Research Journal


Monday, August 16

I realized after I made the previous model and a later conversation with Dr. Noé that my model was actually inaccurate, since the ray leaving the sphere also incurs a change in momentum upon the sphere (not the surrounding medium, as I had previously thought).

My simple model is based on the idea that in a Gaussian beam, each angled ray is match by an equal and opposite angled ray (figure below, a). Assuming small dot size, rays will strike the bead in the same location in pairs, as shown in the figure above. To determine whether ray pairs of greater incidence angles produce a greater change in force than rays parallel to the vertical, I used a basic ray diagram (figure below, b), Snell's law, and the Fresnel equations.

To revise my previous model, I had to find the angle that the ray actually leaves the sphere. If we call the angle the ray enters from the vertical Θi and the distance from the center that the ray strikes d, then the center angle Θc = arcsin(d/r). We can use Snell's law n1*sinΘB = n2*sinΘR to find ΘR=(n1/n2)*sin(Θc+Θi). The refracted ray forms an isosceles triangle in the sphere since the radii are legs of equal length, so we know that the two angles labeled ΘR are congruent. We then know that the angle between the vertical and the aforementioned triangle is (180-2ΘR) - (180-ΘC) = ΘC-2ΘR, and the exiting angle is ΘB due to Snell's law, so Θf = ΘB + ΘC - 2ΘR.

When all variables are expressed in terms of d/r and Θi and the percent reflected versus transmitted is taken into account, the following is the graph of the transverse (blue) and axial (red) forces.

As shown above, the basic shape of the graph is still the same, just with steeper slopes. This can be shown further by comparing together the axial forces before (first graph, red) and after (blue) the collision, and the transverse forces before (second graph, red) and after (blue) the collision.

This increased change in momentum is expected since the final rays have now been refracted twice, in the initial entering of the sphere and upon leaving the sphere. This graph, as seen in the comparisons of transverse trapping forces, actually shows using the revised model that there may be an even larger increase in transverse trapping forces due to rays entering at a steep angle. On a 2-dimensional scale, the next step that I'd like to take is looking at not only the first transmitted ray, but also subsequent transmitted rays escaping after internal reflections. For a ray pair striking at a large d/r (away from the sphere center), up to 25% of the ray's initial power may still be inside of the sphere after the first internal reflection. Dr. Noé also suggested to me that it would be a good idea to look at how this model can be translated to a 3-dimensional scale, or at least understand how the two are connected by resolving a Gaussian beam into perpendicular components.


Monday, August 9

I've been working recently on modeling in Matlab the axial and transverse trapping forces on a particle in optical tweezers using the ray optics model in order to predict whether, theoretically, the transverse trapping forces should increase or decrease using higher order modes. The idea that vortices (with regions of higher intensity away from the beam axis) can improve trapping forces is based on the assumption that rays coming in at a steeper angle from the microscope objective provide stronger trapping forces. Padgett's paper on the trapping efficiency of LG modes in tweezers suggests both that rays coming in at a steeper angle don't improve transverse trapping forces (using a mathematical model) and that LG modes do not significantly improve trapping efficiency. However, in my experimental results, I have found that intensity distributions that have higher intensity rays relative to the central axis of the beam do, in fact, increase trapping efficiency. Even if trapping efficiency is not actually increased, due to truncation of the beam at the microscope objective, my results do suggest that off-axis rays coming in at steeper angles do provide a greater trapping force than the on-axis rays.

I based this mathematical model on the assumption that the beam spot size after focusing from the objective is significantly smaller than the size of the bead--a reasonable assumption, as the spot size should be less than 0.5 μm using my setup, while the latex spheres were ~10 μm. Using the ray-optics model of tweezers, I calculated the change in momentum of a light ray as it either refracted through the latex sphere (Snell's law) or reflected off of the latex sphere, taking into account the theoretical reflection and transmission coefficients as predicted by the Fresnel equations (which took a surprisingly long time for me to figure out).

The following graphs are of the axial and transverse trapping forces on a bead due to a pair of rays at varying angles, assuming (due to small beam spot size) that the two rays hit the same location on the bead. The general idea is to see whether, at the same point on the particle, ray pairs of (a) lesser or (b) steeper angles lead to an overall greater change in momentum of the particle.

In the axial direction, I found as expected that rays coming in at steeper angles lead to a larger backwards gradient force and should increase axial trapping efficiency, as shown in the graph below. It can also be noted from this graph that rays must be coming in from at least 10-15 degrees in order to produce a backwards gradient force--meaning the numerical aperture must be at least 0.23-0.34 to start to balance the scattering force.

Notes on Graph Interpretation:

  • These results are dimensionless, since I'm not quite clear yet on how to calculate the force from a change in momentum (F=Δp/ t , but I'm not sure where to get the time from).
  • The green lines are the x and y axes.
  • The x axis represents the x position of the ray striking the bead, or d/r where d is the x position and r is the bead radius.
  • The y axis represents the change in momentum of the rays, meaning that a positive graph will produce a backwards force on the particle.
  • The red line represents the on-axis rays (theta=0), and each subsequent line increases theta by 5 degrees. (The last theta is 40 degrees, since this is approximately the largest angle that rays can enter at using a NA = 0.85 objective.

    In the transverse direction, I actually found that the trapping force should increase for rays coming in at steeper angles, which is in accordance with my experimental data. This result is evidenced in the graph below. I've 'zoomed in' to the red boxed region to show that, at least near the center of the beam (and up to d/r = 0.5) the higher angled rays have greater forces than the on-axis rays.

    However, this higher change in momentum for off-axis rays is much less pronounced for transverse trapping versus axial trapping. To compare the two, below is a graph of the axial and transverse change in momenta on the same axes.

    The minor issues that I'm having with these models is, firstly, that I'm really not sure how the momentum of light changes when it refracts through a medium. In this model, I'm assuming that the overall magnitude of the momentum of the ray does not change (which should be accurate, since for light p=E/c or p=h/λ and none of these variables actually change). However, the speed of the light does slow down when it goes through a medium of higher IOR--and in classical mechanics, this means that the momentum would decrease. I read a bit more into this, and this article both clarified and confused me a bit more, by basically stipulating that light can either increase or decrease in momentum when travelling through a higher IOR, depending on whether its particle or wave nature is more prominent. I wasn't really sure how to deal with this, or whether it even mattered overall, so I stuck with the assumption that the magnitude of the momentum doesn't change. Secondly, I'm assuming in this model that the particle does not absorb any light and the Fresnel equations apply ideally to the rays.

    I'm not clear based on Padgett's paper whether we're actually comparing the same values in our models, but a possible source for discrepencies (apart from the possibility that some of my assumptions are false) is the regime of optical trapping that we're comparing. As I've talked about before, there are some differences in trapping particles significantly larger than the wavelength of light (the ray-optics regime) and close to the wavelength of light (Lorenz-Mie theory, which incorporates part of the dipole approach). I'm specifically modeling particles that are much larger than the wavelength of light, and there may be major differences in forces when you take into account the electromagnetic forces on a smaller particle.


    Friday, August 16

    I thought I'd do a quick update on the last few days of my time in New York and what I've been up to the past few days. The poster session went well and I got to explain my project to a few people; it was also interesing to see all of the hard work that everyone else had put into their projects.

    After saying some goodbyes, I went to lab for a few hours and was able to get the remaining data that I needed. This was primarily the rest of the videos of the spheres falling out of the trap, using the new mirrors and lenses that came in. This setup has a final power of ~19 mW instead of the original ~10 mW. I now will be able to compare the trapping efficiencies for different orders of vortices, as well as also analyze how these efficiencies relate to the power of the vortex coming out of the objective.

    After arriving back in California, I've kept pretty busy with summer homework and thinking about college, but I've been able to get some work on my tweezers project done the past few days. I spent quite a bit of time trying to calculate the differences in speed that particles in focus (the latex spheres) vs. particles on the miscroscope slide move across my computer screen, as it's the particles on the slide surface that I track to find the speed that the stage was moving. I was able to calculate the theoretical working distance of the objective based on the NA and the objective diameter, which also allowed me to calculate the corrected working difference after the change of the image distance from 160mm to 230mm. However, I realized that if I wanted to calculate the actual depth of the particle in solution I'd have to know how much of the final lens is illuminated at this new distance, since that would change the effective objective diameter--and there's really no way to know that unless you know the internal workings of the objective (length, which sets of lenses are in it and their respective focal lengths, etc.). In summary, by not using the 160mm image distance, the optics become a lot more complicated and I've realized that even if I had data for the axial trap strength, I would only be able to use this comparatively and not quantitatively for an actual accurate force.

    What I was able to actually accomplished was a corrected magnification. Before, I had done a theoretical calculation that had yielded an imaging system magnification of ~3200X. I analyzed pictures of 10 different trapped beads and averaged their heights and widths separately to find a magnification in the x direction of 3040X and in the y direction of 2940X. I repeated this process for a bead on the microscope slide cover when a bead was trapped (which I made sure was at a consistent depth for every trap) and found that the bottom moves ~7.2% faster than the trapped sphere on my screen. This will allow me to make force corrections; I'll make sure to update again when I have all of the forces calculated and graphed.


