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pslct034

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<title>Holography</title></titleStmt>

<publicationStmt><distributor>BASE and Oxford Text Archive</distributor>

<idno>pslct034</idno>

<availability><p>The British Academic Spoken English (BASE) corpus was developed at the

Universities of Warwick and Reading, under the directorship of Hilary Nesi

(Centre for English Language Teacher Education, Warwick) and Paul Thompson

(Department of Applied Linguistics, Reading), with funding from BALEAP,

EURALEX, the British Academy and the Arts and Humanities Research Board. The

original recordings are held at the Universities of Warwick and Reading, and

at the Oxford Text Archive and may be consulted by bona fide researchers

upon written application to any of the holding bodies.

The BASE corpus is freely available to researchers who agree to the

following conditions:</p>

<p>1. The recordings and transcriptions should not be modified in any

way</p>

<p>2. The recordings and transcriptions should be used for research purposes

only; they should not be reproduced in teaching materials</p>

<p>3. The recordings and transcriptions should not be reproduced in full for

a wider audience/readership, although researchers are free to quote short

passages of text (up to 200 running words from any given speech event)</p>

<p>4. The corpus developers should be informed of all presentations or

publications arising from analysis of the corpus</p><p>

Researchers should acknowledge their use of the corpus using the following

form of words:

The recordings and transcriptions used in this study come from the British

Academic Spoken English (BASE) corpus, which was developed at the

Universities of Warwick and Reading under the directorship of Hilary Nesi

(Warwick) and Paul Thompson (Reading). Corpus development was assisted by

funding from the Universities of Warwick and Reading, BALEAP, EURALEX, the

British Academy and the Arts and Humanities Research Board. </p></availability>

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<date>23/06/2000</date><equipment><p>audio</p></equipment>

<respStmt><name>BASE team</name>

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<person id="nf0934" role="main speaker" n="n" sex="f"><p>nf0934, main speaker, non-student, female</p></person>

<person id="sm0935" role="participant" n="s" sex="m"><p>sm0935, participant, student, male</p></person>

<person id="sm0936" role="participant" n="s" sex="m"><p>sm0936, participant, student, male</p></person>

<person id="sm0937" role="participant" n="s" sex="m"><p>sm0937, participant, student, male</p></person>

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<item n="speechevent">Lecture</item>

<item n="acaddept">Physics</item>

<item n="acaddiv">ps</item>

<item n="partlevel">UG1</item>

<item n="module">Optics</item>

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<u who="nf0934"> <kinesic desc="overhead projector is on showing transparency" iterated="n"/> holography is a very modern <pause dur="0.3"/> part <pause dur="0.4"/> in optics <pause dur="0.6"/> it's very complicated subject <pause dur="0.4"/> as well as interesting <pause dur="0.6"/> it's possibly one of the most interesting things <pause dur="0.2"/> <trunc>m</trunc> most of the interesting topics that <pause dur="0.6"/> we have discussed in the lecture <pause dur="0.6"/> # <pause dur="0.3"/> and # <pause dur="0.3"/> it is going to be in a very simplified manner <pause dur="0.7"/> what i'm going to show you <pause dur="0.4"/> so <pause dur="0.2"/> don't be surprised if <trunc>y</trunc> if i'm just <pause dur="0.3"/> if i just throw formulas at you <pause dur="0.6"/> # that <pause dur="0.2"/> are <pause dur="0.2"/> are the final result don't expect any complicated mathematics the mathematics in holography are very very complex <pause dur="0.7"/> so the intention that i have today with holography is to just <pause dur="0.4"/> explain to you what it is <pause dur="0.6"/> # <pause dur="0.2"/> make you understand the basic principles of holography <pause dur="0.4"/> and make you feel comfortable with the idea <pause dur="0.5"/> so that's the intention <pause dur="1.4"/> there isn't much math <pause dur="0.6"/> but <pause dur="0.2"/> there are some very interesting though complex ideas regarding <pause dur="0.4"/> waves in optics <pause dur="0.6"/> and # <pause dur="1.0"/> i would ask you to pay a little bit of attention and try to think <pause dur="0.3"/> on the way <pause dur="1.4"/> okay <pause dur="1.5"/> i am sure that you <pause dur="0.2"/> all <pause dur="0.3"/> have heard before the word holography <pause dur="0.5"/> you know that it

is technique that produces three-dimensional images <pause dur="0.7"/> and # <pause dur="0.2"/> the question is <pause dur="0.4"/> what is it that's different <pause dur="0.2"/> in holography compared to two-dimensional <pause dur="0.4"/> photographs <pause dur="1.5"/> what is that we miss <pause dur="1.4"/> when we've got a normal photograph <pause dur="0.3"/> or we've got <pause dur="0.2"/> our television screen <pause dur="0.5"/> what we see is just a two-dimensional flat image <pause dur="0.4"/> we don't see depth <pause dur="1.1"/> basically what we see is just irradiance <pause dur="1.0"/> so <pause dur="0.6"/> light intensity <pause dur="0.2"/> goes on the screen it gets reflected and that information goes into our eye and we see <pause dur="0.3"/> a two-dimensional image <pause dur="1.2"/> but <pause dur="0.5"/> we miss something <pause dur="1.1"/> the what we miss is information <pause dur="1.0"/> and that information that we miss <pause dur="0.2"/> is the phase <pause dur="0.3"/> of the reflected <pause dur="0.5"/> wavefront <pause dur="2.2"/> as we all know <pause dur="0.3"/> a wave can be described by two things <pause dur="0.8"/> can be described by <pause dur="0.2"/> the amplitude <pause dur="0.5"/> which effectively defines the irradiance <pause dur="0.6"/> and the phase <pause dur="1.2"/> so in two dimensions <pause dur="0.2"/> what we see <pause dur="0.5"/> is simply irradiance <pause dur="0.4"/> but we don't see phase <pause dur="1.2"/> with techniques of holography <pause dur="0.5"/> what we see <pause dur="0.2"/> is both <pause dur="0.4"/> irradiance <pause dur="0.3"/> and phase <pause dur="0.4"/> and this is how we end up seeing a three-dimensional image <pause dur="1.5"/>

now the question is <pause dur="0.2"/> that if we want to see <pause dur="0.3"/> both the irradiance <pause dur="0.2"/> and the phase <pause dur="0.3"/> we need to have a mechanism <pause dur="0.4"/> from which we can code <pause dur="0.4"/> that information <pause dur="1.9"/> and when we talk <pause dur="0.2"/> about <pause dur="0.5"/> phase <pause dur="0.4"/> then <pause dur="0.6"/> sometimes it's easy to think <pause dur="0.4"/> interference <pause dur="2.8"/> and basic idea of holography <pause dur="0.3"/> is to encode <pause dur="0.6"/> both information <pause dur="0.5"/> phase <pause dur="0.4"/> and amplitude <pause dur="0.7"/> in form of interference fringes <pause dur="2.0"/> later on we'll see how <pause dur="0.6"/> we can achieve that <pause dur="1.5"/> right <pause dur="0.6"/> and what i'm going to show you now <pause dur="0.4"/> after i just made a <pause dur="0.4"/> short introduction <pause dur="0.6"/> is <pause dur="0.6"/> give you a schematic representation of what happens in holography <pause dur="0.9"/> holography is defined <pause dur="0.2"/> # is separated sorry <pause dur="0.4"/> into two parts <pause dur="0.3"/> one part is <pause dur="0.2"/> the recording of the information <pause dur="0.9"/> the other part is <pause dur="0.2"/> the reconstruction <pause dur="0.4"/> of the information <pause dur="0.5"/> so keep that <pause dur="0.3"/> balance <pause dur="0.5"/> so you can keep <pause dur="0.3"/> good control on what's being said in the lecture <pause dur="1.0"/> right <pause dur="0.9"/> now <pause dur="0.3"/> here i'm going to show you two <pause dur="0.8"/><kinesic desc="reveals covered part of transparency" iterated="n"/> figures <pause dur="0.2"/> oops <pause dur="0.6"/> i don't want to ruin that <vocal desc="laughter" iterated="y" dur="1"/><pause dur="1.8"/> so we've got two figures here <pause dur="1.1"/> i do not can you can you see it clearly <pause dur="0.8"/> is it <pause dur="0.3"/> okay <pause dur="1.8"/> okay <pause dur="0.4"/>

