Hedzer A. Ferwerda

SCATTERING AND ABSORPTION OF TURBID MATERIALS DETERMINED FROM REFLECTION MEASUREMENTS .2. MEASURING METHOD AND CALIBRATION

A new experimental method has been developed to determine the scattering and absorption characteristics of a turbid material. Existing methods usually require transmission and reflection measurements carried out on a thin slab of the material under study; this method is based on reflection measurements carried out on bulk material. This will be of great advantage in many applications. This paper describes the measuring system and indicates the area of application of the method. Calibration measurements have been carried out to substantiate the approach.

Discussion of a ‘‘coherent artifact’’ in four‐wave mixing experiments

In this paper, we discuss the nonlinear optical effects that arise when stochastic light waves, with different correlation times, interfere in an absorbing medium. It is shown that four‐wave mixing signals are generated in several directions that spectrally track the incoming light fields. This effect is particularly relevant to transient hole‐burning experiments, where one of these signals could easily be misinterpreted as a genuine hole‐burning feature.

Fully relativistic treatment of electron-optical image formation based on the Dirac equation

The theory of image formation for an electron microscope is based on the non-relativistic Schrodinger equation, whereas present-day electron microscopes operate with acceleration voltages of the order of one hundred to several hundreds of kilovolts, in which case relativistic effects become important. We present a fully relativistic theory of image formation, based on the appropriate Dirac equation. It is shown that, within certain approximations, always valid for todays electron microscopes, a very simple expression for the current density can still be derived in terms of wave functions that are solutions to the relativistically covariant Klein-Gordon equation. The following paper presents the analysis of the often stated possibility to obtain the relativistically correct current density from the non-relativistic current density just by replacing the values of the non-relativistic momentum by the correct relativistic expression.

Analytic calculation of the radiance in an anisotropically scattering turbid medium close to a source

We present a method to calculate the radiance due to an isotropic point source in an infinite, homogeneous, anisotropically scattering medium. The method is an extension of a well known method for the case of isotropic scattering. Its basic mathematical ingredient is the Fourier transform. Its great advantage is that it also works very close to the source and not just far away from it, as is the case with most other methods. In principle, the method works for any phase function that can be expanded in a finite number of Legendre polynomials. Here, the simple example of linear anisotropic scattering is worked out numerically and the result is compared with Monte Carlo simulation. Good agreement is found between the two.

THE NON-RADIATING COMPONENT OF THE FIELD GENERATED BY A FINITE MONOCHROMATIC SCALAR SOURCE DISTRIBUTION

We separate the field generated by a spherically symmetric bounded scalar monochromatic source into a radiative and non-radiative part. The non-radiative part is obtained by projecting the total field on the space spanned by the non-radiating inhomogeneous modes, i.e. the modes which satisfy the inhomogeneous wave equation. Using residue techniques, introduced by Cauchy, we obtain an explicit analytical expression for the non-radiating component. We also identify the part of the source distribution which corresponds to this non-radiating part. The analysis is based on the scalar wave equation.

The Fully Relativistic Foundation of Linear Transfer Theory in Electron Optics Based on the Dirac Equation

The fully relativistic quantum mechanical treatment of paraxial electron-optical image formation initiated in the previous paper (this issue) is worked out and leads to a rigorous foundation of the linear transfer theory. Moreover, the status of the relativistic scaling laws for mass and wavelength, as advocated in the literature, is elucidated.

Frits Zernike--life and achievements

We present a review of the life and work of Frits Zernike (1 888-1 966), professor of mathematical and technical physics and theoretical mechanics at Groningen University, The Netherlands, inventor of phase contrast microscopy.

STATISTICAL ASPECTS OF IMAGE HANDLING IN LOW-DOSE ELECTRON-MICROSCOPY OF BIOLOGICAL-MATERIAL

Publisher Summary In low-dose circumstances the image intensity distribution recorded on the micrograph is a realization of a stochastic process. This noise process that is directly related to the way in which images are recorded has been investigated in this chapter. The stochastic nature of the recorded image has a consequence that the results of image processing also become stochastic quantities, for example, the results obtained with an algorithm for phase retrieval. The chapter discusses the properties of the various methods and algorithms that are proposed in the literature for solving the phase problem when they are applied to low-dose imaging conditions. It mentions the basic integral equation that relates the object wave function to a recorded intensity distribution in the image plane. In order to keep the equations as simple as possible, one lateral dimension of the images only is treated in the chapter. For electron microscopes with square diaphragms (if there are any), the extension to two lateral dimensions is straightforward. The chapter discusses the contrast between imaging of the substructure of biological specimens by means of an electron microscope and low-dose imaging. The imaging of the substructure of biological specimens by means of an electron microscope is greatly limited by the radiation sensitivity of these objects. In low-dose imaging, however, the contrast is very noisy. Because of this poor signal-to-noise ratio, the evaluation in particular of nonperiodic object structures is very cumbersome.

Derivation of the equation for an ultrashort pulse in a fibre

Pulses propagating in a non-linear dispersive (glass) fibre can be described by the non-linear Schrodinger equation if the pulse is longer than a picosecond; for shorter pulses, this equation must be extended. In this paper we systematically derive this extended equation using the method of multiple scales. By using an inherent freedom in the method of multiple scales, a technique is developed such that perturbation terms are greatly simplified. The limits of validity of the derived equation are discussed. It is shown to be valid for pulses longer than 30 fs.

ANALYTICAL CLOSE-TO-SOURCE INVESTIGATION FOR AN ISOTROPIC POINT SOURCE IN AN UNBOUNDED, ANISOTROPICALLY SCATTERING MEDIUM

The diffusion approximation, which is often used to describe the propagation of light in biological tissues, is only good at a sufficient distance from sources and boundaries. Light- tissue interaction is however most intense in the region close to the source. It would therefore be interesting to study this region more closely. Although scattering in biological tissues is predominantly forward peaked, explicit solutions to the transport equation have only been obtained in the case of isotropic scattering. Particularly, for the case of an isotropic point source in an unbounded, isotropically scattering medium the solution is well known. We show that this problem can also be solved analytically if the scattering is no longer isotropic, while everything else remains the same.