Zbigniew Jaroszewicz

Nonparaxial design of generalized axicons

The geometric law of energy conservation is utilized in evaluating the phase transmittance function for axicons with arbitrary distribution of the on-axis intensity. Several simple analytical solutions are presented, and a computer-generated holographic version of the uniform-intensity axicon is examined.

Phase retardation of the uniform-intensity axilens

A method for determining the phase-retardation function of the uniform-intensity axilens is discussed and compared with that of an earlier publication [Opt. Lett. 16, 523 (1991)]. Within the presented formulation good agreement is achieved between the geometrical-optics prediction and the numerically evaluated diffraction integral.

Apodized annular-aperture logarithmic axicon: smoothness and uniformity of intensity distributions

We show that the apodized annular-aperture logarithmic axicon preserves excellent uniformity of the on-axis intensity, energy flow, and lateral resolution. Numerical evaluation of the Fresnel diffraction integral leads to results very close to geometrical-optics predictions. Once again the geometrical law of energy conservation turns out to be a useful tool in designing axicons.

Imaging with extended focal depth by means of lenses with radial and angular modulation

The paper presents imaging properties of modified lenses with the radial and the angular modulation. We analyze three following optical elements with moderate numerical apertures: the forward logarithmic axicon and the axilens representing the radial modulation as well as the light sword optical element being a counterpart of the axilens with the angular modulation. The abilities of the elements for imaging with extended depth of focus are discussed in detail with the help of structures of output images and modulation transfer functions corresponding to them. According to the obtained results only the angular modulation of the lens makes possible to maintain the acceptable resolution, contrast and brightness of the output images for a wide range of defocusing. Therefore optical elements with angular modulations and moderate numerical apertures seem to be especially suitable for imaging with extended focal depth.

Axicon-the Most Important Optical Element

Last year, the optics community celebrated the 50th anniversary of the formal naming of the axicon. Long before that, however, axicons generated vivid discussions and disagreements, often of fundamental importance to our understanding of optics.

Lens axicons: systems composed of a diverging aberrated lens and a perfect converging lens

A description is given of axicons obtained as a tandem of one diverging lens that has third-order spherical aberration and one perfect converging lens. The asymptotic representation obtained with the help of the nonuniform stationary phase method allows the determination of such principal features of the focal segment as the intensity distribution and the width of the central core along the optical axis. The obtained results are compared with the numerical evaluation of the corresponding diffraction integral. The analyzed system contains four special cases: the doublet of both lenses, the setup of the perfect converging lens placed in the front of the aberrated diverging lens, the setup of the aberrated diverging lens placed in the primary focal plane of the perfect converging lens, and the defocused Galilean telescope. A short discussion of the aberrated-lens bending factor as well as of choice of the most convenient system geometry is also included.

Simple lens axicon

We present the design of a cemented doublet-lens axicon made from spherical surfaces only. Compared with diffractive axicons, refractive cone axicons, and earlier lens axicons with aspheric surfaces, this element is inexpensive and easy to manufacture even with large apertures. The lens axicon is based on the deliberate use of the spherical aberration of the surfaces. The design principles of the element and its characterization, numerically and experimentally, are presented in detail. Although performance was traded for simplicity and robustness, the results show that the lens axicon has the main axicon properties: a narrow, extended line focus of relatively constant width.

The Light Sword Optical Element—a New Diffraction Structure with Extended Depth of Focus

Abstract This letter introduces a novel diffraction structure, the light sword optical element, with extended depth of focus.

Cell parameter determination of a twisted-nematic liquid crystal display by single-wavelength polarimetry

Optical transmittance of a 90-twisted nematic liquid crystal cell inserted between crossed or parallel polarizers is neither sensitive to the molecular twist sense nor to the exchange between the extraordinary and the ordinary birefringence axis at the input face of the cell. In this article, the equivalence between a twisted-nematic liquid crystal cell and the combination of a retardation wave plate and a polarization rotator is fully exploited to understand the physical origin of these ambiguities. We determine, in a simple way, cell parameters by means of standard cell transmittance measurements when both crossed and parallel polarizers are rotated simultaneously. We show that this procedure, which is subjected to the aforementioned ambiguities, can be completed by additional polarimetric measurements. In particular, we demonstrate that the twist angle, twist sense, retardation, and the rubbing direction can be univocally determined by experimental measurement of the Stokes parameters of the light tran...

Diffractive axicons in oblique illumination: analysis and experiments and comparison with elliptical axicons

Axicons in oblique illumination produce broadened focal lines, a problem, e.g., in scanning applications. A compact mathematical description of the focal segment is presented, for the first time, to our knowledge, and the results are compared with elliptical axicons in normal illumination. In both cases, analytical expressions in the form of asteroid curves are obtained from asymptotic wave theory and caustic surfaces. The results are confirmed by direct diffraction simulations and by experiments. In addition we show that at a fixed angle an elliptical axicon can be used to compensate for the adverse effects of oblique illumination.