Polarized Light Microscopy

The Quarter Wavelength Retardation Plate

The quarter wavelength retardation plate is a common optical accessory for polarized light microscopy that operates by introducing a relative phase shift of 90 degrees between the orthogonal wavefronts (ordinary and extraordinary) passing through when the plate is illuminated with linearly polarized light. A phase shift of 90 degrees between the ordinary and extraordinary components converts the incident linear polarized light vibrations into either elliptical or circularly polarized light. Quarter wavelength retardation plates are useful for the qualitative analysis of conoscopic and orthoscopic images, and for the assessment of optical path differences in birefringent specimens.

The simple anatomy of a quarter wavelength retardation plate is presented in Figure 1 for a typical commercial unit. Retardation materials employed in construction of the plate vary according to the application, but usually consist of either an optical mineral thin section (such as quartz or mica) or a highly aligned birefringent linear organic polymer sandwiched between two isotropic optically flat glass plates. Regardless of the material used in producing retardation, the optical path difference (usually inscribed on the retardation plate frame) and optical axis orientation of the birefringent retarding material must be carefully controlled so that the plate can add a known retardation value to both the high and low refractive index azimuths of orthogonal wavefronts. As illustrated in Figure 1, the birefringent retardation material is positioned in the window of a rectangular frame that is inserted into the microscope optical pathway at a 45-degree angle with respect to the transmission orientations of the polarizer and analyzer. The direction of the slow (high refractive index) axis of the wavefront ellipsoid is indicated on the retardation plate frame as a double-headed arrow accompanied by the Greek symbol for "gamma" (g). In most cases, the slow axis orientation is perpendicular to the long dimension of the retardation plate frame, although this fact should be verified before attempting to use the instrument. Modern quarter wavelength retardation plates are built in a frame having standardized DIN dimensions (6 x 20 millimeters) that will enable their use in a variety of microscopes.

The quarter wavelength retardation plate is designed to introduce a relative retardation of exactly one-quarter wavelength (in the green or 550 nanometer region), or 90 degrees, between the ordinary and extraordinary wavefronts passing through the plate when the birefringent retardation material is illuminated by linearly polarized light at a 45-degree incident angle to the index ellipsoid, as illustrated in Figure 2. The resulting phase shift converts the linear input wavefront to a circularly polarized output wavefront. This action occurs because the orthogonal ordinary and extraordinary components have equal amplitudes when linear light oriented at a 45-degree angle to the principal (the fast or slow) axes is incident on a quarter wavelength retardation plate. In a similar manner, the quarter wavelength plate will convert an incoming circularly polarized wavefront into a linearly polarized wavefront.

Commercial quarter wavelength retardation plates are specified by their linear retardation, which is 137 nanometers for the device illustrated in Figure 1 that is designed to operate in light having a principal wavelength of 548 nanometers (in the green region). In polarized light microscopy applications, the quarter wavelength plate is utilized in a similar manner to the full wave retardation plate in order to determine whether the combination of a weakly birefringent specimen and the plate (oriented at a 45-degree angle to the polarizer and analyzer) yield higher or lower order interference colors. However, the quarter wavelength plate has been largely supplanted by the full wave retardation plate due to the superior sensitivity of the latter in producing color changes that can be readily observed. In cases where birefringent specimens display higher order interference colors between crossed polarizers without a retardation plate, then the quarter wavelength plate can often be used to advantage over the full wave plate to determine optical path differences.

This concept is illustrated in Figures 3(a) and 3(b) for a polished thin section of tactic skarn, which contains inclusions that exhibit first and second order interference colors in polarized light without the presence of a retardation plate or compensator. When a first order retardation plate is employed to determine the optical sign of this birefringent ore, the interference colors are shifted up the Michel-Levy chart by a single wavelength and can lead to confusion during quantitative analysis. Conversely, using a quarter wavelength plate instead produces the customary first order yellow for the fast optical axis (Figure 3(a)) and second order blue hue for the slow axis (Figure 3(b)), allowing for easier identification of the optical properties.

The primary use for quarter wavelength retardation plates is to determine the optical sign of birefringence from interference figures observed in conoscopic mode with a Bertrand lens (Figures 3(c) and 3(d)). Insertion of a quarter wavelength retardation plate resolves the center of a uniaxial interference figure (Figure 3(c)) into two dark spots (Figure 3(d)). If the dark spots are positioned at right angles to the slow vibration axis of the compensator crystal (in quadrants two and four; Figure 3(d)), then the sign of birefringence for the crystal is positive. Conversely, if the dark spots are positioned parallel to the compensator crystal slow axis (in quadrants one and three; Figure 3(d)), the crystal has a negative sign of birefringence. Note that other rings in the interference pattern are translated either towards the center or the periphery of the pattern according to the optical sign. The interference pattern in Figure 3(c) was generated conoscopically using a polished thin section of the mineral lamproite, which exhibits negative birefringence. A similar technique can be employed to determine the optical sign of birefringence for biaxial crystals.

The extinction bands in polarized light images can be eliminated for image analysis purposes by inserting crossed quarter wavelength retardation plates into the microscope optical path with the specimen sandwiched between the two plates. In effect, the retardation introduced by the first quarter wavelength plate is precisely cancelled by the second, so that light reaching the analyzer contains only the retardation introduced by the specimen itself. In practice, one of the retardation plates is inserted into the nosepiece or intermediate tube slot with the slow vibration axis oriented Northeast-Southwest (by convention in modern microscopes). The second plate must be placed between the polarizer and the specimen (usually in or very near the condenser) with the slow axis oriented Northwest-Southeast. The two plates should be fabricated from the same material in order to completely eliminate extinction bands. If the two plates are accurately aligned, a minimum change of polarization colors will be observed in birefringent specimens as they are rotated through 360 degrees with the microscope circular stage. Images of purified riboflavin (Vitamin B2) crystallites in polarized light (Figure 3(e)) alone, and with quarter wavelength retardation plates inserted beneath the stage and above the objective rear aperture are illustrated in Figures 3(e) and 3(f), respectively. Note that the extinction regions of the spherulitic crystallite present in Figure 3(e) have been eliminated by the application of two quarter wavelength plates (Figure 3(f)), which more clearly defines the texture.

