Compact description of substrate-related aberrations in high numerical-aperture optical disk readout

Optical disks are read out by focusing a beam of high numerical aperture (NA) through the substrate. Deviations of the thickness from the nominal value result in spherical aberration; tilting the substrate results in coma. Exact analytical expressions for the rms aberration per micrometer thickness mismatch (for spherical aberration) and per degree tilt (for coma) are derived. The paraxial estimates for these sensitivities proportional to NA4 (spherical aberration) and NA3 (coma) underestimate the exact values by a factor of approximately 2 for the value NA = 0.85, corresponding to the new Blu-ray disk format. Expansion of the aberration function in Zernike aberrations shows that the exact aberration functions are well described by the lowest-order Zernike spherical aberration (A40) and coma (A31) term for all but the very highest NA values.     

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.     

Reduction of the spherical aberration effect in high-numerical-aperture optical scanning instruments

In modern high-numerical-aperture (NA) optical scanning instruments, such as scanning microscopes, optical data storage systems, or laser trapping technology, the beam emerging from the high-NA objective focuses deeply through an interface between two media of different refractive index. Such a refractive index mismatch introduces an important amount of spherical aberration, which increases dynamically when scanning at increasing depths. This effect strongly degrades the instrument performance. Although in the past few years many different techniques have been reported to reduce the spherical aberration effect, no optimum solution has been found. Here we concentrate on a technique whose main feature is its simplicity. We refer to the use of purely absorbing beam-shaping elements, which with a minimum modification of optical architecture will allow a significant reduction of the spherical aberration effect. Specifically, we will show that an adequately designed reversed-Gaussian aperture permits the production of a focal spot whose form changes very slowly with the spherical aberration.     

Evaluation of microlens properties in the presence of high spherical aberration

Microlenses can be generated with various fabrication technologies. Some of these technologies cause large spherical aberrations in the resulting microlenses. We describe an algorithm based on Rayleigh's quarter-wave criterion, which allows the evaluation of lens parameters for those microlenses. Specifically, we investigate numerical aperture, focal length, and space-bandwidth product with respect to applications in optical microsystems. We apply our algorithm to different types of microlenses, three gradient-index lenses, and one surface-relief lens. The experimental results demonstrate that our algorithm provides a helpful characterization method for microlenses with large aberrations.     

Effect of compensation for spherical aberration on the transverse displacement of laser speckle patterns

When a rough surface illuminated by coherent light is displaced perpendicularly to the optical axis of an imaging optical system the speckle pattern in the conjugate plane is transversally displaced too. This displacement has two components. The first one is proportional to the object displacement, and the second one depends on wave-front aberrations and, consequently, is strongly related to the optical system that is used. Usually, well-corrected photographic objectives are used for the measurement of transverse displacements by double-exposure laser speckle photography. Since in well-corrected objectives aberrations tend to compensate one another, it seems that the complementary displacement of the speckle pattern, caused by aberrations, is near zero and does not affect the accuracy of the measurement. Here it is analytically shown that the compensation of spherical aberrations does not guarantee a negligible complementary displacement. From the results obtained it follows that well-corrected objectives for laser speckle photography can be regarded as a particular class of photographic objectives, since they not only yield high-quality images but also minimize complementary displacement.     

Asymptotic behavior of the spatial frequency response of an optical system with defocus and spherical aberration

Asymptotic expressions are derived for the two-dimensional incoherent optical transfer function (OTF) of an optical system with defocus and spherical aberration. The two-dimensional stationary phase method is used to evaluate the aberrated OTF at large and moderately large defocus and spherical aberration. For small aberrations, the OTF is approximated by a power series in the aberration coefficients. An accurate approximation (in elementary functions) to the OTF is obtained for a defocused optical system with a circular pupil. We experimentally demonstrate the validity of the OTF approximations in sharp-focus image restoration from two defocused images. A digital focusing method is presented.     

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.     

A readout scheme providing high spatial resolution for distributed fluorescent sensors on optical fibers

Optical fiber sensors using fluorescent probes distributed along the fiber cladding are of great interest for monitoring physical and chemical properties in their environment. The location of an emitting fluorophore along a fiber can be determined by measuring the time delay between a short, exciting laser pulse propagating in the fiber core and the returning fluorescence pulse. However, fluorescence lifetimes limit the spatial resolution, since a minimum separation of the fluorophores is required to resolve returning light pulses. For many applications, a closer spacing of sensor regions is desirable. We present a new method for the readout of closely packed fluorescent chemosensors located in the cladding of an optical fiber. By using a second fiber as an optical delay line, the minimum spacing between adjacent sensor regions can be well below the fluorescence lifetime limit. Since the coupling between the two fibers is evanescent, the attenuation of the excitation pulse is low, making long arrays of sensor regions feasible. This is particularly important since the one-dimensional combinatorial chemistry method developed by us allows for efficient preparation of diverse linear arrays. Detection sensitivities of 10(-7) mol/L are demonstrated, with the potential for significant improvement.     

