basic of polarizing microscopy

Basics ofPolarizing Microscopy

K E Y W O R D

Polarized light

Linearly polarized light

Circularly polarized light

Elliptically polarized light

Polarizing plate

Polarizing filter

Polarizing prism

Polarizer

Analyzer

Crossed nicols

Parallel nicols

1

1.Properties of polarized light

■1.1 Polarized lightTransverse wave light whose vibration possessdirection is called polarized light. Light from anordinary light source (natural light) that vibratesin random directions (Fig. 1.1) is called nonpo-larized light. In contrast, while light with verticalvibration that travels within a single plane (Fig.1.2a) is called linearly polarized light, circularlypolarized light (Fig. 1.2b) and elliptically polar-ized light (Fig. 1.2c) are types of light in whichthe vibration plane rotates forward.

● Fig. 1.1 Natural light (nonpolarized light) ●

A polarizing plate (polarizing filter) or polarizingprism is often used as the device to changenatural light to linearly polarized light (see 1.7).Configuring the primary and secondary polariz-ing devices in the orthogonal directions of eachtransmitting linearly polarized ray will cut thelight. Such state in which the primary lightpolarizing device is the polarizer and the sec-ondary device is the analyzer is called crossednicols. Parallel nicols is the state in which theanalyzer is rotated to make the direction of thetransmitting linearly polarized light match withthe polarizer, and the amount of light transmit-tance is maximized. (Fig. 1.3b).

● Fig. 1.3 a) crossed nicols and b) parallel nicols ●P: polarizer A: analyzer

● Fig. 1.2 Types of polarized light ●

The vibration direction of light is perpendicularto the progressing light. The vibration directionof natural light points to all the directions.

a. linearly polarized light b. circularly polarized light c. elliptically polarized light

Each figure on the left-hand side shows decomposition of each polarized light into twomutual perpendicular linearly polarized light.

K E Y W O R D

Component P

Component S

Brewster angle

Calcite

Double refraction

Ordinary ray

Extra ordinary ray

Anisotropy

Optical axis

2

When light reflects off the surface of water andglass, its reflectance varies with the directionof polarization (Fig. 1.4a). Comparing the twooscillation components, Component P is parallelto the plane of incidence and has 0 reflectancewhile Component S is perpendicular to the planeand has higher reflectance. The 0 reflectance ofComponent P is caused by the existence of anangle of incidence, known as the Brewsterangle. In other words, the reflected light at thisangle is linearly polarized, and can be cut outwith a polarizing plate. In photography, a polariz-ing filter is used in order to remove reflectionfrom the surface of water and glass (Fig. 1.4b).The Brewster angle against the surface ofwater (n =1.33) and the surface of glass(n=1.52) is 53｡07' and 56｡40', respectively.

■1.2 Polarization by reflection

● Fig. 1.4 a) Difference of reflectance is due to vibration direction of light ●

An object whose image passes through a cal-cite CaCO3 crystal appears doubled (Fig. 1.5a).This phenomenon is called double refraction orbirefringence, which occurs when light that islaunched through a crystal material is dividedinto two linearly polarized light rays havingmutually crossing vibration directions, and thenrefracted. Among these two light rays, the onethat follows the law of refraction is called anordinary ray, while the other one is called anextraordinary ray. Their speed and index ofrefraction differ from one another.

A crystal that refracts in such way is called ananisotropy. Light passing through an anisotropyis generally divided into ordinary and extraordi-nary rays, but toward a certain direction calledoptical axis, they travel together. When thathappens, the double refraction phenomenondoes not occur. (see 1.4).

■1.3 Double refraction

● Fig. 1.5a. Double refraction phenomenon due to calcite ●

● Fig. 1.5b. Double refraction phenomenon due to diagram ●

● b) Effectiveness of polarizing filter (left: without filter right: with filter) ●

tanq1=nq1: Brewster angle

Air

θ：Angle of incidence

reflectiveindey

Ejection light oflinearly light

Calcite C : optical axis

Ejection ray oflinearly polarizedlight

Extraordinaryray

ordinaryray

K E Y W O R D

Optically uniaxial crystal

Optically biaxial crystal

Principal section

Optically positive crystal

Optically negative crystal

Optical character

Index surface

Principal refractive

3

■1.4 Optically uniaxial crystalAnisotropy can be divided into an opticallyuniaxial crystal and an optically biaxial crystalaccordinng to the optical properties. An opti-cally uniaxial crystal has one optical axis whilean optically biaxial crystal has two axes. Amaterial classification in terms of optical prop-erties is as follows:

optically isotropicbody

optically anisotropy

non-crystal

isoaxial system crystal

optically uniaxial crystal

optically biaxial crystal

tetragonal system crystal

hexagonal system crystal

rhombic system crystal

monoclinic system crystal

triclinic system crystal

The optical axis and the direction of a beam oflight determine the vibration direction of extraor-dinary and ordinary rays in an optically uniaxialcrystal, and the section containing both rays iscalled the principal section. The ordinary raysoscillate vertically through the principal sectionwhile the extraordinary rays oscillate within theprincipal section (Fig. 1.6).

● Fig. 1.6 Vibration direction of ordinary rays and extraordinary rays of an optically uniaxial crystal ●

Optically uniaxial crystals can be divided into two types:optically positive crystals, in which the index ofrefraction of extraordinary rays is greater than that ofordinary rays, and vice versa, called optically negativecrystals (hereafter, positive crystals and negativecrystals). For instance, rock crystals belong to positivecrystals, whereas calcite and sapphires belong tonegative crystals. Positive and negative crystals canalso be said to possess a positive or negative opticalcharacter, respectively.The index of refraction of extraordinary rays varies withthe direction of progression of light rays. Figure 1.7shows the index surface for optically uniaxial crystalswith a) a positive crystal, and b) a negative crystal. Theindex surface expresses the index of refraction towardthe direction of progression of ordinary rays andextraordinary rays in terms of the distance from theorigin. As shown in the diagram, the index of refractionof extraordinary rays inclined by q from the optical axisis ne. The index of refraction of extraordinary raysreaches a maximum or minimum perpendicularly alongthe direction of the optical axis. The indices ofrefraction of the ordinary and extraordinary rays in thisdirection, w and e, respectively, are called principalrefractive indices. The principal refracive indices forsignificant crystals are given in table 1.1.

