ECEN 4606, UNDERGRADUATE OPTICS LAB

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1 ECEN 4606, UNDERGRADUATE OPTICS LAB Lab 1: Basic optics lab skills Original version: Dr. Cundiff and Edward McKenna, 1/15/04 SUMMARY: In this lab, you will take the raw beam out a laser and prepare it for use. In the process, you will learn the basic skills required to perform common tasks in an optics experiment. Much of this material can be understood through basic geometry (e.g. the manipulations of laser beams as perfectly straight rays) or Fourier transforms (e.g. the focusing of light). In general, our lab time is limited, so you will not make much progress with cut and try approaches. THINK about what you want to accomplish, perhaps do a quick CALCULATION to derive component distances or focal lengths, then CAREFULLY mount the components to the table in a stable way and TAKE AND RECORD the data you need. The helium-neon laser on your table puts out a beam similar to a common laser pointer. There are three things wrong with this beam: 1. The beam is not precisely located (x,y) or pointed (θ x, θ y ) 2. The beam has unwanted amplitude and phase variations on its profile 3. The beam diameter is too small You will address each of these in turn by 1. Periscope alignment 2. Low-pass spatial filtering 3. Collimation PRELAB DESIGN: Since this is the first lab, it is a long and complete write up. Read and understand this material before you go into lab or you will spend the entire lab time reading. If you don t understand something, try to figure it out before lab. One way to do this is to read the appropriate textbook and lecture notes sections. Do the prelab designs and have these well documented in your lab book when you come into the lab so that the TA can check it. PROBLEM 1: Design a spatial filter for the Helium Neon laser including the distance, L, from the laser to the objective, the objective choice and the pinhole diameter. Details of this problem are included in step 2 of the lab procedure. PROBLEM 2: Using graphical ray tracing, show that a short focal length objective lens and a longer focal length collimation lens separated by the sum of their focal lengths will expand an incident collimated beam to a larger collimated beam. Using geometry on this drawing, find the magnification ratio (size of the output over size of the input beam). If the first lens is your spatial filter objective and the second collimating lens is one of Version 2.1, 8/27/09 Robert McLeod 1

2 those listed in the equipment section below, what is the range of collimated beam diameters you can achieve? Note that if you want a large beam in a small package, you need a very short focal length objective lens, which can be problematic. TECHNICAL RESOURCES: TEXTBOOK: Chapter 27, Characteristics of Laser Beams LECTURE NOTES: Lecture 1, from Maxwell to Optics. EQUIPMENT AVAILABLE: Microscope objectives: 5X, 10X, 20X Pinholes: 10, 15 and 25 µm diameters Collimation lenses: focal lengths of 50, 100 and 250 mm JDS Uniphase 1103P-3020 Helium Neon laser. The laser wavelength is 633 nm. According to the spec sheet, the beam divergence is 1.3 mrad (full angle), 1/e 2 intensity beam diameter is 0.63 mm. However, we have measured the beam diameter and found that it is closer to 0.65 mm, so use that instead. Spatial filter and lens mounts. Irises. Shear-plate collimation tester LAB PROCEDURE: STEP 0: LASER SAFETY AND OPTICS HANDLING 1. THINK. Think before you place or remove an optic in the beam (Where will the reflection go?). Think before you grab a mount (Where is the delicate coating relative to my fingers?) Think if you know what you are doing (Ask!). 2. AVOID BLINDING YOURSELF OR OTHERS. Keep all beams on the table by using beam blocks. Remove shiny rings, bracelets or anything that might swing off of your body and through the beam. NEVER put your eyes at table level with them open when you reach for your dropped pencil, get in the habit of closing your eyes, then opening them below table level. Reverse this on the way up. Do not sit in the lab with your eyes at table level. Do not spray a beam around the room with a loose mirror. Get in this habit, even if the beams you are working with are both visible and weak. Someday they might not be. 3. DO NOT DAMAGE THE OPTICS. The equipment in the lab would cost about $1M to replace. Even a coated singlet lens can cost several hundred dollars. The coatings are very delicate and are always degraded when cleaned. You must learn to handle the optics correctly in order to participate in the lab. If you destroy or damage equipment and the TA believes this was due to negligence, you will fail that lab session. If you do this multiple times, I will kick you out of the class. a. No food or drink in the lab. Ever. b. If you have a cold, bring tissues and use them. Step outside the lab if you need to. Don t coat either the optics or your lab mates with DNA samples. Sneezes and their by-products are the most common contaminant of optical surfaces. Version 2.1, 8/27/09 Robert McLeod 2

