The focusing characteristics of long-distance flying optics were studied systemically for TEM_(mn) Gaussian beams. The results show that the ABCD law of parameter q can be extended to Gaussian modes of any order when waist radius w in the imaginary part of parameter q is replaced by Rayleigh range Z_(R) of a certain resonator in the equation. The difference between the real focal length and the geometric focal length, defined as (DELTA)f, was calculated for laser applications. A novel self-adaptive optical system was demonstrated for precisely controlling the focusing characteristics of long-distance flying optics. Theoretical analyses and experimental results were consistent.
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