    Saturday, August 3, 2013

    The last few days have been pretty busy, mostly between analyzing data (which is a lot of ImageJ video editing and quantifying the drag force on particles), uploading pictures and graphs from my computer onto my journal, and trying to work out some of the issues that I've been having. One topic that I've been grappling with recently is the overfilling model for a traditional Gaussian beam, which I actually talked to Dr. Noé about today. If you consider that a Gaussian beam has angled rays in the hyperbolic section of its curve, but then straight wave fronts at the beam waist, it seems that the individual rays must curve--which doesn't make a whole lot of sense. However, if they don't have a straight wavefront, it would be very difficult to make a model to actually find the force on a sphere from light pressure. Furthermore, since a sphere isn't actually at the waist of the beam due to the scattering force, even if the wavefront were straight and all the lines hitting the sphere were parallel at the waist, this wouldn't correspond to their angle where they actually hit the sphere. The angle of the rays, the location of the sphere relative to the beam waist, and the size of the sphere must all be taken into account to make an accurate model.

    We also discussed today how we're unable to trap polystyrene spheres (10 μm), while we are able to trap yeast cells (more like 5 μm). There's a possibility that this has to do with the size of the spheres, as they have twice as big of a diameter as the yeast. However, there are other factors that may affect this, such as the buoyant force vs. gravitational force on the object (due to different densities) or the index of refraction of the different materials. I did a little bit of research, and it seems that while yeast are ~1.1g/mL the spheres are more like 1.05g/mL, so perhaps the greater buoyant force on the yeast helps to lift them from the bottom of the microscope slide (which is where the spheres seem to be stuck). However, the index of refraction of polystyrene spheres is 1.59, while yeast are only 1.49-1.53, which I thought would cause the polystyrene spheres to have a higher trapping efficiency, as rays that are further bent will cause a greater change in momentum. I'll look into this more--either the differences in size and density are more prominent than the index of refraction difference, there's other factors that I'm not taking into account, or my reasoning on how index of refraction affects the trapping efficiency is flawed. Hopefully, though, with new dielectric mirrors and AR coated lenses (which we ordered today!) there will be less power lost and enough power then to trap the spheres.

    The last part of today I realized that my previous method of quantifying (or at least comparing) axial trapping forces for vortices of varying topological charges wouldn't work, because the spheres weren't falling back into the trap due to the trapping force, they were sinking back into the trap because of gravity. The concept of seeing what distance the trap center could be moved and still pull the particle back was flawed anyways, I realized later, since the Ftrap=kx only applies to distances very close to the beam waist. I found a nice graph to demonstrate this principle below.

    (Source)

    I'll have to think of a new way to quantify the axial trapping forces, perhaps by measuring the net force due to buoyancy and gravity, and then measuring how much longer it takes the particles to fall into the trap when there's a beam under it? (I actually discovered today that the scattering force in my setup is actually stronger than the backwards gradient force. However, since this is an inverted setup, gravity helps to trap the particles.) On a brighter note, I was finally able to figure out how to upload the pictures I took on Kevin's camera today and posted them on a new Optical Tweezers Pictures page.


    Thursday, August 1, 2013

    I took more videos today, and these came out a lot better. They were more consistent since I added a mechanism to the rotating motor that slowly sped up the translation stage (depicted below).

    I also started trapping with vortices today. I found the efficiency of the spiral wave plate and all of the components that I hadn't before, using a photodiode with a pinhole hooked up to a voltmeter. I used this data to make a graph of the total system efficiencies:

    I then profiled the vortex beam using a photodiode with a 200 μm pinhole attached to an ammeter. The following are the beam profiles of LG modes 1, 3, 5, and 7. The modes with a second trial were readjusted on the spiral phase plate so that they had a centered intensity profile.

    I tried trapping with this beam, which actually worked fine (and I got data to analyze for the drag force). The transverse trapping force is definitely weaker, as the particles fell out of the trap at much lower speeds. However, I had no issues with particles being pushed away by the scattering force as I had previously, and it seems by observation that the axial trapping force is stronger, although I have no data to back this up. I'm trying to quantify the axial trapping force by seeing how far the beam waist can be moved away from the particle before it doesn't return to the trap.


    Wednesday, July 31, 2013

    I took a lot of videos today and starting analyzing them to find the force, which seems to be somewhere between 2 and 3 pN. (I need to separate data for different particle sizes and trials in order to find a more accurate number, but this seems to be in the right range.)

    Jenny Magnes and three of her students from Vassar College came to our lunch meeting and dinner today and they talked about their work with the diffraction patterns of small worms. I think it was really neat to hear that undergraduates were actually doing this type of research in a field really similar to what we're doing in the LTC right now, and it showed that there is a lot of practical application of optics in fields that are completely unrelated, like biology. Since optical tweezers are another example of optics in biology, I explained briefly how optical tweezers work, and later showed the group my setup.

    After I finish analyzing all of my data this morning using a combination of ImageJ, paint, and Microsoft Excel, I think that there are two main things that I should focus on in the next few days: first, trying to use the spiral phase plate with perhaps 2 or 3 different orders of vortices to compare the trapping force. (I also need to figure out whether I'm going to measure the trapping in the axial direction and take measurements for that.) Second, I want to make a model for the optimal overfilling in the dorms tonight and then test tomorrow two or three beam expanders around that size and show experimentally that it's correct. (I already know qualitatively that 9.5 mm entering the aperture is better than 7.9 mm because the latter was unable to trap particles axially due to too high of a scattering force. (However, it's possible that the lateral trapping force decreased, so that's why I want to test more lengths and compare the two.)

    Since I'll probably actually analyze the data at home, I don't have to worry about this now, but there are a few things that I thought of last night that I need to pay attention to when I actually do analyze it. First, I need to consider the differences in the two speeds that I look at for particles (before and after it falls from the trap) and take into account how far apart they are for error bars, as it could have fallen from the trap anywhere in between the two, and a larger difference in speed gives a larger margin of error. Secondly, I need to make sure I know how far the particle I'm trapping is from the bottom so I can calculate the actual speed of the stage vs. the particle, since the particles I'm tracking to calculate the speed of the stage are at a different depth than the particle itself. Lastly, I need to consider all of the forces that act axially on the particle if I want to calculate the axial trap strength (gravity, buoyant force, etc.) since the particle size would then vary the trapping efficiency.


    Tuesday, July 30, 2013

    Today was a lot of calibration and optimizing my setup. When I first started up the tweezers, I noticed that although a few particles could trap well, many of them would actually come into the trap and then fly out of focus. I realized through refocusing on them that they were being pushed by the radiation pressure of the light, which meant that my traps were often actually not stable and had a scattering force greater than the gradient force. I thought about how to remedy this, and it made sense to try and overfill the objective, as this increases the strength of the outer rays and lessens the strength of the head-on ones.

    The first thing that I tried to fix this was moving Lens 3 back farther. This brings means that the focal point is even farther from the 160 mm, but it overfills the aperture and weakens the scattering force. This actually worked a bit, and the particles stopped flying out of the trap axially, but it also greatly weakened the transverse trapping force to the point where I could barely move the particles at all.

    To remedy this situation, I moved the lens back to 43cm from the objective, which makes the focal point 23 cm away from the objective, and moved the camera to the equal distance in the conjugate plane. I then replaced the 125 mm focal length L2 with a 150 mm lens and moved L1 25 mm towards the laser. The beam was now 1.4 mm*(150 mm/25.4 mm--beam expander)*(230 mm/200 mm--lens 3)=9.50 mm when it entered the objective, raising the gradient force to scattering force ratio, and since the focus of Lens 3 was closer to the 160 mm, the transverse trapping efficiency was preserved with a tighter focus.

    My next step was to finish constructing the motorized translation stage, which I actually ended up taking apart and rebuilding from yesterday, since it was messy and a bit flimsy. My more durable solution involved putting a circle of foam tape in the inside of the cutoff wire spool and putting this on the dials, which made a nice tight seal. I then used a stiff card cut into strips as spokes for an outer cardboard ring, which is the outer 'gear' that attaches with tape to the motor in order to have a slower angular rotation rate than a 1:1 ratio would have. This method actually worked very steadily and keeps the two directions separate, and moves just slightly slower than the maximum speed for the particle to fall out.

    I have three choices for testing the maximum speed of the particle in the fluid:

    1. Using the same particle, I could add a thin layer of tape to the motor in order to increase the angular speed of the stage dials, and thus increasing the speed of the translation stage. I could do this in both the x and y directions until it no longer trapped the particle.

      The good: This will allow me to find a more accurate reading since I'm using the same particle instead of switching them off, so there are no variables like different shapes or indices of refraction. It will also change in small increments, for higher precision.

      The bad: It takes a while to get the trap to a location where the particle can move for distances, so it will take a very long time to successfully measure the drag force.

    2. I could instead use a constant speed and constant laser power and instead find the largest trapped particle that will move at the constant speed without falling out.

      The good: This method would be the quickest, and there are no adjustments to do.

      The bad: It's often easy to accidentally let a particle fall out of the trap and mistake it for too high of a speed when really the particle was just out of focus, or had too high/low of an index of refraction to be trapped in the first place. Also, there may be some difference in the trapping strength as well as the drag force for varying sized particles, so this may be inaccurate.

    3. This method I don't think will actually work, since I tried it today and it didn't seem to be working out--but the idea was to take a polarizer and (since the laser is linearly polarized) turn it to different angles to let different percentages of the laser power through, as I=I0cos2θ where θ is the angle between the light's polarization and the polarizer. When I measured the values of the light passing through the polarizer at varying angles, I got results with 0% error: for a current of 6.40 mA at 0 degrees, 30 degrees was 4.80 mA, 45 degrees was 3.20 mA, 60 degrees was 1.60 mA, and 90 degrees was 0.00 mA, all +- .01 mA. However, this 6.40 mA (compared to 8.89 mA with no polarizer) is already a large power drop that may not provide enough force to trap particles. Furthermore, while this is a 72% efficiency for the polarizer at this stage, when I measured the output currents after the objective with and without the polarizer, they were 1.49 mA and 2.98 mA respectively, which is only 50% efficiency--meaning either that the polarizer somehow affects the angle that the light enters the trap and therefore unlinearly affects the light coming out of the trap, or that the detector doesn't pick up as accurate of readings for lower powers of light.

