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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. Janda I. Hanák
Department of Computer science and Engineering
University of West Bohemia
Optical Holography
Martin Janda,Ivo Hanák
Introduction
Wave Optics
Principles
Optical holograms
Outline
o Introduction
o Wave Optics
o Principles
o Optical holograms
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
LASER
Photo vs. Holo
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
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[2t – (p)]• u(p, t) = {A(p)exp[i ((p) – 2t)]}• u(p, t) = A(p)exp[i(p)]exp[-i2t]
Complex Amplitude• u(p) = A(p)exp[i(p)]
re
im
A
u(A, )
~
~Phasor
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
uf=u1 + u2~ ~ ~
Interference of two waves – constructive and destructive
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 = |ur + us|2 = |ur|2 + |us|2 + urus + urus = Ir + Is + 2 I1I2 cos(r – s)
~
~
~
~ ~ ~ ~ ~* *
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
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
t
t
t- Dt
t- Dtt+Dt
t+Dt
Direction ofpropagation
Direction ofpropagation
sdsoi
yxusr
srik
S
cos~,~
|)(|
|))(|exp(
1
Optical Holography
Martin Janda,Ivo Hanák
Introduction
Wave Optics
Principles
Optical holograms
Diffraction – And Again
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
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
Optical Holography
Martin Janda,Ivo Hanák
Introduction
Wave Optics
Principles
Optical holograms
Holography Principles in PicturesRecording
Reconstruction
Photographicplate
Object
Mirror
Laserbeam
Hologram
Image
Mirror
Laserbeam
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
Hologram
Object
Referenceplanarwave
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
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 = {front focal plane}
Fourier Hologram• Recording through lens• {planar image} + {point source}• Reconstruction through lens• Both virtual & real image in focus
Optical Holography
Martin Janda,Ivo Hanák
Introduction
Wave Optics
Principles
Optical holograms
Other hologramsHolographic 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
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
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
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