The Majesty Factor
The Nexus of Contrast, Power, Field — essay by Al Nagler
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After showing the first Ethos 13mm at a number of events since April 2007, we can safely conclude it brings the observing experience to a new level. This is based solely on user's reactions to views of familiar objects, not on any prejudgments, publicity or hype on our part. While we were quite confident of success, we wanted, and still want, to explore all the ramifications of what a sharp 100° field really represents.
Right after NEAF in April, Rodger Gordon, the acknowledged "eyepiece junkie" of all time, wrote me "Definitely the finest wide-angle eyepiece I've ever seen. If God is an astronomer, this is the wide-angle eyepiece he'd choose. You can quote me." Thanks, Rodger. I waited until now to avoid "priming the pump", so to speak before quoting your unbridled enthusiasm publicly.
For some time, I've been pondering just why the response has been so overwhelmingly positive. And if I really understand why, is it possible to quantify? My views of the Double Cluster at Stellafane pointed the way.
The 1991 article I wrote for Sky and Telescope on magnification provides the key. A major conclusion for low power states: "The best view occurs with the highest power that comfortably includes the target object. Higher powers darken the background sky, reveal fainter stars and show more detail. The resulting smaller exit pupil also minimizes the effects of eyesight defects."
Considering the potential of Ethos, let me posit a more general conclusion.
It's clear that the largest possible apparent field for a given true field yields the most magnification for greater resolution, with a darker sky background for more contrast as a result of the smaller exit pupil. I believe this combination of contrast, power and field causes the typical "wow" reaction — the Majesty Factor. I think Tom Trusock said it most succinctly in his Starfest (Canada) report: "The same true field at higher magnification means that you'll see blacker skies and more detail." Dennis di Cicco in his 5-star review of Ethos in his October 2007 Sky & Telescope review noted something similar: "Observing with the 12-inch scope, I typically bounce between a wide-field eyepiece for star-hopping and a high-power one for detailed views. But the Ethos gave me both. The field was large enough to star-hop, and the magnification was high enough to bring out faint stars and resolve details in galaxies and star clusters." (He coincidently also illustrated field sizes using the Double Cluster.)
Let's try to quantify the so-called Majesty Factor. While we cannot quantify the majesty of a great symphony, work of art or edifice, I think a meaningful Majesty Factor is quantifiable for those great deep sky views. Here's how:
Let's consider a range of possible eyepieces with apparent fields of 50°, 60°, 68°, 82° and 100°. Now let's pick an object, (like the Double Cluster) and let's say it's properly framed in the field of a 50° Plössl with a 26-mm focal length in an f/4 telescope so the exit pupil = 6.5-mm. Let's arbitrarily assign a factor of 1 to the power (magnification) of this telescope and a factor of 1 to represent the contrast for the 6.5-mm exit pupil. Therefore, for the given true field:
Now let's replace the Plössl with a 100° (apparent field) Ethos with a 13-mm focal length. This yields the same true field of view at twice the power with twice the apparent field and half the exit pupil. The 3.2-mm exit pupil is only ¼ the area of 6.5-mm, so the sky background darkens by a factor of 4 (contrast factor). The magnification power factor yields twice the detail or resolution. Therefore:
Working out the math for all the apparent fields listed above, we have:
|Apparent Field (°)||Power Factor||Contrast Factor||Majesty Factor|
A simple rule of thumb is that for any two eyepieces having the same true field of view, the Majesty Factor equals the cube of their apparent field ratios. Example is (100°/70°)3=2.92.