    I also had some issues today with making the rose chamber. In theory, this should be a nice chamber: the top made of a cover slide, parafilm walls, and a bottom coverslip to hold in the yeast sample. This is made by heating the parafilm donut onto the cover slide, putting a drop of solution in the middle, and then letting the coverslip dry onto it. I had issues getting the coverslip on right: either there was too much solution and it flowed out, making an unsealed chamber, or there was too little solution and air bubbles appeared. Also, this chamber is very thin and most of the particles are stuck to the bottom, so it's hard to find something to actually trap. I emailed Hamsa and asked her about it, and she said that she had overfilled the sample and then to compensate for the evaporating solution (due to the loose seal) she'd just add water. I think that instead, I'm just going to continue to use the method that I've been using, where I have a cover slip over a hole on card paper, so that the cover slip is supported. The only advantage that I can see of a rose chamber is for upright microscopes, but since this tweezers setup uses an inverted microscope, it shouldn't be a problem.

    The rest of the day I spent taking videos of particles moving through solution, both in the x and y directions. I'll be able to use these later to measure the particle size, measure the speed of the particle when it falls from the trap, and from this calculate the trapping force.


    Monday, July 29, 2013

    I remeasured the efficiency of the tweezers setup this morning, using the photodiode attached to the voltmeter again. I was able to get more accurate readings this time by actually visually looking at where the laser dot was on the photodiode and centering it, as well as turning off the lights to eliminate all of the outside noise. This time the conversion factor was 3.53 mW/mA, and the total efficiency of the system was 30%.

    I found a yeast particle and trapped it, and was able to play around with the camera software and take a series of images. I calculated using the magnification of the system that the yeast particle was 7.1 μm.

    On the topic of magnification, I talked to Dr. Noé about why my theoretical calculations may have been off, and we realized that the focus at 3.2 mm isn't the object distance unless the image is at 160 mm. Instead, you can find the focal length using the focal length equation 1/f=1/i+1/o, where i is the image distance and o is the object distance. This means that the focal length of this objective is 3.14 mm. Using this equation once again to find the object distance if the image distance is 210 mm (which it actually is), I calculated the object to be at 3.18 mm, which gives a magnification of M=210 mm/3.18 mm=65.94. While it's nice to know that I have a corrected calculation, this result unfortunately didn't help my margin of error, as this gives a higher system magnification than before, which was already too high.

    I next finished my setup for the stage translation in the x direction. (Once I perfect the x direction, I'll use this model for the y as well.) I calculated about how fast the stage should be moving for the particle to stay in the trap, using the Stokes Drag Theorem equation F=6πηrν for a 7 μm yeast cell in water, assuming the force of the trap was ~5pN. This came out to less than 100 μm/sec, so I realized that with the motor diameter of 13 mm and the dial diameter of 25 mm that translated the stage at 255 μm/sec, I would need to extend the dial diameter to around 90 mm. I looked around for a while and tried a number of designs, before settling on using an empty plastic wire spool and sawing off the large rings on the end, which I then taped to the dial and wrapped in foam tape to make a nice surface for the tape to stick to. I trapped another particle (5 μm) and was able to capture a video of it as it stayed in the trap for around 300 μm travelling at 91 μm/second (which I calculated from the video shown below, as it took 2.71 seconds to cover 2 1280-pixel screen lengths), which means that the trap was greater than 4.3pN (the drag force on the particle). I think that to find the actual trap strength, I'll try an use one consistent particle and attenuate the beam until it falls from the trap, as the trapping force is directly proportional to beam power.


    Saturday, July 27, 2013

    Dr. Noé opened the lab for around an hour today, so Kevin and I came in and I was able to get some work done. I was able to retake the pictures of the Ronchi gratings and find the magnification of objects under the microscope when they appear on the computer screen. The black and white lines came in pairs an average of 1763 pixels wide, which corresponds to 457 mm on the screen. Compared to the actual line width of 150 lines/inch, which is 0.169 mm/line, this is a magnification of 2700X. Although this is a full 17% off from my calculated value of magnification (3270X), the magnification of the lines to the screen seems to be consistent, so although there may be an unknown conversion factor in my calculations that I'm unaware of, my value of 2700X seems to be accurate.

    The second thing that I was able to do was measure the efficiency of the tweezers setup. I first used the power meter, and measured once again 38mW for the laser, 32mW after the first mirror, and 22mW after the 3rd lens. The power meter, however, is bulky enough that I was unable to measure any other values just due to spacing problems. I then used a photodiode attached to an ammeter in order to measure the output current at various places.

    Table of Output Current and Setup Efficiencies

    I'm not sure if the microscope tube and objective measurements are entirely accurate, just due to the difficulty of seeing whether the beam was focused on the photodiode or not. However, these were the highest values that were hit, and they were hit multiple times, so for now they're that best that I could do (although I will probably remeasure these two places later). The output power was calculated using a conversion factor of 3.5 mW/mA, which was calculated by finding the conversion factor that would make 10.8 mA into 38 mW, as these were the consistent output values for the beam directly out of the laser.


    Friday, July 26, 2013

    This morning I finished writing up all of my lab work in my lab notebook, including the calculations for the magnification factors, my motorized stage design, and some old stuff like mirror efficiencies. The camera came in after lunch, and I spend most of the day just learning how to use it and getting better quality images. I had to make a new mount for the camera since the USB port was hitting the microscope's focusing knobs, but this allowed me to actually get the camera a lot closer to the gold mirror. I took a lot of measurements of the inverted microscope and dichroic mirror setup in order to determine how far the 3rd lens had to be to the dichroic, and because of the close placement of the CMOS camera to the gold mirror, this placement was the closest yet to the 160 mm+200 mm that it's been so far. (The lens' focus and camera are both 210 mm away, which is only 5cm off what it would be optimally.) With these positions finally set in place, I finished the scaled diagram of my setup.

    I was also able to successfully trap dirt particles again under the 40x objective, this time viewed on my computer with the new CMOS camera. I realized for the first time today that the dirt particles look so out of focus because the rings around them that I see aren't due to an unfocused camera, but rather the scattered light around them. The particles I've been trapping I think are actually a lot smaller than I believed at first, because I was looking at the rings around them, not the particles themselves. I was able to see the laser light under this new camera, trap particles, and actually take pictures for the first time.

    Laser dot viewed on bottom of cover slip

    Trapped dust particle

    I lastly was able to redo my calculations for the magnification using the new camera setup. I based my theoretical calculations on the same 2-step magnification process as before, with a 210 mm/3.2 mm magnification from the stage to camera and 0.259 mm/5.2 μm magnification for the pixels of a CMOS camera to computer screen (which I looked up online). The product of these two values yielded a 3270x magnification.

    I tried to find the actual magnification through the same Ronchi grating experiment as before, but I seem to be getting that the magnification is only 2694x, which seems way off, especially given that this time I can analyze the pictures with known pixel counts and widths instead of approximating the CCD size with a diffraction pattern experiment. I'll check in lab to make sure that my scaling factor is right and the pictures don't change size when they're saved.


    Thursday, July 25, 2013

    Well, the tweezers worked again today! I think that yesterday I might've either not had enough water on the slide, or possibly had the objective hitting the card holding the cover slip, which would've made the whole viewing plane skewed and made trapping difficult.

    This morning I worked on calculating the image-to-object conversion ratios for the television screen, so that by measuring something on the TV screen, I can tell how large it actually is. I left my lab notebook in the lab, so I don't have numbers for this report, but I can still describe how I went about this process. First, I predicted how big of a magnification there would be. I measured the TV screen width and height, as well as the width and height of the CCD element. The ratio of the dimensions of the CCD to the TV (width and height separately, as the TV stretches the images to fit the screen) are one of the magnification factors of the object's image. The second magnification factor comes from the microscopic objective, which, being 50x with an image plane at 160 mm, means that the 'focal point' of the objective is at 3.2 mm. Since the CCD element was actually closer to 200 mm away, however, the image magnification was more than 50 times--it was 62.5 times. This number, multiplied by the TV to CCD screen size ratio, gives the overall magnifications in the x and y directions both.

    I next made actual measurements of the magnification. The first step of this was to find something very small of known width; in this case, I used a Ronchi grating. The problem was that I didn't know the width of the lines. To find out, I shined a 632.8nm HeNe laser light through the grating and used the measurements of the first order maximum distance and the wall-to-laser distance to calculate the width of each black line. This can be treated somewhat like a double-slit diffraction experiment, so that the width you end up with is double the width of a single stripe. (I actually went back later and used this experiment to measure the width and height of the CCD element, as it was too small to do with a ruler. I set up the Ronchi grating in front of a laser, moved the CCD until the first order maximum was from one edge to the next, measured the distance from the laser, and then calculated how far the first order maximum was.)

    For finding the width of the Ronchi grating lines, the first time I did these calculations, I ended up with 600 lines/mm, which Dr. Noé pointed out to me was not only way off, but should also most likely be in inches and not millimeters. I first realized that using a computer calculator without scientific notation, I had messed up the decimal places and should've had 6 lines/mm. I remeasured the values just to double check, and discovered that the spacing was actually 150 lines/inch, which is equivalent to 5.9 lines/mm, which was why I was getting the value in millimeters before. (6 lines/mm converts to 152.4 lines/inch, which seemed farther off.) Melia and I checked the Ronchi grating next to millimeter tick marks using a magnifying glass, and my calculations seemed right this time. By measuring the width of these stripes on the TV screen (horizontally and vertically) I was able to calculate the magnification once again, and found a relatively low percent difference from my prediction calculations (~2% and 15% for the width and height respectively).

