Huygens Wavelets Constructive/Destructive Interference, and Diffraction

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00:00:12.23 Hi.
00:00:14.14 I'd like to talk to you about
00:00:18.26 an issue that's very important in light microscopy,
00:00:22.08 which is resolution.
00:00:24.10 And it's a subject that,
00:00:28.20 if you didn't know any better,
00:00:30.08 would seem to be one that is related
00:00:32.20 strictly to magnification.
00:00:34.14 After all, a microscope is a magnifying device,
00:00:36.27 so one might assume that
00:00:40.02 the more magnification
00:00:41.17 the more resolution you have,
00:00:43.21 and that, if you want to make a better image
00:00:48.10 that has more resolution,
00:00:50.01 all you need to do is magnify it
00:00:51.28 more and more.
00:00:53.09 And this may not even seem unreasonable
00:00:56.03 if you think about a photon,
00:00:57.12 which is the particle of light.
00:01:00.02 A photon can pass through the smallest aperture,
00:01:04.01 there's no aperture too small for a photon,
00:01:06.20 and when a photon interacts with matter
00:01:10.11 it interacts with a single electron
00:01:12.29 of a single atom,
00:01:14.14 so, certainly, photons have the capability
00:01:17.07 to resolve things,
00:01:19.20 you'd think, down to the level of atoms,
00:01:23.09 so why not just think about light microscopes
00:01:25.05 as big magnifying devices.
00:01:28.16 I want to tell you that this is
00:01:30.29 an idea that is so obvious
00:01:33.13 that scientists have, over the years,
00:01:35.17 thought about ways of just magnifying
00:01:37.18 more and more.
00:01:38.27 And when I was a young faculty member,
00:01:40.22 I remember hearing words
00:01:43.23 about an invention of a kind of microscope,
00:01:47.20 that was very simple,
00:01:50.19 that actually could generate extraordinary
00:01:55.01 highly resolved images
00:01:56.20 by virtue of high magnification.
00:01:58.00 I want to go through that device with you
00:02:00.02 a little bit, because, in part,
00:02:02.06 it teaches what's wrong with that general premise
00:02:05.23 that magnification is all one needs for light microscopy.
00:02:09.08 And so, in this discussion,
00:02:12.20 we'll talk about what
00:02:15.24 limits resolution in the light microscope,
00:02:17.29 which is diffraction.
00:02:20.14 The paper I'm talking about
00:02:23.00 was published initially in a journal called the
00:02:28.25 Annals of Improbable Research.
00:02:30.23 It's a journal most of you probably don't read.
00:02:33.05 In fact, I didn't hear about it there;
00:02:35.08 I heard about this when it was republished
00:02:38.02 in another journal called JUNC
00:02:42.13 -- "junk" --
00:02:45.14 which is The Journal of Unpublished Chemistry,
00:02:46.25 also a slightly obscure journal.
00:02:48.03 And it was the work of Cann and Pruna,
00:02:50.11 and you can find this paper from 2002,
00:02:53.10 and let me just read you the abstract of this work.
00:02:56.03 The title of the paper was
00:02:58.10 "Iterative XEM:
00:03:01.03 A Novel Technique for Imaging of
00:03:03.22 Single Protein-Protein Interactions".
00:03:06.09 And it is, according to the authors,
00:03:09.12 "A revolutionary new microscopy technique
00:03:11.19 that makes it possible to achieve
00:03:13.28 subatomic resolution levels by
00:03:17.04 using standard copying machines."
00:03:20.08 That's right,
00:03:22.17 and the X in XEM is Xerox
00:03:24.00 and the E is enlargement microscopy,
00:03:26.29 Xerox enlargement microscopy.
00:03:29.15 "The process consists of iterative enlargements of enlargements.
00:03:31.26 The authors present several examples,
00:03:33.20 including a 15,392 magnification image of" one salt
00:03:37.07 and a 1.3 million
00:03:40.11 "magnified image of a deuterium ion."
00:03:41.29 This sounded very amazing
00:03:44.03 and so I read the paper
00:03:45.21 and here's a picture from the paper
00:03:47.26 showing the investigator at the copying machine
00:03:50.11 wearing his goggles --
00:03:52.03 why, I don't know exactly.
