Journal



Thursday, July 21st

I was able to quickly fix my set up, the problem was with the mode matching lens I was using was too small for the two cylinder mode converter. With that fixed I've been able to (mostly) get rid of the problem of destroying the LG beam. The lenses that focus the beams will sometimes distort the LG beam, but this can either be fixed by playing with the mode converter or by trying to line up the lenses better. Overall, its not as bad as the problem I was having with the one cylinder lens set up. Another problem was with the rectangular and hexagonal apertures I was using. I didn't realize it at first, but I wasn't using just plain apertures. After shining a regular TEM00 beam through them I noticed the pattern formed had an array of points of light. There were diffraction gratings in the apertures and this partially explained a lot of the patterns.

I've been getting a lot of work done and this can be seen on my "LG and Apertures" page where I've been uploading the pictures I've been taking. I've been using a double slit, a 1000 micrometer circular aperture, and a homemade rectangular aperture. Pete (from the machine shop) said he'd be able to make a rectangular aperture for me, but for now I've just been using an aperture I cut out of a brass strip. It's certainly not perfect, but it seems to be giving good results in that the pattern I see depends on the OAM, but I'll have to see what the better one gives me before I can say anything for sure. I got some pretty cool results with the circular aperture though. The number of dots in the center of the pattern says what the charge is and as one lens is moved I noticed that the pattern rotates. It would be interesting to see if the pattern rotates in the opposite direction if the charge is reversed, so I'll test that today. *Edit: So I tested it and it worked out! When I reversed the topological charge of the beam and I moved the second lens after the aperture I saw that the pattern rotated in the opposite direction. I now have a few more things to test: 1) How does this pattern change with a smaller aperture 2) Is there a way to see the sign of the beam without having to translate a lens? Maybe information about the sign is encoded in the spiral shape around the central core ie its orientation 3) Does the speed of the rotation depend on the charge of the beam?

Tuesday, July 19th

Yesterday I was talking with Marty and he brought up a problem with the overall set up of my laser cavity and lenses, so I've spent a lot of time trying to fix it and thinking what the implications of the problem could be. The thing is I've been working with the single cylinder set up that was designed by a previous student, Hamsa Sridhar. An issue brought up by another student is that with a single cylinder mode converter the LG beam formed can be destroyed and the laser mode will revert to that of a HG mode. With my set up on Friday I was able to get some interesting patterns using the rectangular and hexagonal apertures. However, as Marty pointed out, when the aperture was removed, the LG laser mode reverted back to an HG mode. As brought up by Annie, a previous student, a spherical lens can undo the effect of the Gouy phase that led to the LG beam using the single cylinder set up. With this in mind I redid the triangular aperture experiment and once again when I removed the triangular aperture I saw an HG mode. I'm curious as to how the astigmatism that remains affects the diffraction because on the one hand I was able to reproduce the previous experiment, but on the other hand the astigmatism can't be fully ignored.

With this in mind, today I made the two cylinder mode converter. I'm still having some issues with it because when it's refocused it's partially destroyed (doesnt fully become an HG beam). In theory this shouldn't happen and I have to look over my setup and read the paper about it. With the triangular aperture experiment the two lenses that focus the beam still end up distorting the LG beam. This may be due to the quality of the LG beam produced and is hopefully a different problem than what I was seeing with the single cylinder set up.

Friday, July 15th

Today was pretty interesting, I got some useful results out of my rectangular and hexagonal apertures. In my previous experiments with them I didn't have my lenses in the right place so I was getting the old rectangular and hexagonal patterns with some slight alterations due to the core of the vortex. However, after putting a focusing lens after the apertures to see the pattern in the far field and then using a lens to magnify it I was able to see an interesting pattern on the screen that gave information on the OAM of the beam. With both the rectangular and hexagonal aperture I noticed that as I changed the topological charge of the beam I was able to change the pattern. With both I saw that the pattern had a certain number of holes and the number of holes gave the charge. However, as the charge was increased the pattern became less clear as the holes were harder to differentiate. This may be due to the fact that with the HG 40 beam the incident beam had an already low intensity and/or due to the limitations of the setup. Unfortunately I wasn't able to take pictures of the patterns because my cellphones camera wasn't of high enough resolution and Lauren's camera had the same problem. In order to take a picture I'm either going to have to try and use the mavica camera or try to magnify the pattern so that everything is easier to see.

