Optics Laboratory Spring Semester 2017 University of Portland Laser Safety Warning: The HeNe laser can cause permanent damage to your vision. Never look directly into the laser tube or at a reflection from a shiny surface. The HeNe laser emits in the visible (red, 633 nm), the diode lasers that we use emit in the near-infrared (IR) (780 nm). Only use diffuse reflectors (such as a white 3 x 5 card) for viewing the HeNe laser beams. The diode laser beam can also be viewed on a white card in a dark room or on a special IR card which emits in the visible when illuminated with an IR beam. Protect co-workers from accidental exposure to the laser beam; always block laser beam close to the laser when the experiment is left unattended. Notes on Handling Optics: Always treat the surfaces of lenses and mirrors with care. Never touch the optical surfaces. Use lens tissues to handle optical components or handle the components only by their edges. Always assemble components over a table surface and do not lift the components any higher off the table than necessary. 1
Advanced Laboratory: Optics Spring 2017 University of Portland Laboratory 1: Geometrical Optics Special thanks to the Department of Physics at Oregon State University for portions of this laboratory. Equipment: Item Qty Source (part number) Helium-Neon Laser 1 Thorlabs (HRR020) Optical Rail 1 Thorlabs (RLA2400) Rail Carriage 3 Thorlabs (RC1) Lamp 1 Pasco (OS8470) 100 mm lens 1 Newport (KPX094) 200 mm lens 1 Newport (KPX106) 25 mm lens 1 Newport (KPX076) -25 mm lens 1 Newport (KBC046) Index card 2 Filter holder 1 Thorlabs (FH2) Aluminum mirror 2 10D10ER.1 Iris (adjustable) 2 Thorlabs (ID12) Meter stick 1 Metric tape measure 1 2
Part 1: Alignment Project For many situations, it is convenient if the laser beam is parallel to the top of the optical table and aligned above a line of holes on the table. This will make insertion and adjustment of other components much easier. We will align our laser in a U-geometry with the optical rail in the last arm of the U (see Fig. 1). The rail can be bolted to the table and has carriages that ride on the rail. Components can be mounted on the carriages so that they can be easily moved along the optical axis as defined by the rail. HeNe Laser Mirror Optical rail Mirror Figure 1: U-geometry for optical alignment. The HeNe laser is already mounted to the optical table. The mirrors are mounted in mirror mounts. The post on the mirror mount fits into the post-holder tube/base plate assembly which can be mounted to the optical table using the bolts provided. Locate the first mirror in the approximate position shown in Fig. 1. It is a good idea to locate objects on an optical table a small distance in from the edge of the table so that they are not easily bumped by someone walking by. With the laser turned on, adjust the position of the mirror so that the beam travels approximately parallel with the edge of the table. 3
Mount the optical rail on the table along a set of bolt holes a few rows in from the edge of the table so that the rail is along the third arm of the U. We now want to adjust the mirrors so that the third arm of the U is along the axis defined by the optical rail. We also want to ensure that the laser beam is parallel to the table top. To do this, mount the second mirror on the optical table and position it close to the beginning of the optical rail such that the center of the mirror is above the center line of the rail. Set up two adjustable irises on the optical rail, one as close to the mirror as possible and one as far away as possible. (Note: Do not remove the irises from their posts; they can be easily damaged.) Adjust the iris heights to be as nearly equal as you can. We now want to direct the laser beam through these two holes which define our optical axis. Close the irises down. Adjust the first beam steering mirror so the beam reflected off the second beam steering mirror goes through the first iris. Now adjust the second beam steering mirror so the beam passes through the second iris. Note that this adjustment should do little to perturb your first adjustment since the first iris is so close to the second beam steering mirror. That is the trick! You may have to open the irises some to start and iterate a few times to get it just right, but the procedure should converge very rapidly. Note how the beams move and play with this arrangement enough so that you can quickly and correctly determine which knob need to be adjusted and which direction the knob must be turned to move the beam the correct direction (left, right, up, or down). Note the kinematic construction of the mirror mount; there are two orthogonal pivots about a single point. Leave the laser beam aligned so that you can use it in Part 3. 4
