Motic Polarizing Microscope to Analyze Birefringence with Fixed Retardation Plates and Variable Compensators Part II

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In Part I of this series on Polarizing microscopy, I described how to use a Motic BA310 Polarizing microscope to determine Birefringence as an aid to identifying various chemicals and fibers. The Michel-Lévy chart can be used to estimate birefringence by identifying the maximum interference color in the specimen between crossed polarizers and knowledge of the specimen thickness. There Michel-Lévy chart however only provides an estimate of the birefringence. First-order colors (black to grey) are difficult to determine accurately and determining which order a particular interference color is with the chart isn’t always straightforward. This is where fixed and variable retardation plates can be helpful and permit more accurate measurements of birefringence. I will describe the most common retardation plates and the more accurate Sénarmont compensators.



Over the last 170 years, there have been about 100 different kinds of compensators but only the simple fixed ones and a couple of variable ones have been readily available in the last two or three decades (J.G. Delly). Retardation plates have a fixed optical path difference and compensators have a variable optical path length and are used when accurate measurements of birefringence are required. Today most wave plates and compensators are made to fit Standard DIN (Deutsches Institut für Normung - German national organization for standardization) size of 6 mm wide and 20mm long polarizing microscope slots. Earlier wave plates and compensators were often smaller (see photo above top right showing a Leitz Berek compensator which does not fit a modern polarizing microscope). Rotating compensators allow more precise birefringence measurements, they are expensive (several thousand dollars) and are not offered by all microscope companies.

Table of Contents:

  1. What is Full Wave Retardation Plate? And what is it used for?
  2. What is Sign of Elongation?
  3. What is a Quarter Wave Plate?
  4. How to use a Sénarmont compensator?
  5. Summary

Full Wave Retardation Plate

Tint Plate

The full-wave plate is also called a red plate, lambda (λ) plate, gypsum plate, quartz plate, selenite plate, 1st order plate, sensitive violet or color tint plate. This waveplate adds or subtracts from 530 to 560 nm wavelengths (the actual value depends on the manufacturer) when placed into the light path. When inserted between a crossed polarizer and analyzer at a 45-degree angle the background appears a pink- magenta color. This is the color of white light with green light subtracted due to destructive interference – hence it is also called a red plate.

A full-wave plate is used to add or subtract ~550 nm (green) from the polarized light and will cause interference colors by the specimen to move down and or up an order on the Michel-Lévy interference chart depending on the orientation of the crystal. If the interference colors move up it is having an additive effect and if it coincides with the length of the crystal or fiber, the fiber has a positive sign of birefringence, if it moves down to a lower order it is subtracting in this orientation of the crystal and it is called negative. This is referred to as the sign of elongation of the fiber or crystal.

The full-wave plate can also be used to enhance the contrast and color of specimens viewed between crossed polarizers that are weakly birefringent showing first order black and grey (see below). Full wave retardation filters can be made from quartz, mica, calcite, selenite, gypsum, or linear organic layers. The slow axis (maximum refractive index of the plate) is marked as a double arrow (see above) and it runs across the width of the 6 mm plate.  The wave plate is placed between the polarizer and analyzer at a 45-degree angle and it can help estimate retardations within about 2 nm accuracy by someone experienced.

Amino Acids

Above are crystalized amino Acids Beta-Alanine and L-Glutamine   A) viewed in a microscope by bright light B) viewed in a microscope in cross Polarized light showing that these crystals are anisotropic 100X. When the amino-acid crystals are thin they appear as shades of grey with no color between polarized light – these are first-order black and grey on the Michel-Lévy chart (see below).  After adding a full-wave plate into the light path, the colors are bumped up an order in interference colors.

Crystals of Amino Acid Viewed in polarized light

Above photo show crystals of amino acids Beta-alanine and L-Glutamine 40X in polarized light showing only 1st order grey interference colors because these crystals are very thin – 100X Polarized light microscopy.