In summary, the quarter wavelength retardation plate is capable of detecting optical path differences of (plus or minus) one-half wavelength by rotating the stage through 90 degrees. In this regard, the plate has a sensitivity range lying between the Bräce-Köhler and quartz wedge compensators and overlaps with the de Sénarmont compensator. Unlike many of the adjustable compensators, the quarter wavelength retardation plate can be effectively used in white light, but the most accurate results are obtained when the plate is coupled to the wavelength for which the crystal was prepared (for example, 548 nanometer green light for a 137 nanometer plate). The retardation plate can also be used to produce circularly polarized light by inserting it into the optical path above the polarizer.

Contributing Author

Polarized Light Microscopy

The First Order (Full Wave) Retardation Plate

Optical path differences ranging from a fraction of a wavelength up to several wavelengths can be readily estimated using a first order (or full wave) retardation plate. This versatile tool is known by several names, including a red plate, red-I (red-one) plate, lambda (l) plate, gypsum plate, selenite plate, sensitive violet, or simply a color tint plate, and adds a fixed optical path difference between 530 and 560 nanometers (depending upon the manufacturer) to every wavefront in the field. The first order retardation plate is a standard accessory that is frequently utilized to determine the optical sign (positive or negative) of a birefringent specimen in polarized light microscopy. In addition, the retardation plate is also useful for enhancing contrast in weakly birefringent specimens.

The elegantly simple anatomy of a first order retardation plate is presented in Figure 1 for a typical commercial unit. Retardation materials employed in construction of the plate vary according to the application, but usually consist of either an optical mineral thin section (such as gypsum/selenite, quartz, calcite, or mica) or a highly aligned birefringent linear organic polymer sandwiched between two isotropic optically flat glass plates. Regardless of the material used in producing retardation, the optical path difference (usually inscribed on the retardation plate frame) and optical axis orientation of the birefringent retarding material must be carefully controlled so that the plate can add a known retardation value to both the high and low refractive index azimuths. As illustrated in Figure 1, the birefringent retardation material is positioned in a rectangular frame that is inserted into the microscope optical pathway at a 45-degree angle with respect to the transmission orientations of the polarizer and analyzer. The direction of the slow (high refractive index) axis of the wavefront ellipsoid is indicated on the retardation plate frame as a double-headed arrow accompanied by the Greek symbol for "gamma" (g). In most cases, the slow axis orientation is perpendicular to the long dimension of the retardation plate frame, although this fact should be verified before attempting to use the instrument. Modern first order retardation plates are built in a frame having standardized DIN dimensions (6 x 20 millimeters) that will enable their use in a variety of microscopes.

The first order retardation plate is designed to introduce a relative retardation of exactly one wavelength (in the green or 550 nanometer region) between the ordinary and extraordinary wavefronts passing through the plate when the birefringent retardation material is illuminated by linearly polarized light at a 45-degree incident angle to the index ellipsoid. As a result, green wavelengths emerge from the retardation plate crystal still linearly polarized and having the same orientation as when they entered the retardation material (parallel to the polarizer). These wavelengths are perpendicular to the analyzer, thus are absorbed and do not pass through. The orthogonal wavefronts of all other wavelengths will experience some degree of retardation (less than a full wavelength) and will emerge from the retardation plate having varying degrees of elliptical polarization. These wavefronts are therefore able to pass a component vector through the analyzer. Subtracting the green wavelengths (blocked by the analyzer) from white light yields bright magenta-red, which results from a combination of all visible light spectral colors when the green wavelength band is missing. The magenta color observed in the microscope when a first order retardation plate is inserted into the optical train is a direct result of the events described above and is the origin for much of the common nomenclature describing this important qualitative tool.

The behavior of a quartz first order retardation plate in polarized white light, symbolized by a combination of red, green, and blue wavefronts, is reviewed in Figure 2. Without a specimen in the optical pathway (Figure 2(a)), the retardation plate induces an elliptical polarization vector to the red and blue waves as they pass through, but the green light travels through the quartz crystal as a linearly polarized wavefront that is absorbed by the analyzer. As a result, only a component of the red and blue waves is able to pass through the analyzer to produce a spectrum of white light minus the green wavelengths, which is seen in the microscope as a bright magenta background.

When a birefringent specimen with a wavefront ellipsoid parallel to the retardation plate is inserted into the optical pathway (Figure 2(b)), the relative retardation of orthogonal wavefronts is increased across the viewfield so that the color (red) now exhibiting linear polarized behavior is shifted to longer wavelengths. The blue and green wavelengths are elliptically polarized and interfere at the intermediate image plane to form a hue similar to second order blue (an addition color). Rotating the specimen by 90 degrees alters the relationship between the wavefront ellipsoids (Figure 2(c)) so that they are now perpendicular. In this case, the relative retardation of the orthogonal wavefronts is decreased across the viewfield and the shorter (blue) wavelengths emerge as linearly polarized light (only to be absorbed by the analyzer). Elliptically polarized green and red wavelengths ultimately recombine to form a first order yellow (subtraction) interference color.

Inserting a first order retardation plate into the optical path of a polarized light microscope introduces a dramatic display of interference colors in thin, birefringent specimens that is not only aesthetically beautiful, but also highly useful as an indicator of several optical properties. Quantitative evaluations of relative retardation and determinations of the index ellipsoid orientation are readily achieved with a first order retardation plate. In geological and materials investigations, first order retardation plates are often employed to determine specimen thickness and to identify birefringent crystalline and polymeric materials. The tool is capable of measuring retardations with an accuracy of approximately 2 nanometers in specimens that have relatively low (one-third of a wavelength) optical path differences.

With simple uniaxial birefringent materials, the first order retardation plate can be employed to determine whether the extraordinary wavefront is slower or faster than the ordinary wavefront and thus determine the sign of birefringence. If the extraordinary wavefront is slower than the ordinary wavefront, the specimen displays positive birefringence. Conversely, a negative sign of birefringence is observed in specimens that have an ordinary wavefront that is slower than the extraordinary wavefront. First order retardation plates are ideal for use with specimens that have very low order (or only gray-level) interference colors when observed in the polarized light microscope. Before attempting an analysis of birefringence, specimens must first be oriented with the index ellipse in a diagonal position (45-degree angle) with respect to the microscope polarizer and analyzer. The two vibration (ordinary and extraordinary) azimuths will then run Northeast-Southwest and Northwest-Southeast, whereas the polarizer is oriented East-West and the analyzer North-South (as seen in the microscope viewfield).

