Optical Engineering

Part 2: Materials, dispersion, glass map Herbert Gross

Summer term 2020 www.iap.uni-jena.de 2 Contents

. Wavelengths . Atomic interaction and dispersion . Abbe number . Dispersion formulas . Partial dispersion . Normal line . Glass map Important Test Wavelengths

 in [nm] Name Color Element 248.3 UV Hg 280.4 UV Hg 296.7278 UV Hg 312.5663 UV Hg 334.1478 UV Hg 365.0146 i UV Hg 404.6561 h violet Hg 435.8343 g blue Hg 479.9914 F' blue Cd 486.1327 F blue H 546.0740 e green Hg 587.5618 d yellow He 589.2938 D yellow Na 632.8 HeNe-Laser 643.8469 C' red Cd 656.2725 C red H 706.5188 r red He 852.11 s IR Cä 1013.98 t IR Hg 1060.0 Nd:YAG-Laser

Chromatical Evaluation of Optical Systems

. Chromatical performance evaluation of optical systems: Usage of one main (central) wavelength and two secondary wavelenghts

1st secondary 2nd secondary Main wavelength wavelength wavelength e 546.07 green F' 480.0 blue C' 643.8 red

d 587.56 yellow F 486.1 blue C 656.3 red

. Additional definition of wavelengths at the boundaries of the used spectral range, e.g. - one further wavelength near to the UV edge (g, i) - one further wavelength near to the IR-edge (s,t) 5 Atomic Model of Dispersion

2 2 2 . Atomic model for the refractive index: 2 Ne f j  j nr  i ni    2 2 2 oscillator approach of atomic field interaction 2 c0m j 2 c    j i j j

. Sellmeier dispersion formula: B 2 n2  A j corresponding function  2 j  C j

. Special case of coupled resonances: 2 B 4 B  example quartz, degenerated oscillators n2  A  0  j 2 2 2  2 C  o  j1 j

n (UV) (UV) (IR) (IR) 1 2 visible 3 4 7

6

5

4

3

2 nvis()

1 log  [mm] 0 -1 0 1 10 0.4 0.7 10 10 6 Dispersion and Abbe number

. Description of dispersion:

Abbe number n 1 n  n  n F ' C' refractive index n . Visual range of wavelengths: 1.8 typically d,F,C or e,F’,C’ used 1.75 ne 1 ne  nF '  nC' 1.7

SF1 flint . Typical range of glasses 1.65 ne = 20 ...100 1.6 . Two fundamental types of glass: Crown glasses: 1.55 n small, n large, dispersion low BK7 Flint glasses: 1.5 n large, n small, dispersion high crown 1.45  0.5 0.75 1.0 1.25 1.5 1.75 2.0 7 Abbe Number and Achromatization

1 1 c  , c  . Curvatures cj of the radii of a lens 1 2 r1 r2

. Focal power at the center wavelength e Fe  (ne 1)(c1  c2 )  (ne 1) c for a thin lens

. Difference in focal powers for outer nF '  nC' Fe wavelengths F', C' F  FF '  FC'  (nF '  nC' ) c  (ne 1)c  ne 1 n e

ne 1 with the Abbe number n e  nF '  nC'

1 1 . Focal length at the center wavelength fe   Fe (ne 1)c . Difference of the focal lengths for outer nC'  nF ' nC'  nF ' fe wavelengths f  fF '  fC'   2   (nF ' 1)(nC' 1)c (ne 1) c n e . Achromatization condition for two thin F F 1 1 lenses close together F  1  2   0 n1 n 2 f1n1 f2n 2 8 Dispersion formulas

. Schott formula n  a  a  2  a  2  a  4  a  6  a  8 empirical o 1 2 3 4 5

. Sellmeier 2  2 n()  A  B 2 2  C 2 2 Based on oscillator model    1    2

2 . Bausch-Lomb 2 4 D E  n()  A  B  C  2  2 empirical  2 2 F (   o)  2 2   o

a a . Herzberger n()  a  a 2  2  3 o 1 2 2  2 2 2 Based on oscillator model o  o 

mit o 0.168mm

. Hartmann a1 a4 Based on oscillator model n()ao   a3   a5   9 Relative Partial Dispersion

. Relative partial dispersion : n Change of dispersion slope with  1.54 Different curvature of dispersion curve 1.53 . Definition of local slope for selected i - g g - F wavelengths relative to secondary 1.52 F - C colors F - e C - t 1.51 C - s n1  n2  P  n() 12 nF '  nC' 1.5 . Special -selections for characteristic ranges of the visible spectrum 1.49

 = 656 / 1014 nm far IR 1.48   = 656 / 852 nm near IR 400 500 600 700 800 900 1000 1100  = 486 / 546 nm blue edge of VIS g : 435 nm e : 546 nm UV edge d : 588 nm  = 435 / 486 nm near UV main color i : 365 nm F' : 480 nm C' : 644 nm  = 365 / 435 nm far UV UV edge F : 486 nm C : 656 nm s : 852 nm t : 1014 nm 1. secondary 2. secondary color color IR edge IR edge 10 Partial Dispersion and Normal Line

. The relative partial dispersion changes approximately linear with the dispersion for glasses

P P1,2  a1,2 n d  b1,2 0.6 . Nearly all glasses are located on the normal line in a P-n-diagram PgF

0.55 . The slope of the normal line depends on the selection of wavelengths

. Glasses apart from the normal line 0.5 PCs shows anomalous partial dispersion P

0.45 n P12  a12 n d  b12  P12 80 60 40 20

these material are important for chromatical correction of higher order 11 Relative Partial Dispersion

. Preferred glass selection for apochromates

N-SF1 N-SF6 N-SF57 N-SF66 P-SF68 P-SF67

N-FK51A N-PK52A N-PK51 N-KZFS12 N-LAF21 N-KZFS4 N-LAF35 N-LAF33 N-LAK10 N-LASF41 N-KZFS2 N-LAF37 12 Glass Diagram

. Usual representation of glasses: diagram of refractive index vs dispersion n(n)

. Left to right: Increasing dispersion decreasing Abbe number Ranges of the Glass Diagram

Two major families of glass types, depending on chemical ingredients:

1. Crown: Low index, low dispersion n 2.00 n e 54.7 for ne 1.6028 1.95 n e  49.7 for ne 1.6028 1.90

1.85 LaSF 2. Flint: High index, high dispersion 1.80 SF LaF 1.75 LaK flint n e 54.7 for ne 1.6028 glass 1.70 n e  49.7 for ne 1.6028 BaSF TiSF 1.65 crown glass SSK BaF 1.60 SK F TiF PSK BaLF BaK LF 1.55 LLF KF PK K 1.50 BK FK TiK n 1.45 85 80 75 70 65 60 55 50 45 40 35 30 25 20