantly more defocus error than the high F-ratio F/15 instrument. That’s a natural consequence of the former’s shallower depth of focus, which makes accurate focussing more difficult. The achromat will almost certainly be closer to its ‘sweet spot’ from the outset.
Fig 5. Plot showing how an artificially produced ‘seeing error’ affects the profiles
Take a look at Fig 5, which models how seeing might affect both telescopes. Note that the achromat is evaluated at the solid line, which is actually about 0.05 Strehl points below its peak, and commensurate to the effect of introducing a 0.037 RMS wave P-V of spherical aberration. Thus, in effect, the analysis is comparing a F/15 achromat with 0.037 RMS error to a shorter focus apochromat with 0.050 RMS error. As outlined above, that’s a perfectly valid justification.
Consider the left hand side of the vertical e line in Fig 5. Suppose we were to introduce a focussing error corresponding to the mean defocus range in each of the telescopes, then the apochromat ends up at position indicated by 2, that is, at 0.78 Strehl. The F/15 achromat would decrease to 0.79 Strehl (marked by the 4 on the graph). Next, Vladimir modelled poorer atmospheric conditions by introducing a ‘seeing’ error of 0.1 wave RMS (depicted in the lowermost plots of Fig 5). Again, concentrate your gaze at the left hand side of the e line. During this period of seeing, the apochromat’s Strehl would be set oscillating between 0.52 at its lowest to 0.78 (1-2 on the graph) at its highest point. The achromat image would also oscillate between 0.50 and 0.79 (3-4 on the graph). It is important to note that this analysis was done with respect to the achromat’s peak diffraction intensity (solid red line). The situation would be considerably improved for the achromat if one were to analyse the situation with respect to the encircled energy within its first diffraction minimum (top dashed red line).
Bizarrely, the OSLO data predicts that the situation for the apochromat would be significantly different depending on which side of the e line the scope is focussed. That’s because of the asymmetry of the Strehl curves with respect to this line. Indeed, repeating the above analysis on the right hand side of the vertical axis results in a slightly improved result for the apochromat. In fact, the F/15 achromat enjoys a near constant (9%) defocus error centred on the e line, while the apochromat’s defocus error can vary between 6-13%. What is especially relevant here is the range of possible defocus error on the top plot. In the achromat it is nearly steady, while in the apochromat it can be somewhat smaller than that, or somewhat larger. The worse the seeing, the greater this range will be in the apochromat, consequently producing significant focussing errors as seeing fluctuates.
Indeed, during poorer bouts of seeing, it is easy to see from Fig 5 that the apochromat will be the first to transgress the boundary where the focusing error becomes readily noticeable. Larger focussing inaccuracies, as might be experienced during prolonged moments of bad seeing, have a much more dramatic effect on the low F ratio apochromat than they do on the long focus achromat. For example, a seeing error that causes a shift in best focus position corresponding to a doubling of the plot decentre in Fig 5 would increase the maximum possible error in the apochromat to nearly 20% contrast loss (0.67 vs. 0.83 Strehl), while the effect on the achromat would, in comparison, still be negligible.
Steady she goes
As I explained previously, my experiences with double stars were founded mostly upon on a comparison between a 4” F/15 classical achromat and a number of lower F ratio (F/6-F/9) ED doublets of similar aperture. Indeed, all of the best attested reports from other amateurs that have conducted field tests have compared long focus achromats to shorter focus apochromats. I reported getting more mileage out of the long focus achromat, as it seemed to confer an advantage on nights of average or slightly below average conditions.
And what of the ‘steadier’ images I and a number of observers have witnessed and reported? This is what Canadian amateur, Clive Gibbons had to say some months back, comparing his 4”(100mm) F/15 achromat to his ED 100mm F/9 apochromat. “When I say steadier image, I mean that the diffraction ring(s) and Airy disk of the star appear to be more stationary. Less tremor and/or blurring. Looking through the 100mm f/9 scope would show a star at 5 or 6 on the Pickering seeing scale. Switching to the 100mm f/15 scope appeared to kick the seeing up to 7 or even 8. It was a significant jump.”
Independent tests carried out by amateurs, Jim Barnett and Ging-Li Wang of Petaluma California U.S.A., using similar instruments (i.e. a long focus achromat versus a shorter focus apochromat) revealed similar results in very unfavourable conditions.