Part 2: Thin Lenses In this experiment we will investigate the thin lens equation: 1 S 0 1 + S i = 1 f We will determine the focal length (f) of a lens or a combination of lenses by carefully measuring the object ( S 0 ) and image ( Si ) distances. A negative lens alone cannot produce a real image; therefore, a combination of a positive and a negative lens will be used to determine the focal length of the negative lens. The light source will be a lamp. The lamp has an aperture at the output end that generates the image of an arrow. This will be the Object for the experiment. The optical source, lenses, and screen (white card) are all mounted on the optical rail. The rail is bolted to the table and has carriages that ride on the rail. Components can be mounted on the carriages so that they can be easily moved along the optical axis as defined by the rail. A white card (screen) is mounted on the far end of the optical rail. The Image will be formed on this screen. Optical rail screen lamp Figure 1: Experimental Set-up. 5
Converging (Positive) Lens (1) Turn on the lamp. (2) Place a 100 mm focal length lens in the post holder on one of the carriage rails. Locate the lens approximately 125 mm from the object. Record the measured distance between the lens and the object along with an estimate of the of your measurement in the table below. (3) Slowly move the screen toward the lens until a crisp image is seen. The distance from the lens to the screen is the image distance. Record this value and the estimated in your measurement in the table below. Also briefly describe the image (upright, inverted, magnified, minified) (4) Repeat steps (2) and (3) for an object distance close to the values of 150, 200, 400, and 600 mm. Record the object and image distances in the table below. (5) Using the thin lens equation calculate the focal length of the lens using your data. Compute the in your measured value. Find the average value of your results and compute the in this value. Compare your result with the specified value of 100 mm. Converging Lens: Data Specified focal length: 100 mm Sample Ray Diagram S0 Si 6
Object Distance (S0) + estimated Image Distance (Si) + estimated Calculated Focal Length (f) + calculated Description of Image Upright/inverted, magnified/ minified Average Value: favg = 7
Diverging (Negative) Lens A diverging lens has a negative focal length and forms a virtual image. Since only a real image can be projected on a screen, a combination of lenses will be used to determine the focal length of the diverging lens. (1) Place a diverging lens into a holder on one of the carriage rails with its concave side facing the object a distance of approximately 100 mm from the lamp. Measure the distance from the object to the lens and record it as the object distance (S01). Include an estimate of the of your measured value. (2) Place the converging (positive) lens whose focal length you just measured at a distance of more than 100 mm beyond the diverging lens. Measure and record the distance plus. Obtain a sharp image on the screen and measure the image distance from the positive lens. Measure and record the distance and. (3) Since you know the focal length of the converging lens and you have measured the image distance, you can calculate the object distance that would be required for this image distance if only the positive lens were present. (The image of the diverging lens is the object for the positive lens.) Subtract the calculate object distance for the positive lens from the spacing between the two lenses. This is the image distance for the diverging lens and will be negative. (4) Calculate the focal length of the diverging lens from the thin lens equation. Remember to use the correct signs for the image and object distances. Compute an for this calculated value. (5) Repeat steps (2) through (4) for a few different locations for the converging lens. (6) Compute an average value and for the focal length of the diverging lens and compare your results with the specified value. Why might the of this measurement be larger than that found for the converging lens? 8
Diverging Lens: Data Specified focal length: -25 mm Sample Ray Diagram S01 d Si2 Si1 S02 Object Distance (S01) + estimated Distance between lenses (d) + estimated Measured Image distance (Si2) + estimated Calculated Object Distance (S02) + calculated Calculated Image Distance (Si1) [Si1 = S02 d] + calculated Calculated Focal Length (f) + calculated Average Value: favg = 9
Part 3: Expanding a Laser Beam Many times when a laser is used in an optical system, there is a requirement for either a larger beam or a beam that has a small divergence (i.e. doesn t change size over the length of the experiment). In some cases the size of the beam becomes critical, for example; when measuring the distance from the Earth to the Moon, a beam one meter in diameter travels to the Moon where is has expanded to several hundreds of meters in diameter and when the return beam intersects the Earth s surface it is several kilometers in diameter. The signal returned from this expansion is millions of times smaller than the original signal, so that the divergence of a laser beam must be reduced to produce a strong, detectable signal. Even in the case of earthbound experiments, higher degrees of collimation are required for many applications. The output intensity distribution of many laser beams (including the HeNe laser) is symmetric about the beam axis; the intensity varies with radial distance r from the axis and can be modeled as a Gaussian function given by the expression: 2 ( ) 2r I r = I 0 exp. 2 r1 2 The distance r 1 is the radial extent of the beam when the intensity has dropped to 1 e of its value on the beam axis I 0. The Gaussian intensity distribution is shown in Fig. 1. The distance d is designated the beam diameter. Figure 1. Gaussian intensity distribution. 10