Amino Acids Full wave plate

Above are crystals of amino acids Beta-alanine and L-Glutamine 40X in polarized light after insertion of a full-wave plate (550 nm) into the light path. The light grey colored crystals now appear to range from 1st order orange to 2nd order blue (550 to 750 nm) as each interference color is moved up order by the wave plate. If we subtract 550 nm from 750 nm (2nd order blue) it indicates the original retardation in the blue areas was about 250 nm and the birefringence of the crystals is approximately 0.005 to 0.008. If we measured the exact thickness of the crystal we could determine the birefringence more accurately.

Sign of Elongation

Synthetic anisotropic fibers can have two refractive indices. The sign of elongation refers to whether the maximum refractive index lies parallel to the long axis of the fiber or orthogonal to it. If it runs parallel the fiber is said to have a positive sign of elongation and if it runs across the fiber it has a negative sign of elongation.

Human Scalp Hair

Grey human scalp hair immersed in water A) Crossed polarizers B) after the addition of a full wave retardation plate C) hair rotated 90 degrees D) rotated 90 degrees including a full wave retardation plate (550 nm). The maximum refractive index of the full wave plate runs NE to SW. In B the retardation plate subtracts from the birefringence and in D it adds to the birefringence which indicates the sign of elongation is positive and runs parallel to the fiber. In A the retardation from the Michel-Lévy Chart is estimated to be a 2nd order orange 975 nm. The hair above is 80 µm in diameter and was mounted in water. Because water can alter the birefringence I now immerse hair fibers in oil immersion fluid with a refractive index of 1.5180 (Cargille). Below I measured the Birefringence of hair fibers to be 0.0084 using the Sénarmont compensation method described. In water, I calculate the birefringence of human hair as:


Birefringence = Retardation / thickness nm (multiply width in microns x 1000 to convert to nm)

= 975nm/ 80 µm x 1000 to convert to nm

= 0.012

In the literature, I found Birefringence value for human hair was approximately 0.007 depending on the humidity. 

Optical path difference  =  (Ne – No) x t   

Optical path difference = Birefringence.

Birefringence is the difference between the two refractive indices. Ne is the refractive index of the refracted extraordinary ray, No is the refractive index of the ordinary ray which passes unchanged through the crystal. T is the thickness of the crystal measure in microns then converted to nm (1000 nm – 1 µm). The birefringence can be a positive or negative value.  If No > Ne it is a negative crystal, if Ne > No it a positive crystal.

The Quarter Wave Plate

1/4 wave plate

The 1/4 wave pate is used similar to the full wave retardation plate, by placing it in the optical path between the polarizer and analyzer at 45 degrees it will add or subtract about 137 nm (550/4 = 137.5 nm). This will move the interference color up or down about ¼ of an order on the Michel-Lévy chart and can help determine the interference order. The phase shift of 90 degrees by the ¼ wave plate also converts linear polarized light into circular or elliptically polarized light. The slow axis is marked as a double arrow on the wave plate and is usually across the width. The ¼ wave plate is made of quartz, mica, or an organic polymer. The ¼ wave plate is used to advantage over the full wave plate in specimens displaying higher-order colors.

Human Hair

The above figure shows a human scalp hair A) Crossed polarizers b) Crossed polarizers with ¼ wave plate and C) Crossed polarizers with a full wave plate 550 nm D, E, F) Same as above but the fiber was rotated 90 degrees. The small black arrows show the direction of the max refractive index (slow axis) of the wave plates). By comparing whether the wave plate moves the colors up (to the right) or down (to the left) in orders on the Michel-Lévy chart it is possible to determine the sign of elongation of the hair. If the slow axis of the wave plate is over the slow axis (max refractive index of the fiber) the color moves up toward a higher order otherwise it moves down. If the slow axis moves up the max refractive index is parallel to the fiber and the fiber is said to have a positive sign of elongation otherwise it has a negative sign. The pictures show the hair slow axis corresponds to that of the quarter and full wave plate when it is oriented NE to SE and therefore has a positive sign of elongation.

Another primary use of the ¼ wave plates is to determine the sign of elongation by examining the crystals interference patterns in conoscopic mode using a Bertrand lens. For more information on interpreting interference patterns see J.G. Delly (2017).


