First-order statistics of Jacobi elliptic functions having random phase with an application to holography
- 1 January 1984
- journal article
- Published by AIP Publishing in Journal of Applied Physics
- Vol. 55 (1) , 1-3
- https://doi.org/10.1063/1.332865
Abstract
The first-order statistics (probability density function, characteristic function, probability of exceeding a specified value, first two moments) of the Jacobi elliptic functions cn(θ,k) and sn(θ,k) are evaluated when θ is a random variable uniformly distributed over the period T=4K(k). The resultant expressions reduced to those of the corresponding trignometric functions cos θ and sin θ as k→0. An application of the formal results is made to the holography of vibrating surfaces.This publication has 5 references indexed in Scilit:
- Time-average hologram interferometry of periodic, non-cosinusoidal vibrationsApplied Physics A, 1975
- Characteristic Fringe Function for Time-Average Holography of Periodic Nonsinusoidal VibrationsApplied Optics, 1975
- Hologram Interferometry of Nonsinusoidal Vibrations Analyzed by Density FunctionsJournal of the Optical Society of America, 1971
- Interferometric Vibration Analysis by Wavefront ReconstructionJournal of the Optical Society of America, 1965
- Interferometric Hologram Evaluation and Real-Time Vibration Analysis of Diffuse ObjectsJournal of the Optical Society of America, 1965