Interaction of Light Waves with Phase Specimens
Upon encountering a phase specimen, an incident illumination wavefront is deformed according to the geometry, refractive index, and thickness of the specimen. This interactive tutorial explores the variety of deformations observed in wavefront shape as specimens having differing characteristics are illuminated with a planar beam of light.
The tutorial initializes with a rectangular specimen (represented by a dark gray box) appearing in the window, and having an arbitrary refractive index of 1.50 (approximating the refractive index of a glass block). The specimen is surrounded by a medium of lower refractive index (1.30 by default). A continuous series of planar wavefronts impact and pass through the specimen proceeding from the left-hand side of the window to the right. As each wavefront passes through the specimen, it is deformed and retarded (or advanced) according to the geometry, refractive index differential, and thickness of the specimen.
In order to operate the tutorial, use the sliders, radio buttons, and pull-down menu to alter the specimen and surrounding medium parameters to induce changes in the wavefronts interacting with the specimen. The Specimen Width and Specimen Height sliders control these geometrical parameters and can be employed to produce simple linear changes to the specimen and corresponding wavefront shape. Increasing the width for a specimen having a higher refractive index than the surrounding medium produces a larger amount of retardation in the portion of the wavefront passing through the specimen. In contrast, the same maneuver with a specimen that has a lower refractive index than the medium will advance the wavefront. Increasing the height of the specimen results in a larger deformation in a direction parallel to the wavefront.
The refractive index ratio between the specimen and surrounding medium can be adjusted with the Surround RI: Specimen RI slider. The specimen refractive index range is 1.20 to 1.50, while the surrounding medium refractive index is fixed at 1.30 (approximating buffered aqueous saline). The wavefront style can be toggled with a pair of radio buttons between Planar Wavefronts, which have a sharp leading edge that gradually decreases in intensity, and Linear Wavefronts, represented by a line. Several specimen geometries, including Rectangular, Complex, and Elliptical, can be selected using the Specimen Shape pull-down menu.
An incident wavefront present in an illuminating beam of light becomes divided into two components upon passing through a phase specimen. The primary component is an undeviated (or undiffracted; zeroth-order) planar wavefront, commonly referred to asurround (S) wave that passes through and around the specimen, but does not interact with it. In addition, a deviated or diffracted wavefront (the D-wave) is also produced, which becomes scattered over a wide arc (in many directions) that increases with specimen size.
Incident light that is scattered by non-absorbing, transparent phase specimens is retarded in phase by one-quarter wavelength relative to those light waves that do not interact directly with atoms and molecules comprising the specimen. In a manner similar to propagation of light through a medium, scattering involves the interaction of a light wave with an atom and the subsequent re-emission of light by that atom. When an electromagnetic wave (such as that comprising in an incident light wave) interacts with an atom or molecule, electrons are translocated in an oscillatory fashion in response to the changing electric field of the wave. A new electromagnetic wave is re-emitted as the electrons are accelerated first in one direction and then in another. When the electrons are at rest, the emitted field is zero. Thus, the electromagnetic radiation produced is proportional to the rate of change in the velocity of the charge, or the acceleration of the charge. Because in a simple harmonic motion the acceleration is a quarter-wavelength behind the velocity, the emitted light wave lags a corresponding quarter-wavelength behind the incident wave.
As an illuminating wavefront passes into a non-absorbing medium, such as a thin glass plate in water, at each level some of the atoms in the plate interact with the incident light wave and re-emit light that is retarded in phase by a quarter-wavelength. Each atom acts as a point source, and collectively, the emitted wavelets form a new plane wave that lags one quarter-wavelength behind the incident wavefront that has passed through or around the atoms in the glass plate. This newly retarded wavefront is of low amplitude and constructively interferes with the incident wavefront to produce a resultant wavefront that is retarded by a small fraction (approximately one-twentieth) of a wavelength, as illustrated in Figure 1(a). Due to destructive interference, lateral scattering is essentially zero. The net result, for a thin glass plate immersed in water, is a slightly embossed region in the incident wavefront (see Figure 1(b)). Restated, the embossed portion of the wavefront can be regarded as the sum of the incident wavefront (zeroth-order light) and the low amplitude wavefront of the scattered or diffracted light that is retarded by a quarter-wavelength. As the process is continually repeated (for thicker and irregular specimens), the resultant wavefront is increasingly retarded relative to a wavefront that does not pass through the specimen.
A flat glass plate contains numerous planes of atoms that span large regions in two dimensions. However, the plate (as do most biological and materials specimens) also contains edges with atoms that scatter light retarded by a quarter-wavelength relative to the incident wavefront. The wavelets created at edges propagate in all directions but do not form a plane wave that propagates along the optical axis or in the direction of the incident wavefront. Light diffracted by the edges of a specimen is retarded by a quarter-wavelength relative to the zeroth-order incident illumination, and the thicker the edge, the greater the intensity of this diffracted light. Thicker specimens diffract more light than thinner specimens, but the phase relationship remains the same (retarded one-quarter wavelength).
Douglas B. Murphy - Department of Cell Biology and Anatomy and Microscope Facility, Johns Hopkins University School of Medicine, 725 N. Wolfe Street, 107 WBSB, Baltimore, Maryland 21205.
Kenneth R. Spring - Scientific Consultant, Lusby, Maryland, 20657.
Matthew Parry-Hill, Cynthia D. Kelly, and Michael W. Davidson - National High Magnetic Field Laboratory, 1800 East Paul Dirac Dr., The Florida State University, Tallahassee, Florida, 32310.