A) Muscavite (mica) crystal interference patterns in crossed polarizer light B) the addition of ¼ wave plate and C) the addition of a full wave plate. Wave plates can also be used with conoscopic observations to determine the sign of elongation and type of crystal – uniaxial or biaxial.

The Sénarmont Compensator


The Sénarmont compensator is a more accurate ¼ wave fixed retardation plate calibrated for use with 546 nm light that is provided by an interference filter or the e-line 546.1 nanometers from a mercury arc-discharge lamp. The high refractive index (slow direction) or Z-axis is oriented parallel to the polarizer direction and at 45 degrees to the wave plate. The mica in a Sénarmont compensator is cut to a more precise thickness than the more common quarter-wave plate because it is used quantitatively (Delly 2017). An interference filter 546 nm (I used a 550 nm) is needed along with a rotating polarizer with graduations accurate to 0.1 degrees.

Motic Analyser with Vernier

The above photo shows a Motic analyzer with Vernier for recording the rotation required for the specimen to become dark or nearly extinct when using an interference filter and the Sénaramont method. The human hair I used did not become completely black as the cuticle and cortex of the hair have different birefringence values and the total extinction value is, therefore, an average of the two.

The following is a description of the steps using a Sénarmont compensator based on J.G. Delly (2017).

  1. With the polarizing microscope set the specimen directly under the center of the eyepiece cross hair and have the microscope polarizers crossed.
  2. A narrow beam of parallel light rays is required, therefore swing the top lens of the condenser out and close the aperture diaphragm to obtain axial (parallel) light.
  3. Rotate the stage and note that the fiber disappears (becomes black) when it line ups with either the vertical or horizontal cross hair (polarizer and analyzer).
  4. Rotate the stage to 45 degrees to bring the specimen to maximum brightness (position the fiber NE to SW so the high refractive index of the compensator is aligned with the fiber). Note the fiber interference color. 
  5. Insert a full wave retardation plate so the background turns magenta (pinkish–violet) and note the retardation color of the fiber and whether the sign of elongation is positive or negative. 
  6. Remove the first order red plate and insert the Sénarmont compensator (1/4 wave plate) and put the 546 nm (green interference filter) on top of the light source. You should see a green filament on a black background. 
  7. Rotate the analyzer from its 0 positions until the part of the specimen or fiber is a black as possible (extinction) and record the reading on the Analyzer Vernier to one-tenth of a degree. For the most accurate results, it’s bests to repeat the readings several times and average the values. 
  8. To calculate the retardation let the analyzer rotation be Ɵ, then the retardation R in nm will be obtained from: 

R = Ɵ x λ   ( λ = wavelength of 550nm or 546 nm interference filter)



λ /180 will be a constant – I used a 550 nm interference filter which results in 550/180 = 3.055 nm per degree. Therefore if the angle of rotation was 179.8 degree x 3.055   Retardation = 549.2 nm. Knowing the retardation and thickness the birefringence can be calculated (described in Part I of this article).

Human hair immersed in oil immersion fluid

Human scalp hair immersed in oil immersion fluid. A) Hair in crossed polarized light showing 1st order yellow to red B) Hair after insertion of a full wave retardation plate the filament exhibits 3rd order interference color indicating its sign of elongation is positive. C) Hair in crossed polarized and a 550 nm interference filter. D) Shows the hair after turning the analyzer until the hair beneath the eyepiece cross hair becomes dark or black.

Measurement of the Analyzer showed that this occurred at 179.8 degrees. The hair was 62.5 microns thick. The birefringence value calculated is 549.2 nm/ 62.5 x 1000 nm = 0.0088 similar to previously published values of human hair 0.007 to 0.015 (R. K. Curtis and D. R. Tyson, 1976; A. Kharin et al., 2009).


Birefrigence = Retardation/thickness 62.5 microns x 1000 nm  = 0.0088.