Could there be optical explanations to support these impressions gathered in the field? The surprising properties of the long focus achromat, embodied in the Sacek Effect, provide a robust explanation. One of the first things you’ll notice if you look through a high quality classical refractor is that the Airy disks really ‘pop’, by which I mean, they are clearly discerned with very subdued diffraction rings. Now, both spherical aberration and defocus have the effect of subtracting light from the Airy disk and adding it to the diffraction rings (Fig.6).
Fig 6. Showing the nominal and apparent Point Spread Function (PSFs) of the diffraction rings centred round the Airy disk. Their appearance to the eye is depicted on the far right and shows the effect of increasing amounts of spherical aberration.
But, due to significantly less corrected defocus error in the farther non-optimized wavelengths, relatively more energy in the achromat is farther away from central maxima. This is further enhanced by its slightly larger central maxima, containing more energy than what the peak intensity implies - meaning than less remains in the rings. See http://www.telescope-optics.net/polychromatic_psf.htm for more details.
For example, if the peak polychromatic Strehl in both the achromat and apochromat is taken to be 0.90, the energy transferred to the rings will be ~ 0.10, or 10% of total energy in the apochromat. In the achromat, however, the energy transferred to the rings is empirically approximated (to fit ray-trace results) to be ~ 1-0.90(F+3)/(F+2), where F is the focal ratio of the instrument considered. Thus, for F=15, the energy outside central maxima is approximated by 1-0.90(18/17) = 0.05, or 5%. This is better illustrated with the encircled energy graphs depicted in Figure 4 above.
Observers judge atmospheric conditions by measuring the extent to which these rings degrade from moment to moment. If the rings are brighter, atmospheric turbulence will cause them to jiggle about more. Because the long focus achromat exhibits lower spherical aberration and suffers less from a focussing inaccuracy, the bright rings surrounding the Airy discs will be far more subdued, even in fairly bad seeing, compared with the less well corrected apochromat, with its greater defocus sensitivity and greater spherochromatism (which also brightens the rings). These data, together with the greater elevation of the classical refractor away from body and ground heat, would almost certainly cause the observer to report that the images are steadier.
Pause for thought
This study has demonstrated some remarkable and hitherto unconsidered optical properties of long focal length achromats. What the data point to is that there is no single, dramatic advantage of long-focus achromats over their fast apochromatic rivals with respect to apparent image stability. It is likely to be a compounded effect involving the interaction, to a greater or lesser degree, of all of the following factors:
- Generally better e-line correction,
- Lower sensitivity to focus inaccuracy due to seeing-induced best focus shift,
- A reduction of displaced energy around central maxima - the Sacek effect,
- More coarse focusing action unless the fast apochromat has 10:1 microfocuser and
- Higher elevation of the objective above the ground, avoiding ground (and body) turbulence.
How, I hear you ask, do triplet apochromats fair in this study? Well, without getting into details, triplets will have an e-line correction that is, on average, better than in doublet apochromats. Triplets have less tight tolerances (though nothing quite like the classical refractor) than doublet apochromats. This means that lower F ratio triplets would probably have a somewhat higher polychromatic Strehl in actual use, though not necessarily significantly more so than the F/15 achromat considered here. The long scope would certainly have less of an edge. Only seeing induced focussing inaccuracy and reduced elevation off the ground may conspire against the finest models in this genre.
In this paper, we have introduced the concept of image stability. It is defined as a telescope’s ability to resist defocus. If we consider two telescopes of the same optical design, then it is reasonable to conclude that their stability will scale as the ratio of the square of their respective F numbers. The work demonstrates that depth of focus is a valuable asset in increasing the optical versatility of the refractor in regard to serving up stable, high contrast images. Its great utility stems from its protective role in maintaining the scope’s best performance level.
Many observers have waxed lyrical about the beguiling images served up by a quality, long focus achromat. Indeed, many have reported that there is certain "Je ne sais quoi" about the views they deliver. Just ask amateur Siegfried Jachmann (Utah, U.S.A) about the images served up by his 9” F/14.8 Clark refractor or Bob Royce’s 6” F/15 Vanilla achromat. These findings provide fresh insight into what this might be. The remarkable polychromatic Strehl profile of the long focus achromat is especially noteworthy. For me, it pays testament to the uniqueness of the classical achromat as an instrument that is closely related to, though subtly different from, the apochromat. I have previously spoken of the achromatic image as playing with the eye in a ‘different’ way to the apochromat. I cannot help but think that the data provided in Figure 3 lends credence to that statement.
