-1 Based on 150mm aperture 150x (1mm exit pupil) and 5.5 ULM 7/10 stability skies.
-2 Based on a 6th mag star, 150mm aperture 600x (.25mm exit pupil) and 5.5 ULM 10/10 stability skies.
-3 Without dewshield.

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The Stars

The image at left was rendered by dblCalc assuming perfect seeing and almost perfect transparency. The scope emulated possessed no obstruction whatsoever in the light path. 96 percent of each stars light ended up in its airy disk. The remainder is seen as an harmonically distributed series of concentric diffraction rings surrounding each disk. The size of this disk is not dependent on the true size of the actual star being rendered. It is dependent on the amount of light collected by the telecope aperture and concentrated toward a virtual disk where the bulk of the photons converge. The angular size of that convergence point in arcseconds - as discussed above - varies secondarily with telescope archetecture but primarily with telescope aperture in accordance with the laws of diffraction. Ideally it is said that the angular displacement of any airy disk is equal to 122 / round diameter or aperture (in mm) of a telescopes photon collecting surface or medium. (The number 122 is specific to green light. Angular displacement is greater in red light and less in violet. Thus, theoretically two "blue" stars may be more easily resolved by the same aperture as two orange ones.)

The double Castor depicted above consists of two stars (spectral classes A1V&A2Vm) - the primary of magnitude 2.0 and secondary of magnitude 2.8. The average apparent size of these two stars is .89 arcsecs while the centers of the pair are separated by 3.3 arc seconds. The pair itself revolves in true binary fashion around a common center of gravity. The Castor system is - in reality - more complex than this. There are in fact four stars in the Castor complex. The other two members are much more distant (greater than 1 arcminute) and faint (slightly brighter than magnitude 9). These are not included in the dblCalc rendition.

It would take an exceptional scope and sky to give the view rendered above. The fact that a multiplicity of diffraction rings are visible is no knock against the optics. Under the conditions described above, a six inch instrument reveals stars down to magnitude 14.5 and beyond. Under conditions of such great transparency fainter diffraction rings are revealed. How Castor might be displayed by our four 6 inch instruments under more likely conditions (5.5ULM & 8/10 stability) is to be explored later.

Albireo is widely regarded as one of the prettiest pairs of color visible in the northern hemisphere. Due to its relative brightness (magnitudes 3.1 & 5.1) and wide separation (34 arc seconds) the pair is easily resolved in all telescopes. But what makes it an especially interesting study is the enigmatic nature of its colors. In a fully chroma-corrected telescope the pairs should show true to spectral type (K3II+B0V). Admitting of color-temperature relationships the pair would appear warm yellow and bluish white. The rendition seen at right - like the Castor pair also rendered as through near perfect seeing conditions - uses gold and blue as the base colors. Since all our scopes are assumed chromatically correct, there is little point in comparing them colorwise on this pair. But there is a point to be made. For you see, where large apertures are used - or where insufficient magnification is applied the quality of a stars presentation is at variance with the notion of an "airy disk". In addition, low magnification also tends to blend diffractions rings together into an expansive aura - or glowing region - surrounding the pair. Compounding this phenomenon - and in most cases exceeding it in effect - are added the vagaries of magnification used, brightness of the pair, atmospheric conditions, and the quality of optical surfaces, coatings, and media of refraction which tends to scatter rather than concentrate light. Finally there remains one subtle relationship between scope archetecture, color intensity, and aethetics of view for where more light is concentrated in the airy disk, piquancy of color is amplified and even low magnification stars appear better resolved while displaying greater contrast to the background sky. Thus at low powers very fine optics presents pin-prick stellar images against a very dark - high contrast sky.

Although dblCalc rendering is insensitive to some of the factors described above (optical surfaces & media) it does admit of variation in airy disk sizes and ring brightening due to obstructions in the light path. It is also sensitive to magnitudinal reach of the varying scope types - something that has a very real effect on stellar presentation. Our basic question though comes down to this: Do any of our scope types show a visible advantage when observing bright-wide pairs such as Albireo?

