Design and fabrication of a diode-side-pumped Nd:YAG laser with a diffusive optical cavity for 500-W output power

A ray-tracing code has been developed, and the design parameters of the laser pump head were analyzed in terms of crystal diameter, doping concentration, and optical cavity diameter. According to the numerical analysis, we fabricated an efficient diode-pumped Nd:YAG laser and experimentally obtained 500-W output power. The output power is close to the numerically calculated output power of approximately 450 W and corresponds to an optical-to-optical conversion efficiency of 46.7% and an optical slope efficiency of 49%.     

Image-quality metrics for characterizing adaptive optics system performance

Adaptive optics system (AOS) performance is a function of the system design, seeing conditions, and light level of the wave-front beacon. It is desirable to optimize the controllable parameters in an AOS to maximize some measure of performance. For this optimization to be useful, it is necessary that a set of image-quality metrics be developed that vary monotonically with the AOS performance under a wide variety of imaging environments. Accordingly, as conditions change, one can be confident that the computed metrics dictate appropriate system settings that will optimize performance. Three such candidate metrics are presented. The first is the Strehl ratio; the second is a novel metric that modifies the Strehl ratio by integration of the modulus of the average system optical transfer function to a noise-effective cutoff frequency at which some specified image spectrum signal-to-noise ratio level is attained; and the third is simply the cutoff frequency just mentioned. It is shown that all three metrics are correlated with the rms error (RMSE) between the measured image and the associated diffraction-limited image. Of these, the Strehl ratio and the modified Strehl ratio exhibit consistently high correlations with the RMSE across a broad range of conditions and system settings. Furthermore, under conditions that yield a constant average system optical transfer function, the modified Strehl ratio can still be used to delineate image quality, whereas the Strehl ratio cannot.     

Effect of telescope alignment on a stellar interferometer

For a ground-based stellar interferometer, we investigate the effect of wave-front distortions that are due to telescope alignment errors and other factors. We apply the results to the IR/Optical Telescope Array (IOTA) interferometer. We present the computational method used in our simulation program to calculate explicitly the wave-front shape from an arbitrarily misaligned telescope. We calculate the wave-front shape and variance for a suite of misalignment conditions and interpret these results to find allowable tolerances on the positions and tilts of the telescope mirrors. We calculate the expected Strehl ratios from a total of ten types of factor, including telescope alignment, that are expected to be important in a real interferometer. Ranking the expected wave-front perturbations, we find that three of them, the wave-front curvature from atmospheric turbulence, the servo system time constant, and the flatness of the relay optics surfaces, are more significant than the telescope alignment factor. We compare observational experience at IOTA with our model estimate of the overall Strehl ratio in the visual and the infrared, finding moderately good agreement and, more important, a guide for future instrumental improvements.     

Strehl ratio and modulation transfer function for segmented mirror telescopes as functions of segment phase error

We derive the Strehl ratio for a segmented mirror telescope as a function of the rms segment phase error and the observing wavelength, with and without the effects of the atmosphere. A simple analytical expression is given for the atmosphere-free case. Although our specific results are in the context of the Keck telescope, they are presented in a way that should be readily adaptable to other segmented geometries. We also derive the corresponding modulation transfer functions. These results are useful in determining how accurately a segmented mirror telescope needs to be phased for a variety of observing applications.     

Nonaxial Strehl ratio of wavefront coding systems with a cubic phase mask

An approximate expression of the peak position of the point-spread function (PSF) of wavefront coding systems with a cubic phase mask (CPM) is derived and verified by simulation results. An approach called the nonaxial Strehl ratio (NASR) is used to evaluate the performance of wavefront coding systems with defocus aberrations. The characteristics of the NASR are investigated. The relationships between the NASR and the similarity of out-of-focus modulation transfer function (MTF) and recoverability of blurred encoding images are presented, and some useful guidelines are given for the optimization of phase mask parameters according to these relationships.     

