Wavefront Fields in DIC Microscopy
Wavefront fields traversing the optical train of a differential interference contrast (DIC) microscope undergo several reorientations as they encounter various polarizing, phase retarding, and beamsplitting elements present in the system. Linearly polarized light emerging from the polarizer is separated into orthogonal components upon entering the birefringent condenser Wollaston (or Nomarski) prism and is then sheared at the boundary between the prism wedges. This interactive tutorial explores the wavefront relationships involving polarized and orthogonal wavefront components in both de Sénarmont and traditional Nomarski optical configurations.
The tutorial initializes in de Sénarmont DIC mode with non-polarized, semi-coherent wavefronts (represented by yellow disks) emerging from the left-hand side of the tutorial window and passing through the polarizer (gray disk) to form linearly polarized light. The polarized light, whose electric vector vibration orientation is coincident with the polarizer transmission axis, next encounters the quarter-wavelength retardation plate (light blue disk) and travels through the fast axis of the birefringent crystal to emerge, once again, as linearly polarized light. The third component in the optical train is a Wollaston prism oriented with the shear axis at a 45-degree angle to the transmission and fast axes of the polarizer and retardation plate, respectively.
Upon entering the Wollaston prism, the linearly polarized light is separated into orthogonal components (an ordinary and an extraordinary wavefront) and traverses the lower prism wedge before being sheared at the interface between wedges. At the prism wedge boundary, the ordinary and extraordinary wavefronts also exchange identities as they enter the upper prism wedge. Separated orthogonal wavefronts exit the Wollaston prism and diverge into space either together or with one wavefront ahead of the other, depending upon the bias retardation introduced by rotating the polarizer in the de Sénarmont compensator or by translating the Wollaston prism in a traditional DIC configuration.
Wavefronts are represented in the tutorial by a disk with a double-headed arrow indicating the orientation of the electric vector. Dark blue disks symbolize both linearly polarized light and the ordinary wave component from an orthogonal pair. In contrast, red disks correspond to the extraordinary wavefront produced by either the birefringent retardation plate or the Wollaston prism. 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 the model to a new position.
The orientation of incident linearly polarized light with respect to the retardation (quarter-wavelength) plate fast axis 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 or right (negative and positive values, respectively), an increasing amount of light is passed through the slow axis of the retardation plate (indicated by a series of red disks exiting the light blue disc). As the slider is moved farther to the right or left, the size of the red disks increases and the size of the dark blue disks decreases proportionally (representing varying degrees of elliptically polarized light). Positive values of the slider result in the extraordinary wavefront (red disks) preceding the ordinary wavefront (dark blue disks) and vice versa. When the slider is positioned at the extreme left or right (plus or minus 45 degrees), the dark blue and red disks are equal in size (signifying circularly polarized light). Phase differences between the ordinary and extraordinary wavefronts, which are introduced by rotating the polarizer, result in the introduction of bias retardation. Wavefronts emerging from the Wollaston prism are either in the same phase (no bias retardation) or shifted in phase (bias retardation; either the ordinary or extraordinary wavefront emerges from the prism first) depending upon the position of the Polarizer Rotation slider.
In order to operate the tutorial, introduce varying amounts of bias retardation into the optical train using the Polarizer Rotation slider when the virtual optical train is in de Sénarmont mode, and then drag the model to different positions in the window to view the effects of polarized wavefronts passing through the system. Alternatively, the Wollaston Prism Translation slider produces the same net result when the tutorial is in Nomarski DIC mode. Progression of the wavefronts (colored disks) through the optical train can be suspended by clicking on the Pause button. The speed of the colored disks 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.
Regardless of whether bias is introduced into a differential interference contrast system by translating the objective Nomarski prism or by rotating the polarizer on a de Sénarmont compensator, the net result is the same. In a properly configured microscope that is aligned for Köhler illumination, an image of the light source and condenser prism is transferred by the optical system (condenser and objective) onto the inverted second Nomarski prism located at the objective rear focal plane. The linear phase shift across the face of the condenser prism is precisely compensated by an opposite phase shift in the objective prism. Translation of the objective prism along the shear axis does not alter the phase shift distribution, but instead, adds or subtracts a constant phase difference across the entire microscope aperture. In the same manner, rotating the polarizer in a de Sénarmont compensator also introduces a variable and controlled phase difference. The matched prism system enables image formation to occur with the same bias retardation for every wavefront pair projected from the condenser aperture, irrespective of the route through which it traverses the specimen to reach the objective.