● Fig. 1.7 Index surface of an optically uniaxial crystal ●

● Table 1.1 Principal refractive indices of significant crystals (wavelength = 589.3 nm) ●

Crystal name

rock crystal (quartz)

calcite

sapphire

ω

1.5443

1.6584

1.768

ε

1.5534

1.4864

1.760

● : vibration directionof ordinary ray(perpendicular toprincipal section)

- : vibration direction ofextra ordinary ray(within principal sec-tion)The principal sectionis surface of space.

a. positive crystal

(The ellipse is exaggerated)

b. negative crystal

c : opticalaxis

K E Y W O R D

X' direction

Z' direction

Optical axial angle

Phase difference

Retardation

4


In double refraction, the vibration direction of light withfaster progression is called the X' direction, while theslower progression is called the Z' direction. As for thevibration direction, the positive crystals represent thedirection of extraordinary rays, whereas the negativecrystals express that of the ordinary rays in the Z’direction of optically uniaxial crystals. In the test plateand compensator of a polarizing microscope (see3.2.8), the Z' direction is displayed for investigatingthe vibration direction of the light for specimens.Generally, even optically biaxial crystal will separate intwo rays, and yet they are both extraordinary rayswhose speed differs according to the direction of itsprogression. See Fig. 1.8 for the index surface of opti-cally biaxial crystals. a, b, and g show the principalrefractive indices of optically biaxial crystals. The anglethat constitutes the two optical axes (2Ω) is calledthe optical axial angle.

● Fig. 1.8 Section of refractive index of an optically biaxial crystal ●

● Fig. 1.9 Relationship between direction of optical axis and double refraction of a crystal ●

■1.5 RetardationAfter being launched into an anisotropy. phasedifferences will occur between the ordinary andextraordinary rays. Fig. 1.9 shows the relation-ship between the direction of the optical axisand double refraction. In cases (a) and (b) in Fig.1.9, relative surges and delays, i.e., phase differ-ences, d, will occur between the two rays. Onthe contrary, no phase difference can be seen inFig. 1.9c because light rays advance in thedirection of the optical axis.

The phase difference for extraordinary and ordi-nary rays after crystal injection is given next.

δ=2πd (ne-no)/λ　　(1.1)l indicates the light wavelength, d the thicknessof double refraction properties. ne and no are therefraction indices of extraordinary and ordinaryrays, respectively.Here, the optical path difference R is calledretardation and can be expressed as follows.

δ=δλ/2π=d (ne-no) (1.2)R is the value of the deviation of two light raysin a double refraction element, converted tomid-air distance; it is expressed in a direct num-ber (147 nm, etc.), a fraction or the multiple(λ/4, etc.) of the used wavelength.

OP : Direction ofoptical axis

2Ω : optical axialangle

o : ordinary raye : extraordinaryray

←→ : Direction ofoptical axis

Direction of arrows express thevibration direction.

K E Y W O R D

Optical strain

Photoelasticity

Dichroism

Glan-Thompson prism

Nicol prism

5


■1.6 Optical strainWhen stress is applied to an isotropic bodysuch as glass or plastic, optical strain occurs,causing the double refraction phenomenon, andthat is called photoelasticity. By observing theoptical strain of various materials by means ofpolarization, the stress distribution can be esti-mated (Fig. 1.10).

■1.7 Light polarizing devicesAs stated in 1.2, a polarizing plate and polarizing prismare generally used as the polarizing devices to convertnatural light into linearly polarized light. Their respectivefeatures are given below.(1) polarizing plateA polarizing plate is a piece of film by itself or a filmbeing held between two plates of glass. Addingsalient iodine to preferentially oriented macromole-cules will allow this film to have dichroism.Dichroism is a phenomenon in which discrepanciesin absorption occur due to the vibration direction ofincident light polarization. Since the polarizing plateabsorbs the light oscillating in the arranged direc-tion of the macromolecule, the transmitted light raysbecome linearly polarized. Despite its drawbacks of1) limited usable wavelength band (visible to nearinfrared light), and 2) susceptibility to heat, thepolarizing plate is inexpensive and is easy toenlarge.

(2) polarizing prismWhen natural light is launched into a crystal havingdouble refraction, the light proceeds in two sepa-rate, linearly polarized lights. By intercepting one ofthese two, the linearly polarized light can beobtained; this kind of polarizing device is called apolarizing prism, and among those we find Glan-Thompson prism (a) and Nicol prism (b).A polarizing prism has higher transmittance than apolarizing plate, and provides high polarization char-acteristics that cover a wide wavelength band.However, its angle of incidence is limited and it isexpensive. In addition, when used in a polarizingmicroscope, this prism takes up more space than apolarizing plate and may cause image deteriorationwhen placed in an image forming optical system. Forthese reasons, a polarizing plate is generally usedexcept when brightness or high polarization isrequired.

● Fig. 1.10 Optical strain of plastic ●

● Fig. 1.11 Polarizing prism ) ●(a. Glan-Thompson prism b. Nicol prism)

express direction ofoptical axis

K E Y W O R D

Extinction position

Diagonal position

6

2.Fundamentals of polarized light analysis

Light does not transmit in a crossed nicolsstate, but inserting an anisotropy between apolarizer and an analyzer changes the state ofthe polarized light, causing the light to passthrough. When the optical axis of a crystal withdifference of d is placed between the crossednicols at an angle of q to the polarizer's vibra-tion direction, the intensity of the injected lightis expressed as (2.1).