Tilt angular anisoplanatism and a full-aperture tilt-measurement technique with a laser guide star

A method is presented for sensing atmospheric wave-front tilt from a laser guide star (LGS) by observing a laser beacon with auxiliary telescopes. The analysis is performed with a LGS scatter model and Zernike polynomial expansion of wave-front distortions. It is shown that integration of the LGS image over its angular extent and the position of the auxiliary telescope in an array reduce the tilt sensing error associated with the contribution from the downward path. This allows us to single out only the wave-front tilt of the transmitted beam on the uplink path that corresponds to the tilt for the scientific object. The tilt angular correlation is analyzed in the atmosphere with a finite turbulence outer scale. The tilt correlation angle depends on the angular size of the telescope and the outer scale of turbulence. The tilt sensing error increases with the auxiliary telescope diameter, suggesting that an auxiliary telescope must be small. The Strehl ratio associated with the contribution from the downward path is in the range from 0.1 to 0.9 when the relative telescope diameter D/r(0) varies from 4 to 93 and the turbulence outer scale is in the 10-150-m range. Tilt correction increases the Strehl ratio compared with the uncorrected image for all the system parameters and seeing conditions considered. The method discussed gives a higher performance than the conventional technique, which uses an off-axis natural guide star. A scheme for measuring tilt with a beam projected from a small aperture is described. This scheme allows us to avoid phosphorescence of the main optical train for a sodium LGS.     

Modeling of a Diode-Side-Pumped Nd:YAG Laser

We have developed a unique numerical laser model by use of a commercial physical optics software package. The experimentally measured lasing threshold, slope efficiency, power output distribution, and phase front have been derived. This model is particularly powerful for monitoring the effects caused by thermal distortions encountered in power scaling lasers. Extrapolations have been made through parametric studies to predict changes required in the laser design that would optimize the performance of the laser.     

Continuous radial superresolution filters with large focal depth

A new set of continuous superresolution filters is proposed which exhibits a radial superresolution performance with an extended depth of focus in an optical system by properly choosing the design parameters. Numerical simulation results of the performance parameters of the superresolution gain, the radial central core size, the Strehl ratio, the side-lobe factor and the depth of focus with different design parameters for the optimized patterns are displayed. We also give a design example for this kind of filter characterized by a birefringent element inserted between two parallel polarizers. This kind of filter would be useful in fields such as optical data storage systems.     

Effect of wavefront corrugations on fringe motion in an astronomical interferometer with spatial filters

Numerical simulations of atmospheric turbulence and adaptive optics (AO) wavefront correction are performed to investigate the time scale for fringe motion in optical interferometers with spatial filters. These simulations focus especially on partial AO correction, where only a finite number of Zernike modes are compensated. The fringe motion is found to depend strongly on both the aperture diameter and the level of AO correction used. In all the simulations the coherence time scale for interference fringes is found to decrease dramatically when the Strehl ratio provided by the AO correction is < or = 30%. For AO systems that give perfect compensation of a limited number of Zernike modes, the aperture size that gives the optimum signal for fringe phase tracking is calculated. For AO systems that provide noisy compensation of Zernike modes (but are perfectly piston neutral), the noise properties of the AO system determine the coherence time scale of the fringes when the Strehl ratio is < or = 30%.     

Strehl ratio of a Gaussian beam

We discuss the Strehl ratio of systems with a Gaussian pupil and determine the range of validity of its approximate expression based on the aberration variance. The results given are equally applicable to propagation of Gaussian beams. The uniform and weakly truncated pupils are considered as limiting cases of a Gaussian pupil. We show that the approximate expression for Strehl ratio in terms of the aberration variance yields a good estimate of the true value for a strongly truncated pupil but a much smaller value for a weakly truncated pupil.     

