mit 2.71/2.710 optics 12/06/04 wk14-a- 1 holography preamble: modulation and demodulation the...

MIT 2.71/2.710 Optics

12/06/04 wk14-a-1

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


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Modulation & Demodulation

• Principle borrowed from radio telecommunications• Idea is to take baseband signal (e.g. speech, music, with maximum frequencies up to ~20kHz) 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 each• After selecting the desired station, the receiver follows a process of demodulation which recovers the baseband signal and sends it to the speakers.


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Types of modulation

• Amplitude modulation (AM)

• Frequency modulation (FM)

• Phase modulation (PM)

• Digital methods (Amplitude ShiftKeying – ASK, Frequency ShiftKeying – FSK, Phase Shift Keying– PSK, etc.)

used in radio at lowfrequencies only (“AMband” = 535kHz to1.7MHz) ; as we will see,it is an almost-exactanalog of holography

dominant in commercialradio (“FM band” =88MHz to 108MHz) ;there is an analog inoptics, called “spectralholography,” but it isbeyond the scope of theclass


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Amplitude modulation

f x(baseband)

modulated

uc: carrier frequency


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AM in the frequency domain

spectrum of f x spectrum ofmodulated f (x)


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spectrum of f x spectrum ofmodulated f (x)

(zoom-in) (zoom-in)


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modulation in the space domain

modulation in the frequency domain:two replicas of the basebandspectrum, centered on the carrierfrequency


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Modulation

multiplication

simple carrier tone

modulated f (x)


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Demodulation

multiplication

simple carrier tone

modulated f (x)

must accommodatebaseband spectrum

low-passfilter


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Demodulation[m

odul

ated

spec

trum

Spectrum of


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Demodulation

LP filter pass-band

[mod

ulat

ed

spec

trum


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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? YES → photography (known since the 1840’s)• Can we imprint wavefront information on an optical wave? YES → holography (Gabor, late 1940s)


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Photography: recording

Image removeddue to copyright

concerns

incident illumination(laser beam or white light)

Imaging system

film records intensity information


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Photography: reconstructing theintensity

incidentillumination

(laser beam orwhite light)

imaging system

at the image plane, an intensity pattern is formedthat replicates the originally recorded intensity


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Holography: recording

♣in general, the illumination must be quasi-monochromatic,and spatially mutually coherent

with the reference beam throughout the wavefront

Image removeddue to

copyrightconcerns

incident illumination(laser beam ♣

imaging system

reference beam(split from the

same laser

film records the interference pattern(interferogram) of the object wavefront

and the reference wavefront


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Holography: reconstructing thewavefront

imaging system

illumination:replicates the

reference beam

what is the field at the image plane?


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The field being imaged is:


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take the simplest possible reference wave, a plane wave:

spatial frequency

then the reconstructed field is:


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propagatesat angle:


on-axis

fields departing from thehologram


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on-axis

not wanted

fields departing from thehologram

wanted


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Filtering the wavefront:bandlimited signal

has bandwidth

within circle of radius


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Filtering the wavefront:bandlimited signal

has bandwidth becauseTerm


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Filtering the wavefront:Fourier transform description


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originalspectrum

autocorrelation of the original spectrum

original spectrum but phase -- conjugated:

inside-out, or “pseudo-scopic”


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not wantedwanted


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a low-pass filter ofpassband w or slightlygreater permits thedesired term topass, and eliminatesthe undesirable terms and .


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the field at the image planereplicates the original S stored in the hologram

4F system with Fourier plane filter

illumination:replicates the

reference beam

hologram:


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Potential problem: spectra overlap!



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Spectra should not overlap, i.e.



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Leith-Upatnieks vs Gabor hologramLeith-Upatnieks

Image removeddue to

copyrightconcerns

Imageremoved dueto copyright

concerns

Gabor


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Analogy between the Leith-Upatniekshologram and amplitude modulation (AM)AM Radio Holography

Modulation Recording

Demodulation Reconstruction

modulated

modulated low-pass

filter

low-passfilter

Image removeddue to

copyrightconcerns


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Image locations and magnification

Image removed due to copyright concerns

aaa


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Image locations and magnification

Transverse Magnification

Axial Magnification


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Holography of Three-Dimensional Scenes



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Orthoscopic and Pesudoscopic


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Holography of Three-Dimensional Scenes



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Transmission and Reflection Holograms



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Transmission and Reflection Holograms



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Rainbow hologram (Record)


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Rainbow hologram (Reconstruct)

mit 2.71/2.710 optics 12/06/04 wk14-a- 1 holography preamble: modulation and demodulation the...

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