The pair at left is moderately close and magnitudinally disparate Antares - a double whose low sky position often frustrates resolution attempts by northern hemisphere obervers. It should be interesting to see how our four scope archetectures compare under the kinds of conditions likely to be seen outside the skies middle third. It is also obvious that the pair shows significant color as well as brightness contrast. Like Betelgeuse of winter skies, Antares A of the summer is the classic "red giant" (spectral class M1Ib). (Such aged stars are swollen with remnant hydrogen and helium gas pressed outward by a proportionately small but massively radiant nearly exhausted nucleus.) At spectral class B2 and magnitude 5.4, its confrere is actually bluish-white appearing green under the suasion of its .96 magnitude (visual) companion. One question of note here is whether dblCalc will reveal any variances among the four scope archetectures in terms of resolving Antares disparate secondary under marginal seeing conditions...

For northern latitude observers our next pair (Iota Leonis) provides no seeing excuse for failure to clearly reveal the 4.1 magnitude primary's 6.7 magnitude companion. Two factors make resolution of this pair a challenge however. At 1.5 arcseconds separation, the secondary lies right on the first diffraction ring thrown up by the primary. The second factor of course, is the relative faintness of that secondary which may easily be overwhelmed by its first diffraction ring. A scope of exceptional optics - of even 4 inches aperture - should reveal the secondary since it lies within a more distant first diffraction ring. And a scope of good optics larger than six inches should reveal a brighter secondary outside the closer diffraction ring. But at separations in the 1.6 arc second range and at 6 inches of aperture the picture gets more complicated. Will all our scopes plainly reveal the secondary???

Our penultimate pair (KU 60) is located well within a one degree field southwest of Delta Cephei. Though faint, this duet of red dwarves (M2V spectral) are not dissimilar in brightness (magnitudes 10 & 11) and are separated by a mere 2.4 arcseconds. Given this separation, all four virtual six inchers should be able to resolve the pair through 6/10 or better stability skies. But which scope will accomplish the task of revealing that two faint specs of light are in fact twain?

Our final pair (Gamma Virginis) is a true binary consisting of a two 3.5 magnitude plus stars whose 168.7 year cycle of great eccentricity and relative proximity to the Earth results in wide variations in apparent separation. By March of 2005 the pair should be beyond resolution of any amateur telescope not experiencing superb seeing stability conditions (0.38 arc seconds). The last time this pair approached its 2005 separation (in 1836) the largest available telescope in the world (the 240mm archromatic refractor at Pulkovo Observatory in Estonia established by FGW Struve in 1825) was just able to elongate the pair. Meanwhile as late as the year 2000, the pair could be resolved by any four and a half inch scope possessed of diffraction-limited optics. Our question is - as the gap closes between 3.6 magnitude Porrima A and 3.7 magnitude Porrima-B how long will our various scope apertures "be able to hang in there" and truly resolve the pair?

Let's start peeking through the scopes shall we???

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Raw Resolution: How Close Can They Be?

The timeline at left is Astro.Geekjoy's best effort at interpreting an orbital chart for Porrima during the resolution window for 6 inch apertured scopes 2002-2003. As you can see I have listed minimum aperture requirements based on perfect seeing and non-obstructed scopes. By January 2003, we have arrived at the limit of clean resolution under ideal conditions for such six inch instruments. But what is of greater interest here is to assume that sky conditions are at best 9/10 pickering (stable, non-walking, uniformly illumined first diffraction rings around 3rd magnitude stars at 1mm exit pupils - 152x). At what point in the timeline would we last be able to cleanly resolve Porrima as it progresses toward orbital perihelion in its current cycle?

At right is the last resolve view of the Porrima pair separated at .87 arc seconds. This separation corresponds to the orbital appearance of the pair in November 2002. At such a time a very fine apochromatic refractor would reveal two distinct airy disks approximating at their frontiers at some 560x magnification. A careful look at the two stars shows a faint - yet clearly discernable - first diffraction ring circumscribing both stars. Even at magnitude 3.6 such a fine instrument and sky leaves little in the way of contrast robbing distraction to the eye. This well-hewn view is a tribute to the fact that our apochromat packs a whole lot of light into those .87 arcsecond sized airy disks.

