How does a binocular (or telescope) perform in different light conditions? Which targets can be seen, which remain invisible? This is a very fundamental question that has frequently been addressed during the first half of the past century. The twilight index, initially suggested by A. Kuehl in 1929 and subsequently promoted by H. Koehler and R. Leinhos of Zeiss, is a rather simple attempt to approximate binocular performance. It has gained a somewhat questionable reputation, rating e.g. a 12x42 binocular higher than a 8x56 binocular in twilight conditions.
What is less known is the fact that Max Berek, principal optical designer at Ernst Leitz (Wetzlar), has worked out a fully consistent theory of binocular performance during the 1940s. He started with a model of visual target detection , which he successfully combined with the properties of optical instruments to determine the detection thresholds of targets during visual observations .
Because the original work of Berek was written in German language, it gradually got lost in history. I have picked up the loose threads and transferred Berek's model of target detection into a rather versatile numerical formalism. Original data, listed in cumbersome tables, are now replaced with analytically interpolated functions which enable a convenient evaluation on the computer. The formalism is combined with a recent universal formula to estimate the pupil size of the human eye under virtually any condition . I have computed and discussed the performance of various different binoculars in a writeup, which is now published , and may (in slightly modified form) be downloaded here.
 M. Berek, Zum physiologischen Grundgesetz der Wahrnehmung von Lichtreizen, Zs. f. Instrumentenkunde 63, p. 297 (1943)
 M. Berek, Die Nutzleistung binokularer Erdfernrohre, Z. Phys. A 125, p 657 (1949)
 Andrew B. Watson, John I. Yellott, A unified formula for light-adapted pupil size, Journal of Vision 12, p. 1 (2012)
 H. Merlitz, Performance of binoculars: Berek's model of target detection, J. Opt. Soc. Am. A 32, p. 101 (2015)
Last updated: June 2015