What is Twilight Factor?
When looking at specs for binoculars, I see a line item called "Twilight Factor" and it has a number like 16, 18.3, 20.5, etc...
What is this number telling me?

Multiply the magnification by the objective size in millimetres (for example a 12 x 50 = 600)

Then calculate the SQUARE ROOT of this number ( in this case it would be 24.5 )

The HIGHER the Twighlight Factor , in theory at least the BETTER the binocular will perform in POOR or FADING light.

So whilst exit -pupil (arrived at by dividing objective size by magnification --in this example about 4.2) provides increased BRIGHTNESS as it increases, there comes a stage in lighting conditions where increased MAGNIFICATION helps you see things better in darker situations.

Both of these factors, twilight factor and relative brightness are very important --but do not tell the whole story.

ACTUAL brightness and TWILIGHT PERFORMANCE are also affected very much by QUALITY of glass and coatings and optical designs incorporated ( e.g prism types )

So a top quality $1000 10x40 for example may very likely in reality outperform a $100 12x50 in terms of TWILIGHT PERFORMANCE , even though the math would lead you to believe otherwise .

TWILIGHT PERFORMANCE is in my opinion a very important and often under-rated and overlooked factor with binoculars.

Hope this helps - regards -Kenny.

The original thread is at
What is Twilight Factor?

What Is Visibility Index?
Various noted individuals over the years have adopted scales that attempt to represent relative performance of binoculars, based on some ratio of magnification and aperture. Roy Bishop created the Visibility index that is Mag x Aperture. Alan Adler created the Astro Index that is Mag x Sqrt Aperture. EdZ created an index call the Binocular Performance Index (BPI) see CN Reports - Binoculars - How to Understand Binocular Performance (Feb. 2003) that adapted a scale based on the Adler Index (mag x sqrt ap), but then applied factors based on quality (coatings, contrast, polish, light cutoff, etc.). While I have always been a stong supporter of magnifiaction having greatest influence, that can sometimes be very misleading. In my opinion, it is of far greater importance to consider the intended targets and then determine on which (mag or aper) you should place greater emphasis.
However, the brief explanation of how the indices are determined is this:
(For purposes of this discussion, I am assuming all instruments of equal quality. If so, my BPI would give the same comparative result as Adler Index.

Roy Bishop Visiblity Index
20x60 = 1200
15x80 = 1200

Alan Adler Astro Index
20xsqrt60 = 155
15xsqrt80 = 135

this thread discusses the difference between Roy Bishop's Visibility Index and Alan Adler's Binocular Index.
Is aperture king? Does aperture rule?

further discussion on the topic of Indexing
What does the 'Visibility Index' tell you?
this has explanations of when these indices apply and when they do not.

Also see this explanation of Binocular Performance Indexing - BPI
this thread explains it in brief. Following in the footsteps of Bishop and Adler, I developed
Binocular Performance Index, BPI, which is Adler index adjusted for quality.

Alan Adler's article referencing his index can be found here
http://www.weatherman.com/binadler.htm

What the BPI attempts to do is rank binoculars dependant on their performance characteristics. A normal binocular gets no adjustment. The binoculars that exhibit the best attributes, contrast, transmission, lack of aberration, get adjusted up. Binoculars that exhibit some aberrations or are not well corrected for contrast and transmission, get adjusted down.

Premium coatings and full exit pupil light distribution contribute to greater total light transmission. Well corrected lenses, high polished finish, premium baffels and premium coatings and premium eyepieces contribute to lower scatter and high contrast and better resolution. Transmission, Contrast and Resolution (these are related in various ways) are considered attributes that will have an overall additive or deductive contribution to performance. I have arbitrarily assumed to use a factor for two of these that would either contribute or deduct 10% from the overall index. I used Adler Index (mag x sqrt aperture) as the base.

I would rank the BPI of two different binoculars as such:

Nikon SE 12x50
premium coatings, premium baffles, low scatter, high contrast
lack of aberrations, high resolution, high transmission
Bishop = 12 x 50 = 600
Adler = 12 x sqrt 50 = 85
EdZ BPI = 85 +10% for contrast +10% for transmission = 103

Barska 15x70 - Celestron 15x70 - 2002(1st) version Oberwerk 15x70
less than normal coatings, more scatter, lower contrast,
higher than normal aberrations, lower resolution, lower transmission
Bishop = 15 x 70 = 1050
Adler = 15 x sqrt 70 = 125
EdZ BPI = 125 -(minus)10% for contrast -10% for transmission = 100

this article explains it in detail
This study includes explanations of the influence of magnification vs aperture as relates to point sources, (stars in clusters)
How To Understanding Binocular Performance Indexing - a CN Lab Report by EdZ
The testing and methodology that led to develoment of the BPI