Strehl Number Research Articles

Adaptive system for correcting optical aberrations of high-power lasers with dynamic determination of the reference wavefront

We present the results of the aberration correction of laser radiation wavefront using a dynamic method for determining the reference wavefront. The method, which is based on the processing of synchronously obtained data on the near- and far-field zones, significantly improves the focusing quality with active wavefront correction, especially under conditions of dynamic aberrations. An increase in the Strehl number S from 0.7 to 0.86 is demonstrated when a beam 18 cm in diameter is focused by an F/2.5 parabolic mirror.

Pulse energy limitation of high-power nanosecond lasers due to plasma production in spatial filters

For a neodymium glass laser, which is used to pump the parametric amplifier of the PEARL facility, we investigate the problem of filling the pinholes of vacuum spatial filters with plasma resulting from the ablation of the pinhole surface by laser radiation. The time of plasma expansion is measured and the causes of its appearance are determined, among which the main ones are the spherical aberrations of the lenses of spatial filters, which increase the intensity at the pinhole edges. With the total spherical aberration of the spatial filters, which lowers the Strehl number to 0.15, two nanosecond pulses with energies of 130 – 140 J, delayed relative to each other by 1.8 ns and freely passing through the final spatial filter, are generated on the PEARL facility.

Dynamic phasing of multichannel cw laser radiation by means of a stochastic gradient algorithm

The phasing of a multichannel laser beam by means of an iterative stochastic parallel gradient (SPG) algorithm has been numerically and experimentally investigated. The operation of the SPG algorithm is simulated, the acceptable range of amplitudes of probe phase shifts is found, and the algorithm parameters at which the desired Strehl number can be obtained with a minimum number of iterations are determined. An experimental bench with phase modulators based on lithium niobate, which are controlled by a multichannel electronic unit with a real-time microcontroller, has been designed. Phasing of laser beams at a system response bandwidth of and phase thermal distortions in a frequency band of about is experimentally demonstrated. The experimental data are in complete agreement with the calculation results.

Morphing of Segmented Bimorph Mirrors

Atmospheric turbulence compensation for the next generation of terrestrial telescopes (30–40 m diameter) will require deformable mirrors of increasing size and a number of actuators reaching several thousands. However, the mere extrapolation of existing designs leads to complicated and extremely expensive mirrors. This article discusses an alternative solution based on the use of segmented identical hexagonal bimorph mirrors. This allows to indefinitely increase the degree of correction while maintaining the first mechanical resonance at the level of a single segment, and shows an increase in price only proportional to the number of segments. Extensive simulations using random turbulent screens show that the segmentation produces only moderate reductions of the Strehl number, compared to a monolithic bimorph mirror with the same number of actuators (S = 0.86 instead of S = 0.89 in this study).

The possibility of compensating small-scale wavefront distortions with a Zernike cell and a spatial light modulator in an optical feedback scheme

The possibility of compensating small-scale wavefront distortions in an optical feedback scheme by using a spatial light modulator optically addressed by the output beam of a Zernike cell is theoretically considered. The optimal parameters of the system for compensating sinusoidal distortions and distortions characteristic of phasing of subapertures, the requirements for the elements of the system, the range of compensated distortions, and the quality of compensation are determined. It is shown that the use of this method makes it possible to compensate small-scale phase distortions with a peak-to-peak amplitude of up to 3λ; in this case, the gain in the Strehl number can be as high as 80.

Efficiency of the unstable resonator of a high-power laser with stochastic phase inhomogeneities in the active medium

The specific features of operation of the unstable optical resonator of a large gas laser with an active medium containing stochastic phase inhomogeneities are considered. The output power of the laser, the Strehl number, the angular divergence and average far-field radiation intensity are studied as functions of the spatial scale and structure of random inhomogeneities of the refractive index of the active medium. Physical effects related to the deformation of the radiation pattern caused by a change in the spatial frequency of stochastic perturbations are analysed.

On the possibility of compensating for small-scale wave-front distortions using a Zernicke cell and an optically controlled spatial light modulator

The possibility of compensating for small-scale wave-front distortions using a spatial light modulator which is optically controlled by the output beam of a Zernicke interferometer was studied theoretically. The optimal parameters of the system, requirements of its elements, the range of the compensated distortions, and the compensation quality are determined for the case of compensation for sinusoidal distortions. It is shown that this technique allows for the compensation of small-scale sinusoidal phase distortions with a depth of up to 3λ and a 20-fold gain in the Strehl number can be achieved.

Optimization of pulsed-periodic neodymium glass lasers

Results of an investigation aimed at improving the efficiency of pulsed-periodic neodymium glass lasers are presented. The choice of the efficiency criterion of the laser system as the product of the radiation power and the Strehl number made it possible to formulate and substantiate several practical recommendations on the choice of optimum operating-mode—structure parameters of a pulsed-periodic laser.