Which ever way you look at it, a high quality achromat of high F ratio is best seen, not so much as ancestral to the modern apochromat, so much as being its legitimate sibling. Like the fabled Goldilocks, younger brother ‘Apo’ is an all together more sensitive creature. Everything has to be ‘just right’ in order for it to reach its dizzying optical heights. In good seeing, ‘Apo’ serves up better colour corrected images over the visible spectral range. But the compounding effects of greater spherochromatism, larger seeing induced focussing inaccuracy and greater proximity to ground and body heat, conspire to render the short focus apochromat more unstable. In contrast, Elder brother Achro is a ‘big bruiser,’ being far less sensitive to changing temperatures, focussing inaccuracies, and, by virtue of greater elevation off the ground, less prone to convective turbulence. Perhaps most remarkably of all, ‘Achro’ has a secret weapon, buried deep in the wave theory, which gives it an edge over younger brother Apo, especially in relation to image stability.
Through a glass darkly
Science is all about accepting the truth wherever it leads. And there is one final twist to this study that paints a slightly shadier picture of the classical achromat. The analysis was optimised for photopic vision- the kind the eye is most sensitive to when viewing bright objects. But when the eye is confronted with very faint, low surface brightness objects, it switches from photopic (sensitivity peak ~ 550nm) to mesopic vision (sensitivity peak at ~530nm). The consequence of this is that the optimal human visual acuity moves toward shorter wavelengths. As a result, the eye becomes much more sensitive in the blue part of the visible spectrum. I asked Vladimir to explore this question, since I had noted that the peak Strehl in the achromat shifts to a position nearer the common focus of (yellow 580nm) and green (520nm). So, again, he took it to OSLO and explored how the telescopes behaved when the eye was operating in full mesopic mode. The results are very revealing! Take a look at the dashed red and grey lines (plots 1 and 2, respectively) of Figure 7 below, representing the F/15 achromat and the F/6.3 apochromat, respectively, during mid-mesopic vision.
Figure 7: showing how a 4” F/15 achromat and a 4” F/6.3 doublet apochromat would behave if the eye were shifted to mid mesopic vision. The photopic situation is also illustrated for comparison.
As before, the plots compare the achromat with near perfect e-line correction, but with the Strehl plot based on the nominal peak intensity (and thus effectively with about 0.037 wave RMS of primary spherical aberration) with the apochromat with the equivalent of 0.05 wave RMS spherical error. The first thing you’ll notice is that when the eye converts from photopic vision to mesopic vision, the peak polychromatic Strehl falls for both telescopes. This is a direct consequence of both instruments not being optimised at the peak mesopic wavelength. But the affect on the achromat is more dramatic. Because it has significantly greater error in blue wavelengths, the achromat’s peak polychromatic Strehl plummets from 0.86 to just 0.67. In contrast, the apochromat with 0.05 wave RMS spherical error would decline from 0.85 to ~ 0.79 Strehl (the mean of 0.765 and 0.815 depending on the sign of the introduced spherical aberration). Comparing this to the 0.67 Strehl of the achromat puts the difference in overall contrast at ~17%, which is noticeable but not dramatic.
This is bizarre isn’t it? It raises some important questions. In what mode does the eye actually operate under when viewing celestial objects? The answer depends on how bright those objects are, as well as inter-individual variations in spectral sensitivities. In order to achieve the telescope’s limiting resolution, the eye must either be in photopic or in ‘bright’ mesopic mode. Mid mesopic visual mode only kicks in only after the eye has dark adapted itself for at least 10-15 minutes and longer if there is some ambient light pollution. What’s more, it only appears to do so if the object being viewed is below a certain minimum luminance threshold. Fig 8 illustrates this idea nicely. For example, if the eye is viewing objects above a brightness level of ~magnitude +5 for very short periods of time, photopic vision will quickly begin to creep back in again.
Fig 8. Showing how human eye resolution varies with spectral response
Indeed, it only takes a few seconds of exposure to the above threshold illumination to ‘bleach out’ the rhodopsin molecules from the retinal rods and switch the eye to the cone-dominated mode. Bright mesopic mode is still cones-dominated, unlike dim mesopic mode which is rods-dominated. Fig 8 makes it clear that it takes a drop in luminance of the order of four magnitudes to bring the eye from bright-to mid- mesopic mode.
