MIT 2.71/2.710 Optics 12/06/04 wk14-a- 1 Holography Preamble: modulation and demodulation The...
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Transcript of MIT 2.71/2.710 Optics 12/06/04 wk14-a- 1 Holography Preamble: modulation and demodulation The...
![Page 1: 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.](https://reader030.fdocuments.us/reader030/viewer/2022032708/56649e575503460f94b505b8/html5/thumbnails/1.jpg)
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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MIT 2.71/2.710 Optics
12/06/04 wk14-a-2
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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MIT 2.71/2.710 Optics
12/06/04 wk14-a-3
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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MIT 2.71/2.710 Optics
12/06/04 wk14-a-4
Amplitude modulation
f x(baseband)
modulated
uc: carrier frequency
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MIT 2.71/2.710 Optics
12/06/04 wk14-a-5
AM in the frequency domain
spectrum of f x spectrum ofmodulated f (x)
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MIT 2.71/2.710 Optics
12/06/04 wk14-a-6
AM in the frequency domain
spectrum of f x spectrum ofmodulated f (x)
(zoom-in) (zoom-in)
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MIT 2.71/2.710 Optics
12/06/04 wk14-a-7
AM in the frequency domain
modulation in the space domain
modulation in the frequency domain:two replicas of the basebandspectrum, centered on the carrierfrequency
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MIT 2.71/2.710 Optics
12/06/04 wk14-a-8
Modulation
multiplication
simple carrier tone
modulated f (x)
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MIT 2.71/2.710 Optics
12/06/04 wk14-a-9
Demodulation
multiplication
simple carrier tone
modulated f (x)
must accommodatebaseband spectrum
low-passfilter
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MIT 2.71/2.710 Optics
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Demodulation[m
odul
ated
spec
trum
Spectrum of
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MIT 2.71/2.710 Optics
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Demodulation
LP filter pass-band
[mod
ulat
ed
spec
trum
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MIT 2.71/2.710 Optics
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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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MIT 2.71/2.710 Optics
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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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MIT 2.71/2.710 Optics
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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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MIT 2.71/2.710 Optics
12/06/04 wk14-a-15
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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MIT 2.71/2.710 Optics
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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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Holography: reconstructing thewavefront
The field being imaged is:
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MIT 2.71/2.710 Optics
12/06/04 wk14-a-18
Holography: reconstructing thewavefront
take the simplest possible reference wave, a plane wave:
spatial frequency
then the reconstructed field is:
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MIT 2.71/2.710 Optics
12/06/04 wk14-a-19
propagatesat angle:
Holography: reconstructing thewavefront
on-axis
fields departing from thehologram
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MIT 2.71/2.710 Optics
12/06/04 wk14-a-20
Holography: reconstructing thewavefront
on-axis
not wanted
fields departing from thehologram
wanted
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MIT 2.71/2.710 Optics
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Filtering the wavefront:bandlimited signal
has bandwidth
within circle of radius
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MIT 2.71/2.710 Optics
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Filtering the wavefront:bandlimited signal
has bandwidth becauseTerm
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MIT 2.71/2.710 Optics
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Filtering the wavefront:Fourier transform description
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MIT 2.71/2.710 Optics
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Filtering the wavefront:Fourier transform description
originalspectrum
autocorrelation of the original spectrum
original spectrum but phase -- conjugated:
inside-out, or “pseudo-scopic”
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Filtering the wavefront:Fourier transform description
not wantedwanted
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MIT 2.71/2.710 Optics
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Filtering the wavefront:Fourier transform description
a low-pass filter ofpassband w or slightlygreater permits thedesired term topass, and eliminatesthe undesirable terms and .
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MIT 2.71/2.710 Optics
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Holography: reconstructing thewavefront
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:
![Page 28: 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.](https://reader030.fdocuments.us/reader030/viewer/2022032708/56649e575503460f94b505b8/html5/thumbnails/28.jpg)
MIT 2.71/2.710 Optics
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Potential problem: spectra overlap!
Filtering the wavefront:Fourier transform description
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Spectra should not overlap, i.e.
Filtering the wavefront:Fourier transform description
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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
Image removed due to copyright concerns
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Orthoscopic and Pesudoscopic
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Holography of Three-Dimensional Scenes
Image removed due to copyright concerns
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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)