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

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 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.

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 Shift Keying – ASK, Frequency Shift Keying – FSK, Phase Shift Keying – PSK, etc.) used in radio at low frequencies only (“AM band” = 535kHz to 1.7MHz) ; as we will see, it is an almost-exact analog of holography dominant in commercial radio (“FM band” = 88MHz to 108MHz) ; there is an analog in optics, called “spectral holography,” but it is beyond the scope of the class

MIT 2.71/2.710 Optics 12/06/04 wk14-a- 4 Amplitude modulation f  x  (baseband) modulate d u c : carrier frequency

MIT 2.71/2.710 Optics 12/06/04 wk14-a- 5 AM in the frequency domain spectrum of f  x  spectrum of modulated f (x)

MIT 2.71/2.710 Optics 12/06/04 wk14-a- 6 AM in the frequency domain spectrum of f  x  spectrum of modulated f (x) (zoom-in)

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 baseband spectrum, centered on the carrier frequency

MIT 2.71/2.710 Optics 12/06/04 wk14-a- 8 Modulation multiplication simple carrier tone modulated f (x)

MIT 2.71/2.710 Optics 12/06/04 wk14-a- 9 Demodulation multiplication simple carrier tone modulated f (x) must accommodate baseband spectrum low-pass filter

MIT 2.71/2.710 Optics 12/06/04 wk14-a- 10 Demodulation [modulated spectrum Spectrum of

MIT 2.71/2.710 Optics 12/06/04 wk14-a- 11 Demodulation LP filter pass-band [modulated spectrum

MIT 2.71/2.710 Optics 12/06/04 wk14-a- 12 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)

MIT 2.71/2.710 Optics 12/06/04 wk14-a- 13 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 wk14-a- 14 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 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 removed due to copyright concerns 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

MIT 2.71/2.710 Optics 12/06/04 wk14-a- 16 Holography: reconstructing the wavefront imaging system illumination: replicates the reference beam what is the field at the image plane?

MIT 2.71/2.710 Optics 12/06/04 wk14-a- 17 Holography: reconstructing the wavefront The field being imaged is:

MIT 2.71/2.710 Optics 12/06/04 wk14-a- 18 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 wk14-a- 19 propagate s at angle: Holography: reconstructing the wavefront on-axis fields departing from the hologram

MIT 2.71/2.710 Optics 12/06/04 wk14-a- 20 Holography: reconstructing the wavefront on-axis not wanted fields departing from the hologram wante d

MIT 2.71/2.710 Optics 12/06/04 wk14-a- 21 Filtering the wavefront: bandlimited signal has bandwidth within circle of radius

MIT 2.71/2.710 Optics 12/06/04 wk14-a- 22 Filtering the wavefront: bandlimited signal has bandwidth because Term

MIT 2.71/2.710 Optics 12/06/04 wk14-a- 23 Filtering the wavefront: Fourier transform description

MIT 2.71/2.710 Optics 12/06/04 wk14-a- 24 Filtering the wavefront: Fourier transform description original spectrum autocorrelation of the original spectrum original spectrum but phase -- conjugated: inside-out, or “pseudo-scopic”

MIT 2.71/2.710 Optics 12/06/04 wk14-a- 25 Filtering the wavefront: Fourier transform description not wanted wanted

MIT 2.71/2.710 Optics 12/06/04 wk14-a- 26 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 wk14-a- 27 Holography: reconstructing the wavefront the field at the image plane replicates the original S stored in the hologram 4F system with Fourier plane filter illumination: replicates the reference beam hologram:

MIT 2.71/2.710 Optics 12/06/04 wk14-a- 28 Potential problem: spectra overlap! Filtering the wavefront: Fourier transform description

MIT 2.71/2.710 Optics 12/06/04 wk14-a- 29 Spectra should not overlap, i.e. Filtering the wavefront: Fourier transform description

MIT 2.71/2.710 Optics 12/06/04 wk14-a- 30 Leith-Upatnieks vs Gabor hologram Leith-Upatnieks Image removed due to copyright concerns Image removed due to copyright concerns Gabor

MIT 2.71/2.710 Optics 12/06/04 wk14-a- 31 Analogy between the Leith-Upatnieks hologram and amplitude modulation (AM) AM Radio Holography Modulation Recording Demodulation Reconstruction modulated low-pass filter low-pass filter Image removed due to copyright concerns

MIT 2.71/2.710 Optics 12/06/04 wk14-a- 32 Image locations and magnification Image removed due to copyright concerns aaa

MIT 2.71/2.710 Optics 12/06/04 wk14-a- 33 Image locations and magnification Transverse Magnification Axial Magnification

MIT 2.71/2.710 Optics 12/06/04 wk14-a- 34 Holography of Three-Dimensional Scenes Image removed due to copyright concerns

MIT 2.71/2.710 Optics 12/06/04 wk14-a- 35 Image removed due to copyright concerns Orthoscopic and Pesudoscopic

MIT 2.71/2.710 Optics 12/06/04 wk14-a- 36 Holography of Three-Dimensional Scenes Image removed due to copyright concerns

MIT 2.71/2.710 Optics 12/06/04 wk14-a- 37 Transmission and Reflection Holograms Image removed due to copyright concerns

MIT 2.71/2.710 Optics 12/06/04 wk14-a- 38 Transmission and Reflection Holograms Image removed due to copyright concerns

MIT 2.71/2.710 Optics 12/06/04 wk14-a- 39 Image removed due to copyright concerns Rainbow hologram (Record)

MIT 2.71/2.710 Optics 12/06/04 wk14-a- 40 Image removed due to copyright concerns Rainbow hologram (Reconstruct)