no complaints so i can understand that <pause dur="0.2"/> you can see everything clearly <pause dur="3.4"/> now let's see what we've got here <pause dur="3.5"/> before to those who didn't hear it i said that <pause dur="0.6"/> the basis of holography is storing <pause dur="0.3"/> information <pause dur="0.2"/> about both <pause dur="0.4"/> amplitude <pause dur="0.2"/> and phase <pause dur="1.6"/> and let's see what happens <pause dur="1.8"/> we've got <pause dur="0.6"/> here <pause dur="0.4"/> a beam <pause dur="1.1"/> that is broad <pause dur="0.9"/> and it's coming from a laser <pause dur="2.2"/> that beam is split then in two <pause dur="2.0"/> one part of the beam <pause dur="1.2"/> gets reflected <pause dur="0.2"/> on a mirror <pause dur="1.0"/> and shines <pause dur="0.3"/> on a photographic plate <pause dur="1.6"/> so that's one part of the recording <pause dur="0.7"/> the other part of the beam <pause dur="1.2"/> carries on <pause dur="0.7"/> shines on the object <pause dur="0.2"/> that we're studying <pause dur="0.9"/> and then <pause dur="0.6"/> it gets reflected back <pause dur="0.5"/> on the photographic plate <pause dur="1.6"/> so we've got two beams <pause dur="0.8"/> coming from a laser <pause dur="1.3"/> that travel <pause dur="0.7"/> different paths <pause dur="1.5"/> and <pause dur="0.3"/> what do you think <pause dur="0.2"/> is going to happen on that photographic plate <pause dur="0.5"/> when these two beams come together <pause dur="0.6"/> there are two beams that are coherent <pause dur="0.5"/> because they come from a laser <pause dur="0.8"/> and they travel different paths <pause dur="2.2"/> and i'm sure you all know by now after the exam that you did all your homework <pause dur="0.5"/> that what we have <pause dur="0.3"/> is

interference <pause dur="0.6"/> these two beams are going to interfere <pause dur="1.3"/> and what happens when they interfere <pause dur="0.4"/> we're expecting <pause dur="0.3"/> on this photographic plate <pause dur="0.5"/> to have <pause dur="0.4"/> a complex <pause dur="0.3"/> set <pause dur="0.5"/> of <pause dur="0.8"/> dark <pause dur="0.4"/> and bright fringes <pause dur="0.4"/> that's the result of interference <pause dur="0.4"/> and take my word for it at the moment <pause dur="0.5"/> that these fringes <pause dur="0.5"/> are a coded form <pause dur="0.6"/> of the information <pause dur="0.6"/> that you need <pause dur="0.5"/> to have a three-dimensional reconstruction <pause dur="0.2"/> of that object <pause dur="0.8"/> these fringes <pause dur="0.6"/> tell you <pause dur="0.2"/> everything you need to know if you want to have a three-dimensional reconstruction of that object <pause dur="0.4"/> we'll see later the explanation for that <pause dur="1.5"/> right <pause dur="0.4"/> so <pause dur="1.1"/> then <pause dur="0.6"/> when we <pause dur="0.2"/> develop that <pause dur="0.7"/> photographic film <pause dur="0.7"/> we say <pause dur="0.6"/> that we can reconstruct <pause dur="0.5"/> the actual object <pause dur="0.7"/> how <pause dur="1.9"/> that is illustrated <pause dur="0.5"/> on the second figure here <pause dur="1.2"/> and what we have <pause dur="1.0"/> is <pause dur="0.4"/> a laser beam <pause dur="0.3"/> again <pause dur="0.2"/> shining <pause dur="0.4"/> on that <pause dur="0.8"/> photographic plate <pause dur="0.9"/> and these fringes that are there on the photographic plates <pause dur="0.9"/> make <pause dur="0.7"/> an <pause dur="0.6"/> a complex wave <pause dur="0.7"/> to arise on the other side of the plate <pause dur="1.5"/> and <pause dur="0.4"/> believe me at this stage <pause dur="0.3"/> that if you look <pause dur="1.1"/> at an angle <pause dur="0.6"/> through <pause dur="0.4"/> that photographic plate <pause dur="0.4"/> you will see <pause dur="0.2"/> a three-dimensional reconstruction of the original object <pause dur="1.9"/>

so that is the basic idea the very <pause dur="0.3"/> simplistic idea <pause dur="0.3"/> behind holography <pause dur="1.6"/> now <pause dur="0.6"/> what i'm going to do is i'm going to try to explain to you <pause dur="0.2"/> the mechanisms of holography <pause dur="0.4"/> using two different ways <pause dur="0.9"/> one is a pictorial Fourier way <pause dur="1.0"/> and the second one is going to be <pause dur="0.3"/> a direct <pause dur="0.2"/> mathematical <pause dur="0.2"/> simple <pause dur="0.2"/> way <pause dur="0.9"/> they're both important to understand <pause dur="0.7"/> so i'd like to ask you to pay attention to both <pause dur="0.5"/> # ways of dealing with the problem <pause dur="1.3"/> my first explanation is going to be based on <pause dur="0.2"/> Fourier <pause dur="0.2"/> analysis or <pause dur="0.2"/> Fourier optics <pause dur="0.5"/> i'm not quite sure how many of you feel <pause dur="0.4"/> familiar with <pause dur="0.2"/> Fourier analysis <pause dur="0.4"/> can you just <pause dur="0.5"/> put your hands up the ones that feel comfortable with it <pause dur="1.5"/> have you heard of it before <pause dur="0.4"/> at all <pause dur="0.6"/><kinesic desc="put hands up" n="ss" iterated="n"/> you have # <pause dur="0.2"/> # anybody else <pause dur="0.5"/> is it totally new to you Fourier analysis <pause dur="0.8"/> hands up to those that don't know anything about Fourier analysis <pause dur="1.1"/><kinesic desc="put hands up" n="ss" iterated="n"/> ooh okay <pause dur="0.9"/> <shift feature="voice" new="laugh"/> okay <shift feature="voice" new="normal"/><pause dur="0.8"/> now <pause dur="1.5"/> because i wasn't certain <pause dur="1.0"/> which of you know things and which don't <pause dur="0.7"/> i've added <pause dur="0.2"/> an extra <pause dur="0.3"/> some extra information <pause dur="0.8"/> regarding basic things about Fourier analysis <pause dur="0.3"/> most

of them when they most the people when they hear about Fourier analysis they panic they think it's too complicated <pause dur="0.5"/> but <pause dur="0.6"/> if you just try to concentrate <pause dur="0.5"/> on the idea <pause dur="0.2"/> i'm sure that you will all be better than experts <pause dur="1.2"/> so what is Fourier analysis then <pause dur="0.6"/> Fourier analysis <pause dur="0.4"/> is a way <pause dur="0.6"/> to describe <pause dur="0.6"/> an image <pause dur="0.4"/> to describe <pause dur="0.2"/> a signal <pause dur="0.5"/> to describe <pause dur="0.3"/> a function <pause dur="0.3"/> it's a language <pause dur="1.0"/> nothing more or less than that <pause dur="1.0"/> for that particular case when we talk for images <pause dur="0.3"/> we say that Fourier analysis provides the tools <pause dur="0.2"/> to analyse an image <pause dur="0.6"/> how <pause dur="0.6"/> i'll show you <pause dur="0.4"/> first the horrid thing the mathematics <pause dur="2.7"/><kinesic desc="changes transparency" iterated="y" dur="8"/> so that's what it is <pause dur="1.1"/> <trunc>c</trunc> <pause dur="0.2"/> can you see it <pause dur="2.9"/> i think it's quite <pause dur="0.3"/> oops <pause dur="0.7"/> i don't see that <pause dur="0.4"/> surviving <vocal desc="laughter" iterated="y" dur="1"/><pause dur="0.8"/> okay <pause dur="0.8"/> so what's the first formula <pause dur="0.7"/> the first formula shows you <pause dur="0.5"/> how <pause dur="0.2"/> a function <pause dur="0.2"/> F-<pause dur="0.7"/>of-X-and-Y <pause dur="0.5"/> with that particular function and that particular case is an image <pause dur="0.2"/> is an intensity <pause dur="0.8"/> can be analysed <pause dur="0.6"/> in <pause dur="0.6"/> Fourier <pause dur="0.8"/> spatial frequencies <pause dur="1.7"/> of a particular amplitude <pause dur="0.2"/> and phase <pause dur="0.6"/> you must have seen that <pause dur="0.5"/> that <pause dur="0.2"/> integration <pause dur="0.2"/>

