Marek Kowalczyk

Three-dimensional superresolution by annular binary filters

We present a new family of annular binary filters for improving the three-dimensional resolving power of optical systems. The filters, whose most important feature is their simplicity, permit to achieve a significant reduction, both in the transverse and in the axial direction, of the central lobe width of the irradiance point spread function of the system. The filters can be used for applications such as optical data storage or confocal scanning microscopy.

Imaging phase objects with square-root, Foucault, and Hoffman real filters: a comparison

Methods of imaging phase objects are considered. First the square-root filter is inferred from a definition of fractional-order derivatives given in terms of the integration of a fractional order called the Riemann-Liouville integral. Then we present a comparison of the performance of three frequency-domain real filters: square root, Foucault, and Hoffman. The phase-object imaging method is useful as a phase-shift measurement technique under the condition that the output image intensity is a known function of object phase. For the square-root filter it is the first derivative of the object phase function. The Foucault filter, in spite of its position, gives output image intensities expressed by Hilbert transforms. The output image intensity obtained with the Hoffman filter is not expressed by an analytical formula. The performance of the filters in a 4f imaging system with coherent illumination is simulated by use of VirtualLab 1.0 software.

Asymmetric apodization in confocal scanning systems

A new class of superresolution pairs of pupil filters for three-dimensional, two-pupil confocal imaging is proposed. A distinctive feature of these filters is the asymmetry of their impulse response. For synthesizing the amplitude transmittance of such filters the Fourier transform properties of Hermitian functions are employed. It is shown that, with simple phase-only filters that belong to the class in question, either axial or unidirectional lateral superresolution is achieved.

One-dimensional iterative algorithm for three-dimensional point-spread function engineering

We present a new method with which to binarize pupil filters designed to control the three-dimensional irradiance distribution in the focal volume of an optical system. The method is based on a one-dimensional iterative algorithm, which results in efficient use of computation time and in simple, easy to fabricate binary filters. An acceptable degree of resemblance between the point-spread function of the annular binary filter and that of its gray-tone counterpart is obtained.

Spectral and imaging properties of uniform diffusers

The use of thin phase diffusers in coherent imaging systems is analyzed. A condition is derived that must be fulfilled to ensure that no part of incident light is specularly transmitted. This condition is expressed in terms of first-order statistics of the phase of light emerging from a diffuser. It is shown that random diffusers whose amplitude-transmittance argument (phase) is uniformly distributed in the (−π, π) interval do not pass the specular light while their rms phase corresponds to only 0.29 of a wavelength. Such diffusers will be called uniform ones. A method for forming a uniform diffuser is proposed. It is based on a recording of normal speckle patterns in phase-photosensitive materials with consideration of the exposure characteristics. Autocorrelation functions and power spectra of diffuser transmittance are evaluated for two types of exposure characteristics. For both these cases the image contrast of the uniformly illuminated diffuser is calculated.

Analytical formula for calculating the focal shift in apodized systems

We report a quite simple analytical formula for the evaluation of the focal shift in apodized systems, with or without rotational invariance. Specifically it is shown that the magnitude of the focal shift is determined by the product of the Fresnel number of the focusing geometry and the standard deviation of a mapped version of the azimuthal average of the pupil transmittance. To illustrate our approach, several examples are examined.

Annular binary filters for controlling the axial behaviour of optical systems

The one-dimensional (1D) version of the iterative Fourier transform algorithm (IFTA) and a modified error diffusion algorithm are proposed for binarizing rotationally symmetric pupil filters designed to shape the axial impulse response of optical system. The resulting binary masks consist of a set of transparent and opaque annular zones of equal area or equal width. A numerical experiment in which we examine the performance of the binarization methods is carried out. In this experiment the resemblance between the axial diffractive behaviour of the binary version of an axially superresolving pupil filter, and that of the original continuous-tone filter is evaluated. It is shown that the performance of the binary mask obtained with 1D IFTA is much better than that of the annular binary filters obtained by other digital half-toning techniques which preserve the rotational symmetry of binarized pupils.

Laser speckle velocimetry

The main purpose of this review is to present the statistical properties of dynamic speckle produced by a diffuse object that moves with a constant velocity and the velocimetry applications that result from these properties. In this way the space-time correlation function of the speckle intensity variation is examined. Two typical speckle motions: boiling and translation are identified and discussed for various optical configurations in the diffraction and image fields in the case of the in plane object motion. The following measurement methods for the diffuse object velocity are introduced: the autocorrelation method, cross-correlation method, spatial filtering method, and zero-crossing method. There are several versions of the above mentioned methods. Special attention is paid to those which allow us to measure both the magnitude and direction of the velocity. In the vast majority of methods the Gaussian illuminating beam is used. In this review the TEM10 illuminating beam is also taken into consideration. Then the autocorrelation methods of velocity measurement for the case of longitudinal motion are presented. It is shown that for this particular case the moving object need not to be a diffuse one, it can be a reflecting object as well. Possibility of the measurement of velocity which is arbitrarily directed with respect to the axis of the illuminating beam is also discussed. The speckle velocimetry methods in which the velocity is determined by means of a direct tracking and recording of the translating speckle generated by the moving object are mentioned. Finally some measurement systems in which laser speckles are used to evaluate subcutaneous flow of liquids are presented. Such systems were found useful in food conservation and medicine.

Tunable optical sectioning in confocal microscopy by use of symmetrical defocusing and apodization

We present two novel optical methods to achieve a significative improvement in the optical-sectioning capacity of confocal scanning microscopes. The techniques, whose real power is the simplicity with which they can be implemented, consist of a suitable combination of symmetrical defocusing with two different manners of apodizing both parts of the confocal architecture. It is shown that the proposed techniques are useful in both the bright-field and the fluorescence modes and for reflection and transmission geometries.

One-dimensional error-diffusion technique adapted for binarization of rotationally symmetric pupil filters

Abstract Two novel algorithms for the binarization of continuous rotationally symmetric real and positive pupil filters are presented. Both algorithms are based on the one-dimensional error diffusion concept. In our numerical experiment an original gray-tone apodizer is substituted by a set of transparent and opaque concentric annular zones. Depending on the algorithm the resulting binary mask consists of either equal width or equal area zones. The diffractive behavior of binary filters is evaluated. It is shown that the filter with equal width zones gives Fraunhofer diffraction pattern more similar to that of the original gray-tone apodizer than that with equal area zones, assuming in both cases the same resolution limit of device used to print both filters.