In the analysis above, I used the Motic ¼ wave plate and not the more accurate Sénaramont ¼ wave compensator. I have since ordered a Sénarmont ¼ wave compensator and will compare the two once it arrives, but J.G. Delly a leading polarized light microscopy expert has assured me a Sénarmont compensator will provide more accurate results, but it’s OK to use a normal ¼ wave plate for less accurate readings. In conclusion, the Sénarmont compensator can provide much more accurate Birefringence readings than using the Michel-Levey Chart alone. The Sénarmont compensator is good for measuring within one order, for samples showing more than one order, a quartz wedge or other rotating compensator can be used to obtain more accurate readings (J.G. Delly, 2017).


Compensators are birefringent crystals with a known amount of birefringence and include ¼,  full wave, and multiple wave plates (Quartz Wedge). There are also variable wave compensators that can measure retardation accurately down to 0.1 nm by rotating crystals that are calibrated.  Some of these variable compensators cost thousands of dollars. The most economic high-resolution compensator is a Sénarmount which uses light of a single wavelength and a rotating analyzer found on research quality polarizing microscopes like the Motic BA310.

Note that not all fibers are uniquely identifiable by their optical properties, and in those cases, additional analytical techniques are required. Also, dyed fibers can complicate the analysis and make it more difficult to see and determine the correct interference color (J.A. Reffner et al. 2019).

For an in-depth description and step-by-step instructions of how to use a polarizing microscope quantitatively the reader is referred to the magnificent book by J.G Delly (2017). For amateurs interested in experimenting with retardation plates and for photomicrography one can make basic retardation plates using cellophane tape which is suitable for color photomicrography (T.J. Fagan and M. Lidsky, 1974).

By Robert Berdan Ph.D.


I would like to acknowledge J.G. Delly for furthering my understanding of polarized light microscopy, Michel-Lévy charts, the use of compensators, and answering my questions. I strongly recommend his book.


1.R. Berdan (2021) Polarization Microscopy - The Motic BA310 Polarizing Microscope a Review
2.G. Delly (2017) Essentials of Polarized Light Microscopy and Ancillary Techniques - Hooke College of Applied Sciences. Westmont. Illinois. Available on McCrones web site or Amazon
3.J. G. Delly Sénarmont Compensation: How to Accurately Measure small relative retardations (0-1λ) How to tutorials.

4.J.G. Delly The Michel-Lévy Interference Color Chart – Microscopy’s Magical Color Key. You can purchase a print chart from their website.
5.J.G. Delly (2008) Selected topics from Essentials of Polarized Light Microscopy.
6.M.W. Davidson Introduction to Compensators and Retardation Plates – Olympus Microscopy Resource Center.
7.M.W. Davidson The Quarter Wavelength Retardation Plate
8.M.W. Davidson The Quartz Wedge Compensator
9.M.W. Davidson The First Order (Full Wave) Retardation Plate
10.J.D. Griffin, I.D. Johnson and M.W. Davidson Compensators and Retardation Plates
11.K. Fester and M.W. Davidson The de Sénarmont Compensator Polarized Light microscopy
12.J.D. Griffin, I.D. Johnson and M.W. Davidson Quartz Wedge Compensator
13.Raith, P. Raase and J. Reinhardt (2011) ISBN 978-3-00-033606-5 PDF. Guide to Thin Section Microscopy (minerals). Determination of thin section thickness page 27-29. Free download
14.T.J. Fagan and M. Lidsky (1974) Compensated Polarized Light Microscopy Using Cellophane Adhesive Tape. Arthritis and Rheumatism 17: 256-262.
15.Kharin, B. Varhese, R. Verhagen and N. Uzunbajakava (2009) Optical properties of the medulla and the cortex of human scalp hair. J. Biomedical Optics 14 March\April.
16.R . K. Curtis, D. R. Tyson (1976) Birefringence: Polarization Microscopy as a Quantitative Technique of Human Hair Analysis. J. Soc. Cosmet. Chem. 27, 411`-431.
17.B.E. Sorensen (2013) A Revised Michel-Lévy color chart based on first-principles calculations. Eur. J. Mineral 25, 5-10.

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