Confocal reflection readout thresholds in two-photon-induced optical recording

Confocal reflection readout thresholds in two-photon-induced optical recording in photoisomerization polymer are studied both theoretically and experimentally. A threshold of the axial response from a planar reflector with a refractive-index change of the order of 10(-2) is revealed. However, the threshold is reduced to 0.006 when strong forward scattering caused by the recorded bits leads to multiple reflection between the bit and the rare surface, which enhances the image contrast and reduces the readout threshold. The quality of the reconstructed bit image is strongly dependent on the refractive-index mismatch at the sample rare interface as well as the distance between the recorded position and the rare surface.     

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.     

Automatic procedure for aberration compensation in digital holographic microscopy and applications to specimen shape compensation

We present a procedure that compensates for phase aberrations in digital holographic microscopy by computing a polynomial phase mask directly from the hologram. The phase-mask parameters are computed automatically without knowledge of physical values such as wave vectors, focal lengths, or distances. This method enables one to reconstruct correct and accurate phase distributions, even in the presence of strong and high-order aberrations. Examples of applications are shown for microlens imaging and for compensating for the deformations associated with a tilted thick plate. Finally we show that this method allows compensation for the curvature of the specimen, revealing its surface defects and roughness. Examples of applications are shown for microlenses and metallic sphere imaging.     

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.     

Theoretical analysis for spherical aberration induction with low-order correction in refractive surgery

A theoretical foundation for the analysis of ocular aberration correction is developed. It enables a comparative study for two different refractive surgical approaches, namely, the conventional and the Q-preserved treatment modalities. A refractive surgical factor is identified that leads to a simple cubic function for the postoperative asphericity factor for the conventional treatment. A formulation is developed that paves the way for the calculation of the induction of spherical aberration for low-order aberration correction in refractive surgery. Opposite to the general belief, the Munnerlyn shape makes myopic LASIK more prolate, not oblate. A Monte Carlo simulation was conducted for 1000 eyes for these two refractive surgical modalities. It was found that, although the postoperative spherical aberration is similar for these surgical modalities, for the induction of spherical aberration from the ablation target shape, the conventional modality appears to be slightly more predictable.     

Methodology for third-order astigmatism compensation in off-axis spherical reflective systems

The main constraint of classical off-axis reflecting systems is the primary astigmatism that has long been a research topic of interest. This astigmatism in off-axis spherical reflective imaging systems can be eliminated by using the proper configuration. These configurations could be derived from the marginal ray fans equation, and they are valid for small angles of incidence. The conditions for the astigmatism compensation in configurations with two and three off-axis mirrors have been derived and analyzed, which have not been reported previously. The expression that defines the conditions for primary astigmatism compensation in a four-mirror system is presented. This shows that the marginal ray fan equation can be used to obtain the condition for astigmatism compensation of a reflective system with any number of mirrors. The developed methodology is verified by ray-tracing analysis of some examples.     

Dispersion compensation for high bit rate fiber-optic communication using a dynamically tunable optical filter

A detailed analysis of dispersion-compensating fiber-optic filter is provided. Design parameters of the filter that could provide dispersion compensation for wide spectral sources are discussed. The dispersion-compensating fiber filter designed here can be dynamically tuned to compensate for the drift in the laser center frequency caused by temperature change and other deteriorations. The filter can be fabricated by exposing the photorefractive fibers to ultraviolet radiation. A design methodology for fabricating the refractive-index variation along the longitudinal direction of the fiber with appropriate chirp and taper coefficients is also given here. Dispersion-compensation capability of the fiber filter is demonstrated by simulating pulse broadening after transmission in a long fiber and the regeneration of the pulse after dispersion compensation.     

Interband optical absorption in a small-radius quantized spherical film

The electronic conditions and direct optical transitions in a semiconductor quantized spherical film under ‘strong’ quantization regime are considered when the size of the system is smaller than that of a bulk exciton. A physically adequate model is suggested that allows to find analytically the energy spectrum and wave functions of the charge carriers in the layer. In an approximation of simple non-degenerate bands, the absorption coefficient for interband and ‘intersubband’-inband transitions is found. Along with the frequency dependence, the explicit dependence of the absorption coefficient on the geometrical size of the model is revealed.