Optical Engineering. Course outline. Exercise: Selection of telescope

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1 Course outline 4. Optical Engineering Martina Gerken..007 Universität Karlsruhe (TH). Imaging optics. ight propagation across interfaces. Photography and optical lenses.3 Aberrations.4 Plane parallel plates and reflective prisms.5 Depth of focus.6 Magnifying glass and basic microscope.7 Modern microscopes.8 Beam expansion.9 Telescopes.0 Optic design. Optical sensors 3. Optics in data storage 4. Introduction to displays 5. Fourier optics 6. Diffractive optics and holograms 7. Integrated optics 8. Computerized imaging Exercise: Selection of telescope 4.3 Comparison of telescopes 4.4 Collect the advantages and disadvantages of the two telescopes! Decide as a group on one telescope! BRASKO Telescope Bresser Telescope Pluto 4/500 Refractor Terrestrial observation Reflector No spherical/chromatic aberrations Mirror diameter larger, thus more light More compact More expensive Prettier Aberrations due to diffraction on second mirror

2 Important factors for telescope purchase 4.5 Course outline 4.6 Two main tasks of telescope: Magnify small objects Brighten faint objects Useful magnification limited by diffraction Max. Magnification Diameter of objective in mm Image may be magnified more, but image information is limited Analog: Not more detail on newspaper image observable with magnifying glass Aberrations and air turbulence ("Seeing") limit magnification further Max. resolution of terrestrial telescope Hubble-Telescope 0.05 at visible wavelengths arger aperture for brighter images!. Imaging optics. ight propagation across interfaces. Photography and optical lenses.3 Aberrations.4 Plane parallel plates and reflective prisms.5 Depth of focus.6 Magnifying glass and basic microscope.7 Modern microscopes.8 Beam expansion.9 Telescopes.0 Optic design Analytical solution (optical quadrupole) Matrix formulation Sequential raytracing Non-sequential raytracing FDTD Quality of mount is also critical Should not move more than sec after touching Geometrical optics / Ray optics 4.7 Paraxial approximation / Gaussian optics 4.8 Rays describe propagation of light in (most) optical systems sufficiently well, if dimensions X of objects and parts sufficiently larger than: For propagation at small angles relative to optical axis simplified description of optical parts is possible and analytical solutions exist. Wavelength λ << X Coherence length ξ << X Wave properties of light neglected No interference, diffraction, near field effects... n n α β n sinα n sin β n α n β Geometrical optics may be derived from wave optics for wavelength approaching zero Direction of ray propagation is direction of wavevectors

3 Spherical surface in paraxial approximation 4.9 Thick lens with spherical surfaces 4.0 Approximated s n n n r n s Calculation of optical power of thick lens n Optical power D f [D]m - Diopterdpt n n A θ ϕ θ O S r C O s s n n d B F B G For rays parallel to optical axis n s r n n Thick lens: Focal point 4. Front principle plane 4. n n Front principle plane: ocus of intersection of diverging/converging bundle of rays for parallel outgoing rays Front principle point H: Intersection of front principle plane with optical axis d s B F B G s Positive (converging) system Negative (diverging) system s n s' r n s s n nr nd + d d r d n n ' s' n n + r s n r n( n ) + n r n d + d r ( nr nd + d ) ( n ) [ n ( r r ) + d ( n ) ] Focal length is distance from principle point to focal point Source: Schröder/Treiber, Technische Optik

4 Rear principle plane 4.3 Thick lens: Focal length and optical power 4.4 Rear principle plane: ocus of intersection of parallel ingoing rays with diverging/converging outgoing rays Rear principle point H : Intersection of rear principle plane with optical axis n n Positive (converging) system Negative (diverging) system H f B F B G s' f s ' D s ( n ) [ n( r r ) + d ( n ) ] ( n ) [ n ( r r ) + d ( n ) ] n r r n r r Source: Schröder/Treiber, Technische Optik Possible lens shapes 4.5 Special case: Plano-convex and Plano-concave lenses 4.6 For plane surface r This results in f n r Focal length independent of d! Source: Schröder/Treiber, Technische Optik Source: Schröder/Treiber, Technische Optik

5 Special case: Spherical lens 4.7 Special case: Thin lens 4.8 For spherical surface r r r d r For negligible d d ( n ) << n r r This results in f n n r This results in f ( n )( r r ) r r ( n ) f r r n HH ' d n For thin lenses distance between principle planes may be neglected Source: Schröder/Treiber, Technische Optik Notation for imaging surfaces 4.9 Equivalent lens 4.0 System with several stages (e.g. objective with several lenses) may be described by optical quadrupole ( Equivalent lens ) Normally distance of individual systems measured between H und H In case of microscopes tube length between focal points used Source: Schröder/Treiber, Technische Optik Source: Schröder/Treiber, Technische Optik