Thursday, July 14th

Over the past few days I've been getting more work done and with the end of the program coming up I figure I should make a list of important details and observations to help give direction to the coming weeks.

Circular aperture: Observation of strange pattern in the center of the diffraction pattern for a 1000 micrometer aperture but not in any apertures of smaller size. Question of a bad aperture or emergent property?

Triangular aperture: Why does pattern of rotated triangle only appear when a focusing lens is placed after the triangular aperture? Without it, how far would the screen need to be to see this far field diffraction pattern?

How does the triangular aperture affect LG modes of higher radial indices as opposed to higher azimuthal indices, ie modes with multiple rings? So far it appears a kind of hexagonal pattern is made but its not clear with the current setup. There is also the problem of making LG beams with more rings and this question could probably be approached using mathematica or some simulation software. It would also be interesting to see if the pattern can give any information about the input LG beam.

Some papers mentioned using three slits in a triangular shape as opposed to a triangular aperture. Is there any benefit to this approach and will it affect the modes with higher radial indices differently?

Other shapes: How do rectangular and hexagonal apertures affect the LG beams? With the lens placed right after the apertures I get a lattice of points on the screen. Without that lens I've gotten the usual pattern for these apertures but the lines are slanted. This is qualitatively similar to what I've seen with the double slit experiment where I reproduced a pattern described in a paper of what at first glance looks like slanted lines. These apertures are also smaller than the triangular ones so I should see how the position of the apertures affects the pattern and see if I can get anything better if I move them closer

There's also the aperture Pete recently made that kind of looks like a bowtie. What he did was he had one triangular aperture, then rotated the electrode by 180 degrees and made a new hole using that. It would be interesting to see what pattern is formed

Single slit: After seeing what happened with the double slit experiment I decided to try and see what would happen if I used a single slit. What I got was what looked like a regular single slit diffraction pattern, but the top and bottom parts were seperated by a dark spot in the middle. If I look at the math used for the double slit experiment I might be able to see what happens with the single slit one.

Tuesday, July 12th

So these past two days have been pretty productive. Today I got more equipment and I should be getting the triangular aperture tomorrow. I got some old Phy 300 equipment like a rectangular and hexagonal aperture and some double slits. I've also been working more with the circular apertures. When I used the 1000 micrometer circular aperture I saw a strange pattern in the center of the diffraction pattern. When my input beam was an HG 20 or 30 I saw in the center of the beam a pattern that looked like the respective HG beams. However, when I used different sized apertures, like a 150, 200 or 500 micrometer aperture I obtained the usual Airy disk like pattern. My current line of thinking is that either the pattern is an emergent property that can only be seen with a certain size aperture or that the 1000 micrometer aperture has some imperfection that could lead to it. To see which one it is I'm going to look for a similarly sized aperture and see what appears on the screen.

In terms of the other qpertures, I haven't seen anything quite as dramatic. For the rectangular and hexagonal aperture I noticed that when the an LG beam passed through either of them the pattern was at a slant compared to a 00 mode. This slanting was observed in a paper about passing LG beams through a double slit like experiment. In that experiment they explained that the differing phases of beams with OAMs leads to what looks like a slanting of the usual double slit experiment. What happens is that for a given spot on the screen where a normal line would appear, the top half is light and the bottom half is dark or vice versa due to constructive and destructive interference. This pattern only shows up with beams that have OAM since they have an azimuthal phase dependence and this factors in. Also for both the rectangular and hexagonal apertures I noticed that the resulting pattern on the screen did have a lattice of points like the triangular aperture experiment, but not as clean although this pattern did depend on the topological charge.

Thursday, July 7th

This week was pretty short, only three days long with July 4th off and the Friday trip to NYC. I've been able to get a few things done. I talked to Pete Davis from the machine shop about making a triangular aperture (on Professor Metcalf's advice), so I should have a better triangular aperture next week. I was thinking of using lab equipment from the Phy 300 lab because I remember we used different shaped apertures (rectangular and hexagonal), but I might be able to use new eqipement with Pete's help.

