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