After the specimen has been properly oriented, the colors appearing in the microscope eyepieces represent interference that is generated by the additive effects of the specimen and the first order retardation plate. If the specimen slow vibration axis is superimposed over the corresponding axis of the retardation plate, the additive retardation effects will result in higher order interference colors (termed the additive position). However, if the fast axis of the specimen is parallel to the slow axis of the retardation plate, the relative retardation will be decreased and result in lower order interference colors (the subtractive position). As an example, in a relatively thin, elongated birefringent crystal that displays only first order gray intensities under crossed polarized illumination, addition of a first order retardation plate to the optical train will result in quadrants that display blue and yellow interference colors, depending upon the orientation of the crystal. In positive crystals, yellow interference colors are observed when the crystal is oriented Southeast to Northwest, while blue colors result from rotating the crystal by 90 degrees (into a Northeast-Southwest direction). Likewise, negative crystals exhibit yellow colors when oriented Northeast-Southwest and blue colors when oriented Southeast-Northwest.

This effect is illustrated with a pair of synthetic acetate fibers in Figures 3(a) and 3(b). Without a first order retardation plate in the optical path, the fibers appear birefringent with a 140-nanometer first order gray intensity superimposed on a jet black background (not illustrated). When the long axis of the synthetic acetate is oriented Northwest-Southeast and a first order retardation plate inserted into the microscope tube, the fibers acquire a first order yellow hue on a magenta background (Figure 3(a)). Rotating the microscope stage by 90 degrees (Northeast-Southwest) alters the interference color to second order blue (Figure 3(b)). From these results, the optical sign of birefringence for the acetate fibers is judged to be positive.

The sign of birefringence can also be readily determined using a first order retardation plate coupled to observation of conoscopic interference patterns with a Bertrand lens (see Figures 3(c) and 3(d)). When a Bertrand lens is inserted into the optical train of a polarized light microscope (between the objective rear aperture and the observation tubes), the conoscopic image of a uniaxial quartz crystal appears as a series of concentric rings having increasing orders of interference fringes from the center to the periphery, which are superimposed on a darkened Maltese cross (Figure 3(c)). Inserting a first order retardation plate into the microscope nosepiece or intermediate tube divides the image into quadrants that display higher order interference colors (Figure 3(d)). If the first and third quadrants (see Figure 3(d)) of the conoscopic image produce additive interference colors (blue and higher), the crystal is positively birefringent. However, if the second and fourth quadrants add to higher interference colors, the crystal is negatively birefringent. The conoscopic image of quartz (Figure 3(d)) reveals that the optical sign of birefringence is positive in quartz having this crystalline lattice structure. Biaxial crystals can also be examined conoscopically to determine their sign of birefringence.

First order retardation plates are also efficient at increasing contrast in very weakly birefringent specimens that are difficult or impossible to detect using crossed polarized illumination alone. Many of the common birefringent biological assemblies examined in polarized light, such as cell walls, starch granules, lignin, microtubules, and actin filaments, fall into this category. An excellent example is provided by a thin section of human tongue, which displays several birefringent structures (Figures 3(e) and 3(f)) of varying intensity. In crossed polarized illumination (Figure 3(e)), weakly birefringent condensed formations at the edge of the tissue are difficult to image and striated muscle tissue supporting the structures is absent. In contrast, when a first order retardation plate is added to the optical train, the structure of all birefringent features becomes readily apparent (Figure 3(f)) and the higher order (blue and yellow) interference colors provide an indication of the optical sign.

Contributing Author

Michael W. Davidson - National High Magnetic Field Laboratory, 1800 East Paul Dirac Dr., The Florida State University, Tallahassee, Florida, 32310.

Introduction to Compensators and Retardation Plates

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Polarized light microscopy is a valuable tool for revealing the presence and nature of submicroscopic structural motifs in a wide variety of materials ranging from mineral thin sections to fibers and biological specimens. In many cases, molecular ordering in these specimens is an intrinsic material property, but order can also be induced on multiple levels by dynamic shear, stretching, concentration changes, temperature fluctuations, and force fields. When the ordered state involves structural anisotropy, the optical state usually also displays anisotropic effects in polarized light observations. Quantitative measurements of optical anisotropy is therefore useful in the optical analysis of birefringent specimens.

figure1

Optical anisotropy is studied in the polarized light microscope with accessory plates that are divided into two primary categories: retardation plates that have a fixed optical path difference and compensators, which have variable optical path lengths. Addition of a retardation plate or compensator to the polarized light microscope produces a highly accurate analytical instrument that can be employed to determine the relative retardation (often symbolized by the Greek letter Γ) or optical path difference between the orthogonal wavefronts (termed ordinary and extraordinary) that are introduced into the optical system by specimen birefringence. The terms relative retardation, used extensively in polarized light microscopy, and optical path difference (Δ or OPD), are both formally defined as the relative phase shift between the orthogonal wavefronts, expressed in nanometers, according to the equation:

Δ = Γ = t • (ne - no)

where t refers to the thickness of the specimen (the physical distance traversed by light waves through the specimen), n(e) is the refractive index experienced by the extraordinary wavefront, and n(o) is the refractive index experienced by the ordinary wavefront. The terms (refractive index and thickness) on the right side of the equation are collective referred to as the specimen birefringence. From this relationship, it is obvious that specimens having differing thickness and refractive index gradients can display identical optical path differences or relative retardations. Furthermore, if either the birefringence or the thickness of a specimen is known, the other parameter can be easily determined.