When I was reading one of the papers about the triangular aperture I found an interesting paper in the citations. In the paper the researchers discovered that if you block half of a beam that has OAM, you get an interesting pattern on your screen. Even if the knife is vertical, it will appear on the screen that the beam is cut at a slant. Changing the sign of the topological charge will cause the angle of the slant to reverse. Using this knowledge I was able to show that by rotating by cylindrical lens by 45 degrees I could reverse the sign of the charge. Also I discovered that if you diffract an LG beam with a circular aperture you get a strange dark spot in the center of the beam. At one point it looked like in that dark spot was a remnant of the HG mode, but I'll have to see how this pattern holds up. Also Marty pointed out that when I moved the aperture left and right there was an interesting change in the pattern. Where one spot would be bright on one side, it would be dark on the other. Hopefully I'll be able to test this more thoroughly by using different modes to see how the general pattern behaves.

On a side note I discovered by chance a mathematical formula called a Mobius tranformation. It has the same form as the equation for the transformation of the complex beam parameter of Gaussian beam and I found two papers that mentioned this in passing. I was thinking of reading up on this topic more thoroughly to see if I could find anything useful or interesting on it's application to Gaussian beams. I was also able to make more Gaussian beam modes by introducing a diagnol astigmatism into the open cavity laser. I was able to make 8 more laser modes, but only 6 of which were truly new. That's because I made HG03 and 04 modes, but they are turned into the same LG beams as HG 30 and 40 modes.

Tuesday, July 5th

So I've set up a new part of my website for the laser modes I've documented thus far. In total I have 11 different modes, 6 HG modes and 5 LG modes. One HG mode, the HG 31 was not very steady and was oscillating between the HG 31 and 30 mode. I wasn't able to convert that one into an LG mode, but maybe I could try to do that later. For now I'm moving on from trying to make new modes into seeing properties of these modes, ie how they diffract (I still want to introduce a horizonal astigmatism into the laser to see if I can make different modes though). In terms of diffraction through apertures I currently I have two things to use: some circular apertures I found in a lab and a triangular aperture I made.

The triangular aperture is made from three razor blades taped together. I was confused originally about what exactly to make. The papers describe what they use as an annular triangular aperture. I wasn't sure if I needed a triangular aperture or just the border of a triangular aperture, ie 3 thin slits. For now I'm working under the assumption I just need a regular triangular aperture. I haven't been able to reproduce the pattern made in the papers in a clean way, so right now I'm trying to see where the issues are coming up. My first guess was that my set up was to blame, that the triangle wasn't exactly equilateral and that the razor blades weren't all in one plane because I had to lay one atop the other. Thanks to Marty's advice I'm now seeing whether there might be another problem, whether or not my screen is in the far field and if my aperture is in the right place along the path of propagation. That's what I was trying to fix today and at least with the circular apertures I was able to make an Airy pattern, but I'll have to move on from there.

Wednesday, June 29th

Today we all talked about our projects in the seminar room. The program is about half over, so we've been getting more work done. I found a new way to make a Bessel beam using only a circular annular slit in the back focal plane of a thin lens so I think I'll try to do that. We don't have any axicons in the physics department that anyone knows of, so if I want to make a Bessel beam I'd have to use that method.

Marty helped me fix my open cavity laser set up. The Brewster window was dirty, which explained the spots that were forming on it, and that limited the power of the laser. With the window cleaned using just two swipes of methanol we were able to get a brighter laser and to form higher modes by putting a hair in the cavity. I was able to get a HG 30 and 31 mode and I was able to conver the HG 30 mode into an LG 30 beam. The 31 mode was unstable since the hair was moving. We saw it oscillate between the 31 mode and the 30 mode. I saw some even higher modes when moving the hair, but they were also hard to keep for long. I'm going to try and make more high order LG modes and introduce different astigmatisms into the laser cavity to see what modes I can get. In terms of a project, my current idea is to either study the diffraction patterns of these beams or to try and do something with Bessel beams, either just test their properties or use them in an optical tweezers set up.

Monday, June 27th

I was able to make some higher order Hermite Gaussian beams today. In order to do that I had to move the coupling window closer to the brewster window. I was able to make a 2,0 and a 1,1 HG beam, although with the 1,1 HG beam the profile wasn't as clear as it should have been. Dr. Noe explained this as being caused by there being a superposition of different beams. The way the laser was set up, the open cavity wasn't picking up only one mode. This didnt surprise me, the mount of the coupling lens wasn't screwed down to the optical table at the time since I was still looking for where it should be put.

