Holography Preamble modulation and demodulation The principle of

Holography • Preamble: modulation and demodulation • The principle of wavefront reconstruction • The Leith-Upatnieks hologram • The Gabor hologram • Image locations and magnification • Holography of three-dimension scenes • Transmission and reflection holograms • Rainbow hologram MIT 2. 71/2. 710 Optics 12/06/04 wk 14 -a- 1

Modulation & Demodulation • Principle borrowed from radio telecommunications • Idea is to take baseband signal (e. g. speech, music, with maximum frequencies up to ~20 k. Hz) and modulate it onto a carrier signal which is a simple tone at the frequency where the radio station emits, e. g. 104. 3 MHz (that’s Boston’s WBCN station) • One of the benefits of modulation is that radio stations can be multiplexed by using a different emission frequency MIT 2. 71/2. 710 Optics each 12/06/04 wk 14 -a- 2 • After selecting the desired station, the receiver

Types of modulation • Phase modulation (PM) used in radio at low frequencies only (“AM band” = 535 k. Hz to 1. 7 MHz) ; as we will see, it is an almost-exact analog of holography • Digital methods (Amplitude Shift Keying – ASK, Frequency Shift Keying – FSK, Phase Shift Keying – PSK, etc. ) dominant in commercial radio (“FM band” = 88 MHz to 108 MHz) ; there is an analog in optics, called “spectral holography, ” but it is beyond the scope of the class • Amplitude modulation (AM) • Frequency modulation (FM) MIT 2. 71/2. 710 Optics 12/06/04 wk 14 -a- 3

Amplitude modulation f (x) (baseband) modulate d uc: carrier frequency MIT 2. 71/2. 710 Optics 12/06/04 wk 14 -a- 4

AM in the frequency domain spectrum of f (x) MIT 2. 71/2. 710 Optics 12/06/04 wk 14 -a- 5 spectrum of modulated f (x)

AM in the frequency domain spectrum of f (x) (zoom-in) MIT 2. 71/2. 710 Optics 12/06/04 wk 14 -a- 6 spectrum of modulated f (x) (zoom-in)

AM in the frequency domain modulation in the space domain modulation in the frequency domain: two replicas of the baseband spectrum, centered on the carrier frequency MIT 2. 71/2. 710 Optics 12/06/04 wk 14 -a- 7

Modulation multiplication modulated f (x) simple carrier tone MIT 2. 71/2. 710 Optics 12/06/04 wk 14 -a- 8

Demodulation multiplication modulated f (x) simple carrier tone MIT 2. 71/2. 710 Optics 12/06/04 wk 14 -a- 9 low-pass filter must accommodate baseband spectrum

Demodulation MIT 2. 71/2. 710 Optics 12/06/04 wk 14 -a- 10 spectrum [modulated Spectrum of

spectrum [modulated Demodulation LP filter pass-band MIT 2. 71/2. 710 Optics 12/06/04 wk 14 -a- 11

The wavefront reconstruction problem • Wavefront is the amplitude (i. e. magnitude and phase) of the electric field as function of position • Traditional coherent imaging results in intensity images (because detectors do not respond fast enough at optical frequencies) → magnitude information is recovered but phase information is lost • Can we imprint intensity information on an optical wave? MIT 2. 71/2. 710 YES Optics → photography (known since the 1840’s) 12/06/04 wk 14 -a 12 we imprint wavefront information on an optical • Can

Photography: recording Image removed due to copyright concerns incident illumination (laser beam or white light) Imaging system film records intensity information MIT 2. 71/2. 710 Optics 12/06/04 wk 14 -a- 13

Photography: reconstructing the intensity incident illumination (laser beam or white light) imaging system at the image plane, an intensity pattern is formed that replicates the originally recorded intensity MIT 2. 71/2. 710 Optics 12/06/04 wk 14 -a- 14

Holography: recording incident illumination (laser beam ♣) Image removed due to copyright concerns imaging system film records the interference pattern (interferogram) of the object wavefront and the reference wavefront MIT 2. 71/2. 710 Optics 12/06/04 wk 14 -a- 15 reference beam (split from the same laser ♣in general, the illumination must be quasimonochromatic, and spatially mutually coherent with the reference beam throughout the wavefront

Holography: reconstructing the wavefront illumination: replicates the reference beam imaging system what is the field at the image plane? MIT 2. 71/2. 710 Optics 12/06/04 wk 14 -a- 16