before i mean <pause dur="0.4"/> it is very popular <pause dur="0.8"/> here is in two dimensions because we're talking about two-dimensional <pause dur="0.3"/> images <pause dur="1.6"/> so a scene <pause dur="0.5"/> can be expressed <pause dur="0.3"/> as a series of some Fourier coefficients <pause dur="1.0"/> the coefficients are characterized with a capital letter <pause dur="0.5"/> the spatial frequencies are U <pause dur="0.2"/> and V <pause dur="0.7"/> the integration is over the spatial frequencies i'll tell you later what a spatial frequency is so don't <pause dur="0.3"/> don't be demotivated <pause dur="0.6"/> and here is again another expression <pause dur="0.3"/> where i show how these Fourier coefficients <pause dur="0.4"/> can be expressed can be calculated <pause dur="0.3"/> when you know the scene F-of-X <pause dur="1.1"/> so that's <pause dur="0.3"/> basically the mathematical idea <pause dur="0.5"/> the relation <pause dur="0.3"/> between <pause dur="0.3"/> the scene <pause dur="0.6"/> and something <pause dur="0.4"/> that we call Fourier coefficients <pause dur="1.3"/> the important thing about Fourier coefficients is spatial frequency have you heard that term before spatial frequency <pause dur="0.8"/> okay <pause dur="0.6"/> so <pause dur="0.5"/> now let's forget the math <pause dur="0.2"/> and see <pause dur="0.3"/> in practice what we mean <pause dur="2.1"/> so what i've got here <pause dur="0.6"/> is a very simple image <pause dur="0.7"/> on the right <pause dur="0.4"/> which is a step <pause dur="1.5"/> what i've got here

is let's say high intensity <pause dur="1.0"/><kinesic desc="indicates point on transparency" iterated="n"/> what i've got here is no intensity <pause dur="0.9"/><kinesic desc="indicates point on transparency" iterated="n"/> so it's <pause dur="0.9"/> high intensity <pause dur="0.4"/> dark <pause dur="0.3"/> high intensity dark and so on <pause dur="0.3"/> it's a simple function <pause dur="0.8"/> the reason why i picked a simple function is because it's easier to represent <pause dur="0.4"/> but what holds for that particular function holds for <pause dur="0.2"/> the complex image <pause dur="0.5"/> so it's the same thing <pause dur="1.1"/> now <pause dur="0.5"/> to make it more simple <pause dur="1.5"/> what i've done <pause dur="0.3"/> is i've taken one line <pause dur="1.1"/><kinesic desc="indicates point on transparency" iterated="n"/> out of that image one line across that image <pause dur="0.3"/> and that line is shown here <pause dur="0.7"/> as a one-dimensional image <pause dur="1.3"/> and what i want you to see now <pause dur="0.2"/> is how we can reconstruct that <pause dur="0.4"/> sort of complex <pause dur="0.7"/> intensity line <pause dur="0.3"/> using Fourier <pause dur="0.3"/> analysis <pause dur="0.7"/> and that result <pause dur="0.6"/> is shown <pause dur="0.6"/> on the last figure here <pause dur="0.9"/><kinesic desc="indicates point on transparency" iterated="n"/> and what i have <pause dur="0.6"/> is <pause dur="0.3"/> the square of intensity <pause dur="1.7"/> and on top <pause dur="0.5"/> i've drawn a simple <pause dur="0.5"/> sine function <pause dur="1.9"/> then <pause dur="1.0"/> on top of that <pause dur="0.3"/> basic simple sine function <pause dur="1.0"/> i've drawn <pause dur="0.4"/> another sine function of different <pause dur="0.2"/> frequency <pause dur="1.9"/> and on the last figure here if you've got more than two <pause dur="0.4"/> sine functions <pause dur="0.6"/> and these sine functions when you add them up <pause dur="1.0"/> you're going

to have <pause dur="0.6"/> their initial <pause dur="0.2"/> intensity reconstructed <pause dur="0.7"/> so what is Fourier analysis <pause dur="0.2"/> it's a way to break a complex scene <pause dur="0.5"/> into simpler things <pause dur="0.4"/> that you can play with that you can work with <pause dur="0.6"/> what <pause dur="0.5"/> simple sine functions <pause dur="0.3"/> of different amplitudes <pause dur="0.4"/> of different wavelength <pause dur="0.3"/> when you add all these sine functions <pause dur="0.3"/> what's the idea <pause dur="0.2"/> it's to reconstruct <pause dur="0.4"/> your one-dimensional image <pause dur="1.3"/> so that's Fourier analysis <pause dur="0.7"/> and it's shown here <pause dur="0.3"/> in one dimension for a simple image <pause dur="0.8"/> and <pause dur="0.5"/> on the figure above <pause dur="0.2"/> what i'm showing <pause dur="0.4"/> is one sine <pause dur="0.6"/> function <pause dur="0.4"/> shown in one dimension <pause dur="0.5"/> and here it is how that function shows on two dimensions <pause dur="0.9"/> that represents <pause dur="0.2"/> intensity <pause dur="1.4"/> yeah <pause dur="1.1"/> so that's the idea behind Fourier analysis <pause dur="0.3"/> now what <pause dur="0.5"/> i'm wanting you to concentrate if you want to understand the rest is <pause dur="0.3"/> what is spatial <pause dur="0.4"/> frequency <pause dur="1.1"/> that's very important <pause dur="1.6"/> and that is shown on the figure below <pause dur="1.0"/> so what i've done on the figure below <pause dur="0.3"/> is i have taken <pause dur="0.3"/> one of these sine functions <pause dur="0.5"/> and i've plotted it out <pause dur="0.7"/> and i'm saying that the period of that sine function <pause dur="0.3"/>

is <pause dur="0.3"/> T <pause dur="0.7"/> the period <pause dur="0.3"/> is <pause dur="0.2"/> T <pause dur="0.3"/> T is not time <pause dur="0.3"/> just a period of that time function <pause dur="0.5"/> what is its spatial frequency <pause dur="0.5"/> is one<pause dur="0.4"/> over-T <pause dur="0.9"/> that's what it is <pause dur="1.8"/> that's a spatial frequency and spatial frequency <pause dur="0.4"/> can be defined <pause dur="0.7"/> linearly <pause dur="0.2"/> as one-<pause dur="0.2"/>over-T <pause dur="0.7"/> or angularly <pause dur="0.4"/> as i've <pause dur="0.2"/> shown on that <kinesic desc="indicates point on transparency" iterated="n"/> part of the figure <pause dur="0.4"/> where <pause dur="1.0"/> the difference with angular spatial frequency is that <pause dur="0.4"/> it's important <pause dur="0.2"/> from which position you're looking at something <pause dur="0.6"/> so <pause dur="0.2"/> you've got this period <pause dur="0.2"/> of that sine function <pause dur="0.3"/> you're sitting there <pause dur="0.3"/> looking <pause dur="0.5"/> at that sine function <pause dur="0.5"/> and <pause dur="0.2"/> that <pause dur="0.3"/> period is making an angle theta <pause dur="0.7"/> with you with the observer <pause dur="0.5"/> the angular spatial frequency is one-<pause dur="0.3"/>over-theta <pause dur="2.5"/> so <pause dur="0.2"/> what i'm wanting you to remember out of that transparency is that <pause dur="0.3"/> a scene can be analysed <pause dur="0.2"/> in spatial frequencies <pause dur="0.3"/> these spatial frequencies are a way to reconstruct <pause dur="0.3"/> a more complex scene <pause dur="0.7"/> and why is it important to analyse it <pause dur="0.3"/> it is <pause dur="0.3"/> because <pause dur="0.2"/> as the light <pause dur="0.3"/> falls <pause dur="0.2"/> on an object and then gets reflected <pause dur="0.3"/> there is a theory in optics that say <pause dur="0.3"/> that what travels

