Although traditional differential interference contrast (DIC) optical systems introduce bias retardation into the wavefront field by translation of the objective Nomarski prism, the same effect can be achieved through the application of a fixed Nomarski (or Wollaston) prism system and a simple de Sénarmont compensator consisting of a quarter-wavelength retardation plate in conjunction with either the polarizer or analyzer. This interactive tutorial explores the wavefront relationship in a de Sénarmont DIC microscope optical train as the polarizer is rotated with respect to the fast axis of the retardation plate.
The tutorial initializes with three-dimensional images of a polarizer and quarter-wavelength retardation plate (together comprising a de Sénarmont compensator), along with a fixed Wollaston prism, appearing in the window. From the left-hand side of the window, a beam of non-polarized white light is incident on the polarizer. After passing through the polarizer (the gray disc), which has a transmission axis indicated by a long black wedge, the emerging linearly polarized light is oriented with the vibration direction parallel to the fast axis of the quarter-wavelength retardation plate (represented by a black wedge on the light blue disc). In this configuration, the de Sénarmont compensator passes linearly polarized light, which is represented in the tutorial with a blue sine wave accompanied by an oscillating black arrow that traces the electric vector vibration orientation.
Linearly polarized light exiting the de Sénarmont compensator enters the Wollaston prism, and is separated into orthogonal (mutually perpendicular) components consisting of an ordinary and an extraordinary wave. These perpendicular wavefronts are sheared and exchange identities at the junction between the two quartz wedges in the Wollaston prism. The sheared orthogonal wavefronts also diverge at a very small angle (greatly exaggerated in the tutorial) upon encountering the wedge boundary. To enhance visualization, the entire optical train assembly can be rotated within the window by placing the mouse cursor on any component, and then dragging to model to a new position.
The orientation of incident linearly polarized light with respect to the retardation (quarter-wavelength) plate can be altered by translating the Polarizer Rotation slider to either the right or left from its default central position. When the slider is moved to the left (negative values), within a range of 1 and 44 degrees, an increasing amount of light is passed through the slow axis of the retardation plate (indicated by a red sine wave exiting red wedges on the blue disc). The net result is the production of right-handed elliptically polarized light. The opposite effect occurs when the slider is moved to the right (positive values; left-handed elliptically polarized light). Elliptically polarized light is represented in the tutorial by a three-dimensional trajectory of the black arrow, which traces the vector sum of the individual electronic components from each wave (fast and slow).
In order to operate the tutorial, introduce varying amounts of bias retardation into the optical train using the Polarizer Rotation slider, and then drag the model to different positions in the window to view the behavior of polarized wavefronts passing through the system. The sine wave(s) can be halted by removing the checkmark from the Translate Sine Wave check box, or the entire tutorial can be suspended in action by clicking on the Pause button. The speed of the sine wave can be increased or decreased with the Speed slider (the default setting is medium speed), and the tutorial can be re-initialized without reloading by using the Reset button.
A traditional differential interference microscope optical system contains a polarizer located before the condenser and an analyzer (a second polarizer) inserted into the pathway above the objective, usually in an intermediate tube or combined in the frame with the objective Nomarski prism. The polarizer is oriented with the vibration plane transmission axis positioned East-West, while the analyzer is crossed with respect to the polarizer (transmission axis is North-South). Linear polarized light leaving the polarizer is separated into two components by a Nomarski prism housed in the condenser near the conjugate focal plane of the iris diaphragm aperture. Incident wavefronts are sheared by the prism into orthogonal polarized components, rendered parallel by the condenser optical system, and then utilized to illuminate the specimen.
Positioned behind the objective in the optical pathway is a second Nomarski prism (usually housed in an adjustable sliding frame), which is utilized to recombine the sheared wavefronts in the conjugate plane of the rear aperture after they have been collected and focused by the objective. Components of circular and elliptically polarized light from the recombined wavefronts pass through the analyzer and subsequently undergo interference to generate the DIC image at the microscope intermediate image plane.
In a perfectly aligned DIC microscope, the condenser prism is imaged by the condenser and objective lens assemblies onto the objective prism so that wavefront shear is matched at every point along the surface of the prisms, which are inverted with respect to one another. Translating either prism along the shear axis (perpendicular to the microscope optical axis) produces a wavefront mismatch that is uniform across the microscope aperture. Shifting the phase displacement of the ordinary wavefront with respect to the extraordinary wavefront through translation of a prism is often termed introduction of bias retardation in DIC microscopy. As one of the Nomarski prisms is shifted laterally (usually the objective prism), wavefront pairs contributing to the background become increasingly retarded and out of phase with one another. Thus, the polarization vector orientation of light emerging from the objective Nomarski prism can be adjusted from linear (no translation), through varying degrees of elliptical, and even to circular.
Introduction of bias retardation into a DIC optical system produces changes to the intensity (amplitude) levels of phase gradients in the specimen, which result in the generation of orientation-dependent bright highlights and dark shadows superimposed on a lighter background. Intensity gradients occur along the shear axis of the condenser and objective prisms, and generally appear to be originating from a 45-degree angle (northwest to southeast or vice versa) when the specimen is observed in the eyepieces. Shifting the prism in one direction or another across the microscope optical axis will vary the phase relationship between the orthogonal wavefronts, thus reversing the shadow-cast orientation in the specimen. The net result is to render the specimen image in pseudo three-dimensional relief where regions of increasing optical path length (sloping phase gradients) appear much brighter or darker, and those exhibiting decreasing path length appear in reverse.
