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Glossary

The following is a brief introduction to terms that are relevant for observations with a polarized light microscope. For a more detailed explanation of these and other terms that describe physical phenomena or optical devices can be found in the following references (Shurcliff, 1962; Born and Wolf, 1980; Chipman, 1995; Hecht, 2002).

Analyzer

An analyzer is a polarizer that is used to analyze the polarization state of light (see Polarizer).

Azimuth

The azimuth is an angle that refers to the orientation of the slow axis of a uniformly birefringent region. The azimuth image refers to the array of azimuth values of a birefringent specimen imaged with the LC-PolScope. The azimuth is typically measured from the horizontal orientation with values increasing for counterclockwise rotation. Angles range between 0 and 180°, with both endpoints indicating horizontal orientation.

Birefringence

Birefringence is a material property 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. Molecular order usually renders the material optically anisotropic, leading to a refractive index that changes with the polarization of the light. Birefringence is defined as the difference in refractive index for light of different polarization.

Many types of molecular order lead to what is called uniaxial anisotropy, i.e. light propagating through a uniformly aligned material suffers phase retardation that depends on the polarization of the light, except when the light propagates along one unique direction, which is called the optic axis. Light propagating through the anisotropic material along the optic axis experiences the so-called ordinary refractive index (no), which is the same for all polarization directions. However, light that propagates in any other direction through the material experiences differences in the refractive index, depending on the light's polarization. Light that propagates perpendicular to the optic axis experiences the largest difference in refractive index when polarized parallel versus perpendicular to the optic axis. When polarized perpendicular to the optic axis it is the ordinary refractive index no, when polarized parallel to the optic axis, the light experiences the extraordinary refractive index ne. Birefringence is the difference ne-no=Δn and characterizes the anisotropy of refraction of the uniaxial material.

There are also materials whose anisotropy is called biaxial. For their explanation, the reader is referred to the references mentioned at the beginning of the Glossary.

Circularly polarized light

In circularly polarized light the electric field direction rotates either clockwise (rightcircularly) or counter-clockwise (left-circularly) when looking towards the source. While the field direction rotates, the field strength remains constant. Hence, the endpoint of the field vector describes a circle.

Compensator

A compensator is an optical device that includes one or more retarder plates and is commonly used to analyze the birefringence of a specimen. For a traditional polarizing microscope several types of compensators exist that typically use a single fixed retarder plate mounted in a mechanical rotation stage. With the help of a compensator it is possible to distinguish between the slow and fast axis direction and to measure the retardance of a birefringent object after orienting it at 45° with respect to the polarizers of the microscope.

The LC-PolScope employs a universal compensator that includes two electro-optically controlled, variable retarder plates. Using the universal compensator it is possible to measure the retardance and slow axis orientation of birefringent objects that have any orientation in the plane of focus.

Diattenuation

It is the property of a transmitting material in which the transmittance depends on the incident polarization state of light. A diattenuating material will absorb linear polarization along one axis preferentially. It is related to dichroism, which is the same property but usually described in terms of absorption rather than transmission.

Dichroism

Dichroism is a material property that can occur in absorbing materials with a non-random orientation of the light absorbing molecules. Dichroism refers to the difference in the absorption coefficients for light polarized parallel and perpendicular to the principal axis of alignment.

The measurement of optical anisotropy by the LC-PolScope is affected by the dichroism of absorbing materials. In non-absorbing, clear specimens, however, dichroism vanishes and birefringence is the dominant optical anisotropy measured by the LC-PolScope. Like absorption, dichroism is strongly wavelength dependent, while birefringence only weakly depends on wavelength.

Elliptically polarized light

In elliptically polarized light, as in circularly polarized light, the electric field direction rotates either clockwise or counter-clockwise when looking towards the source. However, while the field direction rotates, the field strength varies in such a way that the end point of the field vector describes an ellipse. The ellipse has a long and short principal axis that are orthogonal to each other and have fixed orientation. Any type of polarization (linear, circular or elliptical) can be transformed into any other type of polarization by means of polarizers and retarders.

Ext functions

These are functions that have been added to the macro language by plugins using the MacroExtension interface. More info. These also include hardware control using serial commands as shown here.