Retardation plates are composed of optically anisotropic quartz, mica, and gypsum minerals ground to a precise thickness and mounted between two optical windows having flat (plane) faces, which are designed to introduce a fixed amount of retardation between the orthogonal wavefronts passing through the crystal. More recently, several manufacturers have shifted to the application of a highly aligned and stretched linear organic polymer to produce anisotropic retardation plates. Compensators and retardation plates have varying anisotropic plate thickness and optical properties targeted at producing a specific optical path length difference or relative retardation between mutually perpendicular (orthogonal) plane-polarized light waves when inserted diagonally in the microscope between crossed polarizers. In most cases the optical axis of the retardation material is confined to the surface plane of the anisotropic plate. Incident rays of linearly polarized light enter the plate perpendicular to the optical axis and are separated into orthogonal components that follow the same trajectory through the plate. However, due to refractive index differences introduced by the anisotropic retardation material, one of the wavefronts is shifted in phase (retarded) relative to the other. The wavefronts emerging from a retardation plate or compensator are polarized either in a linear fashion or with varying degrees of ellipticity, depending upon the degree of relative phase retardation.

The three most common retardation plates produce optical path length differences of an entire wavelength (ranging between 530 and 570 nanometers), one-half wavelength (260-280 nanometers), or a quarter wavelength (137-150 nanometers). In addition, a variable optical path length can also be obtained by utilizing a tapering wedge-shaped design that covers a wide spectrum of wavelengths (up to six orders or about 3000 nanometers). The concept of a phase differential resulting from non-equivalent orthogonal wavefront propagation through retardation plates is illustrated in Figure 2. A wavefront passing through a full wave (one wavelength) retardation plate (Figure 2(a)) remains linearly polarized upon emerging and retains the same vibration plane. In contrast, the one-half wavelength plate (Figure 2(c)) rotates the plane of linearly polarized light by 90 degrees, while the quarter wavelength plate (Figure 2(b)) converts linearly polarized light into circularly polarized light (and vice versa). Retardation plates that introduce less than a quarter wavelength of phase shift produce elliptically polarized light.

figure2

A full wave plate is often referred to as a sensitive tint or first order red plate, because it produces the interference color having a tint similar to the first order red (magenta) color appearing in the Michel-Levy chart. Older first order compensators were fabricated by cleaving gypsum to the appropriate thickness to achieve the first-order red color, and may be marked gypsum plate, Gips, Gyps, One λ, or Δ = 530 nm on the retardation plate frame housing. If the plate originated in Germany, it will probably be labeled Rot I. The first order retardation plate is a standard accessory that is frequently utilized to determine the optical sign (positive or negative) of a birefringent specimen in polarized light microscopy.

Quarter wavelength retardation plates (sometimes referred to in the older literature as a mica plate) are usually fashioned from quartz or muscovite crystals sandwiched between two glass windows, in a manner similar to the first order retardation plates. Depending upon the manufacturer, quarter wavelength plates may be marked Mica, Glimmer, 1/4 λ, or Δ = 147 nm. First-order red and quarter wavelength plates are usually mounted in long rectangular frames that slide the plate through the compensator slot and into the optical pathway. Late model microscopes combine these plates into a single framework that has three openings: one for the first-order red plate, one for the quarter wavelength plate, and a central opening without a plate for use with linearly polarized light without compensators. In addition, these plate frames have knobs at each end that are larger than the slot dimensions to ensure the plates cannot be dropped, borrowed, or stolen.

An advanced class of retardation plates enables the operator to introduce variable amounts of phase shift in order to offset specimen birefringence. These devices, as discussed above, are termed compensators and are mounted in a frame that permits rotation or tilting of the anisotropic plate by a variable number of degrees. The quartz wedge is the simplest example of a compensator, and is utilized to vary the optical path length difference in order to match that of the specimen. Inserting the wedge into the microscope optical path increases the phase shift as the wedge thickness becomes greater. Another simple, yet elegant, compensation technique is termed the de Sénarmont method and employs a fixed quarter wavelength plate in combination with a rotating analyzer. Altering the transmission azimuth of the analyzer enables the de Sénarmont compensator to be used as a nulling device to negate the phase shift produced by the specimen through introduction of an equal, but opposite, phase shift. The angle of rotation required by the compensator to cancel specimen birefringence (producing extinction) is used to calculate the relative retardation or optical path length of the specimen.

Depending upon previous knowledge of the specimen, the relative retardation value can be used to determine whether specimen birefringence has a positive or negative sign, calculate the thickness, or actually measure the level of birefringence (the difference in refractive index experienced by the orthogonal wavefronts). From these observations, other important characteristics of the specimen can be elucidated, including the geometry and central motifs for molecular organization. For example, the tangential or radial orientation of polarizable bonds in the molecular structure of a spherical specimen can be ascertained by proper application of a retardation plate or compensator. However, even though retardation plates are useful for determining the geometry and sign of birefringence, it is the variable compensators that propel the polarized light microscope into the class of quantitative analytical instruments.

Practically all research-level polarized light microscopes are equipped with a slot in the body tube above the nosepiece and the objective rear focal plane, but beneath the analyzer. The purpose of this slot is to house a compensator or retardation plate in a specific orientation with respect to the polarizer and analyzer transmission axis vibration directions. Originally, the slot was oriented with its long axis directed Northeast-Southwest as observed from the eyepieces, but more recent microscopes have the direction changed to Southeast-Northwest. In older microscopes, the slot dimensions were 10 × 3 millimeters, but the size has now been standardized (DIN specification) to 20 × 6 millimeters. When the compensators and/or retardation plates are not inserted into the body tube, a cover is often fitted to prevent dust from entering the microscope through the slots.

A primary consideration when using compensators and retardation plates is to establish the direction of the slow axis vibration vector. By convention, this direction will be Northeast-Southwest and will be marked slow, z', or γ, but it is also possible that the slow axis will not be indicated anywhere on the frame. A convenient method of ascertaining the slow vibration axis of retardation plates or compensators is to employ the plate to observe birefringent crystals (such as urea) with a known optical sign in an orientation where the long axis of the crystal is parallel to the Northeast-Southwest direction of the retardation plate. If there is an addition to the optical path difference when the retardation plate is inserted (when the color moves up the Michel-Levy scale), then the slow vibration direction of the plate also travels parallel to the long axis. Alternatively, if there is a difference (subtraction) between the optical paths, then the slow axis of the retardation plate is perpendicular to the long axis of the framework.