actually <pause dur="0.3"/> after the light has been reflected is the spatial frequencies <pause dur="0.3"/> of that particular scene <pause dur="0.3"/> and each spatial frequency <pause dur="0.3"/> is <pause dur="0.4"/> travels <pause dur="0.2"/> on a wave <pause dur="0.4"/> and depending <pause dur="0.4"/> on <pause dur="0.6"/> <trunc>th</trunc> how big that spatial frequency is <pause dur="0.9"/> no <pause dur="0.4"/> the angle that the spatial frequency makes <pause dur="0.3"/> with the central axis <pause dur="0.5"/> is higher <pause dur="0.2"/> for higher spatial frequencies <pause dur="0.8"/> so what i'm saying is that maybe i need to use blackboard for that one <pause dur="0.4"/> what i'm saying is that <pause dur="0.9"/> when you have light reflected <pause dur="0.2"/> off that scene <pause dur="0.4"/> you've got <pause dur="1.6"/><kinesic desc="writes on board" iterated="y" dur="20"/> that's the central axis <pause dur="0.4"/> you've got <pause dur="0.2"/> a spatial frequency <pause dur="0.5"/> travelling <pause dur="0.3"/> let's say straight through <pause dur="0.3"/> which is the zero order but <pause dur="0.2"/> but don't worry about that at the moment <pause dur="0.4"/> you've got <pause dur="1.2"/> another spatial frequency <pause dur="0.3"/> travelling like this <pause dur="0.5"/> you've got another one <pause dur="0.8"/> travelling like this <pause dur="0.6"/> and so on <pause dur="0.7"/> and they propagate <pause dur="0.3"/> these spatial frequencies <pause dur="0.2"/> and because of the lens <pause dur="0.6"/> they just come back together <pause dur="0.2"/> on the image plane <pause dur="0.2"/> they recombine <pause dur="0.2"/> and there you see the final image <pause dur="0.9"/> okay <pause dur="1.4"/> so <pause dur="0.2"/> that's something that we need to remember how the light propagates <pause dur="0.2"/> in terms of

spatial frequencies <pause dur="2.5"/><kinesic desc="changes transparency" iterated="y" dur="13"/> now why is it important <pause dur="3.3"/> is <pause dur="0.2"/> shown <pause dur="0.4"/> and understood <pause dur="1.3"/> from the following transparency <pause dur="2.5"/> so <pause dur="0.8"/> going back to the <trunc>dea</trunc> the idea of holography <pause dur="0.3"/> we said that we've got <pause dur="0.3"/> two <pause dur="0.2"/> parts of a laser beam <pause dur="0.7"/> recombining <pause dur="0.4"/> on a photographic plate <pause dur="0.4"/> and we said that there we've got <pause dur="0.2"/> fringes <pause dur="1.1"/> on that photographic plate <pause dur="0.5"/> and what i'm trying to go # what i'm going to do now <pause dur="0.3"/> is to show you the result of taking <pause dur="0.4"/> one spatial frequency <pause dur="0.6"/> and see the result of that spatial frequency with the original laser beam <pause dur="0.8"/> and if i <pause dur="0.7"/> put up <pause dur="0.5"/> the figure it's going to be easier for you to follow <pause dur="2.2"/>

right <pause dur="0.4"/> so what do i have here <pause dur="0.4"/> this is going to be an attempt to explain to you <pause dur="0.2"/> how the image is recorded <pause dur="0.2"/> with holography <pause dur="0.5"/> yeah <pause dur="1.8"/> so i am taking just <pause dur="0.2"/> one <pause dur="0.2"/> spatial frequency <pause dur="0.6"/> of the scene <pause dur="1.1"/> yeah <pause dur="0.6"/> that particular spatial frequency is shown here <pause dur="1.0"/> in in <pause dur="0.2"/> it is assumed that it makes an angle theta <pause dur="0.6"/> with <pause dur="0.3"/> the reference wave <pause dur="0.5"/> which is the part of the beam that comes straight from the laser <pause dur="0.3"/> and is shown on the photographic plate <pause dur="1.5"/> right <pause dur="0.9"/> the straight

lines <pause dur="0.4"/> represent <pause dur="0.4"/> crests <pause dur="0.8"/> and the dotted lines <pause dur="0.2"/> represent <pause dur="0.5"/> troughs <pause dur="2.0"/> and that is our photographic plate <pause dur="0.2"/> and i need to hurry <pause dur="0.3"/> and that is our photographic plate <pause dur="0.5"/> and <pause dur="0.2"/> the reference beam is assumed <pause dur="0.3"/> in this figure to have a maximum <pause dur="0.6"/> on that photographic plate <pause dur="1.8"/> now <pause dur="0.5"/> what i'd like you to do is to tell me <pause dur="0.3"/> if you can see <pause dur="0.6"/> at which points on the photographic <pause dur="0.2"/> plate <pause dur="0.2"/> i'm going to have <pause dur="0.3"/> maxima <pause dur="0.4"/> occurring <pause dur="0.3"/> from <pause dur="0.2"/> interference between the two beams </u><pause dur="0.7"/> <u who="sm0935" trans="pause"> A B and C </u><pause dur="0.3"/> <u who="nf0934" trans="pause"> that's excellent <pause dur="0.5"/> this is where you have your maxima <pause dur="1.6"/> A <pause dur="0.2"/> B and C <pause dur="1.4"/> now <pause dur="0.4"/> what is going to happen to the light intensity <pause dur="0.3"/> in between these points </u><pause dur="0.8"/> <u who="sm0936" trans="pause"> <gap reason="inaudible" extent="1 sec"/> </u><pause dur="1.0"/> <u who="nf0934" trans="pause"> it will depend <pause dur="0.2"/> on the phase difference between the two beams <pause dur="0.6"/> the classic line from interference <pause dur="1.2"/> so the next step is <pause dur="0.2"/> is to actually mathematically <pause dur="0.4"/> try and calculate <pause dur="0.4"/> how much that phase difference is going to be <pause dur="0.5"/> as a function <pause dur="0.3"/> of position <pause dur="0.3"/> on top of that photographic plate <pause dur="0.7"/> that's our next aim <pause dur="0.2"/> that's what we need to do <pause dur="1.1"/> and <pause dur="0.5"/> now <pause dur="0.2"/> i've got <pause dur="1.3"/> well <pause dur="1.7"/><kinesic desc="reveals covered part of transparency" iterated="n"/> another figure <pause dur="0.2"/> which is basically <pause dur="0.5"/> part <pause dur="0.4"/> of the first one <pause dur="0.5"/>

but only showing the interesting bits for the calculation <pause dur="0.6"/> so again i've got my photographic plate there <pause dur="0.3"/> i've got an axis X on that photographic plate <pause dur="0.5"/> and <pause dur="0.2"/> i've got the angle theta <pause dur="0.3"/> that <pause dur="0.2"/> the spatial frequency makes with the reference wave <pause dur="0.4"/> got the wavelength of my radiation <pause dur="0.3"/> and what i'm wanting to do is to calculate <pause dur="0.2"/> the phase <pause dur="1.1"/> phi <pause dur="0.2"/> phi <pause dur="0.2"/> how do you call it <pause dur="0.2"/> phi <pause dur="0.5"/> yes <pause dur="0.2"/> phi <pause dur="0.2"/> along <pause dur="0.3"/> that photographic <pause dur="0.3"/> plate <pause dur="1.5"/> now <pause dur="1.1"/> you're not supposed to see that bit yet <vocal desc="laugh" iterated="n"/><pause dur="0.9"/> so <pause dur="0.7"/> how much do you think <pause dur="0.3"/> that phase difference is going to change <pause dur="0.3"/> if i travel <pause dur="0.3"/> from B <pause dur="0.3"/> to A <pause dur="0.4"/> where the two maxima occur </u><pause dur="2.4"/> <u who="sm0937" trans="pause"> two-pi </u><pause dur="0.5"/> <u who="nf0934" trans="pause"> exactly <pause dur="0.5"/> so when i go from the two maxima <pause dur="0.4"/> the phase has changed <pause dur="0.3"/> by two-pi <pause dur="1.5"/> therefore <pause dur="0.2"/> taking that into consideration <pause dur="0.4"/> one can write <pause dur="0.2"/> that the phase <pause dur="0.4"/> phi <pause dur="0.3"/> at some point <pause dur="0.3"/> X <pause dur="0.5"/> satisfies that relationship <pause dur="0.2"/> that analogy <pause dur="0.6"/> if you want <pause dur="0.7"/> but phi <pause dur="0.3"/> over two-pi <pause dur="0.2"/> equals <pause dur="0.2"/> X <pause dur="0.3"/> over <pause dur="0.2"/> the length <pause dur="0.4"/> A-B <pause dur="1.2"/> don't worry making notes about that because you've got everything in your <pause dur="0.2"/> handout <pause dur="0.4"/> so <pause dur="1.6"/> you don't you needn't worry about it <pause dur="0.5"/> unless of

