Axial field shaping under high-numerical-aperture focusing

Kant reported [J. Mod. Optics 47, 905 (2000)] a formulation for solving the inverse problem of vector diffraction, which accurately models high-NA focusing. Here, Kant's formulation is adapted to the method of generalized projections to obtain an algorithm for designing diffractive optical elements (DOEs) that reshape the axial point-spread function (PSF). The algorithm is applied to design a binary phase-only DOE that superresolves the axial PSF with controlled increase in axial sidelobes. An 11-zone DOE is identified that axially narrows the PSF central lobe by 29% while maintaining the sidelobe intensity at or below 52% of the peak intensity. This DOE could improve the resolution achievable in several applications without significantly complicating the optical system.     

Phase retrieval for high-numerical-aperture optical systems

We describe a phase retrieval approach for intensity point-spread functions of high-numerical-aperture optical systems such as light microscopes. The method calculates a generalized pupil function defined on a spherical shell, using measured images at several defocus levels. The resultant pupil functionsreproduce measured point-source images significantly better than does an ideal imaging model. Availability of pupil function information will facilitate new approaches to aberration correction in such systems.     

Anomaly in a high-numerical-aperture diffractive focusing lens

We show an anomalous behavior in a diffractive lens in which the spot size at the focus reaches a minimum at a numerical aperture of ~0.5 and then increases significantly at higher values. Theoretical and experimental results are presented, along with a comparison with refractive aplanatic lenses, in which the anomaly does not appear to exist.     

Error analysis for rotating active Stokes-Mueller imaging polarimeters

Retrieval of Mueller matrices from intensity measurements is a noise-sensitive process. In addition, the choice of the method used for extracting Mueller matrix elements greatly influences the precision of the final results. Among available procedures, three have been tested and their robustness analyzed by adding Gaussian noise to computer synthesized data and have been verified by comparing experimental data. As expected, the methods based on classical matrix inversion reach their noise reduction limit even if more data are considered. In contrast, the discrete Fourier transform approach features a remarkable stability. The identified reason is that the retrieval process corresponds to filtering with a periodic kernel.     

Wave-front spacing in the focal region of high-numerical-aperture systems

The wave-front spacing in the focal region of an aplanatic focusing system is investigated by use of the vector theory of electromagnetic diffraction for monochromatic, linearly polarized incident light. It is shown that, in systems of high numerical aperture, the wave-front spacing near the focus is significantly larger than the wavelength of the incident light and that the wave-front spacing changes significantly within a few wavelengths of the focus and can be less than a wavelength.     

Confocal scanning laser ophthalmoscopy improvement by use of Mueller-matrix polarimetry

A new technique for improving the signal-to-noise ratio and the contrast in images recorded with a confocal scanning laser system is presented. The method is based on the incorporation of a polarimeter into the setup. After the spatially resolved Mueller matrix of a sample was calculated, images for incident light with different states of polarization were reconstructed, and both the best and the worst images were computed. In both the microscope and the opthalmoscope modes, the best images are better than the originals. In contrast, the worst images are poorer. This technique may be useful in different fields such as confocal microscopy and retinal imaging.     

Mueller-matrix diagnostics of optical properties of polycrystalline networks of human blood plasma

The work is oriented toward a study of the possibilities of Mueller-matrix diagnostics of optical anisotropy of birefringent polycrystalline networks of human plasma amino acids. The interrelations between the statistical moments from the first to the fourth orders and fractal dimensionalities, which characterize the coordinate distributions of elements of the Mueller matrix for the blood plasma and the physiological state of the human organism, are determined.     

