Adaptive optics for in-orbit aberration correction: spherical aberration feasibility study

We investigate the feasibility of using an adaptive mirror for in-orbit aberration corrections. The advantage of an in situ aberration correction of optical components in the space environment is that the mirror shape can be adjusted in an iterative fashion until the best image is obtained. Using the actuator spacing, corresponding to one half of the Nyquist frequency, the Strehl ratio of the corrected wave front improves to 0.95 when the mirror is fabricated with 6.5 waves of spherical aberration. The Strehl ratio decreases to 0.86 when the number of actuators is reduced by a factor of 4, in a two-dimensional adaptive optics model.     

Holographic optical elements in the presence of spherical aberration and focus error: Some remarks on imaging quality

Abstract

When aberrations are small, it is possible to use wave aberration variance to obtain the position of the best image plane in both conventional and holographic optical systems. However, when aberrations increase, this measurement is not sufficient and it does not provide the correct plane position for the best image. In this paper, two alternative methods for evaluating image quality in spherically aberrated on-axis holographic lenses are compared. These two methods are the standard deviation of the distribution of light intensity and entropy. Both methods are based on the calculation of the diffraction integral and the subsequent analysis of the distribution of light intensity as a probability density function for each image plane being analysed. Even though the results obtained with both methods are identical when aberrations are small, only entropy provides the best image when the value of these aberrations increases.     

Effective spherical aberration compensation by use of a nematic liquid-crystal device

The next generation of optical data storage system beyond DVDs will use blue laser light and an objective lens with a high numerical aperture of 0.85 to increase storage capacity. Such high numerical aperture systems have an inherent higher sensitivity to aberrations. In particular, the spherical aberration caused by cover layer thickness tolerances and--more obvious--by dual-layer disks with a typical separation of approximately 20 microm between the two layers must be compensated. We propose a novel transmissive nematic liquid-crystal device, which is capable of compensating spherical aberration that occurs during the operation of optical pickup systems.     

A multislice approach to the spherical aberration theory in electron optics

Abstract

A multislice, wave-optical approach to the spherical aberration theory in electron optics is presented for the case of magnetic lenses. It is shown that, in order to remedy the inadequacy of a naive attempt carried out by taking the standard multislice equations and simply adding the fourth order terms in the transverse coordinates in the phase both of the transmission function and of the propagation kernel, it is necessary to approximate the Schrödinger equation by a wide-angle differential equation of the parabolic type and to solve it by means of a marching type algorithm. It turns out that the solution can be separated into two parts, describing, as in the multislice method, the interaction of the incoming spherically aberrated axial wavefunction with the field in a slice, and the propagation in a drift space. When the propagation is evaluated by means of the stationary phase method, a differential equation is obtained for the spherical aberration coefficient, whose solution is identical to that obtained by Glaser in his particle approach based on the eikonal.     

Combined amplitude and phase filters for increased tolerance to spherical aberration

Abstract

Analysis of the expression for Strehl ratio for a circularly symmetric pupil allows one to design complex filters that offer reduced sensitivity to spherical aberration. It is shown that filters that combine hyper-Gaussian amplitude transmittance with hyper-Gaussian phase modulation provide five-fold reduction in sensitivity to spherical aberration. Furthermore, this is achieved without the introduction of zeros into the modulation transfer function and deconvolution can restore the transfer function to that of a diffraction-limited imager. The performance of the derived combined amplitude and phase filter is illustrated through the variation of its axial intensity versus spherical aberration. This technique is applicable to imaging in the presence of significant amounts of spherical aberration as is encountered in, for example, microscopy.     

High tolerance to spherical aberrations and defects of focus with a birefringent lens

We report a systematic investigation of the imaging behavior of an optical system consisting of a lens from a uniaxial birefringent crystal sandwiched between two linear polarizers into which primary spherical aberration has been introduced. The proposed system has higher tolerance to primary spherical aberration and has a larger depth of focus than an imaging system found with an isotropic lens. Some specific cases are computed and illustrated graphically.     

Effect of primary spherical aberration on high-numerical-aperture focusing of a Laguerre-Gaussian beam

Effect of primary spherical aberration on the tight focusing of linearly and circularly polarized Laguerre-Gaussian (LG) beams is studied by using the vectorial Debye integral. Results are presented for the intensity distribution and square of the polarization components. In the case of the linearly polarized LG beam with unit and double topological charge, the presence of aberration reduces the residual intensity at the focal point and spreads the sidelobes. If the beam is circularly polarized, the aberration results in an increase in the size of the dark core along with a reduction in the intensity at the periphery of the bright ring. The effect of aberration is also discussed in the context of the fluorescent spot size in the focal plane of a stimulated-emission-depletion microscope.     

Anisotropy in the aberration constant due to galactic rotation

It is shown that in the near future it will be possible to detect the dependence of the aberration constant on the direction to a star caused by our secular rotation. The corresponding corrections to the visible stellar positions will increase the accuracy in determining the Earth's rotation parameters by astro-optical means. Traslated from Izmeritel'naya Tekhnika, No. 3 pp. 12–13, March, 1994.     

