Count the Pleiades
As a small child I remember being driven back to Portland at night after a visit to relatives in the countryside. I laid in the back of the station wagon, peering up at the sky through the rear window. The stars were so brilliant against the darkest black of skies! It hurt my eyes to look at the brightest stars! What a contrast to the washed out city skies of Portland, even in 1960!
Since most astronomical objects are quite dim as seen through the eyepiece, it behooves us to understand the conditions that permit the best visibility. Until recently, I cited the details of how the eye details light and how the eye then the brain proper process the results. I also invested a great deal of time working on a visual detection calculator. Empirical results at the eyepiece suggest, however, that a littany of factors greatly impact detectability. Consequently, it's best to discuss these factors and address them as much as possible.
For example, here is a table of aperture and magnitude values, from Clark, R.N., How Faint Can You See?,Sky and Telescope, pg 106-108, April, 1994. Look at the overwhelming variation caused by the various factors that impact what we see at the eyepiece.
Telescope Limiting Magnitude
Aperture Detection probability
inches 98% 90% 50% 20% 10% 5% 2%
1 9.7 10.2 10.7 11.2 11.7 12.4 13.2
2 11.2 11.7 12.2 12.7 13.2 13.9 14.7
3 12.1 12.6 13.1 13.6 14.1 14.8 15.6
4 12.7 13.2 13.7 14.2 14.7 15.4 16.2
5 13.2 13.7 14.2 14.7 15.2 15.9 16.7
6 13.6 14.1 14.6 15.1 15.6 16.3 17.1
7 13.9 14.4 14.9 15.4 15.9 16.6 17.4
8 14.2 14.7 15.2 15.7 16.2 16.9 17.7
10 14.7 15.2 15.7 16.2 16.7 17.4 18.2
12.5 15.2 15.7 16.2 16.7 17.2 19.9 18.7
14 15.5 16.0 16.5 17.0 17.5 18.2 19.0
16 15.7 16.2 16.7 17.2 17.7 18.4 19.2
18 16.0 16.5 17.0 17.5 18.0 18.7 19.5
20 16.2 16.7 17.2 17.7 18.2 18.9 19.7
22 16.4 16.9 17.4 17.9 18.4 19.1 19.9
24 16.6 17.1 17.6 18.1 18.6 19.3 20.1
30 17.1 17.6 18.1 18.6 19.1 19.8 20.6
36 17.5 18.0 18.5 19.0 19.5 20.2 21.0
Here are the factors and their impact, based on 50 years of observing at the eyepiece of countless telescopes.
1) Observer experience is worth 2 magnitudes (I have a series of sketches of M31 from childhood onward).
2) Observer variation is 1-2 magnitudes.
3) Age matters a magnitude: young kids can see very faint stars; as we get older, our lens yellows and ability to detect fades.
4) Knowing where to look and what to look for worth 1-2 magnitudes.
5) Did I mention averted vision, worth a magnitude or more?
6) Dark adaption continues to produce increasing benefits for hours, ultimately worth maybe a half a magnitude.
7) Field baffling is an overwhelming factor: the difference between nonexistent and fully baffled views can be worth magnitudes.
8) Covering your head with a black cloth also yields improvements, perhaps on the order of a fraction of a magnitude.
9) Time at the eyepiece is worth 1-2 magnitudes (objects gradually become recognizable or detectable over a period of time, then they fade after a prolonged period of continuous observing).
10) Comfort at the eyepiece is worth maybe a magnitude.
11) Sky transparency is such an overwhelming factor; on rare perfect nights Iíve seen scopes perform as if they had almost unlimited aperture; letís call superb sky transparency worth a magnitude or two.
12) Filters are worth 2 magnitudes.
13) The range of visibility, controlled as best as can be for object size and brightness, varies 1-2 magnitudes, occasionally more.
14) Visibility appears to correlate most with aperture, then apparent size (the greater the aperture, the greater the apparent size, limited by the full field of view). Review of observing books by respected authors suggest no favorite exit pupils or magnifications either; additionally there are a variety of approaches favored by experienced observers.
15) True bino viewing from unaided eye up to 22 inches yields consistent results for me: about a 80% gain in stellar limiting magnitude and about a 120% gain in visibility of extended objects; others report discordant results.
Taken in concert, these factors render any predictive tool or theoretical study's conclusions iffy - thereís really no recourse in many cases except to look through the eyepiece. Perhaps itís best to operate by rules of thumb, recognizing the importance of training and telescope baffling and selecting the most pristine nights for the most difficult observations.