A Study of the Possibility of Image Optimization by Apodization Filters in Optical Systems with Residual Aberrations

A systematic study to optimize the image in real optical systems, by fitting the filter transmission function on the exit pupil to different polynomial types is developed. The systems we have treated, whose residual aberrations are larger than the tolerance values, could be carried to tolerance by the use of an adequate filter, making the Strehl ratio higher than 0·8. The influence of the apodization filter on the optical transfer function is also studied.     

Parallel Ray Tracing Using the Message Passing Interface

Ray-tracing software is available for lens design and for general optical systems modeling. It tends to be designed to run on a single processor and can be very time consuming if the number of rays traced is large. Previously, multiple digital signal processors (DSPs) have been used to perform such simulations. This approach is attractive because DSPs are inexpensive, and the time saved through parallel processing can be significant. In this paper, we report a nearly linear relationship between the number of processors, and the rate of ray tracing with as many as 839 processors operating in parallel on the Naval Research Laboratory's Cray XD-1 computer with the Message Passing Interface (MPI). In going from 1 to 839 processors, we achieved an efficiency of 97.9% and a normalized ray-tracing rate of in a system with 22 planar surfaces, two paraboloid reflectors, and one hyperboloid refractor. The need for a load-balancing software was obviated by the use of a prime number of processors.     

Quality parameters analysis of optical imaging systems with enhanced focal depth using the Wigner distribution function

An analysis of the Strehl ratio and the optical transfer function as imaging quality parameters of optical elements with enhanced focal length is carried out by employing the Wigner distribution function. To this end, we use four different pupil functions: a full circular aperture, a hyper-Gaussian aperture, a quartic phase plate, and a logarithmic phase mask. A comparison is performed between the quality parameters and test images formed by these pupil functions at different defocus distances.     

Spectrometer slit-power-coupling calculations for natural and laser guide-star adaptive optics

We use numerical calculations to examine the relation between adaptive optics (AO) turbulence compensation and power coupled through a spectrometer slit for both laser and natural guide-star AO systems. The AO system and observing parameters used are relevant to the Gemini-North 8-m telescope. For this study, we separate residual tilt from residual higher-order aberrations to isolate their relative effects under a variety of operating conditions. Our results demonstrate that slit-coupled intensity is not uniquely determined by system Strehl alone; we show that this is due to the differing effects of higher-order and tilt aberrations on the shape of the compensated point-spread function. For the Gemini spectrometer and AO system, the wider point-spread function halo associated with an added residual higher-order aberration reduces slit-coupled intensity more rapidly than a broad point-spread function core induced by residual tilt.     

Modeling the combined effect of static and varying phase distortions on the performance of adaptive optical systems

The end-to-end performance achieved by an adaptive optical (AO) imaging system is determined by a combination of the residual time-varying phase distortions associated with atmospheric turbulence and the quasi-static unsensed and uncorrectable aberrations in the optical system itself. Although the effects of these two errors on the time-averaged Strehl ratio and the time-averaged optical transfer function (OTF) of the AO system are not formally separable, such an approximation is found to be accurate to within a few percent for a range of representative residual wave-front errors. In these calculations, we combined static optical system aberrations and time-varying residual phase distortion characteristics of a deformable mirror fitting error, wave-front sensor noise, and anisoplanatism. The static aberrations consist of focus errors of varying magnitudes as well as a combination of unsensed and uncorrectable mirror figure errors derived from modeling by the Gemini 8-Meter Telescopes Project. The overall Strehl ratios and OTF's that are due to the combined effect of these error sources are well approximated as products of separate factors for the static and time-varying aberrations, as long as the overall Strehl ratio that is due to both errors is greater than approximately 0.1. For lower Strehl ratios, the products provide lower bounds on the actual values of the Strehl ratio and the OTF. The speckle transfer function is also well approximated by a product of two functions, but only where AO compensation is sufficiently good that speckle imaging techniques are usually not required.     