6 Course outline 4. Matrix optics / ABCD-matrices 4.. Imaging optics. ight propagation across interfaces. Photography and optical lenses.3 Aberrations.4 Plane parallel plates and reflective prisms.5 Depth of focus.6 Magnifying glass and basic microscope.7 Modern microscopes.8 Beam expansion.9 Telescopes.0 Optic design Analytical solution (optical quadrupole) Matrix formulation Sequential raytracing Non-sequential raytracing FDTD x θ x x θ z xi A B s θi ( x, θ ) ( x, θ ) Optical system Propagation of ray at point A completely described by distance x to optical axis and angle θ relative to optical axis s M s Optical system with several components 4.3. Matrix of translation 4.4 x θ 3 θ θ θ x x x3 x 4 4 M M'3 M3'4 M' M33' M44' z x θ x x A B θ z x x + θ θ 0 x + θ s Effect of total system s [ M M... M ] 5 44' 3'4 s M s Output Eingang i Input Ausgang i s s M s 0 Translation Freiraum

7 . Refraction on plane interface Refraction on spherical interface 4.6 x θ θ n x x n z x x + 0 θ n θ 0 x + θ n Snellius at interface Angle depends on radius Convention for curvature and propagation x n n θ x x θ ρ ρ > 0 z 0 s n s M s 0 n Plane EbeneFläche interface 0 s n n n s M s nρ n Spherical SphärischeFläche interface Exercise: Thin lens 4.7 Thick lens 4.8 All important simple optical elements may be described using the tree matrices (Translation, plane interface and spherical interface) Thin lens (convex, concave) Thick lens (convex, concave) Mirror (plane, focusing) Combination of two spherical interfaces and translation Focal length calculated from principal plane x n n n Derive the total matrix for a thin lens! Derive the dependence of the focal length f and the interface curvatures (ens maker's equation for thin lens)! f f z Derive the matrix for imaging with a convex lens! Derive the imaging equation from the resulting matrix! Consider that x has to be angle-independent h h s M n n M M n n s ( ρ, ) ( ) ( ρ, ) SF SI FR Tr SF SI

8 Matrix properties in Gaussian optics 4.9 Optical elements and their system matrices 4.30 M A B C D Focusing: A 0 x Bθ 0 B C D Because of Snellius law: det M n AD BC n Only 3 of the 4 matrix elements may be chosen independently Optical imaging: A B 0 x Ax 0 C D Deflection of parallel rays: θ Dθ Generation of parallel rays: θ Cx A 0 A C B D B 0 Matrix optics for Gaussian beams and polarization 4.3 Course outline 4.3 Matrix optics not limited to Gaussian optics, but may be used for Gaussian beams as well. ABCD-Matrices identical Instead of ray vector s beam parameter q used: q ( z) Aq Cq B + D q i λ R π w Polarization may be included as well in matrix algorithm Jones-vector describes state of polarization Jones-matrices describe optical elements. Imaging optics. ight propagation across interfaces. Photography and optical lenses.3 Aberrations.4 Plane parallel plates and reflective prisms.5 Depth of focus.6 Magnifying glass and basic microscope.7 Modern microscopes.8 Beam expansion.9 Telescopes.0 Optic design Analytical solution (optical quadrupole) Matrix formulation Sequential raytracing Non-sequential raytracing FDTD

9 Sequential ray-tracing 4.33 Non-sequential ray-tracing 4.34 Rays propagates through optical elements in sequential order Used for design of imaging optical systems Microscope, telescope, camera... Rays split on surface and may pass optical elements several times By propagation of Gaussian beams wave phenomena may be included Used for design including stray light calculation Stray light calculation Back lights, luminaires... Source: Source: FDTD: Finite Difference Time Domain 4.35 Common optical design software 4.36 Solution of Maxwell-equations using space and time grid Used for micro- and nanosystems Integrated optics, photonic crystals, plasmonics... Source: At the university additionally COMSO Multiphysics Source:

10 Course outline 4.37 Spectroscopy Imaging optics. Optical sensors. Spectroscopy. Material characterization.3 Distance measurement.4 Angle measurement.5 Optical mouse 3. Optics in data storage 4. Introduction to displays 5. Fourier optics 6. Diffractive optics and holograms 7. Integrated optics 8. Computerized imaging Spectroscopy: Frequency or wavelength analysis of light Applications of spectroscopy Material characterization Sensors Development of light sources Example: Organic light emitting diode intensity / arb. units Spectroscopy 4.39 Spectrometer using absorptive filters 4.40 Optical spectrum characteristic for chemical elements Known since appr. 859 (Kirchhoff, Bunsen), e.g.: e.g.: Fraunhofer-lines in solar spectrum (80, 84) (Absorption spectra) In general: Glowing solid or liquid objects have continuous spectra (e.g. thermal radiation, black body, Planck's law) Glowing gases or vapors have discontinuous spectra (Transition between discrete energy levels in atoms/molecules) Spectrally broad CCDchip is illuminated through sequence of filters Source: Wikipedia and Gerthsen Physik