Holography: reconstructing the wavefront The field being imaged is: MIT 2. 71/2. 710 Optics 12/06/04 wk 14 -a- 17

Holography: reconstructing the wavefront take the simplest possible reference wave, a plane wave: spatial frequency then the reconstructed field is: MIT 2. 71/2. 710 Optics 12/06/04 wk 14 -a- 18

Holography: reconstructing the propagate wavefront s at angle: on-axis fields departing from the hologram MIT 2. 71/2. 710 Optics 12/06/04 wk 14 -a- 19

Holography: reconstructing the wavefront not wanted on-axis wanted fields departing from the hologram MIT 2. 71/2. 710 Optics 12/06/04 wk 14 -a- 20

Filtering the wavefront: bandlimited signal has bandwidth within circle of radius MIT 2. 71/2. 710 Optics 12/06/04 wk 14 -a- 21

Filtering the wavefront: bandlimited signal Term MIT 2. 71/2. 710 Optics 12/06/04 wk 14 -a- 22 has bandwidth because

Filtering the wavefront: Fourier transform description MIT 2. 71/2. 710 Optics 12/06/04 wk 14 -a- 23

Filtering the wavefront: Fourier transform description original spectrum autocorrelation of the original spectrum MIT 2. 71/2. 710 Optics 12/06/04 wk 14 -a- 24 original spectrum but phase -- conjugated: inside-out, or “pseudo-scopic”

Filtering the wavefront: Fourier transform description not wanted MIT 2. 71/2. 710 Optics 12/06/04 wk 14 -a- 25

Filtering the wavefront: Fourier transform description a low-pass filter of passband w or slightly greater permits the desired term to pass, and eliminates the undesirable terms and. MIT 2. 71/2. 710 Optics 12/06/04 wk 14 -a- 26

Holography: reconstructing the wavefront illumination: replicates the reference beam hologram: 4 F system with Fourier plane filter the field at the image plane replicates the original S stored in the hologram MIT 2. 71/2. 710 Optics 12/06/04 wk 14 -a- 27

Filtering the wavefront: Fourier transform description Potential problem: spectra overlap! MIT 2. 71/2. 710 Optics 12/06/04 wk 14 -a- 28

Filtering the wavefront: Fourier transform description Spectra should not overlap, i. e. MIT 2. 71/2. 710 Optics 12/06/04 wk 14 -a- 29

Leith-Upatnieks vs Gabor hologram Leith-Upatnieks Image removed due to copyright concerns Gabor Image removed due to copyright concerns MIT 2. 71/2. 710 Optics 12/06/04 wk 14 -a- 30

Analogy between the Leith-Upatnieks hologram and amplitude modulation (AM) AM Radio Holography Modulation Recording modulated Reconstruction Demodulation modulated MIT 2. 71/2. 710 Optics 12/06/04 wk 14 -a- 31 Image removed due to copyright concerns low-pass filter

Image locations and magnification Image removed due to copyright concerns aaa MIT 2. 71/2. 710 Optics 12/06/04 wk 14 -a- 32

Image locations and magnification Transverse Magnification Axial Magnification MIT 2. 71/2. 710 Optics 12/06/04 wk 14 -a- 33

Holography of Three-Dimensional Scene Image removed due to copyright concerns MIT 2. 71/2. 710 Optics 12/06/04 wk 14 -a- 34

Orthoscopic and Pesudoscopic Image removed due to copyright concerns MIT 2. 71/2. 710 Optics 12/06/04 wk 14 -a- 35

Holography of Three-Dimensional Scene Image removed due to copyright concerns MIT 2. 71/2. 710 Optics 12/06/04 wk 14 -a- 36

Transmission and Reflection Holograms Image removed due to copyright concerns MIT 2. 71/2. 710 Optics 12/06/04 wk 14 -a- 37

Transmission and Reflection Holograms Image removed due to copyright concerns MIT 2. 71/2. 710 Optics 12/06/04 wk 14 -a- 38

Rainbow hologram (Record) Image removed due to copyright concerns MIT 2. 71/2. 710 Optics 12/06/04 wk 14 -a- 39

Rainbow hologram (Reconstruct) Image removed due to copyright concerns MIT 2. 71/2. 710 Optics 12/06/04 wk 14 -a- 40