An analytic function of the two-dimensional probabilities of perception of the human eyes

The probability of perception is an indispensable quantity in the visual observation of meteors. Based on the data of a large number of double-counting observations, Koschack and Rendtel derived a table-listed average perception function P(Δm) in 1990 and Wu gave it a fitting analytic function in 2005. In this paper, a fitting of the perception function in the two-dimensional field of view, P(Δm,R), is given. Both the new analytic function and each order of its derivatives have only a monodromy and are very smooth. This analytic function will be more essential and useful than the average function P(Δm) and may be connected to the two-dimensional structure of the human eyes as an imaging system.