00:03:54.03 And down below is the pipeline
00:03:56.00 of how you generate these images.
00:03:57.10 So, you place a sample of powder
00:04:00.01 or whatever it is,
00:04:01.14 you could put a cell, I guess,
00:04:03.07 on the glass of the copying machine,
00:04:04.16 and then you select the maximum magnification,
00:04:07.08 and you obtain a piece of paper
00:04:10.07 with the enlarged image
00:04:12.22 of the thing you were looking at.
00:04:14.00 Then you take that enlarged image
00:04:15.21 and you put it back on the copying machine
00:04:17.14 and you again select the maximum magnification possible
00:04:20.28 and you take an image,
00:04:22.19 get that piece of paper,
00:04:24.06 put it back in the machine,
00:04:25.20 and doing this several, several times,
00:04:27.06 maybe ten times,
00:04:28.20 you end up with gigantic magnifications.
00:04:30.06 And here is one picture from this paper,
00:04:33.13 images of atomic hydrogen,
00:04:35.10 enlarged 48 times,
00:04:37.02 an incredible magnification of 1.3-roughly-million
00:04:40.28 was achieved with deuterated salt.
00:04:44.11 And for the first time, the author's claim,
00:04:46.12 they could see a single deuterated atom
00:04:50.13 and the quantum fuzziness,
00:04:52.11 the Heisenberg uncertainty,
00:04:54.07 those little dots around the single atom's center.
00:05:00.29 It sounds really impressive,
00:05:02.25 but why isn't this a great idea?
00:05:06.01 Obviously, it's not a great idea,
00:05:07.10 and it's not a great idea for the same reason
00:05:09.12 that, although in the movies, sometimes,
00:05:11.00 when the investigator wants to find out something
00:05:13.27 like the license plate on a car,
00:05:15.23 they just take an image
00:05:17.08 and they keep zooming it up
00:05:18.29 and then they see more and more detail.
00:05:20.11 As you know, if you look at a newspaper
00:05:22.04 and you zoom up more and more,
00:05:24.11 you finally end up with an image
00:05:26.07 which is just a bunch of dots,
00:05:27.25 and you zoom it up more, the dots get bigger
00:05:29.15 and they move apart from it each other,
00:05:31.17 but in fact you're not getting any more information.
00:05:34.02 So it's very obvious to us
00:05:36.02 when we look at images
00:05:37.19 that images have a grain,
00:05:39.20 related to the photographic emulsion
00:05:41.17 or the printing tool you're using,
00:05:44.07 but it's harder for us to imagine
00:05:47.25 that light itself would have an intrinsic grain,
00:05:49.17 that there might be a limit to resolution.
00:05:51.26 But what I'd like to
00:05:54.13 impart in this discussion
00:05:57.08 is that light does have a limit to its resolving power,
00:06:02.03 largely because it has an intrinsic limit
00:06:04.14 related to a phenomenon known as diffraction.
00:06:06.27 Now, if light had traveled just in straight lines
00:06:10.16 from one place to another,
00:06:11.28 in fact, we probably
00:06:14.15 would be able to generate very high resolution images
00:06:17.16 that would be limited just by the size of photons,
00:06:20.07 which, as I said, are infinitesimally small,
00:06:23.01 so we should be able to get a great amount of resolution.
00:06:25.18 To show why that doesn't really work,
00:06:27.20 I'm going to go to discuss, very briefly,
00:06:30.20 the simplest of all optical imaging devices,
00:06:33.24 the pinhole camera,
00:06:35.08 and some of you may have used a pinhole camera
00:06:37.14 when you were a child.
00:06:39.04 Here's a picture of one.
00:06:40.29 It is a box
00:06:45.06 and right near me is the open end of that box,
00:06:48.06 with a pinhole in it,
00:06:50.07 and the pinhole is used to image the world,
00:06:53.13 and in the box one might have
00:06:55.26 a piece of photographic emulsion
00:06:57.05 or maybe a camera that's sitting there,
00:06:59.17 and then the way the pinhole camera works
00:07:02.29 is based on the view,
00:07:05.08 that you'll see is incorrect,
00:07:07.04 that light travels in straight lines.