    With the ratios known, I found that the size of the particles I was trapping was quite small, from <2 μm to 4 μm. I also began working on a motorized setup for the translation stage so that I can find the trapping force using the Stokes' Drag Theorem. Even if this isn't the most accurate way of quantifying the trapping motion, it's a relatively simple way to calculate the trap strength and will serve as a good reference point for later methods of quantifying the trapping force. (Like Brownian motion--Dr. Noé bought a 200Hz CMOS camera, which is awesome! I'll learn ImageJ and the camera software tomorrow and hopefully get that all set up to track the bead motion.)

    For this motorized stage, I'm going to be using a very slow rotating constant, single-speed motor that is going to have some sort of band around it, attached to the stage as well. (Like a gear system without the teeth.) I actually made a mistake at first and thought that I needed an intermediate setup with a varying sized gear. After I realized that this part was unnecessary (and had too much friction force to rotate), I eliminated it and the rubber band attached around the two knobs actually was able to slide the stage. However, this was a very jerky movement due to the elasticity of rubber bands. Right before we left, I tried using a loop of tape, and this actually worked very well. William helped me time how long the stage took to move, and we calculated that it was moving at 255 μm per second--so I will have to find a way to slow the stage down to variable speeds.


    Wednesday, July 24, 2013

    This morning I started to write up my alignment procedure for the optical tweezers, which ended up being a lot more thorough than I expected--hopefully this will, along with a revised and scaled diagram of my setup, allow for the tweezers to be recreated or realigned more easily in the future.

    We heard Giovanni from City College talk today about optical vortices and classical entanglement, which was actually one of the most interesting presentations I've heard, partly because I could actually follow the majority of it, and partly because it was on a topic that I'm actually really interested in--optical vortices. Although the entanglement aspect doesn't have a relation to optical tweezers (as opposed to angular momentum, which I'm thinking of implementing in my setup), I found it fascinating, and it'll definitely be a huge field in the future.

    After our lunch meeting, I actually took a few backwards steps today, which was a bit frustrating. At first I was able to trap a dust particle again, but when I tried to put the camera closer to the gold mirror so that I could also move the 3rd lens closer to its focal point and strengthen the trap, I lost sight of the laser beam on the stage. Trying to get the laser back into focus, I think that I used the fine adjustment focusing knobs too much, and ended up thinking that I had broken the microscope since the objective seemed to suddenly be too tall for the stage. Dr. Noé luckily helped me figure out what was wrong, but then the cover slip fell off of the metal mount into the dirt, so I had to wipe it off and put on a new sample. Surprisingly, I couldn't find any dirt on the cover slip to trap, and the beads seem to not want to cooperate, so tomorrow...yeast.

    I realize how little time we have left, so I've been thinking a lot about what I can do with these tweezers. If there's any chance of still doing a project with Brownian motion, I think my best chance would be to actually buy a QPD. I've read quite a bit about this subject, and I know that the frame rate has to be well over 100Hz (at least 300-500Hz, the higher the better), and camera systems with this high of imaging rates are well over $1K... so not only would QPDs be more accurate, but cheaper as well. Until I know more about this option, I'm planning on finding the image-to-object ratio from the actual particle sizes (when in focus) to their size on the television screen, and then use these measurements to quantify the drag force on yeast particles. This will at least give me a rough estimate on the force needed, and if worse comes to worst, I'll have some sort of data from this--perhaps something that I can compare for different topological charges and polarizations of light? :) Giovanni's talk today reminded me that vortices could easily make a very interesting project as well.


    Tuesday, July 23, 2013

    The tweezers worked today! :) In the morning, I was able to look around on the microscope slide and see the laser light focus on both the top and bottom surfaces of the slide. I put some water back on the spheres and could focus the light on them, but I had to use the 20x objective (due to the thickness of the slide) which meant that the NA wasn't high enough to actually trap the objects.

    I ate lunch with some of the LTC members and Urszula, a friend of Dr. Noé's, who had worked with optical tweezers at Stony Brook a while ago after learning about them from Dr. Noé and Yiyi, a former Simon's fellow. She had some helpful pointers about preparing yeast, the thickness of the microscope slide, and general comments about Brownian motion and the issue of outside noise.

    Right after she left, we took a vial of a few milliliters of tap water and put in a drop of the 10 μm polystyrene spheres. We then put a drop of this solution onto a water bead that was on a makeshift coverslip setup, which consisted of a coverslip on top of a metal bracket with a hole (~1 inch) predrilled in the center, and an extra slide placed next to it to make it wide enough to fit the sideways adjuster. It was slightly uneven vertically, as when we focused the laser light on an interface, translating the stage vertically defocused it since the slide was on a slanted piece of metal. The main issue with this setup, however, was that our bead solution is now too diluted and I can't actually find any of the beads.

    I searched around for beads for quite a while, but all that we could find were small circular dirt particles, medium dirt particles, and large oddly shaped dirt particles. Right when I was about to try a different solution, I noticed a small dirt particle that seemed to be moving with the screen. I moved the stage faster, and it broke free, and then when I moved by it again, it trapped! It's easy to tell when something is trapped because a) it stops drifting and b) it stops wiggling as well. I kept one particle in particular trapped for over 15 minutes before I decided to search for a different one, so it seems like a stable trap.

    I could move the particles in the lateral dimensions (x and y) by translating the stage or by moving the mirror slightly (which is more steady than the stage), and I could move it in the Z direction as well by using the focus knob on the stage to move it up and down. I tried moving around some larger particles, which was kind of fun because you could get them to spin a little bit if you only dragged one half. I tried trapping again on the 20x with the thin cover slip, but this still was unsuccessful, because you can barely see the particles on 20x that you're trapping with 40x. I think that tomorrow I'll try growing the yeast and possibly making a rose chamber, so that I can observe slightly larger particles--the dust that I was trapping was no more than 5 μm in diameter. Perhaps larger particles will have more visible Brownian motion--if not, I may have to think about optical vortices as a project (unless we have a QPD) since the motion didn't seem at all visible on the TV screen. The only other way that I could think of would be adding a magnifying lens to the CCD camera as well. It would still be nice to use Brownian motion, as the Stokes' Drag Theorem requires moving the stage at a constant speed, and this would be very difficult given the sensitivity and variability of the stage translation.


    Monday, July 22, 2013

    I spent the first half of the day delving further into the quantification of Brownian motion, which was actually surprisingly productive, as I think that I may finally understand the complete process of analyzing a particle's motion to calculate trap strength. The only part that I don't fully understand is how to calculate the Fourier transform of a nonperiodic function. Other than that, I figure that if I can explain something, I know it, so I'll try to explain the PSD analysis of a Brownian particle in a trap below. It all starts with the Langevin Equation

    where kx represents the harmonic force of the trap, γdy/dt is the damping force of the fluid, and F(t) is the random thermal force. Since the particle overall doesn't go anywhere, these forces are in equilibrium. This is an approximation, but it works well for micrometer sized particles.

    Next we look at the Fourier transforms of F(t) and x(t) (the position of the particle) , which are F(f) and X(f). Because

    the Fourier transform of dx/dt will be -2πifX(f) due to the chain rule when you take the derivative. Defining the characteristic frequency fc=k/2πγ, we can take the Fourier transform of both sides of the Langevin equation to get

    which simplifies down to

    The square of the magnitude of the Fourier transform of a function gives the functions' power spectrum. This means that

    and

    where Sx(f) and SF(f) are the power spectrums of X(f) and F(f) respectively.

    This means that if you square both sides of the transformed Langevin equation, you can substitute in the power spectrums to get

    Because the power spectrum of F(t) is an ideal white noise it is a constant, and F(t)=4γkBT (which I'm not sure why it's equal to that in particular). Using this, we can rearrange the above equation to get

    For f << fc, we can substitute fc for k/2πγ and see that

    while for f >> fc, the functions falls off as 1/f2. When graphed on a log log scale, we can see that you'll get a nice Lorentzian curve that looks like this.

    The top line should have a value

    so if you graph the power spectrum of the Brownian motion of a particle in an optical trap, and find the value of the power spectrum at low frequencies as well as the corner frequency (where the part where it falls off to a slope of -2 intersects with S0) you can find what k equals, which is the trap strength.

    The rest of the day was slightly less successful. I did realign the mirrors so that everything was at right angles to make later adjustments easier, but for some reason when we tried to trap a particle, we couldn't find the laser spot on the interface of slide and air. We fiddled around with the mirror angles and still couldn't find it, so by then the alignment was off and I just started over from the 2nd mirror. I got everything aligned but had to leave before looking for the laser spot again.


    Sunday, July 21, 2013

    On Friday I came to the lab after our Simon's trip to the Brookhaven National Lab and worked on setting up the lenses again. I actually finished all of the alignment, and it seems to be focusing well under the microscopic objective. The only component I'm not sure about is the 3rd lens, which I'm not entirely clear on where it should go on the optical table just due to the difficulty of measuring distances and having way of telling whether what you're doing is correct. (A possible way would be to check the reflection back on to the mirror, but then you'd have to also somehow mark the spot on the dichroic mirror to make sure that it's correct in both directions.)