Give a particular night, I select for largest aperture and
eyepiece apparent field of view that will frame the object. Most of the
time, the object doesnít fill the field with 6mm exit pupil, so I also
give smaller exit pupils or greater magnification a try, subject to
seeing conditions. I typically find that higher magnification yields
better results, topping off at 1.5 to 2mm exit pupil. Because of the
variation in sky transparency alone, I almost always try again on a
Averted vision works best if you know where to aim your eyes in the field of view. Here's a chart to help.
For extended objects, things are not so simple as the chart for star limiting magnitude. For starters, it is not possible to increase the surface brightness of an extended object by increasing the aperture. An example: take an object of 10 magnitude/ square arcsecond as seen by the unaided eye at night, exit pupil open to 7mm. Now, look at the object through a 10" scope. If there is no magnification to the image, the surface brightness will increase by the ratio of the scope's aperture to the eye's aperture squared, or, (10"/0.3")^2 =~ 1000x. However, in order to fit all of the light from the 10" aperture into the eye's exit pupil, we must use at least 33x. 33x will dilute the image brightness by 33^2 =~ 1000x, so we are back where we started. In fact, because of mirror coatings not reflecting 100%, and the small obstruction caused by a diagonal, the image brightness per area will actually be a little less than with the unaided-eye!
This leads to the interesting conclusion that the brightness of the sky glow as seen in the eyepiece is entirely dependent on exit pupil. At a given location on a given night, no matter the size of scopes, if they are giving the same exit pupil, then the sky glow brightness will be very similar.
What is sky glow brightness? The night sky, even at very dark sites, glows faintly due to zodiacal light and airglow. See Brian Skiff's discussion at http://www.astropix.com/HTML/L_STORY/SKYBRITE.HTM. You can measure the darkness (or brightness) of your night using a sky glow meter available at http://unihedron.com/projects/darksky/. Dark sky sites have readings close to 21.5 magnitudes per square arcsecond. Observing through a telescope with your eye's pupil fully opened results in a sky glow in the field of view equal to that of the night sky. Magnifying the image results in smaller exit pupils, the useful maximum magnification or smallest exit pupil being close to 1mm. The sky glow brightness drops more than 4 magnitudes to close to 26 magnitude as exit pupil shrinks to 1mm.
So how can we see the object in the scope? The eye is a marvelous detector of low contrast faint objects, but the light must fall on large numbers of rod cells so that the eye-brain can detect the slight contrast difference between object and background. The slighter the contrast, the more rod cells that the object's light must fall on in order to generate a signal difference between object and background. By increasing the telescope magnification, the object is magnified so that its light falls on many rod cells. There are two points to consider when an object is in the field of view of an eyepiece. The first is the object combined with the sky glow from the atmosphere that is directly between us and the object, and the second is a point away from the object, which is the sky glow only. The ratio of brightness between these two points is sometimes called the object contrast. This contrast value stays constant despite any increase in magnification because both points are equally dimmed.
The seminal reference on visual astronomy is Clark's book, "Visual Astronomy of the Deep Sky". In it Clark explains and quantifies the visual detection of objects. Clark has added additional comments since the book's publication, at http://clarkvision.com/visastro/omva1/index.html Clark uses data from a World War II study by Blackwell.
Here a brief presentation of the Blackwell data. The eye's detection ability with sky background brightness values from 21 to 26 is:
From the chart we can see that large exit pupils result in the best ability to detect objects over a wide range of apparent sizes. As the exit pupil shrinks, the ability to detect objects declines and becomes concentrated on apparent sizes of about a degree. We can see this by plotting best apparent detection size against declining sky background brightness. Here are two visualizations of the data:
The data and its interpretation has been the subject of intensive discussions between Prof Clark, Nils Olaf Carlin, Harold Lang and myself.
For Nils Olof Carlin's analysis of Blackwell's original data, see blackwel.html. Here, Nils shows that the best contrast comes when the background is dimmed below visual detection and the object is about one degree in apparent size.
Bill Ferris has generated a series of ODM matrices that compare the variables with each other: http://members.aol.com/billferris/odm.htm
I wrote a visual detection calculator that presents the data by aperture and exit pupil. I believe that the whole issue of visual detection needs more observations and possibly a new model. The detector that I wrote uses the Blackwell data. Like any ground breaking study, there remains much to be done. The study was done with two eyes - how does a single eye do? Objects in with complex isophotes need to be studied, distractions of other objects in the field of view needs to be investigated and variations in the color of the objects need to be checked. Also needing observations is variation in the ages of the observers and especially telescope construction features like baffling and cleanliness of optics.
Greg Crinklaw has invested a great deal of time into improving his visual detection calculator based on empirical results at the eyepiece. See his SkyTools software and in particular his comet chasing page.
Last revised Feb 2013