course if it helps you learn things better to which is which is fine by me <pause dur="0.7"/> and now what we want to do is to <pause dur="0.2"/> isolate that phi <pause dur="0.3"/> and we say that the phase <pause dur="0.7"/> is <pause dur="0.4"/> two-pi <pause dur="0.2"/> multiplied by X <pause dur="0.2"/> divided <pause dur="0.2"/> by <pause dur="0.2"/> A-B <pause dur="1.3"/> that calculation though is not finished because what because what we actually want to relate <pause dur="0.4"/> is that phase difference <pause dur="0.2"/> with the angle <pause dur="0.4"/> theta <pause dur="1.2"/> that the spatial frequency makes with the reference wave <pause dur="1.7"/> and how do we do that <pause dur="1.1"/> usual way <pause dur="0.3"/> we use that triangle <pause dur="0.9"/> yeah <pause dur="0.6"/> and from that triangle we're going to substitute <pause dur="0.6"/> the length A-B that is not very helpful to us at the moment <pause dur="1.2"/> and it's quite straightforward to see that the sine of that angle theta <pause dur="0.3"/> is the wavelength lambda <pause dur="0.2"/> over <pause dur="0.2"/> A-B <pause dur="0.3"/> therefore that length <pause dur="0.2"/> A-B is going to be the length <pause dur="0.4"/> sorry the wavelength <pause dur="0.2"/> divided by the sine <pause dur="0.5"/> of the wanted angle <pause dur="1.3"/> therefore <pause dur="0.2"/> our final result is that <pause dur="0.3"/> the phase <pause dur="0.2"/> along the photographic plate <pause dur="0.2"/> as a function of position <pause dur="0.2"/> is going to be two-pi <pause dur="0.4"/> over the wavelength <pause dur="0.3"/> multiplied <pause dur="0.2"/> by the distance <pause dur="0.2"/>

multiplied <pause dur="0.2"/> by the sine <pause dur="0.4"/> of the angle <pause dur="0.4"/> that the spatial frequency makes <pause dur="0.2"/> with the reference wave <pause dur="2.1"/> and now what is it important to see <pause dur="0.3"/> the calculation is quite straightforward i'm sure you all <pause dur="0.6"/> understood it <pause dur="0.7"/> the important is <pause dur="0.3"/> that <pause dur="0.5"/> the phase <pause dur="0.3"/> X <pause dur="0.8"/> that defines if we're going to have intensity maxima <pause dur="0.2"/> or minima <pause dur="1.2"/> is not only a function of position <pause dur="0.3"/> X <pause dur="0.7"/> it is a function <pause dur="0.4"/> of the angle <pause dur="0.3"/> that the spatial frequency makes with the reference wave <pause dur="1.2"/> and what did we say before <pause dur="0.3"/> that a complex scene <pause dur="0.5"/> can be broken into a number of spatial frequencies <pause dur="0.2"/> that travel with different angles <pause dur="1.4"/> where do i want to end <pause dur="0.2"/> i want to say that <pause dur="0.3"/> for each spatial frequency <pause dur="0.5"/> that angle theta is going to be different <pause dur="1.5"/> therefore <pause dur="0.3"/> what we're expecting to see <pause dur="1.1"/> on the photographic plate when you've got a complex object <pause dur="0.5"/> is a very complicated <pause dur="0.5"/> form of of of dark and bright fringes <pause dur="1.3"/> that's what we're expecting to see <pause dur="5.6"/> but before <pause dur="0.5"/> we go to that point the next bit is <pause dur="0.3"/> to see <pause dur="0.3"/> what is going to be <pause dur="0.3"/> the light field on that

photographic plate <pause dur="2.2"/> and the light field on that photographic plate <pause dur="0.7"/> is going to be given <pause dur="0.3"/> by this <pause dur="0.6"/> formula <pause dur="0.2"/> that comes to you <pause dur="0.3"/> like <pause dur="0.2"/> out of the blue now <pause dur="0.3"/> but it really comes from interference <pause dur="0.5"/> the point is not to go through all the steps <pause dur="0.2"/> it's to make you understand what's behind holography <pause dur="0.7"/> yeah <pause dur="0.5"/> and that's the resultant <pause dur="0.3"/> wave <pause dur="0.5"/> of <pause dur="0.7"/> two <pause dur="0.6"/> beams <pause dur="0.6"/> that have got the same <pause dur="0.2"/> amplitude <pause dur="1.3"/> now what's the resultant intensity <pause dur="0.7"/> when the field is like that the resultant intensity <pause dur="0.3"/> as we all know is going to be proportional to the square of the wave time average blah blah <pause dur="0.3"/> and believe me <pause dur="0.2"/> that is going to be given by that equation <pause dur="1.7"/> so what do we see that for one spatial frequency <pause dur="0.3"/> the intensity on the photographic plate <pause dur="0.3"/> is expected <pause dur="0.3"/> to have a constant term <pause dur="1.3"/> and another term <pause dur="1.1"/> who has got a cosine <pause dur="0.8"/> dependence <pause dur="0.8"/> cosine dependence <pause dur="0.2"/> on the phase <pause dur="0.2"/> difference <pause dur="0.9"/> and enough about math how's it going to look like <pause dur="1.7"/><event desc="takes off transparency" iterated="n"/> i'm going to show you <pause dur="0.9"/> here <pause dur="0.6"/> how the fringes are going to look like on that photographic plate

for this simple case <pause dur="0.8"/> and we said <pause dur="0.3"/> that it's going to look like a cosine <pause dur="0.3"/> and indeed <pause dur="2.4"/><kinesic desc="puts on transparency" iterated="n"/> it looks <pause dur="0.2"/> like <pause dur="0.6"/> that <pause dur="1.2"/> which is <pause dur="0.6"/> a cosine <pause dur="0.4"/> function <pause dur="4.1"/> okay <pause dur="1.5"/> so that's <pause dur="0.2"/> now <pause dur="0.3"/> the intensity on the photographic plate <pause dur="0.3"/> and what do we do when we have that information <pause dur="0.5"/> we develop the film <pause dur="0.6"/> and then we say okay <pause dur="0.2"/> now we've got our fringes <pause dur="0.2"/> we want to reconstruct <pause dur="1.3"/> what's the idea behind reconstruction <pause dur="0.8"/> that is very simply <pause dur="0.4"/> shown on that one <pause dur="0.3"/> where you've got now another laser <pause dur="0.3"/> shining on that photographic plate <pause dur="0.3"/> and because you've got intensity variations on that photographic plate <pause dur="0.3"/> you've got a complex wavefront arising <pause dur="0.2"/> behind that plate <pause dur="1.1"/> and you've got <pause dur="0.2"/> a number of spatial frequencies <pause dur="0.3"/> travelling in different <pause dur="0.2"/> directions <pause dur="1.5"/> and what i'm saying is <pause dur="0.3"/> that <pause dur="0.3"/> if one <pause dur="0.2"/> looks <pause dur="0.5"/> from that position <pause dur="0.4"/> he's going to see <pause dur="0.3"/> a three-dimensional object <pause dur="1.1"/> the explanation about <pause dur="0.2"/> reconstructing <pause dur="0.7"/> is going to be <pause dur="0.2"/> from my point of view more successful <pause dur="0.2"/> with the other approach with a direct mathematical approach <pause dur="1.1"/> but that's the end <pause dur="0.3"/> of the first <pause dur="0.2"/> way of