Optical design of the wide angle camera for the Rosetta mission

The final optical design of the Wide Angle Camera for the Rosetta mission to the P/Wirtanen comet is described. This camera is an F/5.6 telescope with a rather large 12 degrees x 12 degrees field of view. To satisfy the scientific requirements for spatial resolution, contrast capability, and spectral coverage, a two-mirror, off-axis, and unobstructed optical design, believed to be novel, has been adopted. This configuration has been simulated with a ray-tracing code, showing that theoretically more than 80% of the collimated beam energy falls within a single pixel (20" x 20") over the whole camera field of view and that the possible contrast ratio is smaller than 1/1000. Moreover, this novel optical design is rather simple from a mechanical point of view and is compact and relatively easy to align. All these characteristics make this type of camera rather flexible and also suitable for other space missions with similar performance requirements.     

Optical performance of symmetrical and asymmetrical Y-branch couplers for plastic optical fibers

The excess loss and output optical power ratio of symmetrical and asymmetrical Y-branch couplers for plastic optical fibers (POFs) are studied in this work. A ray-tracing model for the Y-branch coupler is derived to investigate the effect of coupling parameters on its optical performance. The coupling parameters, namely coupling angle, axial displacement, and refractive index of filling medium between the emitting-end and receiving-end POFs, are studied. The simulated and measured results indicate that the coupling efficiency is sensitive to all these coupling parameters. A minimum excess loss of approximately 0.83 dB is observed for the symmetrical Y-branch coupler. It is found that both the excess loss and the output power ratio are increased with the increase of the refractive index of the filling medium and the total coupling angle (α+β) for the asymmetrical Y-branch coupler. The experimental results indicate that the maximum output power ratio P1∶P2 is found to be 3.8∶1 for excess loss of less than 2.8 dB for the asymmetrical Y-branch coupler.     

Coupling of large telescopes and single-mode waveguides: application to stellar interferometry

The coupling between a turbulence-distorted optical beam and a single-mode waveguide is addressed. The coupling efficiency and the coupled phase are derived, both without aberrations and with small aberrations. These analytical expressions are validated by numerical simulations. Correction with adaptive optics is investigated. In the general case, the Strehl ratio is a pessimistic estimator, and the coupled phase is different and has a smaller variance than the classical phase averaged over the pupil. Application fields are heterodyne detection and stellar interferometry, for which spatial and modal filtering are distinguished.     

区域投影声束追踪法及其飞机表面载荷预测

舱内噪声影响乘客乘坐飞机的舒适性,同时噪声是影响民用飞机获得适航证和市场认可的重要因素之一。在飞机低噪声设计开发中,机体表面高频声载荷的数值预测方法起着至关重要的作用。使用区域投影声束追踪法进行飞机表面的声载荷预测可以解决经典几何声学方法在大空间下计算的不适应性。经典声线追踪法对不同空间下的声线接收域有着严格的要求,文章将飞机模型的单元网格作为模型的单个接收域,将接收域向声源包络面上投影确定接收域应该接收的声能量密度,通过与经典算法在标准模型下的计算结果对比,定量分析了改进方法与经典方法在计算结果与计算效率上的优劣;通过对比商业软件的声线法模块在飞机模型下的计算结果,验证了改进计算方法计算结果的准确性。     

Image degradation due to surface scatter in the presence of aberrations

Image analysis in the presence of surface scatter due to residual optical fabrication errors is often perceived to be complicated, nonintuitive, and achieved only by computationally intensive nonsequential ray tracing with commercial optical analysis codes such as ASAP, Zemax, Code V, TracePro, or FRED. However, we show that surface scatter can be treated very similarly to conventional wavefront aberrations. For multielement imaging systems degraded by both surface scatter and aberrations, the composite point spread function is obtained in explicit analytic form in terms of convolutions of the geometrical point spread function and scaled bidirectional scattering distribution functions of the individual surfaces of the imaging system. The approximations and assumptions in this formulation are discussed, and the result is compared to the irradiance distribution obtained using commercial software for the case of a two-mirror telescope operating at an extreme ultraviolet wavelength. The two results are virtually identical.