I also did some more work with the single optical fiber. I was able to get light out with the single mode fiber but it was obviously much more difficult than the multimode fiber (and less light was probably shining through).

More importantly, I was able to more exactly test some of the measurements I estimated previously. For one, that the beam waist is located at the coupling mirror. This makes sence because for a laser cavity to be resonant, the curvature of the laser must match that of the mirror. The curvative of a flat mirror is infinite (R=Infinity) so at that point the Gaussian beam has infinite curvature. The place of infinite curvature, ie where the beam is flat, is also the beam waist so therefore the beam waist is at the mirror. I also got better values for the focal lengths of the mode matching lens and the cylindrical lens. I was hoping these better measurements would help my calculations (the ones using the equations from Hamsa's paper), but I still need to find the Rayleigh range more exactly. In the days ahead I hope to measure the laser's Rayleigh range and get started on making some higher order LG beams. With higher order LG beams and an axicon I could make higher order Bessel beams. Of course these properties are for ideal Bessel beams which require infinite energy. Bessel beams made using axicons are really just approximations of Bessel beams within a certain region.

Thursday, June 23rd

Today I started playing around with the open cavity laser first hand more. The way the laser beam was set up by who ever used it last, it was emitting a Hermite Gaussian beam of mode TEM 10. I looked at a previous student's paper on converting an HG mode into a LG mode using only one cylindrical lens and a mode matching lens so I thought I'd use the equations she derived to try and form a LG beam. At first I wanted to use the astigmatic mode converter that requires two cylindrical lens, but since in our lab we have a piece of equipment specifically set up for a single cylindrical lens converter, I decided to just use that.

The first problem I had was simply with calculating all the needed quantities. Before I could get started I needed to know the Rayleigh range of the open cavity laser and where its beam waist was located. I decided that for the time being I'd have to estimate the quantities and rely on old student papers from those who also worked with the same laser. Hopefully I can measure the important parameters of the laser directly in the coming days to help my calculations. Regardless, using the values I had and after some calculations, I was able to form a first order LG beam (0,1). After I had that I started to test the properties. I was able to magnify the beam to see it better and I tested how the LG beam behaved when it whent through a variety of optical instruments like polarizers, diffraction gratings and apertures. I plan on trying to create higher order LG beams by using higher order HG beams and then trying to make a Bessel beam if we have the appropriate equipment (ie an axicon). From what I've read a Bessel beam has some useful properties, like how its non-diffracting and can reconstruct itself in a way that makes it useful for optical trapping and guiding cold atoms.

Tuesday, June 21st

The past two days have been interesting. On Monday we did a derivation for Young's double slit experiment. We found, after several approximations, the intensity distribution of the light for small angles. We also saw the Airy disk pattern that is created when the screen is closer to the laser, ie when the approximations for the Fraunhofer range no longer apply. It was interesting to see first hand how changing a variable like the distance to the screen changes the range and how we'd describe it using math. Of course there is in principle one description of the intensity distribution for all distances from the screen, but it's often easier to work with approximations instead.

Today I went to my first REU lunch and got to see Professor Grad talk about old projects. I'm still not certain what my project will be, but I have narrowed it down. I want to work light that has orbital angular momentum (they form optical vortices). I was thinking of forming optical tweezers using LG beams. They have certain advantages over regular gaussian beams in that they can trap particles that gaussian can't, like optically reflective and absortive particles. They can also rotate particles and are better for long distance trapping. Another project idea involves studying the diffraction pattern formed by light with OAM. There were some interesting papers written that Dr. Noe sent me about how the shape of the aperture gives us information about the light's OAM. If the light is shined through an annular triangle aperture than a triangular lattice of points is formed. The lattice's orientation is used to determine whether the light had a positive or negative topological charge (in what direction the helix of the wavefront turns), and the size of the optical lattice determines what the topological charge is (how many times the helix turns).

I found a cool animation showing how the windings of the helix affect the triangular lattice of point after the light has gone through a triangular aperture here: Diffraction animation. I guess I should add learning how to embed movies onto my to do list.

Finally, I also had the chance to play around with the optical fibers today. I set up two mirrors for the laser to bounce off of and then enter the optical fiber. After some turning I was able to see the laser light come out of the other side of the optical fiber. Getting the light to enter the fiber probably took less time than just trying to set everything up. I needed Carrie's help, but eventually we were able to find a second mirror and all the right screws to attach the posts to the optical table.