dealing with holography <pause dur="0.4"/> the Fourier way <pause dur="2.4"/> how <pause dur="0.3"/> are the fringes going to look for <pause dur="0.6"/> a more complicated object <pause dur="2.9"/><kinesic desc="changes transparency" iterated="y" dur="10"/>

they're going to look more complex <pause dur="1.5"/> and <pause dur="1.9"/> they are bound <pause dur="0.4"/> to look <pause dur="0.6"/> more complicated <pause dur="0.5"/> the more complicated the object you are studying is <pause dur="0.4"/> so <pause dur="0.8"/> i'm just showing you here two pictures to see <pause dur="0.4"/> how do they look like <pause dur="3.8"/> one <pause dur="0.2"/> finds it hard to believe that <pause dur="0.3"/> out of that <pause dur="0.4"/> you've got so much information but <pause dur="0.7"/> that's how it is in holography <pause dur="2.0"/> two more points that i need to make <pause dur="0.3"/> is that <pause dur="0.9"/> as we said before <pause dur="0.5"/> when you have a more complex <pause dur="0.2"/> object <pause dur="0.4"/> you're expecting <pause dur="0.2"/> the phase difference <pause dur="0.6"/> phi <pause dur="0.5"/> to give you a more <pause dur="0.3"/> complicated configuration of fringes <pause dur="0.6"/> and <pause dur="0.5"/> if the amplitude of the waves <pause dur="0.3"/> is not the same as we said before <pause dur="0.3"/> then that is going to reflect <pause dur="0.3"/> on how bright <pause dur="0.3"/> these fringes are <pause dur="2.0"/> we'll see more details of that one <pause dur="0.4"/> on the second <pause dur="0.2"/> part of <pause dur="0.5"/> how to work with holography which is <pause dur="0.4"/> something that you may feel more comfortable which is direct <pause dur="0.2"/> mathematical <pause dur="0.4"/> way <pause dur="3.2"/><kinesic desc="changes transparency" iterated="y" dur="23"/> so <pause dur="1.8"/> we're going back <pause dur="0.5"/> to the usual <pause dur="1.2"/> old known ideas about <pause dur="0.4"/>

waves <pause dur="1.0"/> and <pause dur="0.4"/> to remind you again <pause dur="0.2"/> of the <pause dur="0.4"/> idea of holography <pause dur="0.4"/> i'm just going to very briefly show you <pause dur="2.5"/> what we said about recording <pause dur="0.2"/> we said we've got a laser beam it's been broadened <pause dur="0.5"/> part of it shines on that photographic plate <pause dur="0.4"/> and another part <pause dur="0.3"/> of the beam <pause dur="0.4"/> shines on the object and then ends up on the photographic plate <pause dur="0.5"/> so what do we've got <pause dur="0.7"/> we've got <pause dur="0.2"/> two <pause dur="0.4"/> electric <pause dur="0.3"/> fields <pause dur="0.2"/> recombining on a photographic plate <pause dur="0.2"/> usual interference problem <pause dur="0.8"/> right <pause dur="0.6"/><kinesic desc="changes transparency" iterated="y" dur="10"/> so what do we know about the usual interference problem we just write down the two parts <pause dur="0.3"/> of the wave <pause dur="0.6"/> in a simple mathematical <pause dur="0.2"/> form <pause dur="2.0"/> so what's the first equation represent <pause dur="0.2"/> the first equation represents <pause dur="0.2"/> the part of the laser beam <pause dur="0.2"/> that has not been reflected <pause dur="0.2"/> off <pause dur="0.2"/> from the object <pause dur="0.5"/> and that <pause dur="1.0"/> part of the beam <pause dur="0.2"/> we call it the background beam or reference <pause dur="0.2"/> beam <pause dur="1.3"/> and <pause dur="0.6"/> this is why you've got the <trunc>substr</trunc> subscript-<pause dur="0.2"/>B <pause dur="0.5"/> for background beam <pause dur="1.0"/> that's the electric field <pause dur="0.5"/> that is being produced <pause dur="0.5"/> on the photographic plate <pause dur="0.6"/> and is <pause dur="0.4"/> of constant amplitude <pause dur="0.7"/> and <pause dur="0.4"/> of phase

that is a function <pause dur="0.2"/> of position <pause dur="0.7"/> on the photographic plate <pause dur="1.5"/> that's the description of the first part of the beam <pause dur="0.8"/> now we've got <pause dur="0.2"/> the <pause dur="0.2"/> beam <pause dur="0.3"/> that has been scattered <pause dur="0.4"/> by the object <pause dur="0.7"/> that <pause dur="0.2"/> we give the name <pause dur="0.4"/> E-<pause dur="0.2"/>O <pause dur="0.4"/> O stands for object <pause dur="0.9"/> and that <pause dur="0.2"/> is again the amplitude <pause dur="0.2"/> which is now a position <pause dur="0.8"/> of <pause dur="0.8"/> <trunc>i</trunc> it's a function sorry of position on the photographic <trunc>fil</trunc> on the photographic film <pause dur="0.6"/> and <pause dur="0.3"/> a <trunc>f</trunc> # a phase <pause dur="0.6"/> phi <pause dur="0.7"/> with the subscript-<pause dur="0.3"/>O <pause dur="0.4"/> for object <pause dur="0.8"/> which is again a function of position on the photographic field <pause dur="0.8"/> and what we want to do is to calculate <pause dur="0.3"/> the total electric field <pause dur="0.4"/> that arises <pause dur="0.2"/> from these two fields overlapping <pause dur="0.2"/> adding with each other <pause dur="1.6"/><kinesic desc="reveals covered part of transparency" iterated="n"/> and what we do is we say <pause dur="0.3"/> that <pause dur="0.9"/> the field is going to be <pause dur="0.2"/> the addition of these two <pause dur="0.3"/> and <pause dur="0.3"/> the intensity <pause dur="1.0"/> that it is what we are worried about <pause dur="0.4"/> is going to be <pause dur="0.2"/> as we all know <pause dur="0.6"/> the field squared <pause dur="0.6"/> and then time averaged <pause dur="2.2"/> and <pause dur="0.2"/> the result of that calculation <pause dur="0.3"/> is going to be <pause dur="0.7"/> as you all know <pause dur="0.5"/> the amplitude <pause dur="0.4"/> of the background beam squared <pause dur="1.3"/> plus <pause dur="0.2"/> the amplitude of the object beam

squared <pause dur="0.8"/> plus <pause dur="0.3"/> that <pause dur="0.2"/> interesting bit here <pause dur="0.6"/> which is a cosine <pause dur="0.4"/> of the difference <pause dur="0.2"/> in phase these two beams have <pause dur="1.5"/> now never mind about amplitudes and about constants <pause dur="0.4"/> that's <pause dur="0.4"/> that's the key point <pause dur="0.6"/> here <pause dur="1.3"/> so <pause dur="1.0"/> we say then <pause dur="1.3"/> we see <pause dur="0.4"/> that <pause dur="0.2"/> the intensity <pause dur="0.2"/> formed <pause dur="1.1"/> on that photographic film <pause dur="0.6"/> is really a function <pause dur="0.4"/> of the difference in phase between these two beams <pause dur="1.2"/> so what can we say <pause dur="0.3"/> that the intensity <pause dur="0.3"/> is <pause dur="0.2"/> a coded <pause dur="0.2"/> form <pause dur="0.4"/> of the phase difference <pause dur="1.4"/> that's the whole point <pause dur="0.2"/> that i want you to remember on that one <pause dur="2.4"/> right <pause dur="0.3"/> we understood now the importance of the phase <pause dur="0.4"/> that the phase has been recorded <pause dur="0.3"/> on the photographic film <pause dur="0.2"/> but what about the other bit of information which is the intensity <pause dur="0.9"/> and we're saying that the intensity <pause dur="0.7"/> in holography <pause dur="0.5"/> defines the contrast <pause dur="0.4"/> as i said to you before <pause dur="1.2"/> in the scene <pause dur="0.9"/> and that contrast <pause dur="0.2"/> V <pause dur="0.7"/> is <pause dur="0.2"/> the maximum-intensity-minus-the-minimum-intensity over <pause dur="0.5"/> the maximum-intensity-plus-<pause dur="0.3"/>the-minimum that's a simple definition of what contrast is <pause dur="0.8"/> and that contrast relates if you want to amplitude <pause dur="0.5"/> by