Interestingly, for my 4” F/15 achromat, the optimum magnitude for resolving close doubles is considered to be about +5, and that is largely consistent with my own experiences in the field. According to Hirshfeld and Sinnott (Sky Catalogue 2000.0) the Dawes' empirical limit is based on stars that are about three magnitudes brighter than the faintest detectable and which puts the optimum magnitude at no brighter than +7 to +8. Only going to fainter stars with my 4” glass pushes the eye into ‘dim’ mesopic and, ultimately, scotopic mode, with significantly impaired resolution.
Unless you like looking at extremely faint pairs or low-contrast faint fuzzies – and I for one don’t – all indications are that the eye does tend to retain its cone activity (associated with photopic vision) as predominant in general observing. This makes sense in other ways. High quality, long focus achromats are highly favoured for the lovely views of planets, Luna and brighter double stars they serve up, and so the eye could not reasonably be said to be viewing these objects mesopically.
Taking a closer look at the Point Spread Function (PSF) of the achromat for best polychromatic Strehl focus (depicted in the left hand diagram of Fig 9) in mid-mesopic mode, the achromat suffers a few body blows but still emerges fighting fit. For one thing, the FWHM is about 20% lower in the achromat, owing to the effective increase in defocused energy. It is significantly lower than in photopic mode and would negatively affect resolution of very faint double stars.
However, as Fig 9 demonstrates, the 1st bright ring area in the achromat is not significantly more "loaded" with energy, as might be suggested on first examining Fig 7, so the Airy disks of even fairly dim stars in the long focus achromat may still be a shade cleaner than in the apochromat. Specifically, the former’s 1st bright ring is about 32 times fainter than its peak intensity, compared to 28 times fainter in the latter with its averaged 0.050 wave RMS e-line error.
Examining the mesopic MTF (depicted in the right hand diagram of Fig 9) data for best foci, the graph clearly indicates that the apochromat with 0.050 wave RMS has an edge in contrast and resolution of faint low contrast details, acting as if it had ~15% greater aperture (note that this MTF is not applicable for brighter objects). This is mainly due to more energy displaced farther away from the central maxima in the achromat. Thus, if you are a wide-field, deep sky observer, apochromats may be the dream ticket. Certainly, the data suggests that apochromats would be a better tool than achromats in this regard.
Fig 9. Showing PSF and MTF mesopic responses for a 4” F/15 achromat and 4” F/6.3 doublet apochromat.
These results are also consonant with a large body of anecdotal evidence garnered by deep sky observers who use short focus apochromats. There are many reports in the literature attesting to the greater contrast afforded to the apochromatic image on faint objects on the margins of invisibility. That said, it is interesting to note that some celebrated deep sky observers such as John H. Mallas and the late Walter Scott Houston used 4” F/15 achromats (a Unitron and Clark, respectively) to conduct much of their studies. Even so, in light of the data presented in Fig 7 and Fig 9 above, I can now better understand why other visual astronomers of note, such as Steven James O’ Meara, observing from the idyllic vantage of the Big Island of Hawaii, did so well recording the Messier and Caldwell objects using short focus apochromats.
Lend me your ears!
Any good study raises more questions than it answers. Why, for instance, are achromats (and apochromats for that matter) not optimised at peak mesopic wavelengths (somewhere nearer 530nm rather than the Mercury e-line) to better cater for the requirements of the purely visual observer? Truth be told, it might even improve the situation for astro-imagers too! The answer must surely reflect ‘hallowed’ tradition and to some degree the reluctance of refractor builders to conduct new avenues of research.
It may also partly reflect the fact that any achromatization process inevitably involves compromises. An achromatic refractor that is better corrected at shorter visible wavelengths will be less well corrected at other visually important wavelengths. Nonetheless, in discussing the idea with Vladimir further, it appears that an instrument with d-e-F correction (i.e. with d and F Fraunhofer lines brought together), for example, might do significantly better as an all round scope than the standard C-e-F correction seen in most extant achromatic refractors. All said and done, shifting the correction toward the blue end of the visible spectrum might just bring an improvement in performance to the contemporary achromat in general observing. It would certainly make for an interesting optical engineering project!
What does the word ‘classical’ mean to you? If you look up a dictionary, it’ll probably define it as ‘simple’, ‘pure’ or ‘that which has universal appeal’. In bringing this study to an end, I cannot help but draw parallels from the fruits of the Classical World. The ancient Romans produced engineering and architectural marvels the likes of which the world had never seen before. Yet, despite having only a rudimentary (by modern standards) knowledge of the scientific principles involved, this ancient civilization managed to build magnificent things that have stood the test of time. It is only with the benefit of hindsight however, that we can fully appreciate why their technology did so astoundingly well.