Friday, June 17th

We talked more as a group today. Instead of reading papers we did some derivations at the blackboard and Dr. Noe gave us a tour of the lab. We derived the condition for there to be complete internal reflection of light when it travels from a medium of higher index of refraction to a medium with a lower one. This is important in optical fibers because it allows a light to enter and only escape on the other side. This topic also related to what I've been reading about gaussian beams since you want to focus a beam so it can enter the fiber, but if you focus the beam waist to too small a point it will diverge very quickly. It's easy to see this as a result of the equations, but it's still interesting to think about. It's analagous to what happens with diffraction: if you make the aperture smaller than the light ray with diffract more. The simplest explanation for me of this phenomenom with Gaussian beams where there is no aperture is by appealing to the Heisenberg uncertainty principle about momentum and position. We know the position to greater certainty so the there is less certainty with momentum, so it will have a wider range of values and diverge more. I don't think its the greatest explanation but it certainly helps me remember what happens when the beam waist is smaller.

Dr. Noe also gave us certain topics to talk about with the group. My topic was vortices so I'm going to have to read more on the subject and my reading about LG beams and OAM should pay off. As much as I don't like public speaking, I'm sure it'll probably help me learn better. Having to explain something to someone else usually helps clarify the subject for the speaker too. I know there have been times where I've had a problem for homework all figured out and simply talking to someone else helped me understand the conceptual basis of the problem and/or notice an error.

Wednesday, June 15th

I've been learning a lot more about Gaussian beams in the past few days beyond the basic topics. The topic of orbital angular momentum for Gaussian beams appears to be an important topic in quantum computation. As opposed to spin angular momentum, there isn't a limit on how much orbital angular momentum a beam can have. For spin, there's only right and left circular polarization (along with vertical and horizontal linear polarization but the space of spin angular momentum is still 2 dimensional) as opposed to OAM. When looking at the helical wavefront of a light ray with OAM (ie a Laguerre Gaussian beam), we can say the OAM is determined by how quickly the helix turns and obviously there's no limit on the frequency of turns. More importantly the states should all be linear independent (ie you can't express one as a sum of the others as opposed to the case with circular and linear polarizations) and its easy to see this geometrically. This should allow for greater flexibility with quantum computation although I'd have to read more about the subject before I fully understand it.

One thing that tripped me up at first was with the diagrams of light with OAM.

Citation: http://www.aip.org/png/2005/229.htm

Looking at the top picture the first thought I had was that the light rays were actually traveling in a helix when actually what the diagram was representing was the wavefronts and the phases of the light. For me, the best way to think about it is when looking at the helices is to imagine I'm looking at them as they're coming towards me and to think of the different colors as representing different phases. This is done in the second picture and it helped clear up some confusion for me.

On a different note, for the past few days I've gotten a better feeling for how projects are started. I came into the LTC thinking about Gaussian beams and how they might be used in experiments with BECs. To improve my knowledge about gaussian beams I looked for papers on the subjects and found one that related beam shifts to orbital angular momentum. From there I started reading about OAM and that naturally led to such topics as quantum computing and optical tweezers (since there have been experiments with OAM where particles were transferred angular momentum while trapped in optical tweezers). By learning about optical tweezers I've also gotten a better sense of how particles can be trapped by light.

Monday, June 13th

For the past few days I've mostly been reading papers and thinking about what to make my research project about. I recently finished reading about Gaussian beams in the Lasers textbook by Milonni and it's been a good jumping off point to papers online about the subject, although the papers online seem to focus more on higher order modes (ie LG and HG beams). I found some interesting pieces about the geometry of Gaussian beams, one about conjugate planes and how you won't obtain the highest resonance at the Gaussian beam waist and the other related to Riemannian geometry so the math mostly went over my head

After the lab was finished I found an interesting topic about the orbital angular momentum of light. The spin angular momentum is a much older subject and relates to the polarization of light (ie circular, elliptical and linear) while orbital angular momentum relates to the shape of the wavefront forming a kind of helix shape. There was an interesting article about how the OAM of gaussian beam affects four known shifts when the beam is reflected: the GH angular and spatial shift and the IF angular and spatial shift. The Goos Hanchen spatial shift is when a lightthat is reflected is shifted forward with respect to what would be predicted using geometrical optics. The IF spatial shift is similar but is perpindicular to the plane of incidence. The angular shifts for each are similar with the GH angular shift changing the angle of the light ray within the plane and the IF angular shift rotating the reflected light ray. I thought these topics were interesting in and of themselves and according to the recent paper, if the light has OAM there is a coupling of these four shifts. I don't understand how these shifts come about right now but I'm looking forward to reading more about them and trying to understand them.

