Origin and Variation of Image Contrast
Image intensity in differential interference contrast (DIC) microscopy is a function of the difference in optical path experienced by the extraordinary and ordinary wavefronts as they travel through phase gradients in the specimen. This interactive tutorial explores how variations in the level of bias retardation introduced by translating a Nomarski or Wollaston prism affect the optical path difference and resulting specimen intensity in a DIC microscope.
The tutorial initializes with a model of an erythrocyte (human red blood cell) oriented parallel to the shear direction of the incident wavefront and viewed in cross section on the lower left-hand side of the window. The specimen is assumed to be homogeneous, isotropic, and non-birefringent, having a refractive index (n(s)) greater than that of the surrounding medium (n(m)). A sheared wavefront (located beneath the specimen in the window) is created by passage of plane-polarized light through a Wollaston (or Nomarski) prism housed at the condenser front focal plane (not illustrated). The extraordinary wavefront is drawn as a black line and the ordinary wavefront is represented by a red line displaced slightly to the right. For clarity and ease of illustration, both wavefronts are illustrated parallel to the browser window, but in reality, they are oriented mutually perpendicular to each other.
The wavefronts first pass through the specimen to produce an optical path difference created by the refractive index variations between the specimen and its surrounding medium. In the case of a transparent specimen, the optical path difference is determined by the product of the refractive index and the geometrical thickness of the specimen. The portions of the wavefronts passing through the specimen are retarded relative to those that pass through adjacent portions of the surrounding medium.
After leaving the specimen, the wavefronts enter a second Wollaston (or Nomarski) prism that is located in the objective rear focal plane. The function of this prism is to cancel the angular wave splitting (shear) induced by the first prism located before the specimen in the condenser front focal plane. Upon initialization, there is no additional optical path difference introduced by the second Wollaston prism. However, a lateral displacement of the wavefront deformation occurs as shear is eliminated by the objective Wollaston prism. This produces a path difference introduced between the wavefronts in regions where the specimen exhibits large phase gradients. Under these conditions, the optical system of the microscope is in a condition termed maximum extinction, and the specimen image (presented in the DIC Specimen Image window) appears as brightly highlighted regions on a very dark or black background.
For paraxial light rays, the ordinary and extraordinary wavefronts leave the Wollaston prism in phase and arrive at the specimen still in phase. The wavefronts pass through the surrounding medium and regions of the specimen having equal thickness (no refractive index gradients) without introduction of retardation between the waves. In regions (sloped specimen areas) having refractive index gradients, one or both of the wavefronts are retarded when passing through the specimen. At the left specimen edge, the ordinary wavefront is retarded to a greater degree than is the extraordinary wavefront, while the opposite is true for the right specimen edge.
Upon entering the analyzer, the phase differences in the wavefronts result in interference that produces the intensity and contrast variations observed in the microscope eyepieces. The intensity distribution (I) of the differential interference contrast image is given by the equation:
where I(p) is the light intensity that would be observed if the analyzer and polarizer transmission azimuths (vibration directions) were parallel, δ(c) and δ(s) are the phase retardations between the ordinary and extraordinary wavefronts induced by the second Wollaston prism and specimen respectively, and I(c) is the light intensity when the analyzer and polarizer are crossed and δ equals zero. The term I(c) represents stray light in the optical system introduced by a variety of artifacts including birefringence in lens elements, rotation of the polarization plane by highly curved lens surfaces, and imperfect polarization of light by the polarizer and analyzer. The intensity profile of the specimen across the shear axis of the microscope is plotted as a function of lateral wavefront displacement in the upper left-hand corner of the applet window (see the graph labeled Intensity). Adjacent to this graph is a digital image of a typical specimen observed under these conditions (the DIC Specimen Image window).
Specimens produce contrast based primarily on gradients in optical path that occur in the direction of shear in differential interference contrast microscopy. This gradient-dependent contrast generation mechanism occurs because the ordinary and extraordinary wavefronts are separated by less than the optical resolution of the microscope. Regions having constant optical path will produce minimal or no contrast while regions exhibiting large gradients and optical path differences tend to produce images of high contrast. Image contrast is at a maximum in the shear direction between the wavefronts and is minimal in regions perpendicular to the shear direction. As can be seen in the tutorial specimen image, intensity and contrast are very poor at maximum extinction (no bias retardation applied to the optical system). Under these conditions, edges and gradients appear brighter than the background and the overall image assumes the profile of a darkfield image produced by a thin specimen (a bright image on a dark background).
Changes in bias retardation can be introduced by translating the Bias Retardation slider to the left or right. Moving the slider in either direction increases the optical path difference between the ordinary and extraordinary wavefronts and produces a corresponding change in image intensity. When the slider is translated to the left (Positive Bias), the ordinary wavefront is retarded, producing an increase in the optical path difference. In contrast, moving the slider to the right (Negative Bias) retards the extraordinary wavefront in relation to the ordinary wavefront. In both cases, an inversion of brightness distribution is brought about by the optical path differences. A new specimen can be selected using the Choose A Specimen pull-down menu. The oil drop specimens simulate situations where the specimen refractive index is either higher (High RI) or lower (Low RI) than that of the surrounding medium.