Telescope Reviews: Ground Truth for the Bortle Scale

Tony,

First let me tell that my personal NELM estimates / SQM readings agree very well with what you reported.

I'd like to point the discussion to another aspect that is not considered as intensively as it should (according to my humble opinion). It is visual acuity.

Several years ago Bradley Schaefer released an article in Sky & Telescope. I do not remind of the exact title (maybe "How faint can you see?") and the issue it was publisheed in, but I suppose that CN readers know of it. Schaefer gives a BASIC program, implementing this model. It has a bunch of parameters and is fairly complex.

Bill Gray implemented this model in a version of Guide, allowing to calculate the fst. One day I played with this new feature in Guide, but I was disappointed a bit: I simply cound not reproduce a 7.3 mag dark sky I found when observing from the Austrian Alps. Select high altitude, dry air, sun and moon near nadir - just did not get much darker values as 6+. So what was on with this model? Was it wrong at all? I could not imagine this to be true because Bradley Schaefer has done so much research and Bill Gray is a very precise programmer. A miracle remained.

A free implementation of Schaefer's model comes from Paul Rodman, ther author of the AstroPlanner software: Visual Limiting Magnitude (by P. Rodman)

As I came across this program, I detected what was the most importnat parameter you have to "generate" really dark skies. It is the Snellen parameter. Snellen was a Dutch ophthalmologist who introduced a measure for visual acuity. This Snellen parameter assigns a value of 1 to people with average acuity. Smaller values mean that you can see smaller detail. So acuity affects NELM - and it drives NELM more than other parameters Schaefer incorporated in his elaborate model.

Then in a German astronomy magazine, Jürgen Kemmerer published an article on night myopia. Many people are affected by night myopia, even if they do not wear or need no glasses in daylight. Jürgen reported that with his new "astro glasses" (perfectly fit to compensate his night myopia) his personal NELM improved by more than one magnitude.

Last week one of my observing fellows reported that he now wears glasses - and gained about one magnitude.

Putting together the puzzle pieces seems easy to me:

Observation: NELM estimates of several observers under the same conditions differ much more than what they perceive when using a telsescope. Explanation: when using a telescope, everyone cares to focus precisely. Without the telescope, night myopia takes its toll
Observation: if you look for published correlations of NELM and SQM readings, you will find that they can brought to good match if you shift verticclly. The overall shape of that curves is more or less the same. Explanation: the Snellen parameter corresponds to a constant offset in NELM, as Schaefer showed.

So I suggest to agree on one of the suggested NELM <--> BSB (background surface brightness) curves. Schaefer gives

BSB = 21.58 - 5 log(10^(1.586-fst/5)-1) - 2.5 log(Snellen)

for this. I find this practical, as you simply put in the figures instead of interpolating in a table. And this formaula can be reversed, yielding fst = f'(BSB, Snellen).

What remains to be done is to find a personal Snellen value for you. This could be done with a least squares fit of some (fst,SQM) points. If you have only one estimation, then the Snellen is directly derived from the offset you estimated compared with the Snellen value of 1.

So every observer could determine his/her Snellen value. Some observers can do this together. If they have more than one SQM at hand, they could average the devices' readings.

With knowledge of a personal Snellen value you can contribute NELM estimates and they can be transformed to what an SQM should have given. If you have an SQM, there's no need for the extra mile, but for those without an SQM it would be a better solution than plain estimation.

If it turned out that this works, collecting LP data could be improved. And for logging / sharing of observations it would allow for better comparison of findings (assumed the observers given their Snellen values when reporting observations).

I'm planning a small field campaign during the next year. In our local observers group, some SQMs are in stock. We want to go to several places with dark (6.2 or so, for better skies I had to drive hundreds of miles) and not so good skies.

If you think that this is a helpful or at least reasonable approach, we could try to collect our findings. I know that some guys in the US have darker skies than we in Germany. The best SQM reading I ever got from my regular observing site 30 km from home was 20.80. In the Austrian Alps i read off 21.65, what is great. But this place is too far to drive to more often than once a year. And the weather is not reliable there.

On the other hand: observations under brighter skies (4 to 5 mags NELM) were helpful, too.

Regarding the original topic, the Bortle scale: I find it useful because it does *not* rely on pointlike test objects as stars. Having test targets (OCs, ...) with a more than pointlike angular size will reduce the scattering of estimations. But IMO the Bortle scale is too coarse: on two different nights, according to the descriptions the same Bortle rating had to be given, but one night was definitely better. The Bortle stages correspond to about half magnitude steps. But while observing, I occasionaly found that the sky had become a bit brighter or darker than, say, the previous hour. I noticed this from eyepiece observations, not from periodic NELM estimations. Pulling out the SQM it clearly showed that the impression of change was right. I am pretty sure that I will notice a change of 0.2 magnitudes. And my fellows tell the same.

So a "half step addendum" to the Bortle scale would be very nice. How do you think about this? Has anyone suggested such an extended scale? Maybe even John Bortle himself? I just don't know.

Clear and dark skies to all of you!

Tom