    Dr. Noé got out some of the 10 μm latex spheres on Friday as well, and we looked around at them a bit on a normal microscope slide by diluting the solution with water. We found that you could actually focus in and out to see spheres at different heights within the solution, and the spheres that were the highest in the solution actually were moving (although this may have been due to convection currents rather than actual Brownian motion). I was a little worried when I saw that if you hit the table or anything surrounding, it caused the whole image to move dramatically. This will make measuring Brownian motion accurately very difficult, and I'll have to either be really careful while collecting data, or find some way to inhibit the vibrations.

    On Sunday I read a lot more about Fourier transforms (which I think I can understand now). I also worked more on the setup diagram for the tweezers, which is shown below.

    Lastly, I did the estimation problem for the week. The question was: How much power could be produced in 12 hours if all of the roofs of Stony Brook were covered in solar panels? Using an estimated 1000mx1000m area for Stony Brook, I said that 5% of campus was covered in roofs. I looked up the intensity of sunlight (1kW/m^2), which, assuming solar panel efficiency of 15%, means that the solar panels covering the roofs would be storing 7.5MW of power. Since we're looking for the amount of energy stored in 12 hours (43200s), this would be 3.2x10^11 J, or 9.0x10^4 kWh--which is actually enough power to run a 100W light bulb for a century.


    Thursday, July 18, 2013

    I thought today was going really well for a bit, when I pretty much had the beam focused through the lens of the objective, could see the As on the diffraction grating in the CCD camera, and was overall good to go. After lunch and Sam's talk on laser safety, however, Dr. Noé stopped by and pointed out that a good way to check whether your beam is centered is to take out the microscopic objective and put a mirror there, to see if the beam reflects back towards the 2nd mirror. I gave this a shot, and soon discovered that although my beam was centered when it left the objective, it wasn't centered going in, and my whole alignment was actually off. I spend a really long time trying to fix the alignment of the dichroic mirror, and eventually realized that the 2nd mirror was part of the problem, so I decided to mount it on an optical rail along with the beam expander.

    Overall, I figured out that my whole beam expander was very slightly misaligned. Being a perfectionist, I decided to realign the expander, which proved to be extremely time consuming. I ended up using two apertures, and never actually finished, so at least I know what I'm doing tomorrow. At least this time I know what I'm doing, and hopefully I won't make the same mistake twice and will try to align everything well in the first place!


    Wednesday, July 17, 2013

    The main project for today was realigning the beam expander, which turned out to be not as aligned as I thought it had been when I put in the second lens. I figured out that when you put in the 25.4 mm focal length lens, it makes a really big spot on the wall that's hard to center. However, if you put in the 125 mm focal length lens first, then it's easier to precisely place the beam in the right position. This, along with using a polarizer to attenuate the beam, made focusing the lenses accurately a lot easier. Even with this new method, however, I found it challenging to get the beam centered, just because the slightest errors in one optical element can make the beam even farther off when you add a new element. In the end, I got the beam very well centered on the far wall, but the reflections from the lenses back onto the mirror seem to be off. I could go back and realign them, but I don't think that at this point it's necessary to be overly precise, so I'll leave them where they are unless an issue comes up.

    We toured Eden's lab just down the hall, which is basically focused on encrypting and reading information for single photons. The setup designs on the tables were incredible to look at, even if I didn't entirely understand what was going on, just for their complexity. I thought what was particularly interesting was the probabilistic nature of what they do: they don't have to create a single photon in their experiments, they only have to create a single photon on average. Another part that I found interesting was the use of an acousto-optic modulator, just because it's always cool when you use two different separate elements like light and sound and use them to manipulate each other.

    I lastly mounted the better gold mirror and set it up on a movable mount, and then attached the dichroic mirror underneath the inverted microscope. I roughly aligned the two mirrors, and actually got the beam to focus through the objective (yay!). After that, we left for dinner, which Dr. Noé was nice enough to take us to. I learned tonight that 'pineapple chicken' at this Chinese restaurant actually means chicken served in half a pineapple. It was really good food, and it was nice to get off campus for once!


    Tuesday, July 16, 2013

    Today was almost all construction and hands-on work, which was a really nice change from all of the reading I've been doing. I started the day by measuring the efficiencies of the different mirrors that I'll be using and mounting the golden mirrors. Marty came by and taught me how to clean mirrors using lens cleaning paper and methanol, which was really helpful. Below is a table of the mirror efficiencies that I recorded, before and/or after cleaning them. (The initial laser output power was measured to be 38mW.)

    My next major task for the day was to get the inverted microscope to work. I figured out how to work the power supply and turn on the illumination source, which Marty and I discovered has a filament that isn't aligned along the optical axis. We tweaked it around a bit until it ended up roughly in the center, which we tested by closing the aperture and seeing whether a bright dot was still visible in the center when it was almost completely closed. After cleaning the heat filter glass in the illumination source, I next set up the gold mirror at a 45 degree angle underneath the objective and put the CCD camera facing towards it.

    I learned today that microscopy is actually a rather imprecise art--although the focal length of the microscopic objective was 160 mm, the CCD camera (without any focusing lenses) was placed almost double the distance and we were still able to produce a clear, focused image by shifting the stage. We successfully viewed a Ronchi diffraction grating by hooking up the CCD camera to a TV monitor, and then viewed the finer images of 30 μm 'A's on a diffraction grating that Rachel gave us. The holes of the A's (5-10 μm) were clearly visible, which is a good sign since this is the size of the least that I'll most likely be using.

    With the microscope now working, I decided to start setting up the rest of the tweezers. I put in place the silver mirror that reflects the laser beam as soon as it comes out of the laser, and aligned it with the 3rd row of holes on the table. I then set up the Keplerian beam expander using two plano-convex lenses, with f1=25.4 mm and f2=125 mm, which gives a 5x magnification and expanded the 1.4 mm beam to almost 7 mm. I looked at the laser point on a far wall as compared to where it had been before the expansion, and it both was still centered and had approximately the correct diameter.

    I worked a bit on tomorrow's pizza lunch presentation, and also made a diagram of my setup on Creately (shown below). Tomorrow I plan on putting into place the aperture to clean up the beam, clean the lenses used in the Keplerian beam expander, and put in the rest of the mirrors and the 3rd lens in order to focus the laser in the microscope.


    Monday, July 15, 2013

    I realized today that I should really find out what I'm going to be doing with optical tweezers and my project before I actual start a definitive setup, since the equipment that I'm using will possibly change the setup, and then I'd just have to redo it. That meant most of the day was going back to theory, which was actually really helpful because I think that after a long afternoon of reading papers I think that I finally understand how the quantification of Brownian motion works (...mostly).

    I read a bit about eigenvalues and eigenfunctions this morning for fun, since I thought that they were more relevant than they actually were. Basically, if you have a matrix A, an eigenvector (v) is a matrix that can be multiplied by matrix A so that A*v=λ*v, where λ is the eigenvalue, some constant. This eigenvector basically doesn't change direction when the transformation matrix A is applied to the system, by means of scaling, rotation, shearing, etc. In the diagram below, for example, the blue and purple vectors are eigenvectors, while the red ones are not. Once you know the eigenvalue of a certain matrix, you can find the eigenvectors that correspond to that eigenvalue by plugging it in to the equation A*v=λ*v and solving the system of equations for the components of eigenvector v.

    I also went back and reviewed complex numbers and polar form, before moving on to Brownian motion. I went through a very large number of articles, and finally figured out that the power density spectrum actually is the Fourier transform of the displacement due to the motion of a Brownian particle, as measured either by a QPD or high frame-rate camera--although a QPD is much preferable, as the sample frequency (which I finally figured out is the x axis of the PSD vs frequency graph!) should be much higher than the corner frequency that the graph drops off at. For traps of weak strength (which I'm pretty sure is what my tweezers will be categorized as compared to the multiple Watt laser traps), it actually might be okay to use a lower sample frequency due to the lower corner frequency of the weaker trap. I actually found a program written for Matlab that takes your position data and automatically makes the PSD vs frequency graph, which was really cool--if I get stuck on any concepts, I could possibly look into the code behind their programs to see the calculations behind it.

    Now that I have a bit more confidence with Brownian motion, I think that I'll be able to come up with an actual project. Dr. Noé and I had talked about quantifying Brownian motion in the axial direction, but as far as I can see, the major problem with this is that you need to be able to see the motion of the particle, which you can't in the axial direction--so far. I had two ideas, one that had to do with Doppler shifts (which would probably be very complicated and hard to detect), or using a single photodiode and getting rid of the condenser on the microscope and using the intensity of the beam that hits the photodiode to calculate the bead's axial position, since the bead acts like a lens and refracts light, so a difference in axial position will change the amount of beam that hits the diode (as long as the beam is always filling at least the whole diode). Again, both of these ideas seem very complex, and I don't really think either would be practical, but I'll ask Dr. Noé about them.

    If neither of these ideas works out, I'm most interested in going back to working with optical vortices--either for optimizing the topological charge vs trap strength for different bead sizes, or for developing a way of trapping beads of lower index of refraction than the surrounding medium in the center of an optical vortex. I went back and read some more about optical vortices today, specifically about creating different charges and orbital angular momentum, and I think it'd be really cool to be able to actual create some sort of rotating optical trap. (If I want to do that, though, I'd probably better start soon.)


    Friday, July 12, 2013

    After reviewing the estimation problem (which we were actually all surprisingly close on) about the angular resolution of the human eye (which turned out to be somewhere around 10^-4, we all went to the conference room and had a meeting. Samantha went over plotting in Python, and afterwards we browsed through some websites like the American Journal of Physics and Optics Info Base. I saw a few interesting articles about Brownian motion in optical traps and optical trapping for undergraduate research labs, so I wrote those down and will read them over the weekend.