Meanwhile through our 20% obstructed RV-6 we are able to resolve a still closing Porrima pair down to some .81 arc seconds in separation. This separation value is achieved three months later in our interpolated chart. The price we pay for this additional window of resolution is a slightly but definitely brighter first diffraction ring. Still the game little long-focus reflectors view is outstanding. There is little to distract the eye from contemplating the pristine beauty of such a well-yoked pairing...

An additional increase in the central obstruction diameter allows us to continue resolving a .75 arc second separate Porrima for an additional two months. But here that 34% central obstrcution starts to reveal that there is, in fact, a price to be paid for this additional high contrast resolution. For now the first diffraction rings of both stars are very obvious - and should sky stability begin to degrade the view would degenerate unacceptably. Thus despite the perfection of all those glass curves and mirrored surfaces we are now put in a position where sky conditions become the dominant influence over the pleasures of observation...

Turning now to the Mak Newt rendition at left we once again see an improvement in the diffraction ring situation. Meanwhile we lose the ability to resolve Porrima in February of 2003. But there is something also of note. Can you also detect the fact that the airy disks are not quite as bright in comparing the Mak Newt airies to the classic newtonians? Certainly one would never notice such a thing at the eyepiece but in fact Porrima is slightly less intense through the two catadioptics - with their additional light handling media and surfaces - than through the classic newtonian. This slight difference is made perhaps a bit more obvious when comparing the Maksutov images with the refractor's...

So what's the answer? In simple terms, the MCT will in fact continue to resolve Porrima for a period extending two months after the pair appears elongated through the other three models. Thus, if you had only a single criterion upon which to base a telescope decision - and that criterion was raw, high contrast image resolution - get a Mak Cas...

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Disparate Doubles: Plainly Revealing Faint Companions

Although our 6 inch MCT walked away from the competition in raw resolution we are already quite up on the fact that those overbright diffraction rings are going to leave the scope rather "challenged" when it comes to low contrast studies such as faint detail on the Gas Giants. But there is a class of doubles that do - in fact - require exceptional low-contrast resolution in order to deliver the views. And that class of doubles is what we here at Astro.Geekjoy like to call "doubles of disparate magnitude". In fact most double star pairs are of this class - for it is rare for two suns - like Porrima - to form in any solar system that manage to "share-balance" their masses and set off on a parallel course of stellar evolution. But despite their relative frequency, it takes some special conditions to make this type double unresolvable. Consider, if you will - any secondary that is simply too faint for that telescope to detect under the conditions, or one that may be bright enough but is otherwise overwhelmed by scattered light from the primary -or some other source...

One might think that the ability to resolve our first class of disparates - those with a secondary lying inside the first diffraction ring of the primary - may be more easily resolved by scopes that manage to deflate airy disks due to large central obstructions. And this might be true in some pair instances. However, when it comes to faint stars closer to primaries there is also the fact that such secondaries need to "catch the eye". And for that to occur stars need to compact as much of their light into airy disks as possible.

The second class of disparates have more to do with the particular foibles of the aperture involved. Based on the harmonic relationship between aperture and airy disk size we know that the radius of the first diffraction ring of any star lies at a distance some 244/aperture (in mms) away from the center of the airy disk. In the case of a 152mm scope that places the first diffract at 1.6 arc seconds. Thus any secondary whose airy disk juxtaposes against the first diffraction ring gets "photonically entangled" with it. The result - in the most extreme cases - is a secondary detected as a static "brightening" attached to an otherwise unstable diffraction ring displaying other "unfixed brightenings" randomly seen on that same ring. The ability to distinguish such diffraction-ring entangled secondaries is often subject to the observers experience - or perhaps - the observers tendency to engage in the "power of positive thinking"!

A third class of disparates has to do with faint secondaries located in light scatter associated with brighter stars. In a six inch telescope of decent optics one may detect such scatter regions around stars as faint as 7 magnitudes brighter than the limiting telescopic magnitude of the scope through that sky. Meanwhile scopes possessed of rough surfaces, poor coatings or ineffective baffles may be severely pressed to give any indication of a secondary star whatsoever.