Reconstruction algorithm for high-numerical-aperture holograms with diffraction-limited resolution

A fast algorithm is proposed for the reconstruction of digital holograms that are recorded at high numerical aperture. The method directly evaluates the Rayleigh-Sommerfeld diffraction integral by use of a fast convolution algorithm. A shift parameter that accounts for the coordinate system's transverse displacement of the object plane and the hologram plane is introduced in a discrete representation of the diffraction kernel. Combination of the samplings reconstructed with different shift values yields diffraction-limited resolution over the full field of view. The algorithm is suitable for various applications such as holographic microscopy and metrology. Simulation and experimental results are presented.     

A study on the short—wavelength and high—numerical—aperture phase—change recording

In this paper, we discuss the phase-change recording at a short-wavelength (514nm) and a high numerical aperture (0.85). Effects of recording power and pulse width on the size of the recording marks are studied. The minimum recording mark with a length of approximately 220nm has been observed. The capacity of about 17GB for a single-layer disc of a 12cm diameter can be obtained. The maximum carrier-to-noise ratio reaches 45dB at a writing power of 13--14mW.     

Characterization of sub-10-fs pulse focusing with high-numerical-aperture microscope objectives

Dispersion precompensation with a prism sequence and a third-order dispersion mirror resulted in negligible broadening of sub-10-fs pulses at subwavelength spot sizes when the pulses were focused with microscope objectives and moderate apertures. At larger apertures, lens chromaticity and spherical aberration led to an effective pulse broadening of up to 1.3x , depending on the aperture size and the detector position. The data suggest that intensities exceeding 10(14) W/cm(2) can be produced directly from femtosecond pulse oscillators.     

Investigation of limits of applicability of the pBRDF model for active polarimeters

The polarimetric bidirectional reflectance distribution function is modeled for active polarimeters. The applicability boundaries of the model are determined based on the comparison of the simulated and experimental data.     

Enhanced spectral broadening of short laser pulses in high-numerical-aperture holey fibers

The influence of the structure of holey-fiber cladding on the spectral broadening of femtosecond laser pulses is experimentally studied. These experiments demonstrate that the spectral broadening of 70-fs pulses of 800-nm Ti:sapphire laser radiation transmitted through 2- and 3-μm-pitch holey fibers can be enhanced by a factor of about 1.5 by increasing the air-filling fraction of the fiber cladding from 16 up to 65%. Received: 23 April 2001 / Revised version: 18 June 2001 / Published online: 18 July 2001     

Focusing of partially coherent Bessel-Gaussian beams through a high-numerical-aperture objective

The focusing properties of partially coherent Bessel-Gaussian beams passing through a high-numerical-aperture objective are studied based on vectorial Debye theory. Expressions for the intensity distribution, degree of coherence |mu|, and degree of polarization P are derived near the focus. Numerical calculations are performed to analyze the influences of varying corresponding parameters on the intensity distribution, |mu|, and P in the focal region. It is shown that the intensity, |mu|, and P in the focal region are all influenced by varying the effective coherent length L(c) of incident beams and maximal angle alpha determined by the numerical aperture of the objective. Also, the linearly polarized incident field is found to be depolarized after it is focused by a high-numerical-aperture objective.     

First- and second-order statistics of partially coherent, high-numerical-aperture optical fields

The intensity probability distribution as well as the cross-spectral density of partially coherent optical fields generated through high-numerical-aperture illuminations are analyzed, and novel effects, not apparent in paraxial optical fields, are described. It is shown that the intensity probability distribution significantly differs from what can be expected from a small-angle analysis, and the number of degrees of freedom for the distribution is higher. It is further shown that the cross-spectral density of a high-angle optical field is a function of the coordinate difference along the propagation direction of the field.     

Noise equalization in Stokes parameter images obtained by use of variable-retardance polarimeters

An imaging variable retardance polarimeter was developed and tested by Tyo and Turner [Proc. SPIE 3753, 214 (1999)]. The signal-to-noise ratio (SNR) in the reconstructed polarization images obtained with this system varied for the four Stokes parameters. The difference in SNR is determined to be due to differences in the Euclidean lengths of the rows of the synthesis matrix used to reconstruct the Stokes parameters from the measured intensity data. I equalize (and minimize) the lengths of the rows of this matrix by minimizing the condition number of the synthesis matrix, thereby maximizing the relative importance of each of the polarimeter measurements. The performance of the optimized system is demonstrated with simulated data, and the SNR is shown to increase from a worst case of -3.1 dB for the original settings to a worst case of +5.0 dB for the optimized system.     

