Optical Design with Zemax for PhD - Basics
Lecture 15: Illumination II 2019-02-20 Herbert Gross Speaker: Uwe Lippmann
Winter term 2018/19 www.iap.uni-jena.de 2 Preliminary Schedule
No Date Subject Detailed content Zemax interface, menus, file handling, system description, editors, preferences, updates, 1 17.10. Introduction system reports, coordinate systems, aperture, field, wavelength, layouts, diameters, stop and pupil, solves Basic Zemax Raytrace, ray fans, paraxial optics, surface types, quick focus, catalogs, vignetting, 2 24.10. handling footprints, system insertion, scaling, component reversal Properties of optical aspheres, gradient media, gratings and diffractive surfaces, special types of surfaces, 3 07.11. systems telecentricity, ray aiming, afocal systems 4 14.11. Aberrations I representations, spot, Seidel, transverse aberration curves, Zernike wave aberrations 5 21.11. Aberrations II Point spread function and transfer function 6 28.11. Optimization I algorithms, merit function, variables, pick up’s 7 05.12. Optimization II methodology, correction process, special requirements, examples 8 12.12. Advanced handling slider, universal plot, I/O of data, material index fit, multi configuration, macro language 9 09.01. Imaging Fourier imaging, geometrical images 10 16.01. Correction I Symmetry, field flattening, color correction 11 23.01. Correction II Higher orders, aspheres, freeforms, miscellaneous 12 30.01. Tolerancing I Practical tolerancing, sensitivity 13 06.02. Tolerancing II Adjustment, thermal loading, ghosts 14 13.02. Illumination I Photometry, light sources, non-sequential raytrace, homogenization, simple examples 15 20.02. Illumination II Energy transfer, Etendue 16 27.02. Physical modeling I Gaussian beams, Gauss-Schell beams, general propagation, POP 17 06.03. Physical modeling II Polarization, Jones matrix, Stokes, propagation, birefringence, components 18 13.03. Physical modeling III Coatings, Fresnel formulas, matrix algorithm, types of coatings Scattering and straylight, PSD, calculation schemes, volume scattering, biomedical 19 20.03. Physical modeling IV applications Adaptive optics, stock lens matching, index fit, Macro language, coupling Zemax-Matlab / 20 27.03. Additional topics Python 3
Contents
• Transfer of energy in optical systems • Etendue 4
Energy Transfer in Optical Systems
. Differential flux of power from a small area element dAs with normal direction n in a small solid angle dΩ along the direction s of detection s 2 dW d LdWdAS qS Lcosq dWdA S S dA S LdWsdAS n . Integration of the radiance over the area and the solid angle gives a power P dA A 5
Fundamental Law of Radiometry
. Differential flux of power from a
small area element dAS on a small receiver area dAR in the distance r, the inclination angles of the
two area elements are qS and qR respectively
Fundamental law of radiometric energy transfer 퐿 푑2Φ = 푑퐴 푑퐴 푟2 푆⊥ 푅⊥ 퐿 = cos 휃 cos 휃 푑퐴 푑퐴 푟2 푆 푅 푆 푅
. The integration over the geometry gives the total flux 6 Energy Transfer in Optical Systems
n n' marginal ray u h u' w'
w y surface chief ray s' s
• Helmholtz-Lagrange Invariant: 퐻 = 푛 푦 푢 = 푛′푦′푢′ • Corresponds to: • Conservation of Energy • Liouville Therorem (constant phase-space volume) • Constant transfer of information
• Valid for the paraxial approximation only • More general: Abbe Sine Condition for non-paraxial systems 푛 푑푦 sin 푢 = 푛′푑푦′ sin 푢′ 7 Optical Phase Space
• Define a 4-D phase space of spatial coordinates 푥, 푦 and propagation directions (푘푥, 푘푦)
• X and Y components of the wave vector 푘: 푘푥 = 푛 sin 푢, 푘푦 = 푛 sin 푣
x
z
x x x
x
u I u I 8 Etendue
• Volume in 4-D phase space of a light beam:
푉 = 퐺 = න 푑푘푥 푑푘푦 푑푥 푑푦
• In terms of area and solid angle:
2 퐺 = න 푛 푑Ω푝 푑퐴
• Etendue is a measure for the angular and spatial extent of a light beam. • It is also a measure for the „light collecting capability“ of an optical system. • An very simple analogy: • Light Incompressible fluid • Optical system Bucket • Etendue of incoming light Volume of the fluid • Limiting Etendue of the optical system Volume of the bucket 9 Etendue under Free-Space Propagation
1 • From source: 푑퐺 = 푑퐴 푑Ω = 푑퐴 푑퐴 cos 휃 푐표푠휃 푆 푝푅 푆 푅 푆 푅 푟2 1 • From receiver: 푑퐺 = 푑퐴 푑Ω = 푑퐴 푑퐴 cos 휃 푐표푠휃 푅 푝푆 푅 푆 푅 푆 푟2
• Formula is symmetric: • Etendue leaving source equals etendue arriving at receiver • Etendue is conserved 10 Etendue in Optical Systems
• If sine condition is not violated:
퐺 = න 푑푘푥 푑푘푦 푑푥 푑푦 = න 푑 푛 sin 푢 푑푥 푑(푛 sin 푣) 푑푦
= න 푑푘푥′ 푑푘푦′ 푑푥′ 푑푦′ = න 푑 푛′ sin 푢′ 푑푥′ 푑(푛′ sin 푣′) 푑푦′
• Again, etendue is conserved.
• Etendue is conserved: • In free space propagation • In the absence of aberrations • In the absence of scattering • The etendue of an optical system should be larger than the etendue of the light source to ensure most efficient light transport! 11 Some Useful Etendue Relations
• From planar surface area A into full hemisphere: • G = 휋 푛2 퐴
• From planar area into cone with half opening angle 훼: • 퐺 = sin2 훼 휋 푛2 퐴 훼
• Into a linear slit with half opening angle 훼: • 퐺 = sin 훼 휋 푛2 퐴 훼