11 Spectrometers using dispersive elements Material dispersion Goal: Spatial separation of light of different wavelengths e.g., on a screen or a CCD-chip Use dispersive element Material or structure whose effect on light is wavelength-dependent (e.g. prisms, grating) Common types of spectrometers sorted by dispersive element Prism spectrometer uses dispersion due to refraction Grating spectrometer uses dispersion due to diffraction Common types of spectrometers sorted by functionality Monochromator selects small wavelength interval Spectrometer for observation of large wavelength interval Spectrograph Spectrometer + CCD-camera / film etc. Refractive index depends on type of glass and on wavelength dependent Source: Prism spectrometer Refraction in prism 4.44 Prism spectrometer Bild 6.3. aus Naumann Schröder Telescope Deflection angle: Dispersion: Minimum deflection angle for symmetric pass: Advantage: Unambiguous correlation between wavelength and position in image plane Disadvantage: Small dispersion and thus small resolution Angular dispersion Basis of prism Source: Wikipedia and Optik icht und aser von Dieter Meschede Source: Bauelemente der Optik von Naumann und G. Schröder

12 Interference special case Interference general case Interference: Superposition of waves with fixed phase relation. Interference is due to wave character of light and cannot be understood using ray optics. General case: Superposition of fields: Example: Two monochromatic waves of identical polarization and identical amplitude are superposed at position Irradiance (intensity) obtained as temporal average of electrical field, i.e. square of field amplitude A Principle of superposition for fields. Irradiance (intensity) at point Divisor from averaging is: Only for complex field description Interference term results as Interference depends Spatially modulated interference pattern with minima and maxima on polarization Constructive / destructive interference Interference term Grating principle Interference of spherical waves exiting different slits Each slit also causes diffraction Formula for N slits: Phase difference Path difference Difference of opt. paths of two partial waves Constant term Constructive interference / Maximum of intensity for Destructive Interference / Minimum of intensity for Interference term Diffraction term Source: Optics lecture by PD Dr. Seifert, Universität Halle (

13 Grating - intensity with angle 4.49 Grating equation 4.50 Main maxima for constructive interference of all wave parts Maximum intensity at: Effective grating size Example: N 8, d b Diffraction of slit mλ sinθ m sinθ0 ± d Grating. order interference maximum Image of light bulb through transmission grating Source: Optics lecture by PD Dr. Seifert, Universität Halle ( Source: Wikipedia and Optics lecture by PD Dr. Seifert, Universität Halle ( Exercise: Grating period 4.5 Grating ambiguity 4.5 Determine the grating period of the given grating! Gratings are ambiguous! Source:

14 Grating width of maximum 4.53 Grating resolution 4.54 For more illuminated slits maximum is narrower Two wavelengths are resolved if they are at least separated by width of main maximum Resolution in order m for grating for N illuminated slits Source: Optics lecture by PD Dr. Seifert, Universität Halle ( Source: Optics lecture by PD Dr. Seifert, Universität Halle ( Types of gratings 4.55 Blazed gratings 4.56 Amplitude grating Slits as origin of fundamental waves. Phase grating Modulation of optical path! Modulation of phase In ittrow configuration groove have such profiles that incident and diffracted rays are in auto collimation (i.e., α β). Efficiency of grating increased In this case at the "blaze" wavelength λ B we obtain: β α sinα mλ B d Reflection grating often blazed Source:

15 Czerny-Turner monochromator 4.57 Échelle spectrographs 4.58 ight leaving the exit slit (G) contains entire image of entrance slit of selected color plus parts of entrance slit images of nearby colors. Rotation of dispersing element causes band of colors to move relative to exit slit Prism for dispersion in one direction Grating for dispersion in orthogonal direction dθ m dλ d cosθ m Spectrograph with standard prism Source: Source: Spectrograph with Andor patented prism Comparison grating / prism spectrometer 4.59 Exercise: Spectroscope 4.60 Reflection grating 00 rules/mm Width 60mm Prism Glass SF Build the spectroscope! Resolution at 550nm dα dλ 6 0 nm λ 7000 λ 4 n, 79 b 60 mm, α 60 dn dλ 0 4 dδ dλ 4,5 0 nm λ 000 λ nm 4 Observe and sketch the spectrum of an incandescent source and a fluorescent lamp! What influence does the entrance slit have?

16 Compilation of questions 4.6 When may Gaussian optics be used? How are the principle planes of a thick lens defined? What is a thin lens? What are ABCD-matrices and what are they used for? What is the difference between sequential and non-sequential raytracing? How does a spectrometer using absorptive filters work? Sketch a prism spectrometer! What is constructive interference? Sketch the outgoing intensity as a function of angle for a grating! Why is the wavelength determination with a grating ambiguous? What limits the resolution of a grating monochromator? Sketch a grating spectrograph!