Energy and gasdynamic characteristics of a supersonic cw chemical HF laser with a radial-expansion nozzle array

An experimental investigation was made of the energy and gasdynamic characteristics of a supersonic cw chemical HF laser with a radial-expansion nozzle array of 35 cm × 10 cm dimensions. A nozzle—sonic injector configuration was used for reactant mixing. A specific output energy of 254 J g-1 and an absolute laser radiation power of 33.5 kW were reached. The distributions of the Mach number, of the static pressure, and of the total pressure behind a plane shock wave in the flowing active medium were measured in wide ranges of the pressure in an atomic-fluorine generator and of secondary fuel (hydrogen) flow rates. The optical quality of the active medium, characterised by the Strehl number St=0.53, was estimated. The advantages and shortcomings of a laser with a proposed nozzle array configuration were identified. Future investigations were outlined.

Analysis of the spatial scales of optical inhomogeneities in active media of high-power gas-flow laser amplifiers

A harmonic analysis was made of the spatial scales of regular optical inhomogeneities in high-power laser amplifiers with a continuously flowing active medium. The wavefronts of the probe radiation reconstructed by interferometry made it possible to determine the distribution of the Strehl number over the spatial scales of inhomogeneities in the active medium of a cw chemical laser. The greatest contribution to the overall level of optical distortions in this laser came from a large-scale inhomogeneity, whereas small-scale periodic perturbations of the phase had practically no influence on the divergence of the output radiation, because their amplitude did not exceed the permissible limit (1 rad).

Optical homogeneity of the active media of cw chemical HF(DF) lasers

The optical homogeneity of the active media of cw chemical lasers was investigated by interferometry. A study was made of how the optical quality of the active media was influenced by the characteristics of various configurations of nozzle arrays (classical nozzle—nozzle configuration, configurations with discrete supply of the secondary fuel to the supersonic channel, and those with radial expansion or with a honeycomb structure). The dependences of the integral optical homogeneity criterion, the Strehl number, on the main operational parameters of a laser were determined. The optical homogeneity of the active medium was reduced by intensification of the processes which improved the operational parameters.

Calculation of the quality characteristics of adaptive laser systems with phase correction

Approximate expressions are obtained for calculating the main quality characteristics of adaptive systems used in focusing of laser radiation accompanied by phase correction: these characteristics are the average value of the Strehl number and the relative variance of fluctuations of this number. The example of a system with compensation of the average tilt of the phase front is used in estimating the error in the proposed approximations. The general case of different sizes of the measuring and light-emitting apertures is discussed.

Thermal self-interaction of laser radiation in a KrF laser

A theoretical study was made of the spatial and temporal development of small-scale nonlinear optical inhomogeneities in KrF lasers. The dynamics of the heating of the active medium was investigated as a function of the laser radiation intensity. The nonlinear phase shift and the Strehl number were estimated in the constant-intensity approximation. An analysis was made of the stability of the laser beam against small perturbations of its transverse profile. The growth rates of the scattered radiation and the decay integrals were calculated.

Compensation for small-scale phase distortions using a Fourier phase corrector

It is demonstrated experimentally that efficient compensation for small-scale phase distortions of a CO2 laser waverfront can be achieved by using a Zernike cell type of wavefront-reversal system. After passing twice through the phase plate the Strehl number of the beam increases from 0.43 to 0.86 due to the compensation. The main factors determining the quality of the compensation for the distortions are discussed.

Problem of the quality of wavefront correction in adaptive systems

An analytic expression is obtained for an adaptive system controlled by the shift and slope of subapertures. This expression can be used to calculate the Strehl number K allowing for atmospheric distortions of the phase and for the position and angular errors in subaperture setting. The range of validity of this expression is 0.5 ≤ K ≤ 1.

Quality of wavefront correction in adaptive transmitting systems

Simple analytical formulas are obtained for the Strehl number for the case of correction of the phase front of a wave distorted in the atmosphere and incident on an object. A comparison is made of the quality of two types of correction in which the separate segments of a transmitting system are controlled either in respect of displacement or in respect of displacement and inclination.

Influence of microinclusions in glasses on the operation of optical systems transforming laser beams

An analysis is made of the influence of microinclusions on the normalized intensity at a diffraction focus (Strehl number) of an optical system made of glass. It is shown that large microinclusions reduce the Strehl number by no more than 10%.

Strehl number degradation by large-scale systematic surface deviations

Experience shows that optical and radio reflector surfaces may have systematic residual deviations to which the statistical analysis is not necessarily applicable. For large-scale systematic deviations we derive a general expression for calculating the degraded on-axis intensity, i.e., the Strehl number. For this type of deviation we introduce a quasi-rms value, which has the same optical significance as the rms value of random surface deviations. Numerical examples of realistic cases are presented.

Determination of the optimal reference sphere

It has been shown that there exists one reference sphere with respect to which the Strehl number attains a maximal value and the mean square of the wave aberration reaches a minimum. This theorem is valid for small aberrations (≤ λ/4).

Achromatic Schmidt corrector plates

Two types of achromatic Schmidt corrector plate are described; both give an on-axis Strehl number S ⪆ 0.8 over an extended wavelength region. It is found that this specification can only be achieved by combining a positive and a negative plate and by restricting the speed ratio D/N 3 of the system. The theory is illustrated by numerical examples.