Characteristics of Retardation Plates and Compensators

Plate Type

Optical Path Difference(OPD - Nanometers)

Comments

Quarter Wavelength

137-140

Gray Interference TintCircular Polarization

One-Half Wavelength

260-290

Rotates Linearly Polarized Light

Full Wave (First Order)

540-570

First Order Magenta BackgroundBirefringence Sign Determination

Quartz Wedge

0-3000

Variable RetardationFour to Six Orders

Babinet

0-3000

Twin Opposed Quartz Wedges

Berek

0-11,000

Tilting Calcite PlateSeveral Ranges Available

Bräce-Köhler

0-60

Combination Mica Wedges Several Ranges Available

de Sénarmont

0-540 (or 570)

Elliptical PolarizationRotating Analyzer

Elliptic

0-540 (or 570)

Rotating Plate on Vertical Axis

Ehringhaus

0-2800

Twin Rotating Quartz Plates

Soleil

0-3000

Twin Quartz Wedges

Wright

0-3000

Combination Quartz Wedge

Table 1

The most common retardation plates and compensators are the quarter wavelength, full wave, and quartz wedge plates. Other compensators that are available from various manufacturers are listed in Table 1, along with their optical path difference range and selected comments. The Babinet, Wright, and Soleil wedge compensators are variations on the standard quartz wedge plate. In the quartz wedge, the zero reading coincides with the thin end of the wedge, which is often lost when grinding the plate during manufacture. To overcome this difficulty, the Babinet compensator was designed with two quartz wedges superposed and having mutually perpendicular crystallographic axes. As a result, the zero order band is located at the center of the wedge where the path differences in the negative and positive wedges exactly compensate each other, to produce a full wavelength range on either side. In contrast, the Wright wedge is mounted over a parallel compensating plate composed of either quartz or gypsum, which reduces an optical path difference throughout the wedge equal to the parallel plate contribution.

Soleil compensators are a modified form of the Babinet design, consisting of a pair of quartz wedges and a parallel plate. Phase differences introduced through the compensator are controlled by changing the relative displacement of the wedges. The Bräce-Köhler compensator enables precise measurements of exceedingly small retardation values found in weakly birefringent organic specimens and low-strain glasses. The de Sénarmont and elliptic compensators take advantage of elliptical polarization, by employing a rotating analyzer (de Sénarmont) or with a quartz plate that rotates about a vertical axis (elliptic). The Berek compensator consists of a calcite plate cut normal to the optical axis that is tilted about the horizontal axis by means of a calibrated micrometer drum to enable precise measurements of retardation. Twin quartz plates are substituted for calcite in the Ehringhaus compensator, which operates in a manner similar to the Berek compensator. The Berek, de Sénarmont, and Ehringhaus compensators are standard tools for fiber analysis with polarized light microscopy.

Compensators and retardation plates are also commonly used for qualitative applications, such as control of background illumination or to improve the contrast and visibility in weakly birefringent specimens. In a properly adjusted polarized microscope (when the polarizer and analyzer transmission azimuths are exactly 90 degrees apart) the background appears very dark, almost completely black, and details from specimens that are very thin, or have low levels of birefringence, are often obscured. In many cases, the visibility and contrast in these specimens can be dramatically improved if a small amount of compensation (5 to 10 nanometers) is introduced with a compensator in order to increase the intensity of the background. Compensators can also be used to fine-tune the level of phase displacement between the orthogonal wavefronts (ordinary and extraordinary waves) with a target of increasing visibility and contrast of specimen detail. In short, birefringent specimens, particularly those displaying extremely low levels of phase displacement, are often imaged with superior contrast using a compensator than using a polarizer and analyzer alone.

The Quarter Wavelength Retardation Plate

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The quarter wavelength retardation plate is a common optical accessory for polarized light microscopy that operates by introducing a relative phase shift of 90 degrees between the orthogonal wavefronts (ordinary and extraordinary) passing through when the plate is illuminated with linearly polarized light. A phase shift of 90 degrees between the ordinary and extraordinary components converts the incident linear polarized light vibrations into either elliptical or circularly polarized light. Quarter wavelength retardation plates are useful for the qualitative analysis of conoscopic and orthoscopic images, and for the assessment of optical path differences in birefringent specimens.

The simple anatomy of a quarter wavelength retardation plate is presented in Figure 1 for a typical commercial unit. Retardation materials employed in construction of the plate vary according to the application, but usually consist of either an optical mineral thin section (such as quartz or mica) or a highly aligned birefringent linear organic polymer sandwiched between two isotropic optically flat glass plates. Regardless of the material used in producing retardation, the optical path difference (usually inscribed on the retardation plate frame) and optical axis orientation of the birefringent retarding material must be carefully controlled so that the plate can add a known retardation value to both the high and low refractive index azimuths of orthogonal wavefronts. As illustrated in Figure 1, the birefringent retardation material is positioned in the window of a rectangular frame that is inserted into the microscope optical pathway at a 45-degree angle with respect to the transmission orientations of the polarizer and analyzer. The direction of the slow (high refractive index) axis of the wavefront ellipsoid is indicated on the retardation plate frame as a double-headed arrow accompanied by the Greek symbol for "gamma" (γ). In most cases, the slow axis orientation is perpendicular to the long dimension of the retardation plate frame, although this fact should be verified before attempting to use the instrument. Modern quarter wavelength retardation plates are built in a frame having standardized DIN dimensions (6 × 20 millimeters) that will enable their use in a variety of microscopes.

The quarter wavelength retardation plate is designed to introduce a relative retardation of exactly one-quarter wavelength (in the green or 550 nanometer region), or 90 degrees, between the ordinary and extraordinary wavefronts passing through the plate when the birefringent retardation material is illuminated by linearly polarized light at a 45-degree incident angle to the index ellipsoid, as illustrated in Figure 2. The resulting phase shift converts the linear input wavefront to a circularly polarized output wavefront. This action occurs because the orthogonal ordinary and extraordinary components have equal amplitudes when linear light oriented at a 45-degree angle to the principal (the fast or slow) axes is incident on a quarter wavelength retardation plate. In a similar manner, the quarter wavelength plate will convert an incoming circularly polarized wavefront into a linearly polarized wavefront.