Ⅰ(θ)= I｡ sin22θ・sin2 (δ/2)

= I｡ sin22θ・sin2 ( ) (2.1)

Io is the intensity of transmitted light duringparallel nicols, and R is the retardation (equa-tion (1.2)). With this equation, the change inbrightness during the rotation of an anisotropyand of the interference color from retardationcan be explained.

■2.1 Anisotropy in crossed nicols

● Fig. 2.1 Anisotropy between crossed nicols ●

As the equation 2.1 signifies, at certain fourpositions, (90 degrees apart from each other),the anisotropy appears black as its optical axismatches with or becomes perpendicular to thevibration direction. Such positions are called theextinction positions. The brightest position, alsoknown as the diagonal position, is at a 45°. Thedrawings in Fig. 2.2 represent the change inbrightness from extinct to diagonal position andvice versa, while rotating the body.

2.1.1 Change in brightness when rotating anisotropy

● Fig. 2.2 Extinction position and diagonal position of anisotropy ●

πRλ

A : direction of progression of analyzerP : direction of progression of polarizerC : direction of optical axis of anisotropy

A : vibration directionof analyzer

P : vibration directionof polarizer

polarizer

anisotropy

analyzer

K E Y W O R D

Interference color

Interference color chart

The first order

Sensitive color

7

2.1.2 Interference color in anisotropyBy equation (2.1), when the phase difference d of ananisotropy is 0, 2π, 4π, (retardation R 0, λ, 2λ,…, λ represents a single color wavelength) the inten-sity of the transmitted light is 0, or the body appearspitch dark. On the other hand, when the body seemsbrightest, d is p, 3p, 5p,. (R is λ/2, 3λ/2, 5λ/2,…)This gap in light intensity attributes to the phasedifference created between the ordinary and extraor-dinary rays after passing through an anisotropy, nextthrough an analyzer, and eventually to have interfer-ence.

Fig. 2.3 shows the transmittance of light when awedge-shaped quartz plate, having double refractionis placed in the diagonal position in crossed nicols. Inthe case of single color light, the intensity of trans-mitted light creates light and dark fringes. As thephase difference of an ordinary and extraordinary raysvary according to the wavelength, so does the trans-mittance at each wavelength. (See formula 1.1).When observing the wedge-shaped quartz plate ofFig. 2.3 under white light, interference destroys somewavelengths and reinforce others. As a result, bysuperimposing the wavelength of visible light, thecolor appears. This is called interference color.

The relationship between retardation amount ofanisotropy and interference color is shown by theinterference color chart. By comparing the inter-ference color of the anisotropy with the interfer-ence color chart, the retardation of the anisotropycan be estimated. A vertical line is drawn on theinterference color chart to show the relationshipbetween double refraction (ne-no) and the thick-ness of anisotropy. This is used to find out thethickness d of specimens or the double refraction(ne-no). from retardation.

The visible colors in the color chart from zero orderblack to first order purplish-red are called the firstorder colors. The first order purplish-red is extremelyvivid, and the interference color changes from yellow,red to blue just by the slightest retardation. This pur-plish-red is called a sensitive color. Colors between

the first order red and second order red are calledsecond order colors, such as second order blue,second order green. The higher the order of colorsgets, the closer the interference colorapproaches white.

● Fig. 2.3 Transmittance of wedge-shaped quartz plate ●

● Fig. 2.4 Color Chart ●

wedge-shapedquartz plate

Ⅰ（Transmitted light intensity）

λ＝486nm（blue）

λ＝546nm（green）

λ＝656nm（red）

expresses the direc-tion of optical axis

R（retardation）

K E Y W O R D

Addition

Subtraction

8


Figure 2.5 shows the transmittance curve ofthe interference color in relation to retardationaround the sensitive color, and is calculatedfrom equation (2.1). In the sensitive colors,green light cannot be transmitted and thusappears as purplish-red (Fig. 2.5b). If retardationis reduced from sensitive colors, then a wide-range mixed color light from green to red turnsup, observed as yellow, as shown in Fig. 2.5a;increased retardation, contrarily, brings out ablue interference color. (Fig. 2.5c.)

● Fig. 2.5 Retardation and transmittance curve ●

■2.2 Superimposing anisotropyNow we consider two anisotropy overlappingone another; one with the vibration directions oftheir slower light rays (Z' direction) in the samedirection (Fig. 2.6a), and the other perpendicu-larly. (Fig. 2.6b).

When the Z' directions of two anisotropy over-lap, pointing the same direction, the vibrationdirections of the slower polarized light match.The total retardation is equivalent to the numer-ical sum of the retardations.

R=R1+R2 (R1, R2 denote the retardations of anisotropy 1 and 2)This state is called addition (Fig 2.5a). In con-trast the phase difference after passingthrough one anisotropic element is cancelledout by the other phase difference. As a result,the total retardation is the difference betweenthe two anisotropy retardation.

R=R1-R2.This state is called subtraction (Fig 2.5b).Whether the state is addition or subtraction can

be determined from the changes in the inter-ference color when the anisotropy overlap.Shifting of the interference color toward theincrease of retardation is addition, and viceversa for subtraction. Both addition and sub-traction are the determinants for judging Z'direction. (To be discussed further in 4.1.3)Knowing the Z' direction helps determine theoptical character of elongation (see 2.3) Inaddition, when the anisotropy overlap withone at the extinction position and the otherat the diagonal position, the total retardationbecomes equivalent to the retardation of theanisotropy at the diagonal position.

