Jan Herrmann

Least-squares wave front errors of minimum norm

Requirements for adaptive optics and compensating imaging systems lead to wave front reconstruction problems which we formulate as generalized least-squares problems. For a given array of phase-difference measurements, we construct explicit and exact solutions for the least-squares wave front error. Of particular interest are solutions with minimum norm. Two different discretizations for the gradient are used and the reasons for the different results are given.

Cross coupling and aliasing in modal wave-front estimation

A systematic treatment of modal estimation of a wave-front phase from its gradients is given. We introduce a gradient matrix and use it to describe cross coupling of aberrations (lack of orthogonality of its column vectors) and aliasing of aberrations (lack of linear independence of its column vectors).

ATMOSPHERIC-COMPENSATION EXPERIMENTS IN STRONG-SCINTILLATION CONDITIONS

Most atmospheric-turbulence-compensation experiments have been performed under weak-scintillation conditions; conventional phase-conjugate adaptive-optics systems usually provide good correction for these conditions. We have performed an experiment over a 5.5-km horizontal propagation path to explore the efficacy of conventional adaptive optics in strong-scintillation conditions. The experimental results showed a significant degradation in correction as the scintillation increased. The presence of branch points in the phase appears to be the primary reason for the degradation in correction as the scintillation increases.

Phase Compensation for Thermal Blooming

Appropriate correction of the initial phase of a laser beam is shown by numerical computation to be capable of appreciably reducing thermal blooming for a cw beam.

Dynamics and Energetics of the Explosive Vaporization of Fog Droplets by a 10.6-μm Laser Pulse

The explosive vaporization of individual water droplets (5 microm to 25 microm radius) by a 10.6-microm laser pulse has been observed with a high speed schlieren photography system. The hot vapor and the shock wave produced by the explosive vaporization can be clearly seen in the schlieren photographs. The expansion rate of the heated air mass has been measured. Factors affecting the shape of the volume of heated air are discussed, and the energy balance of the process is considered.

Atmospheric-turbulence measurements using a synthetic beacon in the mesospheric sodium layer

We have performed what are, to our knowledge, the first measurements of wave fronts propagated through atmospheric turbulence with the use of a synthetic beacon in the mesospheric sodium layer. The synthetic-beacon wave fronts showed reasonable agreement with those from reference stars. The sodium-layer beacon performance was also compared with that of beacons produced by Rayleigh backscatter in the 6-20-km altitude range.

Properties of phase conjugate adaptive optical systems

The phase conjugate COAT (coherent optical adaptive technique) is investigated for thin, nonlinear lenses, simulating thermal blooming. The iteration scheme applied has convergent and divergent regimes.

Phase variance and Strehl ratio in adaptive optics

Some correction schemes in adaptive optics are performed with the use of the phase reconstructed from measured gradients. For these cases it can be shown that the minimum phase-variance estimator leads to the maximum Strehl ratio, that is, to the maximum peak intensity in the far field.

Aberrations of the perfect grating rhomb

The aberrations caused by a perfect grating rhomb beam sampler are calculated for a diverging beam. In the geometric optics limit a tilt does not appear, whereas astigmatism and higher-order aberrations are introduced by a perfect grating rhomb.

Optimal Control In Adaptive Optics Modeling Of Nonlinear Systems

The problem of using an adaptive optics system to correct for nonlinear effects like thermal blooming is addressed using a model containing nonlinear lenses through which Gaussian beams are propagated. The best correction of this nonlinear system can be formulated as a deterministic open loop optimal control problem. This treatment gives us a limit for the best possible correction. Aspects of adaptive control and servo systems are not included at this stage. We ask for that control in the transmitter plane which minimizes the time averaged area or maximizes the fluence in the target plane. The standard minimization procedure leads to a two-point-boundary-value problem, which is ill-conditioned in our case. We were able to solve the optimal control problem using an iterative gradient technique. An instantaneous correction is introduced and compared with the optimal correction. The results of our calculations show that for short times or weak nonlinearities the instantaneous correction is close to the optimal correction, but that for long times and strong nonlinearities a large difference develops between the two types of correction. For these cases the steady state correction becomes better than the instantaneous correction and approaches the optimum correction.