Commercial quarter wavelength retardation plates are specified by their linear retardation, which is 137 nanometers for the device illustrated in Figure 1 that is designed to operate in light having a principal wavelength of 548 nanometers (in the green region). In polarized light microscopy applications, the quarter wavelength plate is utilized in a similar manner to the full wave retardation plate in order to determine whether the combination of a weakly birefringent specimen and the plate (oriented at a 45-degree angle to the polarizer and analyzer) yield higher or lower order interference colors. However, the quarter wavelength plate has been largely supplanted by the full wave retardation plate due to the superior sensitivity of the latter in producing color changes that can be readily observed. In cases where birefringent specimens display higher order interference colors between crossed polarizers without a retardation plate, then the quarter wavelength plate can often be used to advantage over the full wave plate to determine optical path differences.

This concept is illustrated in Figures 3(a) and 3(b) for a polished thin section of tactic skarn, which contains inclusions that exhibit first and second order interference colors in polarized light without the presence of a retardation plate or compensator. When a first order retardation plate is employed to determine the optical sign of this birefringent ore, the interference colors are shifted up the Michel-Levy chart by a single wavelength and can lead to confusion during quantitative analysis. Conversely, using a quarter wavelength plate instead produces the customary first order yellow for the fast optical axis (Figure 3(a)) and second order blue hue for the slow axis (Figure 3(b)), allowing for easier identification of the optical properties.

The primary use for quarter wavelength retardation plates is to determine the optical sign of birefringence from interference figures observed in conoscopic mode with a Bertrand lens (Figures 3(c) and 3(d)). Insertion of a quarter wavelength retardation plate resolves the center of a uniaxial interference figure (Figure 3(c)) into two dark spots (Figure 3(d)). If the dark spots are positioned at right angles to the slow vibration axis of the compensator crystal (in quadrants two and four; Figure 3(d)), then the sign of birefringence for the crystal is positive. Conversely, if the dark spots are positioned parallel to the compensator crystal slow axis (in quadrants one and three; Figure 3(d)), the crystal has a negative sign of birefringence. Note that other rings in the interference pattern are translated either towards the center or the periphery of the pattern according to the optical sign. The interference pattern in Figure 3(c) was generated conoscopically using a polished thin section of the mineral lamproite, which exhibits negative birefringence. A similar technique can be employed to determine the optical sign of birefringence for biaxial crystals.

The extinction bands in polarized light images can be eliminated for image analysis purposes by inserting crossed quarter wavelength retardation plates into the microscope optical path with the specimen sandwiched between the two plates. In effect, the retardation introduced by the first quarter wavelength plate is precisely cancelled by the second, so that light reaching the analyzer contains only the retardation introduced by the specimen itself. In practice, one of the retardation plates is inserted into the nosepiece or intermediate tube slot with the slow vibration axis oriented Northeast-Southwest (by convention in modern microscopes). The second plate must be placed between the polarizer and the specimen (usually in or very near the condenser) with the slow axis oriented Northwest-Southeast. The two plates should be fabricated from the same material in order to completely eliminate extinction bands. If the two plates are accurately aligned, a minimum change of polarization colors will be observed in birefringent specimens as they are rotated through 360 degrees with the microscope circular stage. Images of purified riboflavin (Vitamin B2) crystallites in polarized light (Figure 3(e)) alone, and with quarter wavelength retardation plates inserted beneath the stage and above the objective rear aperture are illustrated in Figures 3(e) and 3(f), respectively. Note that the extinction regions of the spherulitic crystallite present in Figure 3(e) have been eliminated by the application of two quarter wavelength plates (Figure 3(f)), which more clearly defines the texture.

In summary, the quarter wavelength retardation plate is capable of detecting optical path differences of (plus or minus) one-half wavelength by rotating the stage through 90 degrees. In this regard, the plate has a sensitivity range lying between the Bräce-Köhler and quartz wedge compensators and overlaps with the de Sénarmont compensator. Unlike many of the adjustable compensators, the quarter wavelength retardation plate can be effectively used in white light, but the most accurate results are obtained when the plate is coupled to the wavelength for which the crystal was prepared (for example, 548 nanometer green light for a 137 nanometer plate). The retardation plate can also be used to produce circularly polarized light by inserting it into the optical path above the polarizer.

ntroduction to Waveplates

The interaction of light with the atoms or molecules of a material is wavelength dependent. A result of this dependence is the resonant interactions related to material dispersion. Birefringence is another consequence of such resonant interaction, which is the change in refractive index with the polarization of light. The orderly arrangement of atoms in some crystals results in different resonant frequencies for different orientations of the electric vector relative to the crystalline axes. In turn, this results in different refractive indices for different polarizations. Unlike dispersion, birefringence can be avoided by using amorphous materials such as glass, or crystals that have simple symmetries, such as NaCl or GaAs. We can also “use” birefringence to modify the polarization state of light, which is a useful thing to do in many situations. The optical components that do this “trick” are called birefringent waveplates or retardation plates (or just waveplates or retarders, for short).

Waveplates

By taking just the right slice of a crystal with respect to the crystalline axes, it can be arranged so that the minimum index of refraction is exhibited for one polarization of the electric vector of a linearly polarized wave, as shown in Figure 1. The wave is polarized along the fast axis, since its phase velocity will be a maximum.

A wave is polarized along the fast axis

Figure 1. A wave is polarized along the fast axis.

A linearly polarized wave with its plane rotated 90° will propagate with the maximum index of refraction and minimum phase velocity, as shown in Figure 2. This wave is polarized along the slow axis.

A wave is polarized along the slow axis

Figure 2. A wave is polarized along the slow axis.

The difference in the number of wavelengths shown in Figures 1 and 2 (2 2/3 and 4, respectively) would imply a ratio of the two indices of refraction nfast : nslow = 2 : 3, a much larger difference than in typical natural crystals; the ratio has been exaggerated for clarity.

The propagation phase constant k can be written as 2πfn/c radians per meter, so that a wave of frequency f will experience a phase shift of φ = 2πfnL/c radians in traveling a distance L through the crystal. Thus, the phase shift for the wave in Figure 1 will be φfast = 2πfnfastL/c, and for the wave in Figure 2, φslow = 2πfnslowL/c. The difference between these two-phase shifts is termed the retardation, Γ= 2πf(nslow - nfast)L/c. The value of Γ in this formula is in radians, but is more common to express in ”wavelengths” or “waves”, with a “full-wave” meaning Γ = 2π, a “half-wave” meaning Γ = π, a “quarter-wave” meaning Γ = π/2, and so forth.