● Fig. 2.6 Superimposing anisotropy ●a：addition b：subtraction

a) R=400 nm

b) R=530 nm (sensitive color)

c) R=650 nm

The light within the range fromgreen to purple is transmitted, andappears yellow with a mixed color.

The low number of green portionsresults in purple and red light totransmit, and is seen as purplishred.

The strong transmitting light ofblue and purple emphasizes theblue color.

Optical character of elongation

Slow length

Fast length

Phase plate

Tint plate

Quarter-wave plate

Half-wave plate

Mica

K E Y W O R D

9


■2.3 Optical character of elongationSome anisotropy are elongated in some direction asthe narrow crystals and fibers in rock would be. Therelationship between the direction of elongation and Z'direction can specify the optical character of elongation(zone character). When the Z' direction matches thedirection of elongation, it is said to have a slow length,and when the z' direction crosses the direction of elon-gation, then it has a fast length).

This optical character does not coincide with the posi-tive and negative attributes of uniaxial and biaxial crys-tals. The optical character of elongation is fixed foranisotropy such as crystals (e.g., uric acid sodium crys-tals of gout), and, by using a polarizing microscope, canbe distinguished from pseudo gout crystals (see 4.1.3).

■2.4 Phase plateA phase plate is used in the conversion of linearlypolarized light and circularly polarized light, and inthe conversion of the vibration direction of linearlypolarized light. A phase plate is an anisotropywhich generates a certain fixed amount ofretardation, and based on that amount, several

types of phase plate (tint plate, quarter-waveplate, and half-wave plate) are made. Whenusing a quarter-wave plate, a diagonallypositioned optical axis direction can convertincident linearly polarized light into circularlypolarized light and vice versa (Fig. 2.8).

A half-wave plate is mainly used for changingthe vibration direction of linearly polarized light,and for reversing the rotating direction of circu-larly polarized and elliptically polarized light.

Quarter-wave plates, half-wave plates, andtint plates are usually thin pieces of mica orcrystal sandwiched in between the glass.

● Fig. 2.7 Optical character of elongation ●

● Fig. 2.8 Quarter-wave plate conversion of linearly polarized light into circularly polarized light ●

anisotrophy

optical character ofelongation is positive

optical character ofelongation is negative

direction of elongation

linearly polarized light

linearly polarized light

1/4 wave plate

1/4 wave plate

circularly polarized light

circularly polarized light

Conversion of linearly polarized light into circularly polarized light

Conversion of circularly polarized light into linearly polarized light

K E Y W O R D

Polarizing microscope

10

3. Polarizing microscopes

A polarizing microscope is a special microscope thatuses polarized light for investigating the optical proper-ties of specimens. Although originally called a mineralmicroscope because of its applications in petrographicand mineralogical research, in recent years it has nowcome to be used in such diverse fields as biology, medi-

cine, polymer chemistry, liquid crystals, magneticmemory, and state-of-the-art materials. There aretwo types of polarizing microscopes: transmittedlight models and incident light models. Fig. 3.1shows the basic construction of a transmitted lightpolarizing microscope.

■3.1 Characteristics of a polarizing microscope

● Fig. 3.1 External view and construction of a transmitted light polarizing microscope (BX-P) ●

Observation tube prism

Eyepiece with crosshair

Image formation lens

Bertrand lens

Analyzer

Test plate, compensator

Centerable revolver

Strain-free objective

Rotating stage

Specimen

Polarizing condenser

Polarizer

Transmitted light illuminator

K E Y W O R D


Rotating stage


Centerable revolver

Bertrand lens

Test plate


11

As seen in Fig. 3.1, compared to a typicalmicroscope, a polarizing microscope has a newconstruction with the following added units: apolarizing condenser that includes a polarizer, arotating stage that allows the position of thespecimen to be set, a strain-free objective forpolarized light, a centerable revolving nosepiece that allows optical axis adjustment for the

objective, an analyzer, a Bertrand lens forobserving the pupil of the objective, a testplate, a compensator, and an eyepiece withcrosshair. An incident light polarizing micro-scope like the one shown in Fig. 3.2 is usedfor the observation of metallic and opaquecrystals.

● Fig. 3.2 External view and construction of an incident light polarizing microscope○●

Observation tube prism


Image formation lens

Bertrand lens

Analyzer

Half mirror

Polarizer

Incident light illuminator

Centerable revolver


Specimen

Rotating stage

K E Y W O R D

12


Among the essentials for polarized light obser-vation, for a transmitted light polarizing micro-scope, the polarizer should be placed below thecondenser and the analyzer should be above theobjective. For an incident light polarizing micro-scope, the polarizer is positioned in the incidentlight illuminator and the analyzer is placedabove the half mirror.The polarizer is rotatable 360 with degree gra-dations indicated on the frame. The analyzercan also rotate 90 or 360 , and the angle ofrotation can be figured out from gradations aswell. As fig. 3.3 shows, the vibration direction ofa polarizer should go side to side relatively tothe observant, and go vertically for an analyzer.(ISO/DIS 8576)

■3.2 Constituents of a polarizing microscope

3.2.1 Polarizer and analyzer

● Fig. 3.3 Vibration direction of light polarizing devices ●

A polarizing objective differs from ordinaryobjectives in a respect that it possesses a highlight-polarizing capability. A polarizing objectivecan be distinguished from ordinary ones by thelabel P, PO, or Pol. Objectives which have thelabel DIC or NIC signify their use for differentialinterference, and yet have improved polarizationperformance. The polarizing objectives can eas-ily be adopted for bright field observation, too.There are two factors which determine the levelof the objectives' polarizing performance: 1) theturbulence of polarizing state, caused by theanti-refraction coating of lenses, or the angle ofincidence influencing the refraction on the lenssurface, and 2) a lens strain such as an originallens strain, newly created from the junction ofthe lenses, or from the connection of frame andlenses etc. An objective lens for polarization isdesigned and manufactured to have low turbu-lence by refraction in the polarizing state on thelens surface and to have low lens strain.