On a related note, I'm going to try and figure out how to put diagrams and graphs in my journal. I figure it would be a lot easier to explain these topics if I had some diagrams and it would useful to know how to do this once I want to start putting up my own graphs.

Thursday, June 9th

Dr. Noe got our accounts for the LTC set up today, so I got some good review on using Linux and the Pico text editor (although I'll probably stick to Vi for awhile since I'm comfortable with it but Pico does have its advantages).

Today the whole group got a chance to go to the library and start researching project ideas for overthe summer. For me, the general outline for my project was decided before I came here. This past Fall semester I had Phy 300, Waves and Optics, with Professor Schneble and thoroughly enjoyed learning about light and how it behaves and the chance to work with lasers in the lab. During the spring semester I took a class in thermal physics where I learned about Bose Einstein condensates, a fascinating new form of matter only visible at very cold temperatures. I was looking for research work and noticed Professor Schneble worked with BECs so I contacted him and was happy to be join his group. Of course I first need to learn more about optics, lasers (specifically Gaussian beams) and the such so I'll probably be working on a project involving Gaussian beams and micrscopy although I'm not sure yet what exactly I'll be doing.

Wednesday, June 8th

We started today talking about the small angle approximation. The small angle approximation allows you to say y=sin(x) is approximately y=x for small x. The series expansion of sin(x) is x-x^3/3!+x^5/5!-... so for x<<1 we can ignore all the terms except for the first. A similar expansion for cos(x) allows us to replace it by 1+x^2/2. The small angle approximation is important in optics because it frequently applicable and simplifies derivations.

After this we talked about diffraction and Young's equation for finding maxima in diffraction experiments. This topic came up because we thought diffraction might play a role in the expansion of the spot of light during the pinhole aperture experiment. Our idea was wrong because we assumed the lightrays going through the hole were parallel to each other.

Importantly, today we went over and tried to explain the data we collected yesterday. Today I learned a lot about pinhole apertures, an important tool in the beginning of photography, and how geometry relates to how they work. What I found surprising was how the size of the pinhole did not affect the size of the image after having to think about it and explain it to the group, it now seems much more intuitive.

Tuesday, June 7th

Today was our first day at the LTC. We were able to cover a wide range of topics in a short amount. We saw a very convincing optical illusion involving toy pigs between two parabolic mirrors. It appeared that the pigs were floating above one of the center holes of the mirror. This brought up the topic of real vs virtual images, are the light rays bouncing off the pigs actually converging on that spot (real image) or were our eyes projecting them there. It was in fact a real image as shown by a ray diagram.

We also talked about Euler's equation, a beautiful equation that relates the exponential function e^x and the trigonometric functions in the complex plane: e^(ix)=cos(x)+i*sin(x). This equation is very important in the study of optics because exponentials are easier to work with than trigonometric functions.

An interesting property of ellipses we went over is how light travels within an ellipse. If a light ray starts at a focal point, it will bounce off a wall and hit the other focal point. This can be explained using Fermat's principle that the path a light will travel will be an extremum (maxima, minima or saddle point) of time and that every point on the distance to the first focus plus the distance to thesecond is constant. Therefore if the light ray changes its path by a little bit the change in the it takes to travel to the other focus is unchanged and every point is a saddle point. In our discussions we also talked about the use of the notebook, deriving equations and the importance of units in doing so, what a full length mirror really means (only half your body length is required), the eye, and acoustic optic modulator. The last topic was interesting because it showed how something like sound, which is really a pressure wave of air, can affect lasers that travel through the air.

Finally, today we had the chance to perform some cool experiments with optics outside. We found the focal length of a black reading lens and the diameter of the light spot from the sun on the ground. We repeated this experiment with a large lens (large radius of curvature). Using pinhole apertures we were able to create an image of the sun on the ground, found at what distance from the ground the image was best defined, and experimented with how the distance from the ground and size of the hole affected the image.