1. Optical Holography Martin Janda, Ivo Hanák Introduction Wave Optics Principles Optical holograms Optical Holography Martin Janda, Ivo Hanák Introduction Wave Optics Principles Optical holograms Optical Holography M. JandaI. Hanák Department of Computer science and Engineering University of West Bohemia

2. Optical Holography Martin Janda, Ivo Hanák Introduction Wave Optics Principles Optical holograms Outline o Introduction o Wave Optics o Principles o Optical holograms

3. Optical Holography Martin Janda, Ivo Hanák Introduction Wave Optics Principles Optical holograms Holography What is not holography Holodeck from Startrek What is holography Photography on steroids Both amplitude and phase is recorded Different intensity in different directions Photo vs. Holo

4. Optical Holography Martin Janda, Ivo Hanák Introduction Wave Optics Principles Optical holograms Holography – A Tase Of Principle Fundamental technology Diffraction grating – bends light Can be superposed Effect (bending) persists superposition Hologram  super complex diffraction grating Effect of diffraction grating on a direction of light

5. Optical Holography Martin Janda, Ivo Hanák Introduction Wave Optics Principles Optical holograms Wave Nature of Light Light Light – El./Mag. radiation 300 – 800 nm A Bit of Mathematics u(p, t) = A(p)cos[2  t –  (p)] u(p, t) = R {A(p)exp[i (  (p) – 2  t)]} u(p, t) = A(p)exp[i  (p)]exp[-i2  t] Complex Amplitude u(p) = A(p)exp[i  (p)] ~ ~ Phasor

6. Optical Holography Martin Janda, Ivo Hanák Introduction Wave Optics Principles Optical holograms Interference What is it? Combination of waves Adding two lights together causes dark! What is it exactly? Summation of complex amplitudes u f =u 1 + u 2 ~~~ Interference of two waves – constructive and destructive

7. Optical Holography Martin Janda, Ivo Hanák Introduction Wave Optics Principles Optical holograms Interference Optical intensity Optical quality perceived by human eye Square of complex amplitude’s magnitude Mathematically I = |u| 2 = uu* Intensity of interference ~~~ This all is true only if coherent light is assumed. I = |u r + u s | 2 = |u r | 2 + |u s | 2 + u r u s + u r u s = I r + I s + 2  I 1 I 2 cos(  r –  s ) ~ ~ ~ ~~~~~**

8. Optical Holography Martin Janda, Ivo Hanák Introduction Wave Optics Principles Optical holograms Coherence Purpose Neglect temporal dependence Coherence light -> stable interference Degree of coherence – interference fringes visibility What light is coherent Monochromatic – temporal coherence Coherence length Spherical waves – spatial coherence Coherence area Formal description Binary relation Cross correlation between two signals

9. Optical Holography Martin Janda, Ivo Hanák Introduction Wave Optics Principles Optical holograms Diffraction - Again What exactly is diffraction Everything not being reflection or refraction Interference of many sources Scalar Diffraction Easier in certain environment Huygens-Fresnel principle More precise formulations Kirchhoff Rayleigh-Sommerfeld

10. Optical Holography Martin Janda, Ivo Hanák Introduction Wave Optics Principles Optical holograms Diffraction – And Again

11. Optical Holography Martin Janda, Ivo Hanák Introduction Wave Optics Principles Optical holograms Holography principle Recording Encoding phase and amplitude as interference fringe pattern Two beams interfering Reference beam – known properties Scene beam – recorded light field Complex diffraction grating is created – hologram

12. Optical Holography Martin Janda, Ivo Hanák Introduction Wave Optics Principles Optical holograms Holography principle Recording Encoding phase and amplitude as interference fringe pattern Two beams interfering Reference beam – known properties Scene beam – recorded light field Complex diffraction grating is created – hologram Reconstructing Hologram illuminated with reference beam Diffraction occurs Resulting light field contains original scene beam

13. Optical Holography Martin Janda, Ivo Hanák Introduction Wave Optics Principles Optical holograms Holography Principles in Pictures Recording Reconstruction

14. Optical Holography Martin Janda, Ivo Hanák Introduction Wave Optics Principles Optical holograms In-line Hologram Recording Reference, object, hologram aligned in line Mostly transparent and planar objects Lower spatial frequency Reconstruction Images disturbed by blurred counterparts and zero order Special setup: blurred image became background

15. Optical Holography Martin Janda, Ivo Hanák Introduction Wave Optics Principles Optical holograms Off-axis Hologram Recording Non-zero angle between reference wave and object wave 3D opaque objects Higher spatial frequency Reconstruction Orders diffracted into different directions Clean original optical field

16. Optical Holography Martin Janda, Ivo Hanák Introduction Wave Optics Principles Optical holograms Lens & Fourier Hologram Lens Different optical material: slowdown/diffraction of waves Use of thin lens: assumption on lack of diffraction Back focal plane = F {front focal plane} Fourier Hologram Recording through lens F {planar image} + F {point source} Reconstruction through lens Both virtual & real image in focus

17. Optical Holography Martin Janda, Ivo Hanák Introduction Wave Optics Principles Optical holograms Other holograms Holographic Stereograms Recording of multiple views through slit Reconstruction: only single focus depth Rainbow Hologram 2 Stages of recording Record regular hologram Record rainbow hologram through slit Visible on white light: multiple color images Color Hologram Common hologram: rainbow due to diffraction 3 holograms + 3 wavelengths: larger gamut Achromatic holograms: holographic stereograms Overlapping/coplanar colors

18. Optical Holography Martin Janda, Ivo Hanák Introduction Wave Optics Principles Optical holograms Physical Representations Thin Amplitude Hologram Zero and first order only First order: 6 % of energy Thin Phase Hologram Multiple orders First order: 33 % of energy Volume Hologram Multiple layers of fringes Reflective  transmission Sensitive only to selected wavelength

19. Optical Holography Martin Janda, Ivo Hanák Introduction Wave Optics Principles Optical holograms Holography – A Tase Of Principle Fundamental technology Diffraction grating – bends light Can be superposed Effect (bending) persists superposition Hologram  super complex diffraction grating Effect of diffraction grating on a direction of light

20. Optical Holography Martin Janda, Ivo Hanák Introduction Wave Optics Principles Optical holograms Physical Representations Thin Amplitude Hologram Zero and first order only First order: 6 % of energy Thin Phase Hologram Multiple orders First order: 33 % of energy Volume Hologram Multiple layers of fringes Reflective  transmission Sensitive only to selected wavelength