    I went back to the graphs of the beam profile from the previous day and calculated from the best fit Gaussian curve what the width of the beam was, which was 1.4 mm in both cases. Since the aperture of the microscopic objective is 6 mm, I chose two lenses that would create a beam expander of approximately the correct magnification (25.4 mm and 125 mm, which magnify the beam to 6.9 mm when placed 150.4 mm apart).

    I decided to get a more accurate reading on the overall beam intensity by using the photodetector along with a translational stage, instead of holding it by hand. This gave a very steady reading, which was 39mW when centered both horizontally and vertically. I also measured the intensity after the silver mirror that I was using, which was 33mW (meaning the mirror has an efficiency of 85%). Since this mirror is fairly inefficient, I think it'd be best to either clean it to reduce extra scattering, or find some gold mirrors that are useable, since they have higher reflectivities than silver mirrors.

    I was able to adjust the mirror to shine almost perfectly perpendicular to the incident laser, by setting up two copper rods and screwing them into the table to make sure that the light hit them both in a row. I used a measuring stick to check the height. I then started putting together the beam expander, which was more of a challenge than I thought it would be since there are so many different adjustable variables that you have to keep track of. One of the main problems that I faced was getting the expanded beam to line up with the original beam direction, due to minute errors in the lens' angle. Once it was expanded, it was clear that the lens was quite dirty and could use some cleaning, as well as an aperture to account for the extra scattering and to clean the beam up.


    Thursday, July 11, 2013

    I read a lot more about Brownian motion today, and I think that I'm starting to have a firmer grasp on how it's detected and the theory behind it--although I'm still not quite sure how you get from the root-mean-square-displacement (which is a measurable quantity by assessing the difference in position of a particle between frames) to the power density spectrum, although I know that it has to do something with Fourier analysis. While I do know what Fourier analysis is, and how to do basics like calculate the coefficients, I need to learn about Fourier transforms and perhaps this will help me.

    Other than that, I spend the rest of the day profiling the intensity of the red HeNe laser that I'll be using for the tweezers. My setup consisted of a photodiode with a 200 μm pinhole, attached to an ammeter to measure the output current from the laser. This was translated across the beam using a horizontally translational stage bolted on top of a vertically translational stage. After I found all of the correct components (which took a surprisingly long time!) and centered the photodiode vertically on the beam (which Dr. Noé later pointed out to me was unnecessary for Gaussian beams), I took preliminary measurements to find the approximate maximum of the beam so that I'd know what intensity I should start my measurements at. My first data set came from moving the stage 0.10 mm at a time, from 0.006mA on one end of the beam to 0.003mA on the other, with a maximum of 0.567mA output. I graphed this in Matlab and came up with a best fit Gaussian curve with the intensity scaled from 0 to 1, I=e^(-((x+0.0004896)/.5092)^2). Using this equation, I calculated the beam width where the intensity dropped off to 1/e^2 to be 1.4 mm.

    As you can see from this graph, however, there were some aberrations in the beam--on the sides, there were regions where the intensity went back up before decreasing again. I talked to Marty about this, and he suggested that perhaps the translational stage had been unsteady, since I was at the very end of it and it seemed to wobble past its maximum extension. I moved the setup around a bit so that I'd have more clearance, realigned the laser, made sure that everything was straight, and then redid the measurements using .05 mm increments. This time, the best fit equation was I=e^(-((x+0.0001968)/.4906)^2), it still had a beam width of 1.4 mm, and there were still regions of higher intensity on the outside of the beam.

    The interesting thing was that when we expanded the laser through a lens and looked at it on a far wall, there didn't seem to be any major aberrations or regions of higher intensity on the outside of the beam. Either the aberrations were at an intensity too low for the eye to detect, or there was some sort of reflection going on at the photodiode, since it was only positioned a few centimeters away from the laser due to lack of table space. Overall, though, the results were at least consistent. A future short math problem that I could do would be to calculate the intensity of the beam using my measured currents and converting them to Watts using the conversion factor for red light on that particular photodiode, and then integrating the volume of a 3D Gaussian intensity profile.


    Wednesday, July 10, 2013

    Today was the pizza meeting, and Samantha gave a presentation on her past experiences in research and her analysis of blue stars in the SDSS, which was really cool to hear about, especially since she made it easy enough for all of us to understand. Afterwards, the LTC group talked about everyone's project ideas and how they were progressing. Dr. Noé also showed us some physics books from as early as the 1800s that he purchased recently, which was neat to see.

    The group discussed the spots that we had seen yesterday on the dichroic mirror. Earlier in the morning, I had realized that there were two different sides to the mirror, and after doing some tests with Kevin, we determined that we had been using the wrong side of the dichroic mirror before--the dots only appear if you shine the laser light on the side with the antireflective coating before the dichroic coating. During our discussion, we hypothesized that the dots were most likely internal reflections due to the imperfect nature of the AR coating, as the light would then bounce between the dichroic material (which reflects a small percentage ~8% of the light) and the AR coating. I thought that perhaps the dots didn't appear on the dichroic side because the small percentage of light that was transmitted through the dichroic coating then wouldn't have enough intensity to be visible when only a small percentage is similarly reflected off of the AR coating. There may be other explanations, though, and it would be interesting to test this as a side project. Dave Battin actually stopped by today and later suggested that the dots might be eliminated by using a half-wave plate to create rotationally polarized light, which we could definitely try.

    The rest of the day was continuing with the construction of our tweezers setup. I used the measurements that I had taken in the morning to make 4 wooden rods with holes on the end to 'sandwich' around the laser, attached to 4 metal posts that Dr. Noé had made in the shop. After splitting a piece of wood and finally learning how to use a vacuum cleaner, I ended up with a setup that actually worked fairly well, as the laser in the end was very secure and almost completely flat (although it could have used a bit of improvement, so I'll go back and readjust it later for accuracy).

    As for actual project ideas, I really do like Dr. Noé's idea of devising a method of quantifying Brownian motion in the axial direction. I'll first have to read a lot more though about Fourier analysis, as this is the basis for finding the PSD of a particle affected by Brownian motion.

    Lastly, we left early to go and visit Melanie Roberts and her lab, where she's building an ultrafast laser. Kevin was particularly interested in this, as he had worked in an ultrafast lab, but I think it was a good experience for me and Samantha as well. I thought it was especially cool because it was a homemade laser, and a fiber laser instead of a more expensive Ti-Sapphire laser, which shows that really you can do a lot with less money if you know how to make the setups. Looking at all of the circuits and breadboards really reminded me of when I did electrical engineering at CTY, which along with the construction of the tweezers makes me remember how much fun physics can be once you start an actual project and can see what's happening.


    Tuesday, July 9, 2013

    Today Melia and I started actually putting together the optical tweezers setup, which was exciting! We started with measuring the intensity of the red HeNe laser that we're using, along with the reflectivity of the dichroic mirror. We used a power meter to measure the laser, which actually wasn't very easy--I learned today that one of the hardest parts about optics projects is actually finding optical elements that work together. We actually ended up holding the detector with our hand, and with the help of Dr. Noé we measured the laser power to be 38mV. After a reflection off of a dichroic mirror angled at 45 degrees, the power of the beam was 35mV, and so we calculated the reflectivity to be 92%. One odd thing that we noticed about this dichroic mirror, though, was that instead of reflecting most of the red light and transmitting a small amount through the mirror, the transmitted beam actually seemed to bounce around in the mirror's interior, forming an array of dots within the mirror that seemed to extend back with decreasing intensity.

    Another odd occurrence came up when we tried to measure the reflectivity of the other side of the dichroic mirror. We actually measured with the power meter that the reflected beam was 43mV, which was higher than our original reading for the laser. Furthermore, when we remeasured the beam directly out of the laser before hitting the dichroic mirror, the output voltage was as high as 44mV. (This would be a reflectivity of 98%.) We thought of two possible explanations for this: (1) it might be possible that the laser beam takes some time to 'warm up', and the laser really was at a higher intensity for the second measuring, or (2) our method of measuring the intensity by angling the detector with our hands was highly inaccurate, and it would be beneficial in the future to set up an actual mounted system for the detector so that we can record precise measurements.

    An interesting side note was that when we used a photodetector to try and measure the beam intensity, by attaching it to an ammeter, we got a very different intensity. (We measured the output current as 11.1A, which for red light was equivalent to around 26mV, assuming that the conversion factor that we used, .43mV/A, was correct.) This further leads to the conclusion that a mounted system for the detectors would allow for greater accuracy, as the two should theoretically have equivalent readings, and in practice should at least be closer.

    We next started to make the beam expander using a 25.4mm and 150 mm focal length plano-convex lenses. We soon realized that the problem with this setup was the we didn't have enough short posts for the optical elements, and that we were going to have to eventually raise the beam anyway to hit the dichroic mirror underneath the microscopic objective (which had to be high enough to have another mirror below it). So, we decided to try and raise the laser. After looking at a few different designs for this, including propping it on honeycomb cardboard and styrofoam (or textbooks), we devised a system of metal supporting rods screwed into the table that could hold the laser fairly stably in all 3 dimensions.

    Front view of laser mount design

    It should work well, as long as we can make all of the right components for it, which I'll work on designing and measuring tomorrow. The only downside to raising the laser is that it will be higher off of the table and more prone to vibrational aberrations, which will be heightened by the flexibility of the tall metal rods.


