A novel wave-front sensor that estimates phase from Fourier intensity measurements is described, and an explicit expression is found and numerically evaluated for the Cramtr-Rao lower bound on integrated rms wave-front phase estimation error. For comparison, turbulence-aberrated wave-front phases and corresponding noisy Fourier intensity measurements were computer simulated. An iterative phase-retrieval algorithm was then used to estimate the phase from the Fourier intensity measurements and knowledge of the shape of an aperture through which the wave front passed. The simulation error approaches the lower bound asymptotically as the noise is reduced.
Wavefront sensors that can operate at low light levels, be built from present technology components, and provide accurate wavefront phase estimates in real -time are required for use with adaptive optics systems. The use of estimation theory makes possible the evaluation of wavefront sensors without specification of the wavefront phase estimation algorithms.The Cramer -Rao method was used to find a lower bound on integrated rms wavefront sensor estimation error.In addition to an analysis of the general case, the error lower bound was numerically evaluated for the shearing interferometer wavefront sensor. Computer simulations of the atmosphere and wavefront sensor measurements including noise were performed.Using an appropriate algorithm, the phase was estimated and the resulting phase error was compared with the lower bound.The results support the validity of using the Cramer -Rao lower bound to evaluate wavefront sensor performance.
Fundamental performance limitations of a phase-lock control loop used to coherently combine the output of two lasers are presented. The phase-lock loop is designed to lock the differential phase (frequency and phase) between the two lasers to a specified reference phase. An optical heterodyne configuration is used to determine the differential phase of the laser pair, which in turn is compared with the reference phase to create an error voltage. The error voltage is filtered and used to frequency modulate one of the lasers in an attempt to null the error. An integro-differential loop equation, valid for the linear operating range, is derived in terms of the reference phase, the heterodyne measurement noise, and the various laser phase instabilities. The solution of the equation results in an expression for the phase error variance in terms of the closed-loop noise equivalent bandwidth W(H). An expression for the value of W(H) which minimizes the phase error variance is developed. In addition to the noise effects, the steady-state and dynamic performance of the loop is examined for different loop filters and modulation formats. A design example pairing a CO(2) waveguide and conventional laser is presented. Implications for coherent laser arrays are discussed.
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