For a laser beam propagating through free space, the beam has a minimum diameter at some location along the beam path. This minimum diameter, designated d0, is called the beam waist. Because of diffraction, the beam waist has finite dimensions (i.e. the beam cannot be focused to a point). The divergence or convergence from this beam waist is measured by an angle ( θ ) is subtended by the points on either side of the beam axis where the intensity has dropped to 2 1 e of its value on the beam axis as illustrated in Fig. 2. Fig. 2. Laser beam waist. For a Gaussian beam of a wavelength ( λ ), the product of the beam waist (d0,) and the divergence ( θ ) is a constant, given by: 4λ d 0 θ =. π A beam with a very small beam waist has a large divergence (the beam spreads out quickly from a small minimum). If we want a more collimated beam, the divergence must be reduced, and that can only be done by increasing the beam waist. This process cannot be easily done using a single lens. First, the beam must be diverged with a short focal length lens and then the diverging lens is re-collimated with a large beam waist and smaller divergence. In this experiment you will investigate two types of laser beam expanders the Galilean and the Keplerian. These combinations of lenses form the basis for many refracting telescopes. 11
Divergence of an unaltered HeNe laser You can determine the divergence of the unaltered HeNe beam by measuring the beam diameter at several distances from the laser. Because the intensity falls off smoothly, as illustrated in Fig. 1, you will need to estimate the beam diameter. For a Gaussian beam, the beam diameter (d) varies as the distance (z) from the laser as: d 2 2 2 2 ( z) d + θ z =. 0 You can assume that d0 is the beam diameter measured close to the laser (i.e. the laser beam diverges from the exit of the laser). Use a ruler to measure the beam diameter and in this measurement at several distances about a meter apart from the output of the laser. The distances should be up to 10 meters if possible. Calculate the divergence for the laser beam (a value for θ) based upon the measurements at various values of z. You will find the values of θ are more accurate for larger values of z. Make a table showing your results and compute an average divergence for the laser. The average of measured values should be in the neighborhood of 1 milliradian. Include a calculated for your results. Galilean Beam Expander A Galilean beam expander is illustrated in Fig. 4. It consists of a negative (diverging) lens and a positive (converging) lens. We ll use the diverging lens first to expand the beam and the converging lens to achieve a collimated, expanded output beam. Fig. 3: Galilean Beam Expander 12
Insert a short focal length (-25.4 mm) negative lens into a holder mounted on the optical rail, positioning the lens a few inches from the second mirror. Align the lens by raising or lowering the post in the post holder so that the diverging beam is centered on the iris at the end of the rail. Insert a longer positive focal length lens (200 mm) into a second holder on the rail. Place this second lens about 175 mm from the first lens (the sum of the focal lengths). Again center the beam on the iris at the end of the rail. Carefully adjust the position of the second lens so that output beam is collimated. To do this, you can measure the output diameter of the collimated beam at several distances from the beam expander. Make a sketch of your experimental set-up and label the location of each lens. Measure the beam diameter of the incident and expanded beams and record these values in your laboratory notebook. Keplerian Beam Expander A Keplerian beam expander is shown in Fig. 4. It consists of two positive (converging) lenses. We ll use the shorter focal length lens first to make a beam expander. Fig. 4: Galilean Beam Expander Replace the negative lens with a short focal length positive lens (25.4 mm) and use the same adjustments to center the beams in the lenses. Adjust the distance between the two lenses to be the sum of their focal lengths. Carefully adjust the position of the second lens so that the output beam is collimated. Make a sketch of your experimental set-up and label the position of each lens. Measure the beam diameter of the incident and expanded beams and record these values in your laboratory notebook. 13