    Monday, July 8, 2013

    I started off today by completing the estimation problem from last week, which was two parts: (1) Find the distance and focal lengths of two lenses used to expand a beam that could fill the umbilic torus outside, and (2) find the distance at which you'd see the far-field diffraction pattern. After reading about beam expanders, I completed the first part of this problem by estimating the beam width to be ~1 mm and the width of the umbilic torus to be 5m. This makes the magnification M=500, which means the f2=500*f1. Using these focal lengths, I arbitrarily came up with the measurements for a beam expander; I said that if you had the first focal length f1=10 mm, and f2=5m, and you placed them 5.01m apart, then you would be able to fill the aperture. For the second part, since the distance you see far-field (Fraunhofer) diffraction is 2W^2/λ where W is the width of the aperture, and λ=633nm, the wavelength of a red HeNe laser light, I calculated the distance that the far-field diffraction pattern appears at is 80,000km--which is the equivalent of going around the Earth about 4 times.

    After lunch today, we did our first mini project! Since we had learned about beam expanders, and I'm going to be using one in an optical tweezers setup anyway, we made a setup that would expand a 1 mm red HeNe laser beam to 6 mm (since that's the size of a microscopic objective). We did this by using 2 plano-convex mirrors and a Keplerian setup, where the first lens' focal length was 125 mm and the second was 750 mm, and they were placed 875 mm apart (which is f1+f2).

    We then profiled the Gaussian beam by using a photodiode and voltmeter setup, by moving the photodiode (200 μm) across the beam in increments of 100 μm and recording the output voltage, using a 1 MΩ resistor in parallel with the photodiode to amplify the current. After realizing that we were consistently getting 0.3mV because we had forgotten to turn the photodiode on, we were successfully able to graph our data into an approximate Gaussian curve, as intensity versus position, where intensity is scaled so that it reaches 1.

    Marty came over and talked to us about our procedure and results afterwards. He first told us that we could have started profiling the beam a lot closer to the center, since our first 30 data points were all less than 10mV in a graph that goes over 3.0V, so they're rather superfluous. He also went over the aberrations in our data and possible explanations. For example, since there were 2 or more peaks at the top of our graph, perhaps the stage was bumped back a few μm (as it wasn't bolted very tightly), which would cause us to remeasure the intensity of the same peak. Another explanation would be that there were actual physical aberrations in our lens due to extra scattering, which could be tested by putting an aperture at the focus of the beam expander and reprofiling the beam to cut out the extra scattered light.

    We also realized that our beam was a bit wider than we expected, dropping off to 1/e^2 of the peak intensity at around 4 mm in diameter rather than 6 mm. However, this was because we had a very rough approximation of the laser beam width at 1 mm, and it was probably in reality a bit bigger.


    Friday, July 5, 2013

    We talked about the estimation problem this morning, "what volume of rubber is worn off of all the tires in the US in one year"? Kevin and I actually both got 1.2x106, which was surprising; we were all around the same order of magnitude, with William a bit higher and Melia a bit lower (who was actually probably the closest, according to Google). It was a bit of a relief when she used her answer to calculate that if we spread that amount of rubber across the continental US, it would 'only' be 1 μm thick.

    Afterwards, I went more through the big red optical tweezers binder, and read about how the beam that goes through the microscopic objective should actually be diverging in order to account for aberrations, instead of parallel. I found this interesting and it posed a new project idea: which angle of entry optimizes the trapping force? I also went back over Brownian motion, and I think I understand it a lot better now. What's actually measured is the uncalibrated voltage power spectrum, which is represented by Sv(f)=β2Sx(f), where β is the detector sensitivity and Sx(f) is the power spectrum density (which is what is graphed, see entry from July 2). β is found using an approximation for f>>fc, which works out nicely as β=(Sv(f)*π2*γ/kB*T)1/2. This graph gives the corner or 'roll-off' frequency fc, which is the basis of the calculations that finds the 'spring constant' α of the optical trap, where fc=α/2πγ. (γ is the drag force, as described by the Stokes' Drag Theorem.)

    Other than that, I read a bit more about Fourier optics, covering the structure of a periodic wave and how to find Fourier constants. The book that I was reading, 'Who Is Fourier? A Mathematical Adventure' had an interesting section on the vowels of the Japanese language, which included something called a formant diamond, which was pretty cool. I got into some basic vector math before I ran out of time, but I'll definitely get back to this later.


    Wednesday, July 3, 2013

    Today was pretty uneventful, with the morning mostly consisting of reading. I added to my ideas page a new idea that I got from a reference on an article that Dr. Noé sent me. This was about how instead of having a particle with a high refractive index, you could actually use the optical vortex in the center of an LG beam to trap a low index of refraction particle--something that hasn't been done much, but could have potential application in drug transportation. I'd definitely be interested in exploring this more, if not potentially doing my project on this.

    Other than that, I just went over more of the papers in the 'optical tweezers' binders and found a lot of good references for equations on calculating the trap forces. The problem is that a lot of the papers don't really seem to agree with each other, especially in the sections on Brownian motion. (Which means that I'm probably just interpreting something wrong.) Overall though, I think that my understanding is getting better, and reading more from new sources definitely helps. I also read about spiral phase plates.

    We ate lunch at the hospital which was really nice (and filling!) and when we got back, we explored the LTC a bit. Melia and Rachel made diffraction patterns through circle, triangle, and square apertures. (The triangular one looked really cool.) We then looked at some diffraction gratings, lenses, lasers, beam splitters, etc. just for fun.


    Tuesday, July 2, 2013

    Today we heard a talk by Dr. Simmerling about his work in modeling protein-folding and DNA repair, as well as the basic path to becoming a scientist. It was interesting to hear what he had to say, especially about how the most important thing about science is to really be excited about what you're doing. He also advised us to not focus too narrowly into biology, physics, etc. and instead try to create your own unique subset of science at the interface of multiple subjects, as this is the cutting edge of modern science.

    When we got back to the lab, I was actually pretty productive. In the morning, Melia showed us how to do estimation problems and gave us one for 'homework', so I finished that. I also finally started looking through the optical tweezers binders in the back room and got through almost all of them; they had some very useful articles, and it was really nice to be given relevant articles without having to scroll through Google search. They have some useful calculations for the actual setups of tweezers, which I'm sure I'll find helpful later.

    I spent a good portion of the day going over the quantification of Brownian motion. Basically, an optical trap has the basic form of Felectric=κx, where x is the displacement from the center of the beam. You can use this to solve for trap efficiency Q, along with the equation Q=Fc/Pn, (F is the optical trap force, c is the speed of light, P is the initial laser beam power, n is the index of refraction of the medium of the trap). To find the Felectric, you must map the Brownian motion of the particle based on the displacement power spectrum as measured by the QPD or imaging device (since the voltage power spectrum Sv(f)=β2Sx(f), where Sx(f) is the displacement power spectrum and β is the detector sensitivity. β must actually also be calculated by using the equation

    where kB is the Boltzmann constant, T is the temperature, γ is the drag coefficient as determined by the Stokes' Drag Theorem, where γ=6πηr (η is the fluid viscosity), and Pv is the plateau value approximated by the following graph that follows the shape of a Lorentzian.

    I actually just noticed that the power displacement spectrum Sx(f)=kBT/γπ2(fc2+f2), which is weird because if you plug that in to the original equation that I had, you get that Sv(f)=Pv/(fc2+f2), (which is weird because so much cancels out, but it seems to work), where fc is the corner frequency of the above graph, which splits the graph into 2 sections: the first (lower frequency) has a constant power density spectrum (I think that this is the plateau value?) and the second (higher frequency) decays as 1/f2. Well, now I just feel like I have a ton of equations floating around (including the Langevin equation κΔx+γdx/dt=Fstoch(t) where the Fstoch is the random thermal force, which is supposedly important, although I have no idea where it fits in here), and I'm really not entirely sure what they all mean, but I guess I'll read some more and figure that out tomorrow.

    Other than that, I started reading a bit about Fourier transforms, but then I realized the paper I was reading was so confusing because there were a bunch of blanks with missing words and equation terms--I should probably look at an actual textbook sometime, like the one that Melia suggested that I saw in Dr. Noé's office.


    Monday, July 1, 2013

    Today was all reading; I basically clarified a lot of concepts that I was shaky on, started learning some math, and wrote down what I know about tweezers in an organized manner. I started out by reading an article on how to improve the quantification of Brownian motion, which will probably be useful if I choose to use Brownian motion as a method of determining trap strength. (Once I find out how the Brownian motion calculations actually work.)

    After all this time, I also finally had something click and I realized that there really was a reason why new experiments suggesting underfilling and old experiments suggesting overfilling clashed: different rules do apply for particles of different sizes after all. It was nice to get some sort of confirmation on that topic, since it had been bothering me. I wrote down everything that I know about the different setups for optical tweezing, and this is a short list of what I came up with, with a (?) denoting what I should probably read more about:

  • Small Particles
    1. These are in the Rayleigh range, where d < < λ.
    2. They fit the dipole approximation.
    3. The trap is diffraction-limited because the particle is so small. (?)
    4. Optical vortices don't improve trap strength because the particle would be in a region of no intensity.
    5. Underfilling the aperture is preferable. (?)
  • Medium Particles
    1. They are in between the Rayleigh and Mie regimes, where d is ~λ
    2. This is the size of most biological particles that studies are being done on.
    3. Particles don't fit either the dipole approximation or the ray-optics model.
    4. Vortices have been determined through experimentation to strengthen the trap axially (for particles >2μm, although it is unknown whether they help with lateral forces.
    5. Underfilling helps both axial and lateral trapping forces.
  • Large Particles
    1. These particles are in the Mie regime, where d > > λ.
    2. Vortices improve trapping strength axially, and it is unknown whether they help laterally. (?)
    3. Overfilling improves trap strength, which is where the original theories about overfilling stem from. (?)