00:07:08.24 So, for example,
00:07:11.26 the top of that lamppost is being imaged
00:07:13.10 through this pinhole camera,
00:07:15.02 and the light coming off the top of the lamppost
00:07:17.16 is going in all directions.
00:07:19.23 We know it's going in all directions
00:07:21.05 because you walk around the lamppost,
00:07:23.01 you look at it from any vantage point,
00:07:24.13 you can see the top of the lamppost,
00:07:25.21 so light be coming from there in all directions.
00:07:29.23 And because the pinhole camera has just a small pinhole,
00:07:31.28 only a small number of rays of light
00:07:34.23 actually get through the pinhole
00:07:36.14 and they continue in the angle
00:07:38.23 they go through the pinhole
00:07:41.02 to generate light at the very bottom of that image plane
00:07:44.27 in there,
00:07:46.07 so you have an inverted image of the lamppost.
00:07:50.07 And, similarly, the light from the bottom of the lamppost
00:07:53.02 goes in all directions,
00:07:54.11 but only a small subset of the rays
00:07:55.27 get through the pinhole,
00:07:57.05 and they end up in the top.
00:07:58.22 so you end up with an inverted image of the object.
00:08:01.09 And you might think about this
00:08:04.11 that if you wanted higher resolution
00:08:06.19 you might just move this piece of paper
00:08:09.15 further and further away from the pinhole,
00:08:13.11 and that should make a bigger and bigger image,
00:08:14.28 and you should be able to catch everything.
00:08:16.16 You might think, however,
00:08:18.13 that part of the problem with resolution
00:08:20.02 is that the pinhole is finite in size,
00:08:22.19 so that more than one ray from the top of the lamppost
00:08:26.27 gets through the pinhole,
00:08:28.13 so there's a little fuzziness to that image
00:08:30.19 related to the size of the pinhole.
00:08:32.10 Indeed, if you make the pinhole bigger and bigger,
00:08:34.12 the image gets fuzzier and fuzzier.
00:08:36.15 If you get rid of the pinhole altogether
00:08:38.20 and just put a piece of paper there,
00:08:40.06 you're not going to see an image at all,
00:08:41.21 because the light is coming in all possible directions.
00:08:44.09 So you might say, well,
00:08:45.29 if we want more resolution
00:08:47.24 out a pinhole camera,
00:08:49.10 why not make the pinhole smaller?
00:08:50.28 Then, rather than having several rays
00:08:53.11 from the top of the lamppost getting through,
00:08:55.07 only one ray might get through,
00:08:57.02 and now we should get a sharper image.
00:08:59.13 And it turns out, and this is the failing of ray optics
00:09:02.11 and the failing of light microscopes
00:09:04.25 to get more and more resolution out of magnification,
00:09:07.08 is that as you make that pinhole smaller and smaller,
00:09:09.26 as shown here,
00:09:12.29 when the pinhole is infinitesimally small,
00:09:14.25 you still get light through
00:09:16.06 -- it takes longer to get an image because it's slower --
00:09:19.05 but the image is degraded tremendously.
00:09:21.20 The smaller the pinhole gets,
00:09:23.13 the image gets fuzzier,
00:09:25.26 just as it gets fuzzier when the pinhole gets bigger.
00:09:27.12 There's an optimum sized pinhole;
00:09:30.06 if it's too big or too small, the image is fuzzy.
00:09:31.29 And that fuzziness, in this case,
00:09:33.24 is due to the fact that if the light
00:09:36.16 gets through that pinhole,
00:09:38.03 if the hole is very small, the light bends
00:09:40.01 -- it's bent in many different directions.
00:09:42.06 This is know as diffraction.
00:09:43.18 I'm going to explain what diffraction is
00:09:45.22 in detail in a moment,
00:09:47.12 but it is diffraction that
00:09:49.13 really screws up the pinhole camera
00:09:51.09 and it screws up regular light microscopes as well.
00:09:53.25 In order to understand diffraction,
00:09:55.12 we have to think about
00:09:59.15 the idea that light is not traveling in rays,
00:10:02.02 but rather traveling as waves.
