Wavefront Relationships in de Sénarmont and Nomarski DIC
In differential interference contrast (DIC) microscopy, the spatial relationship and phase difference between ordinary and extraordinary wavefronts is governed either by the position of the objective prism (Nomarski DIC) or the relationship between the polarizer and a thin quartz retardation plate in a de Sénarmont design. This interactive tutorial explores the similarities and differences between the wavefront relationship in the two microscope configurations.
The tutorial initializes with a de Sénarmont DIC microscope optical train bearing a condenser Wollaston prism and an objective Nomarski prism appearing in the window. A beam of linearly polarized light emerges from the polarizer and becomes separated into two orthogonal components before entering the lower Wollaston prism (labeled the Condenser Prism) and being sheared at the quartz wedge interface. In the tutorial, the ordinary wavefront is represented by short red lines (parallel to the browser window) on a black ray trace, while the extraordinary wavefront is depicted by black dots (perpendicular to the browser window) on a red ray trace. The sheared orthogonal wavefronts are rendered parallel by the condenser and pass through the specimen before being collected by the objective and focused onto the interference plane of the Nomarski prism (the Objective Prism). Recombined wavefronts emerge from the objective prism and pass through the analyzer to complete their journey through the virtual DIC microscope. Note that the raytrace paths are simplified schematic diagrams and not intended to accurately represent the actual refracted wavefront field passing through the optical system.
The microscope can be changed from a de Sénarmont to a traditional Nomarski configuration by toggling the Imaging Mode set of radio buttons (labeled de Sénarmont and Nomarski). In Nomarski imaging mode, the beam of linearly polarized light emerging from the polarizer first enters the lower Wollaston prism (labeled the Condenser Prism) before being separated into two orthogonal components and sheared at the quartz wedge interface. In de Sénarmont mode, the Polarizer Rotation Angle slider controls the relationship between wavefronts leaving the quarter wavelength retardation plate. The optical path difference between wavefronts is determined by the position of the polarizer, with respect to the retardation plate (prior to entry into a Wollaston or Nomarski prism), in de Sénarmont mode. However, in Nomarski mode, the Objective Prism Position slider is utilized to the create a similar optical path difference.
In order to operate the tutorial, use either the Objective Prism Position (Nomarski mode) or Polarizer Rotation Angle (de Sénarmont mode) slider to translate the objective prism laterally across the optical path of the microscope or rotate the polarizer, respectively. As the waveform relationship is altered, the Emerging Waveform (depicted in the upper right-hand corner of the tutorial window) changes from linear, through varying degrees of elliptical, and finally, to circular. When the waveform has some degree of elliptical or circular character, a portion of the light emerging from the objective prism can then pass through the analyzer to form an image. The Specimen Gradient slider can be utilized to increase the optical path gradient across the specimen, which will also produce a change in the waveform emerging from the objective prism. The speed of wavefronts traveling through the virtual microscope can be increased or decreased using the Applet Speed slider.
Bias has been traditionally introduced into the differential interference contrast microscope by translating the objective Nomarski prism back and forth along the optical axis using a fine adjustment knob located at the end of the mounting frame (usually positioned in the microscope nosepiece housing or an intermediate tube). An alternative technique, 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). At maximum extinction, the fast axis of the retardation plate is aligned with the transmission axis of the polarizer, and 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) 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. 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, while rotating the polarizer in the other direction will alter the vector trajectory to generate a left-handed elliptical sweep.
When the orientation of the polarizer transmission axis reaches either plus or minus 45 degrees (equivalent to one-quarter wavelength 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 prism and become sheared. 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.
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. As previously discussed, 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.
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, Robert T. Sutter, and Michael W. Davidson - National High Magnetic Field Laboratory, 1800 East Paul Dirac Dr., The Florida State University, Tallahassee, Florida, 32310.