3.2.2 Polarizing objective (strain-free objective)

● Fig. 3.4 Polarizing objective ●(ACH-P series and UPLFL-P series)

A：Vibration direction of analyzer

P：Vibration direction of polarizer

K E Y W O R D


Cross moving device

Rotating stage

Universal stage

Bertrand lens

13

3.2.3 Polarizing condenserA polarizing condenser has the following threecharacteristics: 1) built-in rotatable polarizer, 2)top lens out construction when parallel light illu-mination at low magnification is required, and 3)strain-free optical system, like the objectives.

● Fig. 3.5 Polarizing condenser (U-POC) ●

3.2.4 Polarizing rotating stageAs illustrated in 2.1.1, rotating an anisotropy betweencrossed nicols changes the brightness. For this reason,in polarized light observation, the specimen is oftenrotated to the diagonal position (the position where theanisotropy is brightest). In other words, rotatability ofthe polarizing stage and centerability are fundamental(see 3.3).360°angle gradations are indicated in the areasurrounding the rotating stage, and, using the vernierscale, the angle can be measured to an accuracy of0.1°. A cross moving device is also equippedexclusively for moving specimens.A universal stage with multiple rotating axes may alsobe used to enable the observation of specimen frommany directions.

3.2.5 Bertrand lensA Bertrand lens projects an interference imageof the specimen, formed in the objective pupil,onto the objective image position (back focallength). It is located between the analyzer andeyepiece for easy in and out of the light path.See 4.2 for how to use the lens.

● Fig. 3.6 Polarizing rotating stage (U-SRP) ●

Centerable revolving nosepiece


Test plate

Compensator

γdirection

K E Y W O R D

14


The optical axis of the objective changesslightly according to the lens. Since the stageneeds to be rotated for polarizing observation,the objective and the optical axis of the tubemust coincide exactly with one another. In orderfor the optical axis to completely match evenwhen the lens' magnification is changed, arevolver with optical centering mechanism isinstalled in each hole. (see 3.3).

3.2.6 Centerable revolving nosepiece

●Fig. 3.7 Centering revolving nosepiece (U-P4RE) ●

This is an eyepiece with a diopter correctionmechanism which has a built-in focusing platecontaining a crosshair. By inserting the pointpin into the observation tube sleeve, the vibra-tion direction of the polarizer and analyzer canbe made to agree with the crosshair in thevisual field.

3.2.7 Eyepiece with crosshair

● Fig. 3.8 Crosshair ●

The test plate is a phase plate used for verify-ing the double refractivity of specimens, deter-mining the vibration direction of pieces, and forretardation measurement; a quarter-wave plate(R=147 nm) or a tint plate (R=530) are someexamples. The γ direction shown on the testplate indicates the Z' direction.The compensator is a phase plate that canchange and measure the retardation. SeeChapter 5 for more details.

3.2.8 Test plate and compensator

● Fig. 3.9 Test plate with compensator ●

K E Y W O R D

Orientation plate

15

■3.3 Preparation for polarizing microscope observationIn polarized light microscopy, always performthe optical adjustments, e.g. centering of therotatable stage, adjusting the optical axis ofobjective lens and vibration direction of a polar-izer, before the observation.(1) Adjusting the stageIn a polarizing microscope, the stage isoften rotated during observation. Thus, it isnecessary that centering of the rotatablestage is in alignment with the optical axis ofthe objective.Insert a standard objective (normally 10x)into the optical path and rotate the stage.Manipulate the two stage centering knobsto bring the center of a circle, which istraced by a point on a specimen on thestage to align with the intersection of thecrosshair of the eyepiece. (Fig. 3.10).

(2) Adjusting the optical axis of the objectiveFor stan dard objectives, as explained in (1)above, the centering of the rotating stagealigns with the optical axis of the objective.For objectives with other magnifications, thecenterable revolving nosepiece adjusts thecentering of the objective optical axis.For objectives other than 10x, insert theobjective into the light path. Then, rotate thestage and turn the screw of the centerablerevolving nosepiece to make the optical axisalign with the rotating center of the stage.

(3) Adjusting the polarizerWhen the calibration of the polarizer is 0°,the vibration direction must correctly alignwith the crosshair in the visual field. To dothis, an orientation plate, which is a crystalspecimen whose optical axis is parallel tothe standard plane, is used. If the vibrationdirection of the polarizer is not in alignmentwith this optical axis, the orientation plateappears bright. In order to darken it, adjustthe polarizer and analyzer and fix them atthe position where the standard plane of theorientation plate is parallel with the horizon-tal line of the crosshair (Fig. 3.11). For somepolarizing microscope, the analyzer isalready built into the mirror unit and its vibra-tion direction is controlled.

● Fig. 3.10 Centering adjustment of the stage ●

● Fig. 3.11 Adjustment by the orientation plate ●

orientation plate(B2-PJ)

standard plane

Make it parallel

crosshair in aneyepieceorientation plate

K E Y W O R D

Orthoscope

One nicol

16

3.Polarizing microscopes

Observation of an anisotropy by a polarizingmicroscope is generally done with illuminationof lower NA but without the top lens of the ordi-nary condenser lens. This observation is calledorthoscopic observation. In order to investigatethe optical properties of a crystal, etc., interfer-ence fringes that appear on the exit pupil of theobjective can be observed during polarizing lightobservation. This observation method is calledconoscopic observation. Provided below are theorthoscopic and conoscopic observation meth-ods.

a) Vitamin crystal

b) Optical pattern of liquid crystal

c) Rock

d) Emulsion

● Fig. 4.1 Example of anisotropy observation via crossed nicols ●

■4.1 Orthoscopic observationAmong the observation methods of a polarizingmicroscope, the orthoscopic observation is theone in which only the roughly vertical light isexposed to the specimen surface (i.e., low illumi-nation light of NA), and the optical propertiesare observed only in that direction. In ortho-scopic observation, the Bertrand lens isremoved from the light path, and either the toplens of the condenser lens is out, or the aper-ture diaphragm is closed.There are two orthoscopic observations, one iscrossed nicols and the other is one nicol. Incrossed nocols, the polarizer and analyzer areboth used to be crossed, while in one nicol, onlythe polarizer is used.

