Optical Holography

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

Outline

Martin Janda, Ivo Hanák

Introduction Wave Optics Principles

o Introduction

Optical holograms

o Wave Optics o Principles o Optical holograms

Optical Holography

Holography

Martin Janda, Ivo Hanák

Introduction

Principles Optical holograms

LAS ER

Wave Optics

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

Holography – A Tase Of Principle

Martin Janda, Ivo Hanák

Introduction Wave Optics Principles Optical holograms

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

Wave Nature of Light

Martin Janda, Ivo Hanák

Introduction Wave Optics Principles Optical holograms

Light • Light – El./Mag. radiation 300 – 800 nm

A Bit of Mathematics

im

• u(p, t) = A(p)cos[2πνt – ϕ (p)] A • u(p, t) = {A(p)exp[i (ϕ (p) – 2πνt)]} ~ • u(p, t) = A(p)exp[iϕ (p)]exp[-i2πνt] ϕ

Complex Amplitude ~

• u(p) = A(p)exp[iϕ (p)]

u(A, ϕ)

Phasor

re

Optical Holography

Interference

Martin Janda, Ivo Hanák

Introduction Wave Optics Principles Optical holograms

What is it? • Combination of waves • Adding two lights together causes dark!

What is it exactly? • Summation of complex amplitudes uf~ =u~1 +~u2

Interference of two waves – constructive and destructive

Optical Holography

Interference

Martin Janda, Ivo Hanák

Introduction Wave Optics Principles Optical holograms

Optical intensity • Optical quality perceived by human eye • Square of complex amplitude’s magnitude • Mathematically ~ 2 = ~~ I = |u| uu* • Intensity of interference ~ + ~ u |2 I = |u r s ~ 2 ~ ~*~ 2 ~ ~* = |u | + |u | + u u r s r s + ur us = Ir + Is + 2√ I1I2 cos(ϕr – ϕs)

This all is true only if coherent light is

Optical Holography

Coherence

Martin Janda, Ivo Hanák

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

Diffraction - Again

Martin Janda, Ivo Hanák

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 t t−∆t • Huygens-Fresnel principle • More precise formulations

t−∆t t t+∆t

t+∆t

• Kirchhoff  • Rayleigh-Sommerfeld   1 exp( ik | r (s)|) ~ ~ u( x,y) = ∫ o( s) cosαds 

iλ

S

| r (s)|

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 •

Optical Holography

Holography Principles in Pictures

Martin Janda, Ivo Hanák

Introduction

Recording

Wave Optics

Photographic plate

Principles Optical holograms

Object

Laser beam

Mirror

Reconstruction Hologram Image

Laser beam

Mirror

Optical Holography

In-line Hologram

Martin Janda, Ivo Hanák

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

Reference Hologram planar wave

Object

Optical Holography

Off-axis Hologram

Martin Janda, Ivo Hanák

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 = {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 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

Holography – A Tase Of Principle

Martin Janda, Ivo Hanák

Introduction Wave Optics Principles Optical holograms

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