Modeling these three types of disparate resolution behaviors is exceedingly difficult - especially across the full range of sky conditions, apertures, magnifications, pair dissimilarities, and scope types. dblCalc incorporates such modeling but caveats apply here... Despite these difficulties we can at least get a sense of how plainly disparates of Type II (faint secondaries on diffraction rings) may be resolved. And to that end we turn to Spring's Iota Leonis...

At left is our FS-152 view of a ring-entangled Iota Leonis through 8/10 seeing skies. Due to the pairs proximity some 325x is required to distinguish one "star" from another. Notice the slightly distended appearance of the 6.7 magnitude secondary. Here we see light from the first diffraction ring as it combines with luminosity from the star itself. There is something vaguely "un-starlike" about the view of the secondary. An experienced double-star observer would recognize this phenomenon - and as long as the oblate brightening remains fixed in relation to the primary - would be confident that - in fact - a disparate secondary was present.

At the same 325x magnification the view of Iota Leonis through the RV-6 is in fact only slightly distinguishable from that of the FS-152. A closer look at the pair shows a faintly detectable first diffraction ring extending around the primary. In this case though the ring adds little real confusion to the view. The secondary - though now more visibly oblate than in the apochromatic refractor - remains obvious to the eye.

Meanwhile the effect of the MCT's 52% central obstruction requires no special attention on the part of the observer in the image at left. Here the first diffraction ring is clearly seen - but despite its presence - the secondary is easily seen as the fixed brightening. However in real world and more dynamic seeing conditions light present in those brighter rings could conceivably "gang up" and give a sense of a similarly "ring-entangled secondary" where none exists. Under such conditions it would be all too easy to be mislead into thinking that a faint secondary was present...

Finally we return to a view comparable to the newtonians. But again - like the MCT - we might note that the MN-61 scope collects a scosh less light than the newt and should the companion be even dimmer than Iota Leonis-B we might find ourselves guessing about the secondary rather than getting any real sense of certainty.

We might wish to speculate as to how faint such a secondary might be for each scope. So what does dblCalc say? As it turns out - under conditions as described above - the FS-152 and RV-6 should reveal a faint secondary on the 4.1 magnitude's primary's first ring down to magnitude 8.7. Meanwhile the MN-61 and M-603 should accomplish the same task to magnitude 8.5. Of course, we have assumed that all our scopes are of equal optical quality and - but for central obstruction and certain light handling limitations - are identical. (NOTE: The fact that the RV-6, for instance, will show certain diffraction effects associated with a four-vaned spider is not included in our model.)

So given these realities we have to say that - of the four scopes the FS-152 is the "scope of choice" when attempting to resolve Type II disparate secondaries...

It is equally clear that the unobstructed apochromat also goes deeper when revealing more distant disparates beyond the ring system (TYPE III disparates). However, one lingering question remains. Which model will reveal faint secondaries at the theoretical limits of resolution for each type? And perhaps the only answer to that is subject to individual interpretation. For if we play the same trick with Iota Leonis and close the separation of the pair until the two stars are about to merge we find...

... that the 6.7 magnitude disparate secondary is resolvable down to .81 arc seconds through the FS 152. The RV-6 (and MN-61) pushes this further still to .76 arcseconds. While the M603 accomplishes the same resolution trick to .70 arc seconds at some 675x. No surprise here! But who knows what such a pair would really look like through the eyepiece! But at least through dblCalc we can speculate...

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Faux Nebulae: Faint Close Pairs

Charles Messier made himself famous - not for his comets - but for his catalogue of supposedly comet-like objects to avoid during comet-quests. Among those "quasi-cometary" objects two (M40 & M73) actually consisted of two or - a few - stars that gave the appearance of nebulosity where none was present. All this of course, points out that some double star pairs lie right at the edge of resolution - but not because they are "too close" but because they are "too faint"...

Our original view of KR 60 (above right) showed the faint, closish KR 60 pair under ideal seeing conditions. In that rendering, the fact that this is a pair of faint stars is obvious. We can even determine that both components are "red" in color (red dwarves - long-lived stars of low luminosity and low color-temperature). The view through our FS-152 however is appreciably diminished in intensity - due to the 5.0ULM and 6/10 stability skies associated with the dblCalc rendering. However - assuming that there is not an excess of glare on your monitor and its gamma intensity setting is not too low) the stellar nature of this pair is just discernable through the refractor as well.