4.1.1 Observation of anisotropy via crossed nicolsThe most commonly used observation methodin polarizing microscope is crossed nicols obser-vation to inspect the double refractive struc-tures in biology, rock minerals, liquid crystals,macromolecule materials, anisotropic propertiessuch as emulsions, and stress strain.

K E Y W O R D

17

4. Observation method for polarizing microscope

4.1.2 General principles of interference colors and retardationRetardation testing is conducted for investigat-ing an optical anisotropy. Retardation R isexpressed by the equation (1.2) as d (ne-no), theproduct of the width of anisotropy and doublerefraction. By using this equation, the speci-men's double refraction can be calculated fromthe value of thickness d, giving a hint as towhat the anisotropy may be. If, on the otherhand, the value for double refraction is alreadygiven, then the thickness d will be figured out.Furthermore, through the computation of opticalstrains, the analysis of stress can possibly bemade.

In order to determine the retardation, set thespecimen diagonally in crossed nicols,observe the interference colors, then com-pare it with the interference color chartgiven in 2.1.2. However, a high degree ofaccuracy cannot be expected from the retar-dation value derived in this way; measure-ment is restricted to the range of bright col-ors, from primary order to secondary order.This is why a compensator as outlined inChapter 5 must be used in order to performaccurate measurements.

4.1.3 How to use a test plateThe test plate for a polarizing microscope is usedas follows:(1) Sensitive color observationUse of a tint plate in polarization observation ofanisotropy with small retardation enables observa-tion at bright interference colors. In the neighbor-hood of sensitive colors, the retardation changes,and the interference colors alter accordingly butonly more sharply and dramatically. Because ofits sensitivity, any minute retardation can bedetected through interference colors.(2) Measurement of optical character of elonga-tionAs stated in 2.3, measuring the optical characterof elongation for anisotropic elements elongatedin a certain direction enables to identify theunknown anisotropy. Determining the optical char-acter of elongation is performed while using thetest plate and compensator to observe changesin the interference colors (Fig. 4.2).(a) Set the anisotropy in the diagonal position.Look over the interference color of the speci-men in the interference color chart.

(b) Insert the test plate into a slot and observethe changes in the interference colors. If thecolor converts to higher order, then the Z'direction of the anisotropy matches the Z'direction of the test plate. If it changes tolower order, the Z' direction is perpendicular tothat of test plate. Relationship between thedirection of elongation and Z' direction of theanisotropy helps determine the optical charac-ter of elongation.

● Fig. 4.2 Determination of the optical character of elongation ●

If the test plate is put in, the interference color shiftsto higher order. (addition)The Z' direction matches the direction of elongation.The optical character of elongation is positive.

If the test plate is put in, the interference colorshifts to lower order. (subtraction)The Z' direction is perpendicular to the directionof elongation.The optical character of elongation is negative.

Z' directiontest plate

K E Y W O R D

Plechroism

Becke line

18

One nicol observation, in which the analyzer isremoved from the optical path, leaving the polar-izer inside, is mainly used to observe rock miner-als. In crossed nicols observation, theanisotropy appears colored by the interferencecolors. However, because interference colors donot emerge with only one nicol, the specimencan be seen in more natural, original color.Besides inspecting the shape, size, and color ofthe specimen, investigation of plechroisms byrotating the stage and observing the changesin colors can be done.To estimate the index of refraction of crystalssuch as minerals, Becke line is often utilized.The Becke line is a bright halo visible betweenthe crystal and the mounting agent when theaperture stop of the condenser lens is closed(Fig. 4.3). The Becke line is clearly visible whenthe difference of the index of refraction of themounting agent and the crystal is large; itbecomes dim when the difference is smell.Lowering the stage (or raising the objective)moves the Becke line to a higher index of refrac-tion, and raising the stage (or lowering theobjective) moves the line to a lower index ofrefraction. By changing the mounting mediumwhile observing the Becke line, the medium hav-ing the same index of refraction with the crystalcan be determined, and in turn, the crystal’sindex of refraction can be deduced.

When the index of refraction of the crystal is

greater than the index of refraction of the mount-

ing agent:

a) Becke line with a slightly lowered stage

b) Becke line with a slightly raised stage

In the opposite case, the location of the Becke

line is contrary to what is seen in Fig 4-3.

4.1.4 One nicol observation

● Fig. 4.3 Becke line ●

K E Y W O R D

Conoscope

19

■4.2 ConoscopeConoscopic observation is used to obtain theinformation necessary for identifying crystalssuch as rock minerals in uniaxial and biaxialmeasurement as well as in measurement of theoptical axis angle.

4.2.1 Conoscopic optical systemAmong many observation methods using a polarizingmicroscope, the one which studies the pupil surfaceof the objective (back focal plane) with a condenserlens installed is called conoscopic observation. Thepurpose of conoscope is to view the interferencefringes created from the light rays that travelsthrough the specimen through multiple angles, andthus enables the inspection of various optical prop-erties of the specimen in different direction at thesame time. In order to gain the best result, theobjective lens with NA of high magnification isrequired.