Since waves repeat themselves every 2π radians, we could subtract an integral number of 2π's or waves, and for example, call the crystal showing 2π(m+1/4) radian a quarter waveplate. It would not matter, provided it was only used at exactly the optical frequency designed for the waveplate. However, if the frequency was changed, the retardation would change at a rate faster than it would for a plate that had only 1/4 wave retardation. This difference can be noted by calling it a “multiple order quarter waveplate".

Half-Waveplates

The most commonly used waveplates are the half-waveplate (Γ = π) and the quarter-waveplate (Γ = π/2). Half-waveplates can be used to rotate the plane of linearly polarized light as shown in Figure 3.

A half-waveplates rotating the plane of linearly polarized light

Figure 3. A half-waveplates rotating the plane of linearly polarized light.

Suppose a linearly polarized wave is normally incident on a waveplate, and its plane of polarization is at an angle θ with respect to the fast axis. To see what happens, resolve the incident field into components polarized along the fast and slow axes, as shown. After passing through the plate, pick a point in the wave where the fast component passes through a maximum. Since the slow component is retarded by one half-wave, it will also be a maximum, but 180° out of phase, or pointing along the negative slow axis. If we follow the wave further, we see that the slow component remains exactly 180° out of phase with the original slow component, relative to the fast component. This describes a linearly polarized wave, but making an angle θ on the opposite side of the fast axis. The original polarization axis has been rotated through an angle 2θ. The same result will be found if the incident wave makes an angle θ with respect to the slow axis.

A half-waveplate is very helpful in rotating the plane of polarization from a polarized laser to any other desired plane (especially if the laser is too large to rotate). Most large ion lasers are vertically polarized, for example, so to obtain horizontal polarization, simply place a half-waveplate in the beam with its fast (or slow) axis 45° to the vertical. If it happens that the half-waveplate being used does not have marked axes (or if the markings are obscured by the mount), place a linear polarizer in the beam first and orient it for extinction (horizontally polarized), then interpose the half-waveplate normal to the beam and rotate it around the beam axis, so that the beam remains extinct - one of the axes has now been found. Then, rotate the half-waveplate exactly 45° around the beam axis (in either direction) from this position, and the polarization of the beam will have been rotated by 90°. Check this by rotating the polarizer 90° to see that extinction occurs again. If you need some other angle, instead of 90° polarization rotation, simply rotate the waveplate by half the angle you desire. A convenient waveplate mount calibrated in angle is the RSP-1T or GM-1RA.

Incidentally, if a new polarizer doesn’t provide as good an extinction as the ones you used before, it likely means this waveplate isn’t exactly a half-waveplate at the operating wavelength of your interest. Small errors in retardation can be corrected by rotating the waveplate a small amount to move the incident beam's plane of polarization towards the fast or slow axes. Moving towards the fast axis decreases the retardation while moving towards the slow axis increases the retardation. Try both ways and use a linear polarizer to check for improvement in the extinction ratio.

Quarter-Waveplates

Quarter-waveplates are used to turn linearly polarized light into circularly polarized light and vice versa. To do this, the waveplate must be oriented so that equal amounts of fast and slow waves are excited. This is achieved by orienting an incident linearly polarized wave at 45° to the fast (or slow) axis, as shown in Figure 4.

Turning linearly polarized light into circularly polarized light

Figure 4. Turning linearly polarized light into circularly polarized light.

On the other side of the plate, examine the wave at a point where the fast-polarized component is at maximum. At this point, the slow-polarized component will be passing through zero, since it has been retarded by a quarter-wave or 90° in phase. Moving an eighth wavelength farther, we will note that the two are the same magnitude, but the fast component is decreasing and the slow component is increasing. Moving another eighth wave, we find the slow component is at maximum and the fast component is zero. If the tip of the total electric vector is traced, we find it traces out a helix, with a period of just one wavelength. This describes circularly polarized light. Right-hand circularly polarized light is shown in the Figure; the helix wraps in the opposite sense for left-hand. Left-hand polarized light is produced by rotating either the waveplate or the plane of polarization of the incident light 90° in Figure 4.

Setting up a waveplate to produce circularly polarized light proceeds exactly the same as described for rotating 90° with a half-waveplate: first, cross a polarizer in the beam to find the plane of polarization. Next, insert the quarter-waveplate between the source and the polarizer and rotate the waveplate around the beam axis to find the orientation that retains the extinction. Then rotate the waveplate 45° from this position. Half of the incident light should now be passing through the polarizer (the other half being absorbed or deflected, depending on which kind of polarizer being used). The quality of the circularly polarized light can be checked by rotating the polarizer - the intensity of light passing through the polarizer should remain unchanged. If it varies somewhat, it means that the light is actually elliptically polarized, and the waveplate isn’t exactly a quarter-waveplate at operating wavelength of your interest. This may be corrected (as with the half-waveplate) by tilting the waveplate about its fast or slow axes slightly, while rotating the polarizer to check for constancy.

What effect do retardations other than a half-wave or a quarter-wave have on linearly polarized light? Figure 5 shows the effect of λ/4 retardation on linearly polarized light with the plane of polarization making an arbitrary angle with respect to the fast axis.

The result is elliptically polarized light - where the amount of ellipticity is a function of the retardation of the incident plane wave; and the tilt of the axis is a function of the tilt of the incident plane wave. The exception is a half-wave retardation, in which case the ellipse degenerates into a plane wave making an angle of 2θ with the fast axis. Note that the quarter-waveplate does not produce circularly polarized light here, because equal amounts of fast and slow wave components were not used; the incident tilt angle must be exactly 45° with respect to the fast (or slow) axis to make these components equal.

The effect of λ/4 retardation on linearly polarized light

Figure 5. The effect of λ/4 retardation on linearly polarized light with the plane of polarization making an arbitrary angle with respect to the fast axis.

Waveplate Applications

The two most common applications of waveplates have been mentioned: rotating the plane of polarization with a half-waveplate and creating circular polarization with a quarter-waveplate. A quarter-waveplate can also be used to create plane-polarization from circular polarization — just reverse the direction of light propagation in Figure 4. The operation of a waveplate and a summary of how quarter and half waveplates convert one polarization state to another are shown in Figure 6.

