製品 | 2021/5/14

This page is a detailed introduction to the 2-D Birefringence Measurement System "PA/WPA series": measurement principle and equipment configuration, and present a set of measurement examples.

2次元複屈折評価システムPA/WPAシリーズ

Japanese version

Contents

1.Basics of Birefringence Measurement

The 3 components of light

①Amplitude = brightness

光の振幅:明るさ

②Wavelength = color

光の波長:色

③Direction of the Vibration: polarization

In contrast to amplitude and wavelength,

polarization cannot be recognized by human eye,

making it difficult to apprehend intuitively.

Basic Principle of Polarization Measurement

Rotating a polarizer and observe the change of intensity transmitted through the polarizer.

 Polarization & Polarizers

偏光子polarizer

when

Input Direction = Polarizer Direction

       ↓

      100% transmitted

偏光子polarizer

when

Input Direction ⊥ Polarizer Direction

       ↓

       0% transmitted

偏光子polarizer

when 45deg. …

       ↓

       50% transmitted

Polarization and Birefringence

Refractive index = how easily light passes through the material

The higher the refractive index is,
the more time is needed for light to
pass through the material.

※Optical length=Refractive Index x Length

Example: for glass with index n = 1.5, light is slowed down by a factor 1.5.

Birefringence = when refractive index depends on light polarization

Example refractive indices

MaterialOrdinaryExtraordinaryBirefringence(⊿n)
Calcite1.65841.48640.172
Quartz1.54431.55340.0091
Sapphire1.7681.760.008
Ice1.3091.3130.004

Phase shift = Birefringence × Length

Here, we assume that different polarizations are passing through the material at the same point.
Thus, length is the same ⇒ Phase Shift ∝ Birefringence

Impact of Birefringence on Light Polarization

Phase Shift between Each Polarization Component and Total Polarization Resulting.
every state of polarization existing is the result of a combination of 2 perpendicular components.

In Phase

直線偏光linear polarization
直線偏光linear polarization

Linear Polarization

Quadrature

円偏光circular polarization
円偏光circular polarization

Circular Polarization

※ Depending on the phase shift between the 2 components, a different state of polarization results.

We understand that birefringence makes polarization change by introducing a phase shift between the two components.

Material exhibiting birefringence makes polarization change

【non birefringent material】

複屈折birefringence
No change in polarization

複屈折birefringence
Crossed polarizers (cross Nichols): dark
no light is detected.

【birefringent material】

複屈折birefringence
Change of polarization
複屈折birefringence
Even with crossed polarizers, light
is detected due the change of polarization
induced by the birefringent material.

Crossed polarizers completely shut down the light trying to go through

            ↓

A non birefringent material placed between does not change the situation

            ↓

A birefringent material placed between the crossed polarizer appears bright

Birefringence caused by stress

Even in non birefringent materials, internal stress can induce birefringent behavior.

This phenomenon, called “photo-elasticity”, imply that observed birefringence is proportional to the stress applied to the material. The proportionality constant, referred as the “photo-elasticity constant”, is a property of each material.

birefringence= β×stress [force] (1012Pa)

phase shift δ(nm) = β×thickness d (cm)×stress [force] (105 Pa)       

 ~β is the photo-elastic constant for the particular material [ 1012/Pa ]

For example,
a force of 1MPa applied to a 1mm quartz plate results in a phase shift of:

3.5×0.1×10=3.5nm     

Material Photo-elastic constant(10-12/Pa)
Quartz3.5
Polycarbonate75
Acrylic6
Glass0.5
Lead glass0.005

※Natural birefringence of rock crystal quartz is approx.0.01(1.55-1.54).The amount of force to obtain this value by photo-elasticity is 0.003TPa=3GPa, which is very big. In general, birefringence exhibited by the photo-elastic effect is much smaller than in naturally birefringent quartz.

※The major part of the birefringence observed in plastic molded object is thought to originate from molecular orientation, rather than from photo-elasticity. Thus, for this type of object, it is not reasonable to calculate an amount of stress from the birefringence observed. However, differences of birefringence still can be linked to differences of the molding process, thought as a whole. That is why birefringence analysis is a good evaluation technique for plastic molding process.

Summary: Polarization, Birefringence, Phase Shift, Photo-elasticity

Evaluating the distribution of birefringence enables the access to information about internal stress and molecular orientation in transparent materials.

Birefringence in material modifies the polarization of the light going through.

Thus, comparing light polarization in and out allows measuring birefringence in the material.

Birefringence Measurement =Polarization Measurement + Difference Computation.

※A birefringence measurement system must be, as long as we talk about hardware, a polarization measuring device.

Computation Flow

①Polarization Measurement                             

②Phase Shift Computation (from change of polarization)           

③Birefringence Computation (from phase shift and sample thickness)    

④ Internal Stress Computation (from birefringence and photo-elastic constant)

Theoretically, computation of birefringence and internal stress is possible. However, because of the following
reasons birefringence measurement device usually provide data
for ② phase-shift only:
a. sample geometry data is not easy to manipulate in a universal manner
b. phase-shift data is often more relevant than birefringence for most applications
c. the cause of birefringence is rarely internal stress only, but a combination of factors
The user is then free to keep further the computations based on its own knowledge about his sample geometry and material.

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