3 c. Do not touch optical surfaces with your skin. The oil in your skin can permanently damage the coatings and will certainly screw up your experiment. i. Pick up mounted components by the mount. ii. Be careful not to accidentally brush your hand across a mounted component on the table. Think before you move. iii. If you need to mount or unmount an optic, have your TA show you how this is done. If you don t feel confident, ask for their help. Always use a folded lens tissue as a shield between you and the optical surfaces. Touch the lens tissue by its edges the lens tissue will absorb you skin oils and transfer them to the lens. Be prepared for accidentally dropping the optic - place a pillow of lens tissue on the table and keep the optic above it. Handle the unmounted optic only by its non-functional surfaces and at the edges. d. Do not touch optical surfaces with anything else, either. i. Don t lay optics down on their faces except on lens tissue or in their packages. NEVER lay any optic face down on the steel table this is begging for scratches and dust. ii. Bolt all mounted components to the table so they can t be knocked over. Designate an out-of-the-way part of the table as bone yard where you keep unused mounted components lightly bolted to the table. iii. Be careful moving any equipment (wrenches, oscilloscopes) around the table. Imagine that there are thousands of dollars of delicate glass parts sitting there with no protection. This shouldn t be a stretch, because it s true. e. The mechanics are moderately hard to damage, but be careful with steel screws don t over-torque them, don t cross thread them, use washers under screws so the head doesn t chew up the mount. 4. NEATNESS COUNTS. Keep the optical table organized - put all the unused optics in a boneyard, lightly screwed to the table. Put your wrenches back in their holder, even during the lab. Keep anything that isn t optics off of the table electronics go in the overhead rack, notebooks go on the lab benches. Put backpacks and coats somewhere out of the way so you won t trip over them in the dark. Accidents are much more common when a workspace is cluttered. When you are done with the lab, return it to a pristine state move the optics back to the boneyard, discard any papers or trash and generally tidy up. Whenever the TA or I witness you violating these rules, we will stop the surrounding students and point out your mistake. This will serve to educate your colleagues and embarrass you. STEP 1: ALIGN THE LASER BEAM TO A DESIRED AXIS The first step in any laser experiment is getting the beam to enter your experiment at a known position and angle. Since this includes 2 transverse positions and 2 angles, there Version 2.1, 8/27/09 Robert McLeod 3

4 are a total of 2+2=4 degrees of freedom. We thus need 4 measurements and 4 controls (knobs). Think about this, it s important to learn to think this way about laser beams. First we ll establish the measurement tools. Set up two mirrors on tip/tilt mirror mounts in a periscope arrangement as shown below. Mount 3 identical irises on 3 identical post holders with no height adjustment so that you know they are exactly the same height, roughly 6 off of the table. Set one aside for later. Place one iris fairly near M2 (this is a good idea why?) and one as far down the table as possible. To get good angular resolution, you d like as much distance as possible between the two irises. Your job is now to get the laser to go precisely through these two irises. Adjust the mirrors so that the laser hits the center of the first iris. Close the iris as tightly as possible (but don t break it!) and observe the diffraction rings (a bull s-eye pattern) after the iris using a piece of paper. You want to center this bull s-eye on the second iris. You now have 4 knobs (tip+tilt on each mirror mount) and 4 measurements (x+y on each iris). The system is coupled - each mirror knob adjusts position on both irises. Fortunately, only two at a time are coupled (x rotations to x positions, y to y). Think about the system, then iterate until you perfectly center the beam on both irises. This is the foundation of all later experiments, so you want it done well. M2 Iris 1 Iris 2 M1 Figure 1. Component layout for laser beam alignment. Make sure you will be able to insert your spatial filter a distance L after the laser (see Figure 5) according to your prelab design. In your lab book: Sketch your layout including distances and components. Briefly describe your alignment procedure for your future reference. Use simple geometry to estimate the position and angular accuracy that you obtained. In the limit of large distance, the size of the beam on the second iris will increase linearly with distance. How does distance change the product of the position and angular accuracies? This is called the Heisenberg Uncertainly Principle. STEP 2: SPATIAL FILTER THE BEAM. For our later experiments, we want a beam which is flat phase (a plane wave) and uniform in amplitude except for a smooth, Gaussian envelope. The beam from the HeNe Version 2.1, 8/27/09 Robert McLeod 4

5 laser is good, but not good enough. To make it better, we will low-pass filter the beam in spatial frequency in order to remove any high spatial frequency variations. We will do this by taking the Fourier transform of the laser beam and passing this through a low-pass filter in the Fourier domain. This is followed by an inverse Fourier transform, just as in circuit analysis. The figure below illustrates how a single lens takes a Fourier transform. In the diagram on top, a plane wave in the front focal plane incident at an angle θ is focused by a lens of focal length F to a single spot in the back focal plane. As is shown in the electric field plots on the bottom, the distribution in the front focal plane (vs. x) is uniform in amplitude and has a sinusoidal phase. The distribution in the back focal plane (vs. x' ) is a focused spot. This mapping from a sinusoidal phase to a delta function is the foundation of a Fourier transform. The geometry shown allows one to derive the relationship between physical location in the back focal plane (x') and the Fourier spatial frequency (f), f 1 [ ] m x Fλ =. [Eq. 1] 0 Version 2.1, 8/27/09 Robert McLeod 5