Summary of how quarter and half waveplates convert one polarization state to another

Figure 6. Summary of how quarter and half waveplates convert one polarization state to another.

Optical Isolation - A quarter-waveplate can be used in an optical isolator, that is, a device that eliminates undesired reflections. Such a device uses a quarter-waveplate and a linear polarizer or polarizing beamsplitter cube.

Polarization Cleanup - Often an optical system will require several reflections from metal or dielectric mirrors. There is no change in the polarization state of the reflection if the beam is incident normally on the mirrors, or if the plane of polarization lies in or normal to the plane of incidence. However, if the polarization direction makes some angle with the plane of incidence, then the reflection often makes a small phase shift between the parallel and perpendicular components. This is particularly true for metal mirrors, which always have some loss. The resulting reflected wave is no longer linearly polarized, but will be slightly elliptically polarized. This can easily be determined by its degraded extinction when a polarizer is inserted and rotated. This small ellipticity can often be removed by inserting a full waveplate (which ordinarily does nothing) and tilting it slightly about either fast or slow axes to change the retardation slightly to just cancel the ellipticity.

Waveplate Material and Practice

Materials — Many naturally occurring crystals exhibit birefringence, and could, in principle, be used for waveplates. Calcite and crystalline quartz are typical materials used. While they are durable and of high optical quality, the refractive index difference, nslow - nfast is so large that a true half-waveplate would be too thin to polish, therefore impractical to create.

It is also possible to induce small amounts of birefringence into a normally isotropic material through stress. For example, most polymers exhibit birefringence from stress applied in the manufacture. Polymer waveplate material is available in half or quarter-wave retardation. This material can be sandwiched between two high quality windows to make precision zero-order waveplates.

Multiple-Order Waveplates - One alternative to polishing or cleaving very thin plates is to use a practical thickness of a durable material such as crystalline quartz and obtain a high-order waveplate, for example, a 15.5 waveplate for a 1 mm thickness. Such a plate will behave exactly the same as a half-waveplate at the design wavelength. However, as the optical wavelength is changed, the retardation will change much more rapidly than it would for a true half-waveplate. The formula for this change is easily derived from the definition of Γ:

where f0 and λ0 are the design frequency and wavelength, and m is the order of the waveplate. Thus, the rate of change of retardation with frequency σΓ/σf will be 2m + 1 times as large for an mth order plate as a true half-waveplate, (m = 0, or “zero-order” plate). This would be 31 times larger for our 1 mm “15.5-waveplate”. Calculate the frequency or wavelength range required by a given system, and see if the error in retardation will be tolerable over that range with a multiple-order waveplate.

Similarly, the sensitivity of the retardation to rotation about the fast and slow axes is found to be about (2m + 1) times larger for a multiple order plate than a true zero-order half-waveplate. This means much smaller rotations are required to correct for retardation errors. But it also means that light rays not parallel to the optical axis will see a (2m + 1) larger change in retardation. Multiple order waveplates are not recommended in strongly converging or diverging beam portions of an optical system. Similarly, the sensitivity of retardation to changes in length caused by changes in temperature is multiplied by (2m + 1), so that tighter temperature control will be required. A typical temperature sensitivity is 0.0015λ per °C for a visible 1 mm thick half-waveplate.

Multiple-order waveplates can be used when a waveplate is required to be used at two discrete wavelengths, for example, the 488 and 514.5 nm wavelengths of an argon-ion laser or the 532 and 1064 nm wavelengths from an Nd:YAG laser. By choosing the thickness to give a (2m1 + 1) plate at one wavelength and a (2m2 + 1) plate at the other, both wavelengths will see a “half-waveplate” (but not the wavelengths in between). The integers must be selected by a computer program, since the dispersion in index also has to be accounted for, but it is usually possible to find a plate of reasonable thickness provided the two wavelengths are not too close together.

Zero-Order Waveplates - Fortunately, a technique is available for realizing true half-waveplate performance, while retaining the high optical quality and rugged construction of crystalline quartz waveplates. By combining two waveplates whose retardations differ by exactly half a wave, a true half-waveplate is created. The fast axis of one plate is aligned with the slow axis of the other, so that the net retardation is the difference between the two retardations. The change in retardation with frequency (or wavelength) is minimized as shown in Figure 7. Temperature sensitivity is also reduced to a typical value is 0.0001λ per °C. The change in retardation with rotation is highly dependent on manufacturing conditions and may be equal to or greater than that of a multiple order waveplate.

These waveplates are recommended for use in systems using tunable radiation sources, such as a diode laser or white light sources.

Change in retardation with wavelength

Figure 7. Change in retardation with wavelength.

Achromatic Waveplates - Achromatic waveplates consist of two different materials that are carefully choosen to eliminate chromatic dispersion. The most common type is crystalline quartz and magnesium fluoride birefringent crystals in an air-spaced design. Achromatic polymer waveplates are also avaiable which consitint of film stack laminated between two high-precision AR coated N-BK7 windows. Compared to zero-order waveplates, achromatic waveplates offer better retardation accuracy over broadband wavelength ranges, as example of achromatic quartz-MgF2 1/2 waveplate shown in Figure 8.

Achromatic waveplates have better retardation accuracy over a broad wavelength range

Figure 8. Achromatic waveplates have better retardation accuracy over a broad wavelength range.

Berek’s Variable Waveplates - A Berek compensator quantitatively determines the wavelength retardation of a crystal, fiber, mineral, plastic film or any other birefringent material. Berek tunable or variable waveplates have a variable birefringence or thickness that can be tuned to a certain wavelength or shift the retardation value for a single wavelength. If the material’s thickness can be measured, this optical device can be used to learn its birefringence value. The Berek compensator works by measuring the rotation angle of a calcite or magnesium fluoride optical plate that is cut perpendicular to the optical microscope’s axis.

In 1913, Max Berek developed this style of polarization compensator, as a variable waveplate that imposes a quarter- or half-wave retardation at wavelengths between 200 and 2800 nm. This greatly reduced the number of compensation plates needed to conduct quantitative polarized light microscopy.

MKS Newport offers an outstanding variety of Waveplates, Half-Waveplates and Quarter-Waveplates to provide a wide range of solutions to customer needs. Please contact us if you have any questions or special requests.