Extinction

The extinction is defined as the ratio of maximum to minimum transmission of a beam of light that passes through a polarization optical train. Given a pair of linear polarizers, for example, the extinction is the ratio of intensities measured for parallel versus perpendicular orientation of the transmission axes of the polarizers (extinction = I∥/I⊥). In addition to the polarizers, the polarization optical train can also include other optical components which usually affect the extinction of the complete train. In a polarizing microscope the objective and condenser lens are located between the polarizers and significantly reduce the extinction of the whole set-up.

Fast axis

The fast axis describes an orientation in a birefringent material. For a given propagation direction, light that is polarized parallel to the fast axis experiences the lowest refractive index, and hence travels the fastest in the material (for the given propagation direction). See also entry for Slow axis

Linearly polarized light

In a linearly polarized light beam the electric field is oriented along a single axis in the plane perpendicular to the propagation direction.

Macro Language

A macro is a simple program that automates a series of ImageJ commands. The easiest way to create a macro is to record a series of commands using the command recorder. A macro is saved as a text file and executed by selecting a menu command, by pressing a key or by clicking on an icon in the ImageJ toolbar. More info can be found here.

Mode

A Mode in context of OpenPolScope can be defined as an optical property (eg. Birefringence, Diattenuation, etc.) that can be computationally calculated based on n images acquired at n optical states.

OpenPolScope

OpenPolScope.org was created for users and developers of polarized light microscopy techniques. It is an open-access platform for the collection and dissemination of knowledge about the technology, its applications and its further development. The website is maintained by members of the Cellular Dynamics Imaging Group and the Laboratory of Rudolf Oldenbourg at the Marine Biological Laboratory in Woods Hole, Massachusetts.

Optic axis

The optic axis refers to a direction in a birefringent material. Light propagating along the optic axis does not change its polarization, hence for light propagating along the optic axis the birefringent material behaves as if it were optically isotropic.

Plugin

The Mode-Plugin which are specific to Pol-Acquisition and Pol-Analyzer defines the type of device required (VariLC, MeadowlarkLC, generic filter wheel) and a computation algorithm that would produce the computed images.

Polarized Fluorescence

It has its origin in the polarized excitation and emission of single fluorophores. In microscopy, the anisotropy of fluorescence (also referred to as fluorescence polarization or polarized fluorescence) has been used to analyze molecular properties and dynamics, such as rotational diffusion, molecular binding and order-disorder transitions of protein domains, in in-vitro systems and inside living cells.

Polarized light

A beam of light is said to be polarized when its electric field is distributed non-randomly in the plane perpendicular to the beam axis. In unpolarized light the orientation of the electric field is random and unpredictable. In partially polarized light, some fraction of the light is polarized, while the remaining fraction is unpolarized. Most natural light is unpolarized (sun, incandescent light), but can become partially or fully polarized by scattering, reflection, or interaction with optically anisotropic materials. These phenomena are used to build devices to produce polarized light (see Polarizer).

Polarizer

A polarizer, sometimes called a polar, is a device that produces polarized light of a certain kind. The most common polar is a linear polarizer made from dichroic material (e.g. a plastic film with embedded, small iodine crystals that were aligned by stretching the plastic) that transmits light of one electric field direction while absorbing the orthogonal field direction. Crystal polarizers are made of birefringent crystals that split the light beam into orthogonal linear polarization components. A polarizer that produces circularly polarized light, a circular polarizer, is typically built from a linear polarizer followed by a quarter wave plate (see Analyzer).

The LC-PolScope employs a universal compensator that can also be called a universal polarizer because it converts linear polarization into any other type of polarization by means of two variable retarders (see section Polarization optical components).

Retardance

Retardance is a measure of the relative optical path difference, or phase change, suffered by two orthogonal polarization components of light that has passed through an optically anisotropic material. Retardance is also called differential or relative retardation. Retardance is the primary quantity measured by a polarizing microscope. Assume a nearly collimated beam of light traversing a birefringent material. The light component that is polarized parallel to the high refractive index axis travels at a slower speed through the birefringent material than the component polarized perpendicular to that axis. As a result, the two components, which were in phase when they entered the material, exit the material out of phase. The relative phase difference, expressed as the distance between the respective wave fronts, is called the retardance:

retardance R=(ne-no).l = Δn.l,

where l is the physical path length or thickness of the birefringent material. Hence, retardance has the dimension of a distance and is often expressed in nm. Sometimes it is convenient to express that distance as a fraction of the wavelength λ, such as λ/4 or λ/2. Retardance can also be defined as a differential phase angle, in which case λ/4 corresponds to 90° and λ/2 to 180° phase difference.