The view through the RV-6 continues to reveal the stellar nature of the pair. But even now - to this observers eye - some difficulty "holding" the 11th magnitude star with direct vision is experienced. This effect may be attributable to two causes: The RV-6 loses about .3 magnitudes to the refractor in limiting telescopic magnitude. And an additional 6 percent of both stars light is being spread out away from now smaller airy disks into the atmospherically diffused glow-region around both stars.

To this point the fact that two stars are present in the field of view may be ascertained by careful observation through the newt and the apochromat. But what are to make through the same field through the more light-starved Maksutov-Cassegrain also suffering from added diffusion of light based on the largish central obstruction? Certainly something is present in the field - but what? A "mini-dumbbell" planetary? Distant comet? Use of averted vision on the "object" reveals (to my eye) a faint pinch at the waist of the pair. Meanwhile it is only on eye movement (around the field) that the stellar nature of the pair is confirmed. Knowing the effect of seeing conditions, an experienced observer might conclude that they were seeing a faint unresolved double and make an effort to confirm this observation on a better night - or with a scope of better low-contrast detail resolution...

The view through the Maksutov-Newtonian although almost equally afflicted by reduced luminosity as the Mak-Cas is - as we suspect - only a slightly dimmer view of that seen through the RV-6. In fact the "pinch" between the pair is more obvious than through the M603. But it is only with averted vision and movement of the eye across the field of view that we begin to suspect that we are actually seeing a faint double star.

Based on all this we can pretty much conclude that - despite modeling precisely the same observing conditions - the RV-6 and refractor are capable of revealing the stellar nature of our discovery - while the two Maks leave us somewhat in doubt.As in the instance of wide disparate doubles (TYPE III's) we have to give the nod to the FS-152 when it comes to faint closish pairs where contrast is needed to definitively reveal the stellar nature of the double.

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Aesthetics of View

As it turns out for those of us in the northern temperate climes the Swan's Beak makes for great viewing for almost half of the year-long season of the stars. So turning our fine instruments on Albireo - under decent - but not exceptional conditions - we might get views like those that follow through our four virtual scopes:

It would appear that such a fine pairing reveals much of beauty - irrespective of scope type...

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Marginal Seeing

The very finest telescope - despite every effort of refinement - is ultimately beset by three main limitations. The first is that imposed by the observer - not all eyes, optic nerves, and lobes (occipital in particular) are the same. In addition there are limits to what even the best observers can see. The second fetter is imposed by the wave nature of light. Because light is a wave it is subject to diffraction. Diffraction in turn is a property of light that diffuses the motion of lights elementary entities (photons) result in a fixed limit of resolution based on telescope aperture and any blockages encountered by photons along their path. Ultimately the greatest limitation imposed on the view has to do with the atmosphere through which that study is observed.

Seeing conditions can of course be strangely variable - not only from night to night, but from one part of the sky to the next. In general the stars , moon and planets give their best views when culminating at the zenith overhead. But even that situation can be compounded by heat rising from ones own body - or the discomfort that can come from low eyepiece position. As sky location changes during the night the amount of atmosphere through which starlight passed to be gathered by our instruments varies.

The fact that the Earth is a sphere also complicates matters. Although all stars rise and set at the horizon some never make it very high above that horizon even while culminating due south (or north depending on the observers hemisphere). On a night of superb atmospheric stillness overhead (9 of 10 seeing Pickering) stars a mere 10 degrees above the horizon may not even display airy disks. Meanwhile, aside from body heat, there are a host of other local factors that can negatively impact atmospheric stability - heat rising from tarmac or a heated building can also create turbulence zones that effect image quality. In general the further down toward the horizon that a study is seen the more such factors gang up to effect the view. Add to all this factors such as unrefined optics, large central obstructions, or short focal lengths and image quality can even vary from scope to scope.

So, astro.geekjoy will now leave you with four views of the tight, bright disparate pair Antares through our four scope types through 6/10 seeing skies low-down near the horizon. Pick the best one and trust you can afford it!

Other dblCalc Rendered Double Star Views

dblCalc Software Page

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