In a prior thread, I said I would not respond further, but I changed my mind. Opticsmike appears to be into computer graphics. The following link will offer you insight into his model, and the problems with it:

http://www.cg.tuwien.ac.at/research/theses/matkovic/node17.html

**koshkin wrote:**
His calculations seem to be fairly accurate (but) I have only looked at the calculations briefly .....()it seems to be an improvement on the existing measures that some people use ("twilight factor", etc) by taking the size of your eye pupil into account. ..... When I have a little more time I'll look into it in more detail.ILya |

While my wife was having eye surgery yesterday, I had time to look at a couple of examples of the calculations. The first problem that caught my eye was that Opticsmike has optical gain (and therefore perceived brightness) increasing as magnification increases, which is not correct.

Increasing magnification makes the image get dimmer, not brighter. Depending upon your experience with zoom lenses, it is an easy mistake to make. I, too, sometimes make it.

As an aside, zoom lenses can be used as beam expanders for lasers. If you use the largest diameter as a reference, when the laser beam is made smaller, its intensity increases. It is why I sometimes make the mistake, and I will guess it is why Koshkin did not catch it.

Opticsmike defines the variables in his equations as follows:

Theoretical Exit Pupil Intensity Gain = square of the Obj lens diameter divided by the square of the exit pupil diameter. TG = (Od^2/EP^2)

Realistic Exit Pupil Gain = Theoretical Gain X Transmission Factor. RG = (TG x T fct)

Perceived Brightness = cube root of Realistic Gain. PB =(RG)^1/3

Low Light Performance = the square root of the product of Perceived Brightness and Magnification.

LLP = [(RG)^1/3 x Mag]^1/2

The cube root (1/3 power) he uses appears to come from the Stevens work that relates to computer graphics that I don't accept to be true or appropriate for our application. But it is like talking to a liberal; you sometimes have to accept half-truths to discuss something.

I have purposefully omitted the definitons of Theoertical Light Gain and Realistic Light Gain because we cannot measure Luminance with our eyes. In any event, (more half-truth stuff) in those cases where the exit pupil is larger than our eye pupil, he has Light Gain as identical to Exit Pupil Gain.

When we substitute for the variables in his equation and expand it into terms we can readily identify with, we find that

LLP Index = [{(Od/EP)^2 X Trans factor}^1/3 x Mag]^1/2

Remember that the ratio of the obj lens diam to the exit pupil diam is one way to express magnification. While not technically true, it is either identical or often very close. If we substitue magnification for the ratio (Od/EP), we get:

LLP Index = [{Mag^2 x Trans Fact}^1/3 x Mag]^1/2

You can get his LLP index by using this simple formula when the exit pupil is larger than the eye pupil. In other words, Opticsmike would have you believe that the low light performance of a scope is all about magnification. It is easy to prove that isn't true.

For all its faults, the twilight factor is much more reasonable.