00:10:04.21 I'm sure you've all head of the
00:10:07.12 particle-wave duality of light.
00:10:09.24 The first person to
00:10:11.29 understand that light travels in waves
00:10:13.29 was a genius named Christiaan Huygens,
00:10:16.12 and here's his picture.
00:10:18.13 He was a remarkably smart guy.
00:10:22.12 He was a Dutch mathematician,
00:10:24.20 he was an astronomer,
00:10:26.12 he was a physicist,
00:10:27.22 and he was a horologist,
00:10:29.19 which means he studied clocks.
00:10:32.25 His work included early telescopic studies,
00:10:37.02 elucidating the nature of the rings of Saturn
00:10:38.29 and he discovered the moon of Saturn,
00:10:42.05 called Titan.
00:10:43.22 He also invented the pendulum clock,
00:10:45.19 which we still use.
00:10:47.01 It's a very clever idea
00:10:48.17 and it's worth looking up how a pendulum clock works,
00:10:50.15 it's ingenious.
00:10:51.27 And a consideration of extraterrestrial life
00:10:54.19 was his final work before he died,
00:10:57.03 he was interested in whether
00:11:00.03 living things existed elsewhere in the universe.
00:11:04.11 And he was famous for many studies in optics
00:11:07.20 and the centrifugal force
00:11:10.04 is something he studied in great detail.
00:11:13.04 For our purposes,
00:11:15.05 his main claim to fame is wave optics.
00:11:17.21 That was his big idea
00:11:19.12 and it was the idea that light is actually a wave.
00:11:22.13 And this was against
00:11:24.25 a backdrop of Newton,
00:11:26.05 who was a very impressive person, of course,
00:11:28.10 in his own right,
00:11:29.18 who insisted that light was really particles.
00:11:31.11 And I think Newton gets a lot of credit for this
00:11:34.18 corpuscular theory of light,
00:11:36.11 but it was actually Huygens insights into light waves
00:11:39.21 that provided us with understanding of the resolution limits of light.
00:11:43.03 So, let me talk about light as waves.
00:11:45.02 First of all, light travels,
00:11:47.25 apparently, in straight directions,
00:11:50.12 as a laser beam would tell you
00:11:51.26 or a pinhole camera would imply,
00:11:53.28 but, according to Huygens
00:11:56.09 and now it is well accepted,
00:11:58.17 that light that is traveling in one direction
00:12:01.03 is really a wave.
00:12:02.29 It's a plane wave --
00:12:04.09 the light's direction is orthogonal
00:12:07.13 to the oscillation of the light,
00:12:09.08 and so this wave front,
00:12:10.18 this vertical line and the one right behind it
00:12:13.14 and the one right behind it,
00:12:14.19 could be thought of as the breaker waves
00:12:16.28 in an ocean,
00:12:18.24 where one wave hits the shore
00:12:20.07 and then right behind it another wave
00:12:21.26 and after that another wave, and so on.
00:12:23.22 The distance between those peaks of the waves
00:12:26.04 might be the wavelength
00:12:28.02 and if they're straight, arranged straight,
00:12:31.06 they just keep going more or less in a straight direction
00:12:33.11 -- I can go forward or back.
00:12:35.05 It's called a plane wave
00:12:37.09 because it's not actually just a line
00:12:39.15 on the surface of...
00:12:42.17 of, let's say, water,
00:12:44.08 but it's actually a three-dimensional object,
00:12:47.21 it's a plane
00:12:50.17 and behind it is another plane and another plane.
00:12:53.01 So, the plane is in
00:12:55.12 one two-dimensional surface,
00:12:57.29 but right behind it is another one and another one,
00:12:59.20 and these are the things that are oscillating.
00:13:01.19 It's a little hard to get your mind around
00:13:03.24 what a plane wave is
00:13:06.22 when one thinks about something that big,
00:13:08.23 like a piece of plywood oscillating,
00:13:11.14 but that is what a plane wave is.
