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2.1 Refractive index

        Refractive index is denoted by the letter n, while spectrum line or wavelength is denoted by x.

Nineteen spectrum lines’ refractive indices of colorless optical glass provided in table 1 are measured by minimum deviation angle method.

        Test equipment:High precision refractive index tester (SpectroMaster UV-VIS-IR) made by German TRIOPTICS.

        Measurement accuracy:±3×10-6 in the ultraviolet range, ±2×10-6 in the visible range, ±5×10-6 in the near- infrared range.

        Sample requirements: No visible striae, bubbles or stones with naked eye, stress birefringence up to class 1.

        Upon special request, we can provide other characteristic spectrums’ refractive indices, including 253.65nm, 289.36nm, 296.73nm, 312.57 nm, 334.10nm, 388.86nm, 508.58nm, 1064.00nm, 2058.09nm.

        In the spectral range of 365.01nm~2325.42nm, the refractive indices not listed in the handbook can be calculated by the Schott formula (1):

        Where: A0~A5—Calculating constants;

                    λ—Wavelength, μm

                        n—Refractive index (Calculation accuracy at the visible band ±1×10-5)

        Correlative spectrum lines’ refractive indices of low softening point glass (glass starting with D-) in this handbook were tested after -25/H annealing treatment. Refractive index of d line changes with cooling rates βd is given in the handbook, and refractive index nd in cooling rate s can be calculated by formula (2).

 

 Table 1

Spectral Line

Element

Wavelength (nm)

Spectral Line

Element

Wavelength (nm)

i

Hg

365.01

C

H

656.27

h

Hg

404.66

r

He

706.52

g

Hg

435.84

A

K

768.19

F

Cd

479.99

s

Cs

852.11

F

H

486.13

t

Hg

1013.98

e

Hg

546.07

Hg

1128.64

d

He

587.56

Hg

1529.58

D

Na

589.29

Hg

1970.09

He-Ne

He-Ne

632.80

Hg

2325.42

C

Cd

643.85

 

Other spectrum lines’ refractive indices varying with cooling rates are also available if required.

2.2 Dispersion and abbe-number

    The central dispersion is expressed by nF-nC or nF-nC.

    nF-nCnF'-nC'

Abbe-number υd and υe are defined as:

2.3 Relative partial dispersion

    Relative partial dispersion is usually calculated with arbitrary spectrum lines. For example, relative partial dispersion for wavelength X and Y can be expressed by formula (5):

 

      

The values of Pd, c, Pe, d, Pg, F and P'd, c, P'e, d, P'g, Fare given in the handbook.

2.4 Abnormal dispersion 

According to the abbe-number formula, the following linear relationship is tenable for most normal glass:

The deviation value PX, Y of relative partial dispersion can be calculated by the following formula:

Pg, F, PF, e, PC,t and PC,s against H-K6, F4 can be calculated by formula (8):

 

        

2.5 Temperature coefficient of refractive index dn/dt

      Refractive indices of optical glass change with temperatures.The relationship of refractive index change to temperature change is called temperature coefficient of refractive index dn/dt. Temperature coefficients of refractive indices are determined by temperature coefficients of relative refractive indices in the dry air (dn/dt)rel.(101.3KPa) and temperature coefficients of absolute refractive indices in the vacuum (dn/dt)abs..The testing data are provided every 20 from -40 to 80. Temperature coefficients of refractive indices of spectrum lines s, C, d, F are also available if required, and testing temperatures can be extended to 160℃。.

      Temperature coefficients of absolute refractive indices (dn/dt) abs. can be calculated by formula (9), and the temperature coefficients of refractive indices for air (dnair/dt) are indicated in table 2.

Table 2  

Temperature (℃)

dnair/dt(10-6/)

t

C'

He-Ne

D

e

F'

g

-40~-20

-1.34

-1.35

-1.36

-1.36

-1.36

-1.37

-1.38

-20~0

-1.15

-1.16

-1.16

-1.16

-1.16

-1.17

-1.17

0~+20

-0.99

-1.00

-1.00

-1.00

-1.00

-1.01

-1.01

+20~+40

-0.86

-0.87

-0.87

-0.87

-0.87

-0.88

-0.88

+40~+60

-0.763

-0.77

-0.77

-0.77

-0.77

-0.77

-0.78

+60~+80

-0.67

-0.68

-0.68

-0.68

-0.68

-0.69

-0.69

 

2.6 Calculating constants of dn/dt

    The temperature coefficients of absolute refractive indices unspecified in the handbook can be calculated with the aid of equation (10).

Where: n(λ,T0) —Relative refractive index at the reference temperature;

T0—Reference temperature (20 ℃);

T —Targeted temperature (℃);

ΔT—Temperature difference T-T0 (℃);

λ—Wavelength of the electromagnetic wave in the vacuum (μm);

D0, D1, D2, E0, E1and λTK—Constants depending on glass type.

The applied temperature range: -40℃ to +80℃;

The applied wavelength range: 0.3650 μm to 1.014 μm.

2.7 Stress photoelastic coefficient  B

    Stress inside glass can result in change of optical properties, thereby birefringence appears. The relation among optical path difference, stress inside glass and glass thickness is expressed below:

      δ=B∙d∙F……………………………………………(11)

Where: δ—Optical path difference, nm;      

d—Glass thickness, cm;

F—Stress. Pa;

B—Stress photoelastic coefficient.

In this handbook, stress photoelastic coefficient is listed at a unit of (nm/cm/105Pa).

2.8 Internal transmittance τ

    The internal transmittance refers to transmittance excluding reflection losses at the surfaces of the sample. Internal transmittance values are calculated from transmittance measurement of a pair of samples with single beam: measure transmittance of two samples of different thicknesses respectively, and then calculate mathematically.

Test equipment:Hitachi spectrophotometer (UH4150 UV-VIS-NIR)

Measurement accuracy:better than ±0.3%.

Sample requirement:bubble up to class 1, striae up to class B.

In the handbook, internal transmittance of 10mm (τ10) from 280nm to 2400nm can be calculated by formula (12).

………………………(12)

Where: τ—Internal transmittance based on transmittance of samples thicknesses is 10mm       

             △d—Thickness difference of samples d2-d1  ( d2d1), mm,

             T1, T2—Transmittances including surface reflection loss obtained by thickness d1, d2 of the sample

The internal transmittances of different wavelengths for 5mm and 10mm thick glass are shown in the handbook.

 

2.9 Color code λ80(70)5

        Transmitted spectrum performance of optical glass at short wave band can be expressed by the color code λ80(70)5. Measure the transmittance of glass with a thickness of 10mm±0.1mm (including reflection losses at the surfaces), wavelengths λ80 and λ5 respectively corresponding with transmittance 80%, 5% are used to express color code in 5 nm step(round off 2 and round up 3 or more, round off 7 and round up 8 or more of the bits of integers). For instance, if the corresponding wavelength of transmittance 80% is 357nm while transmittance 5% is 324 nm, the color code λ80 / λ5 is 355/325, as shown in figure 1.

figure 1

    For a glass whose ne is higher than 1.85, λ70 is used in place of λ80 as a color code due to a heavier reflecting loss. That is to say, the color code is expressed by λ705.

    The variance range of color code is usually within ±10 nm. Upon special request, we can provide materials with smaller tolerance.

2.10 Internal transmittance  λτ80/λτ5

    For a 10 mm thick glass, wavelengths λτ80 and λτ5 respectively corresponding with internal transmittance 80%, 5% are used to express coloring degree of the glass simply.


 

 

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