Relationship between axial ratio and cross polarization microscope

Antenna Axial Ratio vs Cross Polarization

relationship between axial ratio and cross polarization microscope

Polarized light microscopy (PLM) is a technique which employs the use of polarizing . through the substance at the same rate and these two rays are in phase with interference, and the sample can thus no longer be seen under cross polars. When the sample is rotated to a 45° angle in relation to the polarizers, the. Even the axial ratio of the assembly (∼) was undistinguishable from the axial Figure 22 illustrates dynamic association–dissociation cycles of α- and β- tubulin into microtubules growing to a size visible under the polarizing microscope. by quenching at 2◦C. (From A.L. Hitt, A.R. Cross, and C.R. Williams Jr. J. Biol. Cross polarized CP signal level given axial ratio. The scale works both ways. If the left side is axial ratio, then the right side is X-polarization or vice-versa.

One of the images appears as you normally would expect when viewing an object through clear glass or an isotropic crystal. The other pencil image appears displaced, due to the nature of doubly-refracted light. When anisotropic crystals refract light, the resulting rays are polarized and travel at different velocities as discussed above.

Microscopy: Examples of Using Polarization Microscopy (Shinya Inoue)

One of the rays travels with the same velocity in every direction through the crystal and is termed the ordinary ray. The other ray travels with a velocity that is dependent upon the propagation direction within the crystal. This light ray is termed the extraordinary ray. The distance of separation between the ordinary and extraordinary ray increases with increasing crystal thickness. The two independent refractive indices of anisotropic crystals are quantified in terms of their birefringence, a measure of the difference in refractive index.

This expression holds true for any part or fragment of an anisotropic crystal with the exception of light waves propagated along the optical axis of the crystal. As we mentioned above, light that is doubly refracted through anisotropic crystals is polarized with the vibration directions of the polarized ordinary and extraordinary light waves being oriented perpendicular to each other.

We can now examine how anisotropic crystals behave under polarized illumination in a polarizing microscope. Figure 3 illustrates a birefringent crystal placed between two polarizers whose vibration directions are perpendicular to each other and oriented according to the arrows next to the polarizer and analyzer labels.

White light entering the polarizer on the left is polarized with an orientation in the direction indicated by the arrow next to the polarizer label and is arbitrarily represented by a "red" sinusoidal light wave. Next, the polarized light enters the anisotropic crystal where it is refracted and divided into two separate components vibrating parallel to the crystallographic axes and perpendicular to each other arbitrarily, the "blue" and "red" light waves.

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The polarized light waves then pass through the analyzer whose polarization position is indicated by the arrow next to the analyzer labelwhich passes only those components of the light waves that are parallel to the polarization direction of the analyzer.

Let us now examine more closely how birefringent anisotropic crystals interact with polarized light in an optical microscope. Our subject material is a hypothetical tetragonal crystal having an optical axis oriented parallel to the long axis of the crystal.

relationship between axial ratio and cross polarization microscope

Light entering the crystal from the polarizer will be traveling perpendicular to the optical long axis of the crystal. Figure 4 illustrates the crystal as it would appear in the eyepieces of a microscope under crossed-polarized illumination. Circular polarization is often encountered in the field of optics and in this section, the electromagnetic wave will be simply referred to as light. The nature of circular polarization and its relationship to other polarizations is often understood by thinking of the electric field as being divided into two components which are at right angles to each other.

Refer to the second illustration on the right. The vertical component and its corresponding plane are illustrated in blue while the horizontal component and its corresponding plane are illustrated in green. Notice that the rightward relative to the direction of travel horizontal component leads the vertical component by one quarter of a wavelength.

relationship between axial ratio and cross polarization microscope

It is this quadrature phase relationship which creates the helix and causes the points of maximum magnitude of the vertical component to correspond with the points of zero magnitude of the horizontal component, and vice versa. The result of this alignment is that there are select vectors, corresponding to the helix, which exactly match the maxima of the vertical and horizontal components.

To minimize visual clutter these are the only helix vectors displayed. To appreciate how this quadrature phase shift corresponds to an electric field that rotates while maintaining a constant magnitude, imagine a dot traveling clockwise in a circle. Consider how the vertical and horizontal displacements of the dot, relative to the center of the circle, vary sinusoidally in time and are out of phase by one quarter of a cycle.

The displacements are said to be out of phase by one quarter of a cycle because the horizontal maximum displacement toward the left is reached one quarter of a cycle before the vertical maximum displacement is reached.

Circular polarization - Wikipedia

Now referring again to the illustration, imagine the center of the circle just described, traveling along the axis from the front to the back. The circling dot will trace out a helix with the displacement toward our viewing left, leading the vertical displacement. Just as the horizontal and vertical displacements of the rotating dot are out of phase by one quarter of a cycle in time, the magnitude of the horizontal and vertical components of the electric field are out of phase by one quarter of a wavelength.

The next pair of illustrations is that of left-handed, counter-clockwise circularly polarized light when viewed by the receiver.

Because it is left-handed, the rightward relative to the direction of travel horizontal component is now lagging the vertical component by one quarter of a wavelength rather than leading it.

relationship between axial ratio and cross polarization microscope

Reversal of handedness by phase shift[ edit ] To convert a given handedness of polarized light to the other handedness one can use a half- waveplate.

A half-waveplate shifts a given component of light one half of a wavelength relative to the component to which it is orthogonal. Reversal of handedness by reflection[ edit ] The handedness of polarized light is also reversed when it is reflected off a surface at normal incidence. Upon such reflection, the rotation of the plane of polarization of the reflected light is identical to that of the incident field.

However, with propagation now in the opposite direction, the same rotation direction that would be described as "right handed" for the incident beam, is "left-handed" for propagation in the reverse direction, and vice versa.

relationship between axial ratio and cross polarization microscope

Aside from the reversal of handedness, the ellipticity of polarization is also preserved except in cases of reflection by a birefringent surface. Note that this principle only holds strictly for light reflected at normal incidence.