00:13:13.23 And Huygens appreciated that
00:13:16.10 there were not only plane waves,
00:13:17.26 light traveling in a straight direction,
00:13:19.18 but there were also the possibilities
00:13:21.24 that light would travel out from a point
00:13:24.07 -- you have a point of light like a candle or a small spot of light --
00:13:26.28 the light travels in all directions,
00:13:29.02 and that would be a spherically expanding wave,
00:13:32.02 and that is called a spherical wave.
00:13:34.15 And the spherical wave can expand to larger and larger areas,
00:13:37.20 and, also, maybe a little less intuitively,
00:13:40.15 light can be focused
00:13:42.22 by a converging spherical wave
00:13:45.04 that focuses onto a point,
00:13:46.22 and then once it gets beyond that point
00:13:48.06 it rediverges as a diverging spherical wave.
00:13:51.02 So, light can converge or diverge
00:13:53.22 as a spherical wave,
00:13:55.00 just as plane waves can go in one direction
00:13:57.02 or in the opposite direction.
00:14:00.20 So, that...
00:14:02.27 again, the wavelength would be the distance between the rather...
00:14:05.26 the individual plane waves.
00:14:08.25 Now, if you think about waves this way,
00:14:12.23 this is the amplitude of a wave,
00:14:14.10 that peaks and troughs,
00:14:16.09 the troughs have as much energy in them
00:14:19.01 as the peaks,
00:14:21.04 and we have to think of the intensity of the wave,
00:14:24.22 that is, its energy,
00:14:26.17 proportional to all aspects of the wave,
00:14:29.03 not just the peaks,
00:14:30.26 but the peaks and the troughs,
00:14:32.04 and the way one does this is by
00:14:34.08 understanding something that you can read in many textbooks,
00:14:37.04 that the intensity of a wave
00:14:39.00 is proportional to the amplitude of the wave squared.
00:14:42.19 I want to give you a kind of intuitive understanding
00:14:44.27 why the intensity,
00:14:47.07 that is, what you detect as brightness,
00:14:48.26 is not related to the amplitude of the wave
00:14:50.27 but to the square.
00:14:52.15 And I'll start just by
00:14:54.18 showing you this small oscillation
00:14:58.24 going up and down,
00:15:00.08 and you could imagine holding a piece of rope
00:15:04.28 and moving your hand up and down
00:15:07.18 to generate a standing wave moving forward.
00:15:12.04 My arm is moving up and down
00:15:14.12 roughly in that amplitude.
00:15:16.08 So, that takes a certain amount of work
00:15:18.09 for me to do that.
00:15:20.16 Now, if I wanted to make a wave
00:15:22.14 that was bigger,
00:15:24.01 let's take a wave that's four times bigger,
00:15:25.27 it has the same frequency of peaking and troughing,
00:15:29.04 but now I've got to go a
00:15:31.18 much farther distance up and down
00:15:34.17 to wave this rope,
00:15:36.12 but I've got to do it in the same amount of time
00:15:38.21 as I did this small wave down here,
00:15:40.12 so I've got to go 4 times as far,
00:15:42.28 but 4 times faster.
00:15:45.23 So, generating a 4 times larger wave
00:15:48.13 requires 4 times the force
00:15:50.28 over 4 times the distance,
00:15:53.15 and that is 16 times the energy.
00:15:56.17 So, it takes 16 times as much effort
00:16:00.13 to generate a wave that's 4 times bigger
00:16:02.26 than a small wave,
00:16:04.17 and therefore that light
00:16:06.19 would be considered 16 times brighter
00:16:08.10 than the light below.
00:16:10.15 So when such a wave imparts its energy to a detector,
00:16:12.14 like your retina,
00:16:14.05 we measure the intensity as intensity;
00:16:16.11 hence 4 times the amplitude
00:16:19.00 is 16 times the brightness.
00:16:22.12 Now, the other thing is that
00:16:24.25 the amplitude is moving across space at the speed of light
00:16:28.05 -- this amplitude, this wave is moving forward --
00:16:32.15 and that is just the way
00:16:35.19 the light wave looks at one instant in time,
00:16:37.12 but if we want to know what
00:16:39.15 the cumulative amplitude of that wave is,
00:16:41.07 we first have to square it,
00:16:43.00 which would generate...