Automatic three-dimensional tracking of particles with high-numerical-aperture digital lensless holographic microscopy

We present an automatic procedure for 3D tracking of micrometer-sized particles with high-NA digital lensless holographic microscopy. The method uses a two-feature approach to search for the best focal planes and to distinguish particles from artifacts or other elements on the reconstructed stream of the holograms. A set of reconstructed images is axially projected onto a single image. From the projected image, the centers of mass of all the reconstructed elements are identified. Starting from the centers of mass, the morphology of the profile of the maximum intensity along the reconstruction direction allows for the distinguishing of particles from others elements. The method is tested with modeled holograms and applied to automatically track micrometer-sized bubbles in a sample of 4 mm3 of soda.     

Role of the null space of the DRM in the performance of modulated polarimeters

Imaging polarimeters infer the spatial distribution of the polarization state of the optical field as a function of time and/or wavelength. A polarimeter indirectly determines the polarization state by first modulating the intensity of the light field and then demodulating the measured data to infer the polarization parameters. This Letter considers passive Stokes parameter polarimeters and their inversion methods. The most widely used method is the data reduction matrix (DRM), which builds up a matrix equation that can be inverted to find the polarization state from a set of intensity measurements. An alternate strategy uses linear system formulations that allow band limited reconstruction through a filtering perspective. Here we compare these two strategies for overdetermined polarimeters and find that design of the null space of the inversion operator provides degrees of freedom to optimize the trade off between accuracy and signal-to-noise ratio. We further describe adaptive filtering techniques that could optimize the reconstruction for a particular experimental configuration. This Letter considers time-varying Stokes parameters, but the methods apply equally to polarimeters that are modulated in space or in wavelength.     

Compression of fiber supercontinuum pulses to the Fourier-limit in a high-numerical-aperture focus

A multiphoton intrapulse interference phase scan (MIIPS) adaptively and automatically compensates the combined phase distortion from a fiber supercontinuum source, a spatial light modulator pulse shaper, and a high-NA microscope objective, allowing Fourier-transform-limited compression of the supercontinuum pulses at the focus of the objective. A second-harmonic-generation-based method is employed to independently validate the transform-limited compression. The compressed pulses at the focus of the objective have a tunable duration of 10.8-38.9 fs (FWHM), a central wavelength of ~1020 nm, an average power of 18-70 mW, and a repetition rate of 76 MHz, permitting the application of this source to nonlinear optical microscopy and coherently controlled microspectroscopy.     

Temperature characteristics of a Y-cut Z-propagation LiNbO3 light modulator for application to polarimeters

The temperature characteristics of a Y-cut Z-propagation LiNbO₃ crystal light modulator, with manufacturing errors, in the absence and presence of an electric field have been investigated by analyses and experiments. According to our analyses, when the Z-axis of the LiNbO₃ crystal is at an angle of 0.22° with respect to the normal of the input surface of the crystal, we found the theoretical fluctuation of the normalized output-light intensity with temperature to be less than 7:75 × 10⁻⁶/°C. This magnitude is less than 1% of the theoretical intensity fluctuation of a conventional temperature-compensation LiNbO₃ light modulator. The measured temperature characteristics of a prototype of this modulator were 2 × 10⁻⁴/°C in the absence of an electric field (OFF state) and 2:8 × 10⁻⁴/°C in the presence of an external field (ON state). During a running test of longer than 8 hours at room temperature, the intensity fluctuation of this prototype was 0.01% in the OFF state, and 0.07% in the ON state.