this <pause dur="0.2"/> simple definition <pause dur="1.3"/> and we see <pause dur="0.3"/> that the amplitude <pause dur="0.3"/> of the object <pause dur="0.3"/> E-O-O <pause dur="1.1"/> indeed <pause dur="0.2"/> defines the contrast of these fringes <pause dur="0.7"/> so the contrast <pause dur="0.6"/> and the intensity really <pause dur="0.2"/> of that photographic plate <pause dur="0.3"/> give you all the information you need <pause dur="0.9"/> both <pause dur="0.2"/> information for intensity <pause dur="0.2"/> and phase <pause dur="0.7"/> to reconstruct <pause dur="0.7"/> your original scene in three dimensions <pause dur="3.9"/><event desc="takes off transparency" iterated="n"/> right <pause dur="3.2"/> so that's the bit about <pause dur="0.2"/> recording <pause dur="0.4"/> for the direct mathematical approach <pause dur="0.5"/> what about reconstruction <pause dur="1.2"/><kinesic desc="puts on transparency" iterated="n"/> again <pause dur="1.0"/> i'm showing you very briefly <pause dur="0.3"/> the figure for those that <pause dur="0.8"/> didn't pay that much attention before <pause dur="0.5"/> you've got your <pause dur="0.2"/> reference beam on reconstruction <pause dur="0.5"/> that shines on that photographic film <pause dur="0.5"/> that has all the information encoded <pause dur="0.8"/> and <pause dur="0.4"/> part of the beam <pause dur="1.2"/> is going through <pause dur="0.2"/> and the wavefront that arises <pause dur="0.7"/> behind that photographic field <pause dur="0.6"/> <trunc>ph</trunc> photographic film sorry <pause dur="0.2"/> is giving you the information you need <pause dur="0.3"/> to see <pause dur="0.4"/> that <pause dur="0.5"/> three-dimensional image <pause dur="0.5"/> now one may say <pause dur="0.2"/> hold on a minute <pause dur="0.2"/> you've got two images there <pause dur="0.9"/> you've got <pause dur="0.2"/> one <pause dur="0.3"/> here <pause dur="0.4"/> and <pause dur="0.2"/> one <pause dur="0.2"/> there <pause dur="0.8"/> and indeed you've got two images formed in holography <pause dur="0.4"/> the thing is <pause dur="0.2"/> that the one of them <pause dur="0.2"/> is not good <pause dur="1.9"/> and i'll show

you later why <pause dur="2.9"/> right <pause dur="0.2"/> so let's go now <pause dur="0.6"/> to the mathematics <pause dur="1.3"/> and i'm saying that we've got <pause dur="0.2"/> one laser beam shown <pause dur="0.4"/> on that <pause dur="0.4"/> # photographic film <pause dur="0.9"/> a laser beam <pause dur="0.6"/> and that's <pause dur="1.8"/> its <pause dur="0.4"/> formula <pause dur="0.5"/> how you define that <pause dur="0.5"/> beam mathematically <pause dur="0.7"/> we call it the reconstructive <pause dur="0.5"/> reconstructing <pause dur="0.2"/> wave or reconstructive <pause dur="0.2"/> beam <pause dur="0.4"/> that's the name for it <pause dur="0.3"/> and you've got this R-subscript there <pause dur="0.8"/> and it's <pause dur="0.2"/> very simple to describe it <pause dur="0.7"/> it's a wave <pause dur="0.2"/> it's got its amplitude <pause dur="0.2"/> and it's got its phase <pause dur="0.6"/> that's what it is <pause dur="1.0"/> now that beam <pause dur="0.4"/> reads <pause dur="0.3"/> the information <pause dur="0.4"/> on the photographic plate <pause dur="0.5"/> that reading <pause dur="0.7"/> is mathematically expressed <pause dur="0.8"/> as <pause dur="1.4"/> # multiplication <pause dur="0.9"/> of the <pause dur="0.3"/> wave <pause dur="0.4"/> the reconstructing wave <pause dur="0.4"/> with the intensity <pause dur="0.7"/> on that photographic <pause dur="0.3"/> plate <pause dur="2.3"/> so what i'm saying is that the final wave <pause dur="0.3"/> the emerging wave behind <pause dur="0.4"/> the photographic plate <pause dur="0.7"/> is going to be a multiplication <pause dur="0.5"/> of the reconstructing wave <pause dur="0.6"/> with <pause dur="0.3"/> the <pause dur="0.2"/> intensity <pause dur="0.4"/> of that <pause dur="1.3"/> that is stored on that photographic plate <pause dur="2.0"/> that's how

it is <pause dur="0.9"/> that's the starting point <pause dur="0.4"/> now what's going to happen <pause dur="0.6"/> let's see <pause dur="1.1"/> next bit is okay let's see what happens if we substitute <pause dur="0.6"/> the reconstructing wave <pause dur="0.3"/> with its <pause dur="0.5"/> analytical form <pause dur="0.6"/> and <pause dur="0.5"/> i substituted here the intensity <pause dur="0.6"/> with the formula that i've shown you on the <pause dur="0.2"/> on the previous page <pause dur="0.5"/> nothing new <pause dur="0.3"/> here <pause dur="1.8"/> and what we do <pause dur="0.2"/> is we <pause dur="0.2"/> multiply <pause dur="0.4"/> all that <pause dur="1.3"/> with a constant <pause dur="0.5"/> provided by these two terms <pause dur="1.1"/> and <pause dur="0.2"/> if we do that <pause dur="0.8"/> multiplication <pause dur="0.5"/> we're going to see <pause dur="0.2"/> that <pause dur="0.5"/> it is the reconstructing <pause dur="0.9"/> wave <pause dur="0.6"/> multiplied by this constant <pause dur="1.0"/> and then <pause dur="0.2"/> the second bit of the multiplication is to take <pause dur="0.2"/> all that <pause dur="1.0"/> and multiply it <pause dur="0.3"/> with <pause dur="0.3"/> all that <pause dur="1.6"/> so what's interesting <pause dur="0.2"/> in this multiplication <pause dur="0.4"/> you've got the multiplication of two cosines now <pause dur="0.8"/> the cosine appearing here <pause dur="0.6"/> the cosine <pause dur="0.6"/> there <pause dur="1.2"/> and <pause dur="0.3"/> the result <pause dur="0.8"/> is shown <pause dur="0.5"/> on that <pause dur="0.2"/> second line i'm showing <pause dur="1.5"/> so what do you have here <pause dur="0.5"/> you've got all your constants <pause dur="0.2"/> that you're not <pause dur="0.3"/> particularly worried about at the moment <pause dur="0.5"/> and you've got the cosine <pause dur="0.4"/> of the reconstructing <pause dur="0.2"/> wave <pause dur="0.5"/> multiplied with

the cosine of that phase difference <pause dur="0.3"/> between the reference beam <pause dur="0.5"/> and <pause dur="0.6"/> the object <pause dur="2.0"/> right <pause dur="0.3"/> and when we see cosines multiplied together <pause dur="0.7"/> what do we do <pause dur="0.3"/> we use the known <pause dur="0.4"/> trigonometric formula <pause dur="1.1"/> and <pause dur="0.3"/> finally <pause dur="0.3"/> we've got here <pause dur="2.0"/> the <trunc>f</trunc> <pause dur="0.2"/> the result <pause dur="1.5"/> that <pause dur="0.2"/> is telling you <pause dur="0.6"/> that the final <pause dur="0.2"/> E-F <pause dur="0.3"/> wave that emerges behind the photographic film <pause dur="1.4"/> is <pause dur="1.1"/> the first term <pause dur="1.2"/> that we saw here <pause dur="0.6"/> the reference wave multiplied by constant but that's not giving you any information so basically <pause dur="0.4"/> you're not worried too much as a physicist about that <pause dur="0.7"/> and then you've got the interesting bits <pause dur="0.6"/> you've got <pause dur="1.4"/> the constant here <pause dur="0.4"/> which is <pause dur="0.4"/> the <pause dur="0.7"/> amplitude of the wave arising from the object multiplied by something you're not worried about <pause dur="0.8"/> and you've got <pause dur="0.5"/> the cosine <pause dur="0.9"/> of the <pause dur="0.2"/> summation <pause dur="0.7"/> of these two phase terms <pause dur="0.8"/> do you see what i mean <pause dur="1.5"/> i've taken the multiplication of cosines <pause dur="0.6"/> and i said <pause dur="0.5"/> that cosine-A cosine-B is going to be cosine A-plus-B <pause dur="0.5"/> A being that <pause dur="0.3"/> B being that big term <pause dur="0.5"/> and then i've <trunc>g</trunc> ended up then with that expression <pause dur="1.5"/> and on the third term <pause dur="1.0"/>