The Conoscopic optical system is shown in Fig. 4.4.The linearly polarized light that passes through thepolarizer is converged by the condenser and travelsthrough the specimen at various angles. After that,the linearly polarized light will be divided into ordinaryand extraordinary rays in the crystal, will proceed par-allel to each other after passing through the crystal,then possess the optical properties that are peculiarto the specimen, and the retardation dependent ofthe angle of incidence.The two rays meet on the pupil surface of the objec-tive and their polarization direction is adjusted by theanalyzer, causing an interference. These interferencefringes are called the conoscopic image. First inter-ference fringes, created by the rays parallel to themicroscope optical axis, emerge at the center of theconoscopic image. The light rays which waslaunched at an angle relative to the optical axis cre-ates the second interference fringes, which thenappear in the periphery of the image.The conoscopic image can be easily studied byremoving the eyepiece. However, because the inter-ference fringes will become rather small, an auxiliarylens called a Bertrand lens projects the pupil surfaceof the objective onto the original image position, andenlarges it through the eyepiece.

● Fig. 4.4 Conoscopic optical system●

Conoscopic projection image(observed with eyepieces)

Bertrand lens

Analyzer

Conoscopic image

Objective lens

Crystal

Condenser lens

Polarizer

e:extra ordinary rayo:ordinary ray

K E Y W O R D

Isogyre

20

4. Observation method for polarizing microscope

Conoscopic images of uniaxial crystals differfrom those of biaxial crystals. A flake that hasbeen cut vertically by uniaxial optical axis canbe viewed as a concentr ic ci rcle withpenetrated black cross (isogyre). This crosscenter is the optical axis direction of theuniaxial crystal.As shown in Fig. 4.5b, if an image has twocenters of the interference fringes, then theimage is for a biaxial crystal. By studying thestyle of a conoscopic image, the distinctionbetween uniaxial crystals and biaxial crystals,the optical axis direction, the optical axis angleof biaxial crystals, and the positive and negativecrystals can be attained.

4.2.2 Conoscopic image of crystals

a) Uniaxial crystal conoscopic image (calcite)

b) Biaxial crystal conoscopic image (topaz)

4.2.3 Determination of positive and negative crystal using a test plateThe use of a test plate in the conoscopic imageenables to distinguish positive and negative crystals.In the case of uniaxial crystals, the vibration directionof the extraordinary rays oscillates inside the princi-pal section (the surface including the vibration direc-tion of the rays and the optical axis), and ordinaryrays oscillate perpendicularly to the principal section.For positive crystals, the index of refraction of extra-ordinary rays is greater than that of the ordinary rays,and vice versa for negative crystals.As a result, in uniaxial crystals cut perpendicularly bythe optical axis, the Z' direction of the conoscopicimage appears as shown in fig. 4.6a. Inserting thetest plate into the optical path for a positive crystalchanges the interference colors in the direction inwhich the first quadrant and third quadrant areadded. As for a negative crystal, the interference col-ors move in the direction in which the second quad-rant and the fourth quadrant are added. Observingthe changes in the interference colors upon insertingthe test plate helps determine whether it is a posi-tive crystal or a negative crystal.Figure 4.6b shows a conoscopic image of the uniax-ial crystal when the sensitive color test plate isinserted into the light path. Observing the changes inthe interference colors around the optical axis deter-mines whether the crystal is positive or negative.

● Fig. 4.6 ●a) The Z' direction of the uniaxial crystalconoscopic imageb) Changes while the sensitive color testplate is present in the light path

● Fig. 4.5 Conoscopic images ●

positive crystal negative crystal

positive crystal negative crystal

Z' directionof test plate

a.

b.

Z'Z'

The accurate retardation measurement can beobtained by canceling the retardation createdfrom specimens, and by reading the calibrationmarked at the point. Most typical compen-

* Compensator names are Olympus brand names

** The measuring range of the compensator is that of an Olympus compensator

(compensator measuring ranges vary with manufacturers)

The Z' direction (γ direction) is printed on the compensator to facilitate distinguishing the Z'direction of anisotropy as well as test plate. (see 4.1.3).Detailed information on each compensator is given next.

■5.1 Types of compensators

K E Y W O R D

Compensator

21

5. Compensator

For strict measurement of the retardation ofanisotropy, a device called a compensator, com-posed of a phase plate that can change theretardation, is used. Depending on the compen-sators, measurement methods and measurable

retardation vary, thus it is necessary tochoose the most suitable compensator forthe application. This chapter describes theprinciples and measurement methods of vari-ous compensators.

sators' measuring ranges and applicationsare given below.

● Table 5.1 Measuring range and applications of various compensators ●

Name* Measuring Range** Main Applications

0-11000nm(0-20λ)0-1640nm(0-3λ)

･ Substances with high retardation such as crys-tals, LCDs, fibers, plastics, teeth, bones, andhair.･ Retardation measurement of optical strain･ Determination of the Z' direction of anisotropy

Berek

U-CTB

U-CBE

0-546nm(0-λ) ･ Retardation measurement of crystals, fibers, liv-ing organisms, etc.･ Retardation measurement of optical strain･ Emphasizing contrast for the observation of fineretardation textures･ Determination of the Z' direction of anisotropicbodies

Senarmont

U-CSE

0-55nm(0-λ/10)0-20nm(0-λ/30)

･ Retardation measurement for thin film and glass･ Emphasizing contrast for the observation of fineretardation textures･ Determination of the Z' direction of anisotropy

Brace-kohler

U-CBR1

U-CBR2

500-2000nm(1-4λ) ･ Retardation measurement of rock crystals･ Determination of the Z' direction of anisotropy

quartz wedge

U-CWE

K E Y W O R D

Berek compensator

22

A Berek compensator is a kind of a prism whichmeasures retardation with a calcite or magne-sium fluoride crystal cut perpendicular to theoptical axis. (Fig. 5.1)Turning the rotating dial on the compensatorinclines the prism relative to the optical axis,lengthens the optical path, and increases thedifference between the index of refraction of theordinary rays and extraordinary rays (ne-no),which in turn increases retardation as shown inFig. 5.2.