00:16:45.02 for every trough, now it's turned into a peak,
00:16:48.04 so there are twice as many peaks in the intensity
00:16:50.13 as there is in the wavelength,
00:16:52.06 but that's still one moment in time.
00:16:53.21 But since that wave is moving across space,
00:16:56.12 that's one moment in time...
00:16:58.02 if we integrate that intensity
00:17:00.09 over a full wavelength,
00:17:01.27 we get an intensity that is the addition of all those waves
00:17:04.27 as we move it across that integration.
00:17:07.14 So ultimately, the intensity is
00:17:10.09 a uniform value for the wave.
00:17:11.19 So, we start with this as the backdrop
00:17:13.26 for Huygens' great idea of waves,
00:17:16.04 which was not just that light travels in waves,
00:17:18.20 but that there's an infinitesimally small wave
00:17:21.20 which he called a wavelet,
00:17:23.29 and the wavelet is the component
00:17:26.04 that generates plane waves and spherical waves.
00:17:29.26 This wavelet has properties
00:17:32.06 that are very similar to the way we...
00:17:35.01 think about, in a modern way,
00:17:37.26 photons behave when they're in space.
00:17:39.21 So his ideas,
00:17:41.17 although he didn't think of these as particles,
00:17:43.29 the properties of a photon in space
00:17:45.27 is very much like a wavelet
00:17:48.26 -- its position is not easily determined
00:17:50.16 and it can send its energy in all directions.
00:17:53.26 It's very hard to intuitively understand this,
00:17:57.22 but you'll see that with this one insight
00:17:59.15 one can generate all the properties of a microscope
00:18:02.11 without drawing lines any more
00:18:04.20 -- everything falls out of this
00:18:06.18 without having any idea that light has directionality.
00:18:08.26 So, here is Huygens' postulate,
00:18:12.18 which is that light at its most elemental
00:18:14.01 is a disturbance that propagates in all directions
00:18:17.22 as a spherical wave.
00:18:19.07 He called these elements wavelets
00:18:21.07 and sometimes they're now called Huygens' wavelets.
00:18:23.21 So there is a wavelet there...
00:18:26.01 it would be as if you were dropping
00:18:27.26 stone after stone in water at a regular interval
00:18:30.24 and you're generating waves around it,
00:18:33.07 but because they're spherical waves
00:18:35.01 you're not dropping the stone in the surface of water,
00:18:37.19 but you're making a little explosion maybe in the middle of water
00:18:40.18 and generating spherical wave after spherical wave,
00:18:44.12 sending its energy out in all directions.
00:18:47.01 And, you know, here might be
00:18:49.18 a diagrammatic view of the pulsating light source.
00:18:52.12 The distance between these crests
00:18:56.08 is the wavelength of the light
00:18:57.19 and if it's a higher frequency light,
00:19:00.10 higher energy light,
00:19:02.09 they are gonna be spaced closer together,
00:19:05.03 a shorter wavelength.
00:19:07.06 So, that is one instant in time,
00:19:08.25 shown there, the instantaneous
00:19:10.21 -- what a wavelet looks like at one moment in time --
00:19:12.23 but if one wants to get the intensity one squares it
00:19:15.06 and integrates it over time to get the intensity,
00:19:18.04 so there you have a bright spot
00:19:19.23 and then it distributes itself over space.
00:19:22.11 So, how does this explain plane waves
00:19:24.11 and spherical waves?
00:19:25.26 So, if we look at a plane wave...
00:19:29.16 according to Huygens',
00:19:31.08 a plane wave is just a bunch of wavelets
00:19:32.24 aligned in a straight line or on a plane,
00:19:36.02 and the leading edge of all the wave fronts
00:19:38.27 form a surface and that is the front of the plane wave,
00:19:43.09 and then the next wave front
00:19:46.03 would be right behind it by a wavelength delay,
00:19:49.06 and one wave front after another will be generated
00:19:51.28 through a plane of wavelets.
00:19:54.12 Spherical waves are exactly the same thing
00:19:56.12 except the wavelets, now,
00:19:57.24 rather than being arranged on a flat plane,
00:20:00.07 are arranged on the surface of a sphere,
00:20:02.09 and they can be generating light that's either diverging
00:20:04.17 -- moving away from a point,
00:20:06.18 you know, getting farther and farther apart --
00:20:08.14 or a bunch of plane waves...