which is called <pause dur="0.9"/> the difference <pause dur="1.2"/> i've got <pause dur="0.4"/> cosine <pause dur="0.7"/> of <pause dur="0.2"/> A-<pause dur="0.4"/>minus-B <pause dur="0.5"/> so <pause dur="0.3"/> cosine of <pause dur="0.2"/> all that phase <pause dur="0.3"/> minus <pause dur="0.5"/> all that phase <pause dur="1.2"/> and that's <pause dur="0.7"/> the final wave that emerges <pause dur="0.7"/> behind the photographic plate <pause dur="1.1"/> what does that mean <pause dur="6.0"/><kinesic desc="changes transparency" iterated="y" dur="15"/> to make it more easy <pause dur="1.2"/> i've written out here <pause dur="0.2"/> again <pause dur="1.6"/> the three terms <pause dur="1.1"/> and we're going to make comments on these three terms <pause dur="6.7"/> so the first term <pause dur="0.4"/> as we said before <pause dur="0.5"/> contains not much interesting information <pause dur="0.3"/> just a constant <pause dur="1.5"/> now the second term <pause dur="0.9"/> which we called the sum <pause dur="1.1"/> term <pause dur="0.9"/> what does it contain <pause dur="0.7"/> we saw here <pause dur="1.2"/> it's got an amplitude <pause dur="1.2"/> which is a modified version of E-nought-nought but what does modified mean well it's been multiplied <pause dur="0.8"/> that's what it is <pause dur="1.2"/> and it also <pause dur="0.6"/> contains the phase here <pause dur="0.7"/> contains <pause dur="1.0"/> the factor <pause dur="0.5"/> two-<pause dur="0.4"/>phi <pause dur="1.1"/> i'll remind you <pause dur="0.2"/> that phi is the phase <pause dur="0.3"/> of the wave <pause dur="0.3"/> coming from a laser <pause dur="1.1"/> now it's getting a little bit complex <pause dur="0.2"/> and trust me on that stage <pause dur="0.3"/> that that <pause dur="0.2"/> term two-phi <pause dur="0.3"/> is responsible <pause dur="0.2"/> for the separation of the two images <pause dur="0.6"/> like i've shown you before <pause dur="1.9"/> the appearance of that term <pause dur="0.3"/> makes the two images that

we've seen on the previous <pause dur="0.8"/> figure <pause dur="0.6"/> appear <pause dur="5.5"/> and it also contains information about the phase of the object <pause dur="0.7"/> phi-nought <pause dur="0.4"/> only <pause dur="0.8"/> what's the difference <pause dur="0.2"/> it's got a minus there <pause dur="1.4"/> so that particular term <pause dur="0.5"/> contains information about both the amplitude <pause dur="0.3"/> of the object <pause dur="0.4"/> plus <pause dur="0.5"/> the phase <pause dur="0.3"/> and somebody may say oh okay <pause dur="0.3"/> i've got my amplitude i've got my phase i've got my three-dimensional image <pause dur="0.2"/> no <pause dur="0.2"/> it's not quite right <pause dur="0.2"/> because the phase <pause dur="0.2"/> appears here <pause dur="0.2"/> with a minus <pause dur="0.7"/> what does that mean in practice <pause dur="0.4"/> that that particular image that we called the real image <pause dur="0.2"/> is not right <pause dur="0.4"/> it's upside down <pause dur="1.0"/> so <pause dur="0.2"/> if in reality let's say <pause dur="1.0"/> # <pause dur="0.5"/> something is supposed to <pause dur="0.2"/> be closer to you <pause dur="0.6"/> on that image that bit looks to be <pause dur="0.2"/> further away than you <pause dur="0.6"/> it's the other way around <pause dur="0.7"/> that effect is caused by this minus-<pause dur="0.4"/>phi <pause dur="0.6"/> and the image occurring <pause dur="0.4"/> due to that term <pause dur="0.2"/> is not <pause dur="0.2"/> right <pause dur="0.2"/> is not correct <pause dur="1.9"/> the correct <pause dur="0.5"/> three-dimensional image <pause dur="1.4"/> <trunc>acu</trunc> occurs <pause dur="0.3"/> from the other term on the final wave <pause dur="0.5"/> which is the difference <pause dur="0.6"/> term <pause dur="0.8"/> and if you see <pause dur="1.3"/> in that

difference term <pause dur="0.2"/> you've got the amplitude <pause dur="1.6"/> of the wave <pause dur="0.9"/> coming from the object <pause dur="0.4"/> and now <pause dur="0.3"/> you've got <pause dur="0.2"/> the correct <pause dur="0.4"/> phase <pause dur="0.4"/> phi-nought <pause dur="0.5"/> of the object <pause dur="0.4"/> and that <pause dur="0.7"/> part of the final image <pause dur="0.5"/> is the one that is given you <pause dur="0.5"/> the three-<pause dur="0.4"/>dimensional <pause dur="0.2"/> image in holography <pause dur="4.0"/> so <pause dur="0.6"/> to conclude what we've done today <pause dur="0.8"/> is <pause dur="0.4"/> first thing <pause dur="0.3"/> to remember <pause dur="0.6"/> is the difference between two-dimensional and three-dimensional imaging <pause dur="0.5"/> in two dimensions <pause dur="0.3"/> what we do <pause dur="0.2"/> is we store <pause dur="0.2"/> information about irradiance intensity however you want to put it <pause dur="0.3"/> but we have no information about phase <pause dur="0.3"/> and holography comes and says okay <pause dur="0.5"/> there is a technique where <pause dur="0.2"/> i can store information <pause dur="0.4"/> on both intensity and phase <pause dur="1.0"/> then <pause dur="0.7"/> we shown the basic mechanism <pause dur="0.4"/> of recording and reconstruction <pause dur="0.4"/> in holography <pause dur="0.5"/> and we tried to explain <pause dur="0.6"/> that idea <pause dur="0.2"/> using two ways <pause dur="0.3"/> one way

was based on Fourier analysis <pause dur="0.6"/> and we had to <pause dur="0.5"/> say some things about spatial frequencies and the way they propagate in space <pause dur="0.6"/> and the other way to do it <pause dur="0.3"/> was direct mathematical way <pause dur="0.4"/> by using simple techniques of adding waves <pause dur="0.3"/> and calculating intensities <pause dur="0.2"/> and giving physical meanings to various <pause dur="0.4"/> mathematical results <pause dur="1.9"/> and that brings this lecture to an end <pause dur="0.9"/> thank you for your attention <pause dur="1.1"/> and # <pause dur="0.4"/> i'm sure you will <pause dur="0.2"/> all be pleased to hear <pause dur="0.3"/> that there is no workshop today and there is no second hour today <pause dur="0.3"/> so you're free to go home and <shift feature="voice" new="laugh"/>enjoy your weekend <shift feature="voice" new="normal"/><pause dur="0.7"/> and as about the marks because some people <pause dur="0.2"/> asked me <pause dur="0.2"/> at the beginning of the lecture i haven't done your marking yet <pause dur="0.4"/> i will have by Monday <pause dur="0.5"/> but <pause dur="0.2"/> the gentleman who deals with giving you the marks is Dr <gap reason="name" extent="2 words"/> <pause dur="0.3"/> so don't know when you will know the results of the of the examination you have to ask him <pause dur="1.2"/> that's it

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