To measure the retardation of specimen, tilt theprism to move the black interference fringes ora dot to the desired location, then read thecalibration from the rotation dial (at this point,the retardation of the compensator and that ofthe specimen become equivalent).Use the attached conversion table to determinethe retardation R from the angle that is readout. The table is deriven from calculation usingthe following equation.

（5・1）

Here, C is calculated as follows:

ω, ε: refraction indices for ordinary rays andextraordinary rays

d: prism thickness of the compensator

■5.2 Berek compensator

● Fig. 5.1 Berek compensator ●

● Fig. 5.2 Angle of prism inclination and retardation of Berek compensator ●

R＝C・ 2 　1－sin2θ/ε2－　1－sin2θ/ω2　

（1/ε2－1/ω2）

θ:prism tilting angleC :optical axis

prism tilting angle θ(°)

Retardation

(nm)

C＝　　（1/ε2－1/ω2） d・ω 2

K E Y W O R D

23

Two kinds of Berek compensators are availablefrom Olympus: U-CTB with a large double refrac-tance calcite prism, and U-CBE with a calcitemagnesium prism. U-CTB has a wider measur-

ing range than conventional Berek compen-sators. The typical interference fringes whenusing a Berek compensator are shownbelow.

b) while measuring retardationa) diagonal position

● Fig. 5.3 Berek compensator interference fringes when measuring minerals inside rocks ●

b) U-CTBa) U-CBE

(The above diagram is from a positive fiber. When it is negative, the interference fringes are reversed for U-CBE and U-CTB.)

● Fig. 5.4 Berek compensator interference fringes when measuring fibers ●

K E Y W O R D

Senarmont compensator

24

5. Compensator

A Senarmont compensator is a combination ofa highly accurate quarter-wave plate and arotating analyzer to measure retardation. The

The rays exited from the specimen whose retar-

dation is measured are elliptically polarized light.

Specimen retardation determines the state of

this el l iptically polarized l ight. This l ight

becomes linearly polarized when it passes

through a Senarmont compensator (quarter-

wave plate). The linearly polarized light at this

time is rotated more than when no specimen is

present. The retardation of the specimen deter-

mines the extent of the rotation. The rotation

angle q is the position at which the specimen is

darkened when the analyzer is rotated. The

retardation R is calculated from the rotation

angle q by the following equation:

(5.2)

Since the quarter-wave plate used in the Senar-

mont compensator is normally designed for a

546 nm wavelength, the λ = 546 nm narrow

band interference filter must be used.

An example usage of the Senarmont compen-

sator is shown in the picture below.

configuration of the Senarmont compensatoris shown in Fig. 5.6.

■5.3 Senarmont compensator

● Fig. 5.6 Senarmont compensator configuration ●

● Fig. 5.7 Measurement of muscle with Senarmont compensator ●

a) diagonal position

b) while measuring retardation

● Fig. 5.5 Senarmont compensator (quarter-wave plate) ●

Polarizer

Specimen1/4 Wave plate

Analyzer

Senarmont compensator

R＝　　λ θ 180

K E Y W O R DBrace-kohler compensator

25

■5.4 Brace-kohler compensatorA Brace-kohler compensator is a compensatorfor measuring fine retardation. (see Fig.5.9) Tochange the retardation, rotate the small micaprism with low retardation with optical axis in

The value of retardation R using a Brace-kohlercompensator can be found from the equationbelow, using the rotation angie q.

R＝R0・sin (2・｜θ｜) (5.3)R0 is a constant value individually attached toeach product. An example usage of the Brace-kohler compensator is shown in Fig 5.10.

A Brace-kohler compensator is also used toincrease contrast in polarized light observation,besides retardation measurement. When usinga Brace-kohler compensator to observe a sam-ple with an extremely small retardation, anincrease or a decrease of retardation results instressing the differences in brightness betweenthe place where retardation occurs and itsbackground, and thus simplifies the observa-tion. The Brace-kohler compensator is particu-larly effective during observation in polarizedlight of the double refractive structure in livingorganisms.Two Brace-kohler compensators are availablefrom Olympus: U-CBR1 and U-CBR2. U-CBR1has a measuring range of 0-55 nm (λ/10), andU-CBR2 has 0-20 nm (λ/30).

the center. Turning the dial will rotate theprism.

● Fig. 5.9 Brace-kohler compensator prism (rotation direction) ●

● Fig. 5.10 Measurement of a film with Brace-kohler compensator ●

diagonal position

while measuring retardation

● Fig. 5.8 Brace-kohler compensator ●

Vibration direction of analyzer

Zero position of compensator

=

Vibration directionof polarizer

optical axis

K E Y W O R D

Quartz wedge

26

5. Compensator

A quartz wedge is shown in Fig. 5.12. Movingthe quartz wedge can alter the retardationbecause the retardation continually changes inthe direction of the wedge. Instructions on how to measure the sampleretardation is provided next. Moving the quartzwedge toward the long-side direction makes theblack fringes appear when the sample retarda-tion and compensator retardation cancel outeach other. At this point, remove the specimen,secure the quartz wedge, and determine theretardation by comparing the observable inter-ference color with the interference color chart.The result obtained in this manner lacks accu-racy. Besides measuring retardation, the quartzwedge is also used for determining the Z' direc-tion.

An example of measuring quartz wedge retardation is shown below.

■5.5 Quartz wedge

● Fig. 5.11 Quartz wedge ●

● Fig. 5.12 Quartz wedge prism ●

● Fig. 5.13 Measurement with a mineral crystal quartz wedge. ●

b) while measuring retardationa) diagonal position

optical axis

crystalmoving direction

Quartz wedge

Direction ofoptical axis(Perpendicularto space)

basic of polarizing microscopy

Documents