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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
Outline
Introduction
Wave Optics
Principles
o Introduction
Optical
holograms
o Wave Optics
o Principles
o Optical holograms
Optical
Holography
Martin Janda,
Ivo Hanák
Holography
Introduction
LA
SE
R
Wave Optics
Principles
Optical
holograms
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
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
Wave Nature of Light
Introduction
Wave Optics
Principles
Optical
holograms
Light
• Light – El./Mag. radiation 300 – 800 nm
A Bit of Mathematics
• u(p, t) = A(p)cos[2pnt – j (p)]
• u(p, t) = R{A(p)exp[i (j (p) – 2pnt)]}
~
• u(p,
t) = A(p)exp[ij (p)]exp[-i2pnt]
Complex Amplitude
~
• u(p) = A(p)exp[ij (p)]
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
u~ f=u~ 1 + u~ 2
Interference of two waves – constructive and destructive
Optical
Holography
Martin Janda,
Ivo Hanák
Interference
Introduction
Wave Optics
Principles
Optical
holograms
Optical intensity
• Optical quality perceived by human eye
• Square of complex amplitude’s magnitude
• Mathematically
~ 2 = uu*
~~
I = |u|
• Intensity of interference
I = |u~r + u~s|2
= |u~r|2 + |u~ s|2 + u~ ru~s* + u~*ru~ s
= Ir + Is + 2 I1I2 cos(jr – js)
This all is true only if coherent light is assumed.
Optical
Holography
Martin Janda,
Ivo Hanák
Coherence
Introduction
Wave Optics
Principles
Optical
holograms
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
Diffraction - Again
Introduction
Wave Optics
Principles
Optical
holograms
What exactly is diffraction
• Everything not being reflection or refraction
• Interference of many sources
Scalar Diffraction
• Easier in certain environment
• Huygens-Fresnel principle t+Dt t
t-Dt
• More precise formulations
• Kirchhoff
• Rayleigh-Sommerfeld



1
exp(
ik
|
r
(s ) |)
~
~
u x , y    os 
cosds

i S
| r (s ) |
t-Dt t t+Dt
Direction of
propagation
Direction of
propagation
Optical
Holography
Martin Janda,
Ivo Hanák
Introduction
Wave Optics
Principles
Optical
holograms
Diffraction – And Again
Optical
Holography
Martin Janda,
Ivo Hanák
Holography principle
Introduction
Wave Optics
Principles
Optical
holograms
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
Holography principle
Introduction
Wave Optics
Principles
Optical
holograms
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
Holography Principles in Pictures
Recording
Wave Optics
Photographic
plate
Principles
Optical
holograms
Object
Laser
beam
Reconstruction
Mirror
Optical
Holography
Martin Janda,
Ivo Hanák
In-line Hologram
Introduction
Wave Optics
Principles
Optical
holograms
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
Optical
Holography
Martin Janda,
Ivo Hanák
Off-axis Hologram
Introduction
Wave Optics
Principles
Optical
holograms
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
Lens & Fourier Hologram
Introduction
Wave Optics
Principles
Optical
holograms
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
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
Optical
Holography
Martin Janda,
Ivo Hanák
Physical Representations
Introduction
Wave Optics
Principles
Optical
holograms
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
Physical Representations
Introduction
Wave Optics
Principles
Optical
holograms
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