An alternative technique for introduction of bias retardation, which is growing in popularity, is to mount a quarter-wavelength retardation plate in fixed orientation between the polarizer and condenser prism (termed de Sénarmont DIC compensation, as discussed above). At maximum extinction (matched prisms with no bias applied; see Figure 1(b)), the fast axis of the retardation plate is aligned with the transmission axis of the polarizer. Both optical units can be (and often are) contained within the same housing on the base of the microscope. An alternative location for the de Sénarmont compensator, in microscopes equipped with the appropriate intermediate tube, is between the objective prism and the analyzer.
In order to introduce bias using the de Sénarmont compensator, the polarizer transmission axis is rotated (up to plus or minus 45 degrees; see Figures 1(a) and 1(c)) with respect to the fast axis of the retardation plate, which remains fixed at a 90-degree angle relative to the analyzer transmission axis. When the compensator fast axis coincides (is parallel) with the transmission axis of the polarizer, only linearly polarized light passes through the de Sénarmont compensator to the condenser prism, as illustrated in Figure 1(b). However, when the polarizer transmission axis is rotated, wavefronts emerging from the quarter-wavelength retardation plate become elliptically polarized. Rotating the polarizer in one direction will produce right-handed elliptically polarized light (Figure 1(a)), while rotating the polarizer in the other direction will alter the vector trajectory to generate a left-handed elliptical sweep (illustrated in Figure 1(c)).
When the orientation of the polarizer transmission axis reaches either plus or minus 45 degrees (equivalent to one-quarter wavelength of retardation), light passing through the compensator becomes circularly polarized (again in either a left-handed or right-handed sense). Because elliptically or circularly polarized light represents a phase difference between the ordinary and extraordinary wavefronts emerging from the de Sénarmont compensator, bias is introduced to the system when the wavefronts enter the condenser Nomarski beamsplitter prism and become sheared (Figure 2). Positive bias is obtained when the polarizer is rotated in one direction, while negative bias is introduced by rotating the polarizer in the opposite direction. The amount of retardation introduced by a de Sénarmont compensator can be quantitatively determined according to the equation:
where θ is the rotation angle (calculated in degrees) of the polarizer transmission axis in relation to the fast axis of the retardation plate, and λ is the average wavelength of light passing through the compensator. In the case of tungsten-halogen illumination, the wavelength is often taken to be approximately 550 nanometers for calculations involving bias retardation. With de Sénarmont compensators, bias retardation values ranging between one-twentieth and a full wavelength can be easily measured with an accuracy of 0.15 nanometers.
The effects of bias retardation introduced into the DIC optical system by a de Sénarmont compensator are illustrated in Figure 2 for three settings of the compensator. All of the examples presented in Figure 2 diagram a single wavefront entering the central portion of a Wollaston prism, but a Nomarski prism will operate in the same fashion. When the polarizer transmission axis is aligned parallel to the fast axis of the quarter-wavelength retardation plate (Figures 1(b) and 2(b)), linearly polarized light emerges from the compensator and is incident on the lower wedge surface of the condenser Wollaston prism (as depicted in Figure 2(b)). In a DIC microscope, the incident linearly polarized light is oriented at a 45-degree angle to the fast and slow axes of the lower wedge component of the Wollaston (or Nomarski) prism. Upon entering the prism, the polarized light is separated into orthogonal components, which traverse the fast and slow axes of the lower quartz wedge and become sheared at the boundary between the two prism wedges. Because the linear wavefront exists as a single phase when it enters the prism, the orthogonal components are initially in phase when they are produced at the air-quartz boundary, but undergo phase shifts inside the prism.
As previously described, the gain in phase by the ordinary wavefront in the lower portion of the Wollaston prism is offset in the upper wedge after the ordinary and extraordinary waves exchange identities at the junction between the two wedges. The net result is a cancellation of phase shifts produced inside the prism, and the orthogonal wavefronts emerge from the Wollaston prism in phase with each other (Figure 2(b)). In this condition, the optical system exhibits maximum extinction, and only large phase gradients present in the specimen are visible. These phase gradients are superimposed on a very dark, or black, background and take on the appearance of a darkfield image.
The situation is quite different when the polarizer is rotated in either direction away from the zero position in a de Sénarmont compensator. Wavefronts emerging from the compensator exhibit phase shifts that impart an elliptical or circular character to the vector summation of the orthogonal wave components. When the polarizer is rotated to the left by 30 degrees (negative bias retardation; Figure 2(a)), the ordinary wavefront generated by the de Sénarmont compensator enters the Wollaston prism prior to the extraordinary wavefront, and exits the prism (after exchanging identities) as the extraordinary wavefront ahead of the ordinary wavefront. The basic result is the generation of an optical path difference, which is required for the introduction of bias retardation. The opposite effect occurs (Figure 2(b)) when the de Sénarmont polarizer is rotated to the right (positive bias retardation), and the ordinary wavefront emerges from the Wollaston prism ahead of the extraordinary wavefront.
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 and Michael W. Davidson - National High Magnetic Field Laboratory, 1800 East Paul Dirac Dr., The Florida State University, Tallahassee, Florida, 32310.