00:20:10.06 sorry, spherical wavelets
00:20:12.19 that are each on the same surface of a sphere
00:20:15.11 that are converging to a point
00:20:17.03 -- they would reach the point and then they would rediverge
00:20:20.06 on the other side.
00:20:21.17 So, how does this explain
00:20:24.04 bending of light?
00:20:25.25 Well, here for example is the idea that
00:20:27.17 if you had a plane wave
00:20:29.09 and you have a very small opening,
00:20:30.22 only one wavelet gets through the opening
00:20:33.17 and that wavelet then sends its information
00:20:36.18 in all directions.
00:20:38.17 And so if you have a box with a point source in it
00:20:41.15 and the light is sending it out in all directions,
00:20:43.24 you can trace paths out of that pinhole
00:20:46.29 that are clearly not a straight line from the source,
00:20:49.10 because the light has bent at the pinhole,
00:20:51.16 but the bending in this case is due to the fact that
00:20:54.21 that one wavelet is sending its energy in all directions.
00:20:57.12 So, if you have one wavelet,
00:20:59.09 it's kind of straightforward what diffraction does,
00:21:01.19 but if you have two wavelets from the same source
00:21:05.09 that are synchronously pulsing up and down,
00:21:07.18 then you can get interference of those wavelets.
00:21:10.28 And interference is a very interesting phenomenon
00:21:13.18 and it's interesting especially because this sinusoidal shape,
00:21:17.03 if it ever interferes with another sinusoid
00:21:19.27 of the same frequency,
00:21:24.17 but set off at a different phase,
00:21:26.09 you always end up with another sinusoid.
00:21:29.12 And this is the idea shown here
00:21:31.23 -- interference: if you have waves of one frequency
00:21:34.09 that come from the same source
00:21:36.06 at nearly the same time,
00:21:37.29 they're coherent with each other,
00:21:39.23 which means that they have the same phase,
00:21:42.06 and a predictable phase difference,
00:21:44.27 and when coherent waves coincide
00:21:47.08 they interfere with each other
00:21:48.25 and their amplitudes add,
00:21:50.13 so you can end up with a wave
00:21:52.23 that is double the amplitude of the individuals,
00:21:55.04 when they're exactly in phase,
00:21:58.00 or when they're exactly out of phase, you end up with nothing,
00:22:00.27 and if you're somewhere in between
00:22:03.03 you end up with a phase-shifted wave.
00:22:05.08 So that purple wave is the composite interference
00:22:08.01 of two waves
00:22:10.00 that are being moved one phase relative to the other
00:22:11.26 -- when they're in phase, the purple is the strongest,
00:22:14.20 when they're exactly a half a wavelength out of phase,
00:22:17.10 the purple is flat
00:22:19.05 and you have what's known as constructive interference
00:22:22.16 when they're big
00:22:24.11 and destructive interference
00:22:26.19 when they're exactly half a phase out of...
00:22:30.23 out of phase with...
00:22:32.27 half a wavelength out of phase with each other.
00:22:35.12 So, let's look at this interference of two wavelets,
00:22:38.25 keeping this in mind.
00:22:40.28 So, when multiple wavelets from this same source at the same time
00:22:44.19 -- that is, they're coherent, they're pulsing synchronously --
00:22:46.22 interact,
00:22:48.22 they set up standing waves of constructive and destructive interference
00:22:51.27 -- the classic Young's two-slit experiment,
00:22:54.07 with a light source that ends up
00:22:57.10 through two slits
00:22:58.18 and then you end up with a pattern of bright and dark bands.
00:23:00.07 I'd like to unpack that idea for you
00:23:02.02 because we're gonna use that formalism
00:23:05.00 to understand, ultimately,
00:23:06.25 the resolution limit of the light microscope.
00:23:09.13 So, the light goes through one slit,
00:23:12.06 each slit generates a wavelet,
00:23:14.06 but if you have two wavelets
00:23:17.10 that are coherent with each other,
00:23:19.23 you end up with this very complicated
00:23:22.06 pattern of places where the two waves
00:23:24.03 are in phase or completely out of phase,
00:23:29.09 so they're either constructive or destructive,
00:23:30.21 or somewhere in between.