Spherical gradient-index polymer lens with low spherical aberration

A sphere lens with a spherical gradient index (GRIN) was prepared by the modified suspension polymerization technique. GRIN spheres with quadratic- and linear-index distributions were obtained by two different methods to confirm the effect of the GRIN profile on the focusing property of the sphere lens. It was confirmed in both theory and experiment that the spherical aberration of such GRIN spheres was remarkably decreased compared with that of a homogeneous sphere.     

Correcting ocular spherical aberration with soft contact lenses

Following aberroscopy, aspheric front surface soft contact lenses (SCLs) were custom-made to correct spherical refractive error and ocular spherical aberration (SA) of 18 myopic and five hypermetropic subjects (age, 20.5 +/- 5 yr). On-eye residual aberrations, logMAR visual acuity, and contrast sensitivity were compared with the best-correcting spectacle lens, an equally powered standard SCL, and an SCL designed to be aberration free in air. Custom-made and spherical SCLs reduced SA (p < 0.001; p < 0.05) but did not change total root-mean-square (rms) wave-front aberration (WFA). Aberration-free SCLs increased SA (p < 0.05), coma (p < 0.05), and total rms WFA. Visual acuity remained unchanged with any of the SCL types compared with the spectacle lens correction. Contrast sensitivity at 6 cycles/degree improved with the custom-made SCLs (p < 0.05). Increased coma with aspheric lens designs and uncorrected astigmatism limit the small possible visual benefit from correcting ocular SA with SCLs.     

Helicoid modal analysis of laser oscillators with spherical aberration

A technique for the modal decomposition of laser beams allows an analysis of laser oscillators perturbed by rod spherical aberration. Beam quality can be degraded or improved, depending on whether the beam scale increases or decreases with lens power. Efficient power extraction is problematic, however.     

Delamination and matrix cracking of cross-ply laminates due to a spherical indenter

An investigation was performed to study delamination growth induced by matrix cracks in cross-ply composites resulting from a spherical indenter. The major focus of the study was to understand fundamentally the damage mechanics in terms of matrix cracking and delamination growth, and interaction between them. A nonlinear three-dimensional finite element model based on an updated Lagrange formulation was developed during the investigation. An augmented Lagrangian method was utilized to model the delamination interface condition. A general contact node search algorithm was proposed which can handle complex contact conditions, such as arbitrary slippage and discontinuous curvature. The indentation resulting from the spherical rigid indenter was also modeled. Fracture mechanics was applied to determine the delamination propagation in three dimensions. The strain energy release rates were calculated by a crack-closure technique. The model was verified analytically and experimentally.     

Characterization of trapping force in the presence of spherical aberration

Abstract

Transverse trapping force in laser tweezers is investigated in the presence of spherical aberration caused by the refractive-index mismatch between a cover slip and the water solution where particles are suspended. The transverse trapping efficiency is characterized in terms of the numerical aperture of a microscope objective and the thickness of a sample cell. It has been experimentally demonstrated that the spherical aberration can be compensated for by changing the effective tube length of an objective used for trapping. As a result, the transverse trapping efficiency can be improved by up to 20%. In principle, a further improvement in the trapping efficiency is possible if an objective of an infinitely-long tube length is used.     

Effects of index-mismatch-induced spherical aberration in pump--probe microscopic image formation

Pump--probe fluorescence microscopy has been demonstrated to be a powerful tool for obtaining three-dimensional, time-resolved information in bioimaging applications. However, the use of this technique can be complicated by the fact that the different wavelengths used to achieve pump--probe microscopy can result in wavelength-dependent spherical aberration, thus limiting the usefulness of the technique. We address this issue by investigating the effects of refractive-index-mismatch-induced spherical aberration on pump--probe image formation. We model the effects by considering pump--probe imaging performed with an objective with a numerical aperture of 0.75 focusing through an oil-water interface. Our results show that spherical aberration has the greatest effect in degrading an axial point-spread function. In addition to signal loss, the redistribution of signal strength along the axial direction results in broadening of the FWHM of the plane response function. The inclusion of confocal detection tends to improve image resolution but at a significant loss of signal strength.     

Normalized parameter relating the spherical aberration of a thin lens to the diffraction limit and fiber coupling efficiency

In this paper, we calculate the transverse spherical aberration TA of a thin lens and defines a normalized aberration Y equal to TA divided by the theoretical resolution limit. As a rule of thumb, (a) a thin lens that suffers only from spherical aberration may be considered effectively diffraction-limited as long as Y < 1.6. Similarly, (b) the coupling efficiency of a Gaussian beam to a single-mode fiber may be high even when Y > 1.6, and, specifically, (c) the lens need be diffraction-limited only over a radius approximately equal to the radius (to the 1/e-point) of the Gaussian beam.     

Axial intensity distribution of partially coherent light focused by a lens with spherical aberration

Abstract

The focusing of partially coherent light by a lens with spherical aberration (SA) is studied. The numerical calculation results are given, showing that the axial intensity distribution not only depends on the SA, but also on the coherence of partially coherent light and the Fresnel number of the lens. As the coherence decreases, the influence of the SA on the axial intensity distribution decreases, and the positions of maximum axial intensity shift towards the lens.