6 x x F E E 0 ( x, z) e j ( k x+ k z ) x = z λ F Λ θ Λ E Λ = λ sinθ ( E) ( x,0) = E e 2π j x Λ 0 x λ f x = Fλ λ x = F sin θ = F Λ Fourier Transform λ E = E 0δ x F Λ 1 = E0δ f Λ x arg E Figure 2. Fourier optics applied to an infinite plane-wave being focused by an ideal lens to an infinitely small focused spot (top). The plane wave is shown as finite to conserve paper. This can be viewed as a Fourier transform of a sine-wave to a delta function (bottom) with an appropriate scaling of the coordinates. This can be employed to apply a low-pass spatial filter to a laser beam using basic Fourier-domain filtering concepts. First the beam is focused (Fourier transformed). In the back focal (Fourier) plane, a pinhole is used to pass the on-axis light (low spatial frequencies) and block the off-axis light (high spatial frequencies). The focused beam must then be collimated with a subsequent lens which performs the inverse Fourier transform (step 3, below). All that is required now is to design the filter. We need to pick the lens focal length F (which sets the scale of the Fourier transform plane by Eq. 1) and the pinhole diameter D (which determines the cutoff frequency of our low-pass filter in that plane). We won t have too many choices of these parameters they will be determined by the discrete set of objectives and pinholes we have available. So it will be handy to have one analog knob (in contrast to these two discrete choices) that can make the design work. That knob is the laser beam diameter, d. The beam exits the laser with an initial beam diameter d HeNe and a divergence half-angle θ HeNe. A distance down the table, the beam diameter at the front focal plane of our lens is thus Version 2.1, 8/27/09 Robert McLeod 6

7 d = d + 2θ L, [Eq 2] HeNe HeNe where L is the distance from the laser to the lens. We can thus use this distance to adjust the beam diameter, d, in order to use a limited set of optics. Assuming we have done this adjustment and the beam has a diameter d at the front focal plane of our Fourier transform lens, Figure 2 shows the distribution of the focused spot in the Fourier plane. This Airy disk is the 2D Fourier transform of a uniform circular beam. It is the 2D analog of a sync (sin x / x) function which is the 1D Fourier transform of a rect function. Note an important quantity which shows up in the equations below which is the numerical aperture (NA) of the cone of light, which is defined as the sin of the largest angle in the focusing cone of rays, NA = d/(2 F). r 2π λ 0 ( 0, y, z) 2 E d 2 = F d = 2r 1.22 y λ0 d 2 F λ0 = 1.22 NA [Eq 3] ( x, y, F ) 2 E d 2 sin F d d y d 2 2π F λ 0 Lens F z x d 2 2π F Figure 3. Intensity distribution at the focus of a lens illuminated by a top hat beam with uniform intensity inside a diameter d and zero elsewhere. The right-hand plot is in a normalized coordinate system that applies to any beam diameter, focal length and wavelength. The optimal pinhole diameter D is between λ 0 /NA and 1.22 λ 0 /NA. Common pinholes come in diameters of 5, 10, 15, 25 and 50 [µm]. Common objectives are given in Table 1. This gives us all the pieces we need to design the spatial filter which consists of the λ 0 Version 2.1, 8/27/09 Robert McLeod 7

8 distance L from the laser to the object, the objective power or focal length F and the pinhole diameter D. Table 1. Typical microscope objective specifications [1]. Note that NA in this spec table is the maximum NA that is passed by the lens. In use as a spatial filter objective, the NA of the focused beam will be significantly less than this maximum because the incoming beam diameter d will be much less than the clear aperture of the objective. Power NA F [mm] Working dist [mm] Clear Aperture [mm] 5x x x x x PRELAB DESIGN PROBLEM 1: Design your spatial filter for this laser. Consider objectives of 5x, 10x and 20x, determine the best pinhole diameter D to use and what distance L that is required. When picking your final design, remember you want the beam aligned to the table before you spatial filter it, so your periscope (see Figure 1) will come first this constrains your design. How does the choice of objective impact a) the difficulty of the pinhole alignment and b) the size of your eventual collimated beam given a fixed set of collimation lenses? This is a common trade-off. PROCEDURE: Set up and align your spatial filter. This is a very delicate (probably the most delicate) alignment in a typical optical setup, so we will use a specialized mount that holds both the objective and the pinhole, as shown in Figure 5. This provides the required degrees of freedom and keeps these two components accurately positioned relative to one another. Figure 4. Spatial filter mounts. The microscope objective is on the left and the pinhole is on the right in both cases. The left mount is a 5 degree-of-freedom mount and the right mount is the 3 degree-offreedom mount. Version 2.1, 8/27/09 Robert McLeod 8