When I began this sojourn with you, I had no idea where this study would lead. But now, at journey’s end, I can better understand the experiences I have had with the long scope. What is more, I am deeply humbled by what this research has yielded. The optical properties of the classical achromat not only exceeded my expectations, it has clear advantages in terms of delivering stable, high quality images of bright objects under a wider range of observing conditions than the short focus apochromat considered. Not only is this borne out from a theoretical perspective, it has been demonstrated in the real world, with real telescopes.
This study is also in good accord with the historical record. After all, for the visual observer at least, there isn’t much new under the Sun. It pays to remember that the vast majority of objects contemporary amateurs observe today were actually discovered and thoroughly characterised by visual observers from generations past. And it was through their efforts and unbridled inspiration, that future generations ventured into the dark. History itself attests to both the high quality of the optics they used, as well as the visual skills they brought to the eyepiece. Almost invariably, amateur astronomers from those formative years employed long focus instruments (with high F ratios) to divine the treasures of the celestial realm.
As we have seen, producing a high quality achromatic refractor is far less of a design challenge than a perfectly functioning apochromat. That’s not to say that a lousy optician couldn’t produce a howler of a long focus achromat. Its great depth of focus would be of little utility were it to have moderate spherical aberration. Need I remind you of the Craig Telescope (c. 1852)? Nor does it imply that telescopes of shorter F ratio cannot perform comparably under good conditions with their longer focus counterparts. As the data in Table 1 reveals, they’re just considerably harder to execute well and, like a tropical orchid, more fastidious in their needs.
The future of the apochromat is already assured, but let us be PROFOUNDLY democratic and re-appraise the attributes of the ‘simple’ crown/flint glass. I write these words at a perilous time, when the future of the classical achromat appears uncertain. Advances in the casting and figuring of low dispersion glasses portend to an all but certain relegation of the humble crown-flint achromat to the doldrums of history, eking out an undignified future existence in binocular objectives, or as a ‘cheap’ finder or, worst still, as an ‘antiquarian trophy.’ Yet, this study has pointed out some significant - and frankly unexpected – attributes retained in the classical achromat that might well give it a distinct edge over the shorter focus ED refractor, and, might I add, even a long focus apochromat, especially in regard to the observation and measurement of double stars.
What mad pursuit!
But you know what they say don’t you?
The truth is sometimes stranger than fiction!
The author’s book, Choosing and Using a Refracting Telescope is available now from Springer.
This work, carried out over the course of several months, could not have been completed without the help of many people.
First and foremost, I would like to pay tribute to the brilliant Vladimir Sacek. Without his great learning, insight, patience and attention to technical detail, the present study would never have got out of the blocks. Thank you for having faith in me!
I would also like to extend my sincere gratitude to Professor Bob Abraham of the University of Toronto, Professor Emeritus Iain Nicholson of the University of Hertfordshire, England, Alan French (Upstate New York), William Paolini (Vienna, Virginia) and Chris Lord (Lancashire, England) for reading earlier drafts of the work and for providing positive and useful feedback.
I have to thank a great many people for taking the trouble to field some tests and report their findings on Cloudy Nights (CN) Refractor Forum. Special thanks are extended to Loren Toole, New Mexico, Clive Gibbons, Ontario, Canada, Jim Barnett and Ging-Li Wang of Petaluma California U.S.A. for starting CN threads confirming this interesting phenomenon. Thanks also to Siegfried Jachmann (Utah), Steve Fisher (Utah), Charles St.-George (Kansas), Thomas Jensen (Bornholm, Denmark), Jeff Morgan (Arizona), Andrew Jackson (Sydney, Australia), Erik Bakker (Haren, the Netherlands), John Nanson (Oregon) and Dave Tinning (England)
I also wish to record again my special gratitude to William Paolini, a through and through gentleman who continued to encourage me and offer his unflagging support for this project, even when it looked like no one else would.
Finally, I’d like to thank Mark Harry (Massachusetts), Jared Wilson (California), Ken Hubal (Ohio) and Mardina Clark (Washington), for interesting discussions and contributions. Last but not least, a warm thank you to Richard Day, London, who built the telescope that launched a thousand questions. Keep up the good work!
- The defocus ranges for the achromat and apochromat discussed in Fig 5. are incorrectly labelled. The larger range should be attributed to the achromat.
- Another error occurs on graph 4, where the colors for the achromat and the apochromat are switched.
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