00:23:32.12 And let's now look at this in a little more detail.
00:23:34.20 So, we have a point source
00:23:36.16 generating a diverging spherical wave
00:23:38.18 made up of a bunch of wavelets
00:23:40.22 on that curved surface,
00:23:42.15 which is the diverging spherical wave,
00:23:44.27 of which two wavelets are caught
00:23:46.26 through two pinholes.
00:23:48.08 And one of those pinholes is generating
00:23:51.09 that pattern at one moment in time,
00:23:53.10 and the other pinhole is generating that pattern.
00:23:56.28 And then the peaks and the troughs
00:23:59.13 of these two will interact, generating a pattern,
00:24:02.09 like that.
00:24:04.03 So, let's look at that pattern in a little more detail
00:24:06.25 to understand how this works.
00:24:08.24 So, if we take a position
00:24:10.26 somewhere that is exactly the same distance
00:24:13.18 to the two points...
00:24:15.02 so, for example, this is on a midpoint
00:24:17.02 between those two points,
00:24:19.13 those two distances are exactly the same,
00:24:21.27 the two waves will be both peaking or troughing or in between
00:24:26.22 at every point in time
00:24:28.24 -- there will be no opportunity for destructive interference --
00:24:30.25 and therefore if they're equidistant
00:24:33.13 they'll be constructive interference.
00:24:35.16 However, if we go to a position
00:24:37.15 where one of the distances
00:24:40.11 is exactly half a wavelength longer than the other,
00:24:44.17 then there is going to be
00:24:46.26 absolute destructive interference
00:24:48.13 if there's a half a wavelength difference
00:24:50.24 in those distances.
00:24:52.05 And you can just go to any position in this space
00:24:55.09 and you'll find whether there's constructive or destructive interference.
00:24:58.27 If we put a piece of photographic paper
00:25:01.11 along a vertical line where those two points were,
00:25:05.15 we would end up with bright areas and dark areas
00:25:08.14 in this kind of banding pattern that you see.
00:25:12.02 So, that is what we are going to need
00:25:14.17 to understand how light operates in the microscope,
00:25:18.11 so this should give you a good sense of diffraction,
00:25:22.00 and in a subsequent lecture
00:25:24.03 I'll talk about how this also allows us
00:25:26.23 to derive the point spread function for the light microscope.
00:25:30.00 Thank you.

This Talk

Speaker: Jeff Lichtman

Audience:

Researcher

Recorded: December 2012

Talk Overview

Light has properties of particles and waves. Understanding the wave nature of light is essential to understanding the workings of a microscope. This lecture describes Huygens Wavelets, constructive/destructive interference, and diffraction.

Questions

Higher magnification will always result in higher resolution: True or False?
A pinhole in a pinhole camera has an optimum size. When making the pinhole smaller than the optimal size, the image will get blurred because of:
1. Refraction
2. Less light can travel through the small pinhole
3. Diffraction
4. Magnification
The theory of wave optics was developed by:
1. Isaac Newton
2. Antonie van Leeuwenhoek
3. Christiaan Huygens
4. Robert Hooke
A laser is directed at a lens. Characterize the wave shape of the light before and after the lens:
1. Before: Plane wave, After: Plane wave.
2. Before: Plane wave. After: Spherical wave
3. Before: Spherical wave. After: Plane wave
4. Before: Spherical wave. After: Spherical wave
Diffraction is
1. Focusing of light by a lens
2. The banding pattern seen after passing coherent light through two slits
3. The bending of light that passes through a small opening
4. Scattering of light hitting an opaque surface

Answers

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Speaker Bio

Jeff Lichtman

Jeff Lichtman’s interest in how specific neuronal connections are made and maintained began while he was a MD-PhD student at Washington University in Saint Louis. Lichtman remained at Washington University for nearly 30 years. In 2004, he moved to Harvard University where he is Professor of Molecular and Cellular Biology and a member of the… Continue Reading