9 Place a third iris (aligned to the beam) a few inches in front of the objective so that you can see reflections from the back of the objective on the right side of the iris. Your optical setup will look like this: M2 Iris 1 Iris 3 Iris 2 M1 L Obj. P.H. Steps: Figure 5. Component layout for spatial filtering. a. Use the detector to measure the total laser power. Remember to check that the meter is adjusted for this wavelength. b. For the 5-Axis spatial filter insert the objective and pinhole into the assembly. Note: For the 3-Axis spatial filter start at step e. c. Hold the assembly up to a low power white light source and look through the objective. Adjust the X-Y position of the pinhole so that the white light source (room lighting) is visible and centered in the objective. d. Using the knurled ring, adjust the ring until the light is in focus. e. Insert the spatial filter after the HeNe and monitor the reflection off of the objective lens onto iris #3 to make sure that the beam is normally incident on the objective. That is, the light that is focused by the objective onto the metal of the pinhole should retroreflect onto the laser at the laser aperture. If the reflected spot is far from the laser aperture, adjust the spatial filter orientation. f. Turn the room lights off and look at the front of the pinhole (OBLIQLY NEVER PUT YOUR HEAD AT TABLE LEVEL). You should see a dim red gleam from the pinhole. Adjust the pinhole position to maximize the intensity. g. Place a white card after the spatial filter and adjust the X-Y position of the pinhole until a faint spot is incident on the card. Continue with step f until you get light through the pinhole onto the card. As soon as you see any light on the card, use it as your feedback method. h. Rotate the knurled nut to bring the pinhole closer to the objective and adjust the X-Y position of the pinhole to maximize the intensity on the white card. i. Repeat the previous step until the maximum throughput is obtained. This is indicated by a bright circular blob of light surrounded by a symmetric Version 2.1, 8/27/09 Robert McLeod 9

10 ECEN 4606 Lab 1 Basic optics lab skills pattern at the output. A slight movement of the X-Y position of the pinhole results in the complete disappearance of the diffraction pattern as well. An example is illustrated in the figure below. At the final position, very slight changes in the X-Y positions will dramatically change the beam pattern adjust for the visually smoothest pattern with fewest rings. Figure 6. Output of the spatially-filtered HeNe laser beam. This pinhole was chosen a bit smaller than D = λ0 / NA causing diffraction ringing in the output. In your lab book: Record the total power out of the pinhole and the efficiency of the spatial filter. The efficiency should be fairly high (90% or so) if you have chosen D λ0 / NA. Roughly measure the divergence angle of the spatially-filtered expanding beam. Does this agree with your calculation of the spot size after the objective? If you have a cell-phone camera, snap a picture of the spatially-filtered beam on a piece of white paper and paste it into your lab book. Note any features of the beam (rings, asymmetry, etc) and their potential causes. STEP 3: COLLIMATE THE DIVERGING, FILTERED BEAM Version 2.1, 8/27/09 Robert McLeod 10

11 M2 Iris 3 Iris 1 Iris 2 M1 L Obj. P.H. Figure 7. Final layout including the collimation lens. Move iris 1 beyond the spatial filter and align it to the diverging beam. Insert your collimation lens with the more flatter surface towards the diverging beam and the more curved surface on the collimated side (this minimizes aberrations). Place the shear-plate collimation tester after iris 2 and observe the fringes. Figure 8. Use of the collimation tester 2. If the fringes are curved, you have the lens decentered (in x or y) and/or tilted (in θ x or θ y ). You thus have five degrees of freedom including distance along the table (z). The collimation tester provides one test and the two irises provide the other four by centering the beam on iris 2 and the weak, circular back reflections on iris 1. Achieve the best collimation you can. In your lab book: Sketch the remainder of your setup. Record your procedure and observations. Sketch or photograph the pattern on the collimation tester. Perfectly straight lines indicates a plane wave, while curved lines indicate deviations from this ideal. Straight lines in the center with curves at the edges indicate a paraxially collimated beam with aberrated edges. Congratulations! You now have an aligned, filtered, expanded and collimated laser beam. This is the beginning of most experiments using a laser. 1 From Newport, see 2 For more details, see Version 2.1, 8/27/09 Robert McLeod 11