    Hopefully this will help me with my ideas, as I'm thinking that I could do a project on the optimization of an optical tweezers trap perhaps using parameters that haven't yet been tested, comparing particles of different sizes, or by changing the topological charge of an optical vortex.

    Anyway, apart from these clarifications that I put down on paper, I learned some basic math that I'll definitely find necessary. Most of it was about the structure of Gaussian beams, and the notation used to describe them. In the image below

    w0 is the beam width (from the axis of propagation to the point where I=I0e-2, and w(z) is the beam width defined by the same parameters, at any point z from the center of the beam waist. The Rayleigh range, or zR is the distance from the beam waist to where the area of the wavefront is double the area at the beam waist, so w(zR)=rt(2)w0. I also read a bit about Gouy phase shifts, the radius of curvature of a Gaussian beam, and the complex beam parameter 'q', which helps to calculate the properties of a Gaussian wave at any point along its propagation, by using ray transfer matrix analysis (which I may read about more, especially if it's relevant).


    Friday, June 28, 2013

    We started out today with a whiteboard discussion about the equation that describes a spherical light wave using complex notation, and applying it to the double-slit diffraction experiment. The interference pattern on a far wall has an intensity

    where Ap is the sum of the amplitudes of both waves, Ap' is the complex conjugate of the amplitude, k=2π/λ, and d1 and d2 are the distances traveled by the light from each slit respectively. We then used Euler's equation and the binomial expansion approximation to simplify this equation down to

    for two slits separated by length a that is much smaller than the distance L to the screen, where the distance from the center to the first maximum is y. This is actually really cool, because it means that the interference pattern has the shape of a cosine wave with an intensity between 0 and 4 times the original intensity from one slit. We lastly went over the small angle approximation, which basically says that a very small arc can be treated as a straight line in order to find the angle measure in radians. A laser beam, for example, generally produces a 1 cm diameter beam at 10m, so it has an angle measure of 1 milliradian.

    After our whiteboard talk, I went back to reading about optical tweezers. I found some interesting new articles about how truncating the beam with an aperture before it reaches the microscope objective actually increases the trap strength, so I started my ideas page for my actual project. This took the rest of the day until around 4:30, when we went to the Physics department barbeque, which was a lot of fun. (Plus free food.)


    Thursday, June 27, 2013

    Today consisted pretty much of reading articles about the optimization of optical tweezers trap strength, spatial light modulators, and holographic optical tweezers (apart from our trip to the lab safety lecture). I found out quickly this morning that using calculus to find the scattering and gradient forces would actually be a lot more complicated than I had initially expected, since I'd have to take into account the angle that each beam was coming in from, where the particle would be located (as it has to be slightly past the beam waist), etc. I also found out by reading articles online that experiments have been done recently that actually point to the idea that perhaps it's better to underfill the objective's aperture. This is because a narrower beam will have a stronger lateral trap, as less power is lost than in overfilling, and the light is more concentrated. So in the end, the ideal filling of the aperture depends on whether you want to focus on axial or lateral trapping strength, and there isn't really a definitive answer to this question.

    Dr. Noé showed me brianjford.com, which is a website that includes a cool article about Leeuwenhoek microscopes, which are basically very primitive magnifying devices (the first microscopes), made in the mid-17th century. Leeuwenhoek was actually able to see specimen as small as red blood cells, which is incredible for the limited technology they had at that time. On a similar note, I checked out the website of a previous LTC student who also created a simple microscope, but out of a water droplet.

    I read a bit more about optical vortices, since they come up a lot in the papers about optical tweezers. Apparently, optical vortices also decrease lateral trap strength while increasing axial trap strength, furthering my previous observations about the difference between these two forces. I also learned how spatial light modulators play a huge part in holographic optical tweezers, although even after reading many papers I'm still not quite sure how. I was also a little confused by all of the references to Fourier optics, which I haven't studied at all yet. I think it will probably be useful tomorrow to look at some actual articles in print rather than just online, or read through some of the textbooks specifically for optics.


    Wednesday, June 26, 2013

    Today we had our presentations at noon in the conference room, so the morning was mostly spent reviewing what we had written and making sure that our Powerpoints worked on the projector. The talks all went well! Everybody had something unique to say, which kept things interesting despite the fact that I had limited knowledge about the topics discussed.

    The following talk on research ethics took up most of our lab time, and we got back around 4pm. Dr. Noé and Marty Cohen showed me the poster on the wall about the cooling of neutral atoms and pictures of the Nobel Prize ceremony in 1997, which was actually really inspiring to see.

    Afterwards, Dr. Noé talked to me a bit about possible directions for my project, which included optical tweezers (which I had given my talk about). We went over the function of a Gaussian beam in Excel and plotted its intensity versus radius for a set aperture width, and tried to find out how to overfill the aperture to maximize the trapping force. While we came up with two approximations, they both had their flaws. The first idea, which was to only look at the trapping force as a function of the intensity of the outermost beam (which is what provides the backwards gradient force), neglected to recognize the weakening of the scattering force as the beam widened. The second idea was to find the ratio of the intensities of the outermost beam to the center beam, which could give a better approximation. However, the problem was that this didn't take into account that there are more points on a wave front on the outside than in the center, and so our solution was that you should overfill an infinite amount. This did allow us to come to the conclusion, though, that there should probably be more of an overfill than what the first method would suggest. To figure out the exact dimensions, one would need to use calculus, which I might start working on for fun tomorrow.

    The other ideas that Dr. Noé gave me to consider were using Brownian motion as a method of detecting trap strength (as opposed to measuring the drag force in a fluid) while still using a simpler detection system than a quadrant photodiode (simpler is usually better!), and whether it's possible to create an doughnut beam by using apodization or a similar concept. I'll definitely look into both of these tomorrow, and also read about Maxwell's equations and try to understand them, as I started to look them over earlier today.


    Tuesday, June 25, 2013

    Today we started off by discussing Huygens's principle and interference (not diffraction!) patterns caused by double-slit and single-slit interference. The difference between diffraction and interference patterns is technically that diffraction is from one source while interference is from multiple beams, even though often interference patterns (such as the slit experiments) are caused by the diffraction of light.

    After some more brief discussions about osculating curves, Airy waves, and quantum numbers, we got to work on our presentations for Wednesday. My Introduction to Optical Tweezers is on the evolution of optical trapping and the basic physical principles behind optical tweezers. Dr. Noé showed me a previous student's project that had to do with overfilling the objective of a microscope in an optical tweezers setup to idealize the beam that was focused to trap the sample. Overfilling is useful because then the beams that are responsible for the gradient force (the outside beams) are more intense than if the fringes of the beam were used, and thus create a stronger trapping force compared to the scattering force.

    My readings on optical tweezers were actually really useful in clarifying some of the concepts that I had been unsure of before, like the use of a quadrant photodiode as a position detector for the beam, and how the particle is actually suspended in 3D space using a fluid compartment. Hamsa's Paper on her inverted optical tweezers setup really helped me to understand the actual practical creation of an optical trap, as well as possible ways to measure their effectiveness. However, when I started reading further about optical vortices, I got really sidetracked by a lot of other interesting topics that seemed to keep on branching off into other fields.

    After all the material I read today, there were a lot of topics that I wasn't able to cover or didn't completely understand. (Note: read more about using optical fibers and their usage in trapping, birefringence (they came up a lot in the tweezers setups), different laser modes (like HG, LG, Bessel, and CV beams), q-plates and liquid crystals.)

    The main idea that I spent a while trying to understand and wasn't quite able to figure out conceptually was the actual difference in what is caused by spin angular momentum versus orbital angular momentum. I know that spin is for the photon itself, while orbital is for the path of the photon. The two together must be conserved, and can be transferred (such as when a photon is absorbed). What I got stuck on was the idea of polarized light and how circularly polarized light was caused by the spin of the photon, and yet it could be split (for example, by birefringent prisms) which doesn't seem to make sense, since you can have two separate electromagnetic waves displaced from each other that are both from the same proton. Maybe William's presentation will make things more clear.


    Monday, June 24, 2013

    Today was the first day of the Simons program. After the opening breakfast we went down to the Laser Teaching Center and Dr. Noé showed us some neat optical phenomena like the interference pattern from an interferometer, the 3D image of a pig formed by two concave mirrors, and various demonstrations with polarized light. One of these, which included placing a circularly-polarizing filter in front of a mirror, showed how circularly polarized light has a certain direction of rotation since the reflected light (with the same direction of rotation) could not pass back through the filter, because it was coming from the opposite direction. This is different from linearly polarized light, which when reflected, still can pass through the filter. (The electromagnetic field of linearly polarized light appears the same from the front and back, since a line cannot be inverted, so it doesn't matter which direction the light passes through the filter.) We lastly burned some holes in black paper with magnifying glasses outside before lunch.

    After lunch, we talked about the presentations that we're going to give on Wednesday and titled them. I realized that I still don't know a lot of the technical details about optical tweezers, so I'm going to read some more about their set-ups tonight. Dr. Noé suggested that I look at the work done by Arthur Ashkin and Steven Chu, who were the ones that broke through with the single-beam optical traps. We also discussed Linux, our webpages, and research journals. While it'll probably take some time to get used to keeping a neat research journal, it's also definitely a good idea, as organization hasn't ever been my strongest suit. Overall, I'm excited to start reading and learning more in the LTC!