Birefringence

What is imaged ?

Birefringence and Diattenuation are material properties that can occur when there is molecular order, that is, when the average molecular orientation is non-random, as in crystals or in aligned polymeric materials. Diattenuation can only occur when the material absorbs or otherwise reduces the transmittance of the light passing through the material. Birefringence occurs in absorbing and transparent materials and expresses the difference in refractive index for light polarized parallel and perpendicular to the axis of molecular alignment.

The molecular alignment creates a slow and a fast axis in the material. Light that is polarized parallel to the fast axis travels faster through the material than light that is polarized parallel to the slow axis. This leads to a differential phase shift between the polarization components of the transmitted light. The differential phase shift is called retardance. The Birefringence OpenPolScope measures and presents images of the retardance and orientation of fast and slow axis in the specimen.

Hardware

The OpenPolScope augments the traditional polarizing microscope with specific hardware and software components.

Required hardware components:

General: Wide-field microscope stand with monochromatic light source, such as a halogen lamp with bandpass filter, for best results use strain-free objective and condenser optics;
CCD or equivalent camera supported by Micro-Manager software;
Computer with Windows 7, ImageJ, and Micro-Manager installed.

OpenPolScope specific: LC universal compensator; analyzer for circularly polarized light.

The LC universal compensator is made of a linear polarizer and two variable retarder plates implemented as liquid crystal devices. Unpolarized light enters on the side of the linear polarizer and exits as polarized light whose polarization can be set to any state, including circular polarization and linear polarization of any orientation. The LC settings are computer controlled through an electronic controller box.

The liquid crystal devices for the universal compensator can be custom ordered from several manufacturers.

Unlike the traditional polarizing microscope, which is typically equipped with linear polarizers, the OpenPolScope requires a circular polarization analyzer for measuring linear birefringence in the specimen. A circular polarizer is typically made from a linear polarizer and a quarter wave plate that are bonded together. Circular polarizers are manufactured to a specific wavelength, but are also available as achromatic circular polarizers.

The OpenPolScope Group at the MBL can assist in acquiring and optimizing the installation of hardware and software components. See Services.

OpenPolScope Software

The OpenPolScope software synchronizes the LC settings and image acquisitions, calculates the retardance and slow axis orientation for each resolved image point, and presents the results as images.

Birefringence is one of three imaging modes of the OpenPolScope software which is built as Micro-Manager and ImageJ plugins.

Pol-Acquisition is a Micro-Manager plugin and is used for acquiring images.

Pol-Analyzer is an ImageJ plugin and is used for viewing and reprocessing data. The Pol-Analyzer plugin requires Micro-Manager to be installed for reading image data acquired using Pol-Acquisition.

Retardance is typically measured as a distance in nm, signifying the relative distance between the two wavefronts that are associated with the two polarization components that pass through a birefringent material. The OpenPolScope measures the retardance for every resolved specimen point and presents the results of the computation as the retardance image.

In the retardance image, dark areas correspond to sample regions that have no or little birefringence. They are optically isotropic. Bright areas, on the other hand, correspond to sample regions that are birefringent. Their brightness directly corresponds to the retardance, irrespective of the orientation of the slow and fast axes.

In the orientation image, each pixel value gives the orientation of the slow axis as an angle between 0° and 180° with respect to the horizontal axis in the image. The red lines indicate the slow axis orientation on regular grid points. The orientation lines can be overlaid on any of the images.

In the retardance image with orientation colors, hue represents the slow axis orientation and brightness represents retardance.

orientation image with orientation lines	retardance	retardance with orientation colors

Example

This retardance image was generated using a Nikon Microphot SA equipped with a liquid crystal universal compensator, a 60x/1.4 plan apochromat oil immersion objective and an achromat aplanat oil immersion condenser. The cell in the center is a primary spermatocyte from the crane fly, Nephrotoma suturalis. With the OpenPolScope, birefringence is revealed with striking contrast, regardless of specimen orientation, and thus, the spindle fibers, composed of bundled microtubules, are clearly imaged as bright structures on the non-birefringent (or weakly birefringent) background cytoplasm. At the periphery of the spindle is a mantle of elongated mitochondria, as well as numerous highly birefringent vesicular structures. The pole-to-pole distance is approximately 25µm. Credit: James R. LaFountain, University at Buffalo.

Phase Wrapping

In the above example, the retardance values of cell structures are a few nanometers and therefore way less than half the wavelength of the monochromatic light used for illumination in the microscope. The retardance of other samples, however, such as thick collagen fibers, polymer films, liquid crystalline materials or thick sections of birefringent crystals, can easily exceed this limit, which introduces ambiguity in the measured retardance versus the actual retardance of the sample. This ambiguity is introduced by a phenomenon called phase wrapping and is explained next.

For example, let us assume that the birefringence of the sample is 0.2 and the sample thickness is 2µm, then the retardance accumulated by polarized light passing through the sample is 0.2 x 2µm = 400nm.

Using light of wavelength 546nm, 400nm retardance is more than half the wavelength (276nm) of the imaging light. In this case, the retardance measured by the OpenPolScope algorithm will be 546nm - 400nm = 146nm.

The images or maps of measured retardance values still reflect the changes in specimen retardance, but the measured values have to be reinterpreted because of the ambiguity introduced by phase wrapping.

The graph on the right illustrates what happens when one measures increasing values of actual retardance using green light (wavelength 546nm). Only for values between zero and 546/2 = 273nm, actual retardance values correspond directly to measured retardance values. Higher retardance values than wavelength/2 are folded back by the phase wrapping phenomenon.

The dashed lines illustrate the earlier example of the measured retardance of 146nm when encountering an actual retardance of 400nm.

The measured slow axis orientation or azimuth values also have to be reinterpreted, if they are associated with actual retardance values that are larger than half the wavelength. In the above example of an actual retardance of 400nm, let's assume that the actual azimuth value is 20°. Using the standard OpenPolScope acquisition and processing routines, the measured retardance will turn out to be 146nm and the measured azimuth value will be 20°+90°=110°. In fact, regardless of what the actual azimuth value is, the measured azimuth value will be always orthogonal to the actual azimuth value. In other words the measured azimuth value will be be 90° higher or lower than the actual value. Furthermore, this 90° rotation of the measured slow axis orientation applies to all retardance values that lie between half and full wavelength, as is illustrated in the graph on the right.

When using red light of 633nm wavelength, then the inflection points move further out and an actual retardance of 400nm results in a measured retardance of 233nm. Hence, by sequentially making two measurements using two different wavelength light, the ambiguity can be resolved.

By considering the difference in retardance between the two measurements, one can come up with a clever scheme to find the actual retardance. This "phase unwrapping”, however, is not included in the OPS software.

Additional complications can occur if there are chromatic aberrations in the optics and images, which can make resolving the retardance near inflection points more tricky.