As a practical example consider a mitotic spindle observed in a microscope that is equipped with low numerical aperture lenses (NA ≤ 0.5). When the spindle axis is contained in the focal plane, the illuminating and imaging beams run nearly perpendicular to the spindle axis. Under those conditions, the retardance measured in the center of the spindle is proportional to the average birefringence induced by the dense array of aligned spindle microtubules. To determine , it is possible to estimate the thickness, l, either by focusing on spindle fibers located on top and bottom of the spindle and noting the distance between the two focus positions, or by measuring the lateral extent of the spindle when focusing through its center. The latter approach assumes a rotationally symmetric shape of the spindle. Typical values for the spindle retardance of crane fly spermatocytes and of other cells is 3 to 5 nm and the spindle diameter is about 30 to 40 μm, leading to an average birefringence of around 10-4. It has been found that the retardance value of the spindle is largely independent of the NA for imaging systems using NA ≤ 0.5 (Sato et al., 1975).

On the other hand, when using an imaging set-up that employs high NA optics (NA > 0.5) for illuminating and imaging the sample, the measured retardance takes on a somewhat different context. For example, the retardance measured in the center of a microtubule image recorded with a LC-PolScope equipped with a high numerical aperture objective and condenser lens is 0.07 nm. A detailed study showed that the peak retardance decreased inversely with the NA of the lenses. However, the retardance integrated over the cross section of the microtubule image was independent of the NA (Oldenbourg et al., 1998). While a conceptual understanding of the measured retardance of submicroscopic filaments has been worked out in the aforementioned publication, a detailed theory of these and other findings about the retardance measured with high NA optics has yet to materialize.

Retarder

A retarder or waveplate is an optical device that is typically made of a birefringent plate. The retardance of the plate is the product of the birefringence of the material and the thickness of the plate. Fixed retarder plates are either cut from crystalline materials such as quartz, calcite, mica, or they are made of aligned polymeric material. If the retardance of the plate is l/4, for example, the retarder is called a quarter waveplate. A variable retarder can be made from a liquid crystal device. A thin layer of highly birefringent liquid crystal material is sandwiched between two glass windows that each bear a transparent electrode. A voltage applied between the electrodes produces an electric field across the liquid crystal layer that reorients the liquid crystal molecules. This reorientation changes the birefringence of the layer without affecting its slow axis direction or thickness.

Slow axis

The slow axis describes an orientation in a birefringent material. For a given propagation direction, light polarized parallel to the slow axis travels the slowest in the material,and hence experiences the highest refractive index.See also entry for Fast axis

Waveplate

A retarder or waveplate is an optical device that is typically made of a birefringent plate. The retardance of the plate is the product of the birefringence of the material and the thickness of the plate. Fixed retarder plates are either cut from crystalline materials such as quartz, calcite, mica, or they are made of aligned polymeric material. If the retardance of the plate is l/4, for example, the retarder is called a quarter waveplate. A variable retarder can be made from a liquid crystal device. A thin layer of highly birefringent liquid crystal material is sandwiched between two glass windows that each bear a transparent electrode. A voltage applied between the electrodes produces an electric field across the liquid crystal layer that reorients the liquid crystal molecules. This reorientation changes the birefringence of the layer without affecting its slow axis direction or thickness.

  • Born, M. and E. Wolf (1980) Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light, Elmsford, N.Y.: Pergamon Press.
  • Chipman, R. A. (1995) Polarimetry. in M. Bass (ed.) Handbook of Optics, vol. 2. New York: McGraw-Hill, Inc.
  • Hecht, E. (2002) Optics, San Francisco, CA: Pearson/Addison-Wesley.
  • Oldenbourg, R., E. D. Salmon and P. T. Tran. 1998. Birefringence of single and bundled microtubules. Biophysical Journal 74: 645-54.
  • Sato, H., G. W. Ellis and S. Inoue. 1975. Microtubular origin of mitotic spindle form birefringence. Demonstration of the applicability of Wiener's equation. Journal of Cell Biology 67: 501-17.
  • Shurcliff, W. A. (1962) Polarized Light, Production and Use, Cambridge, MA: Harvard University Press.

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