Make Your Own Digital Spectrometer With Diffraction Grating

Transcription

1 Make Your Own Digital Spectrometer With Diffraction Grating T. Z. July 6, Introduction and Theory Spectrums are very useful for classify atoms and materials. Although digital spectrometers such as Ocean Optics spectrometers have been developed, it s a lot of fun to make your own digital spectrometer. Diffraction gratings can be used to separate light beams of different wavelengths in spectrometers. A diffraction grating is an optical component with periodic structure, which splits and diffracts light into several beams traveling in different directions. The orientations of beams depend on the both spacing of the grating and the wavelength of light. Figure 1: 1

2 The governing equation is dsinθ = n provided d << L0, which is ordinarily true. Therefore measuring the angle θ, counting n from the zero-order pattern, and knowing d(the spacing of grating) in advance, we can calculate, the wavelength of the pertinent spectrum line. Doing this for several values of n increases the precision. sodium doublet is an interesting phenomenon in spectrum. It refers to two bright yellow spectral lines(d1 and D2) of sodium, which are close to each other with the centre wavelength nm. The doublet correspond to the fine splitting of the excited states due to spin-orbit effect. The wavelength splitting is 0.597nm, which can be observed though spectrometer. 2 Experiment Figure 2: The apparatus of digital spectrometer experiment In this experiment, we are building digital spectrometer with optical spectrometer, diffraction gratings(300 lines/mm), camera and PC. The setup is simple(fig. 2), however, a perfect alignment is required. In the experiment, you can not only observe the spectrum lines but also obtain the intensity distribution for each line. Especially for sodium lamp, 2

3 naked-eye observation does not give the intensity distribution of doublet, but with the digital spectrometer we build, it s easy to observe and measure the intensity ratio of the doublet. Light from a mercury source is concentrated on the collimator slit by means of a condensing lens. The collimator produces a beam of parallel light, which is incident on gratings on the photographic slide. The diffraction pattern is observed using the telescope; the angular position of which may be found using the record of camera. The mercury source produces three principal spectral lines and by the use of filters any one of these may be separated out from the rest of the spectrum sufficiently well for the purposes of this experiment. Note: since the mercury source is fairly powerful and produces a certain amount of ultraviolet, you should avoid looking at it directly. 2.1 Procedure (1) Place the light source(mercury lamp) in front of the spectrometer. Adjust their height to keep them in the same level so that the light beam can shine into the collimator without much loss. (2) look into the telescope to see the image of the light source. The telescope has to be in a line with the collimator. Adjust the focus by slightly pulling the eyepiece in or out until a sharply focused narrow upright slit is visible in the telescope. You may also adjust the width of slit in the front of collimator. Do not insert the photographic plate into the beam at this stage. (3) Place the diffraction grating and check if the image of slit(actually it s zeroth order diffraction fringe here) is still in the center of field of view in telescope. If not, you may have to adjust angle of the diffraction grating. (4) Rotate the telescope to look for 1st and 2nd order diffraction patterns. (5) Swing the telescope of the spectrometer to one side so it is not obstructing the path of the light. (6) Be sure the camera is focused at infinity.(pressing the focus bottom for a while and it can switch from automatic focus mode to focused at infinity) If necessary, focus it on an object as far away as possible, possibly down the hallway. Disable the digital zoom. (7) Position the camera directly in front of the diffraction grating and adjust its position until the zeroth and first order interference pattern are visible in the screen. You may also see the second order pattern. Center the pattern. Zoom in appropriately if you want better observation(optical, not digital). 3

4 (8) Record a short video with Virtual Dub and open it in Image J. Use the averaging algorithm to smooth the image. Draw a thin box around the diffraction pattern and then select plot profile under analyze, and record the positions of the maxima in pixels. (the Video Capture Instructions below explain the capture and analysis in greater detail at the end of this manual.) (9) Calibrate your self-made digital spectrometer! (See calibration below) (10) Calculate the distance between each peak and the zeroth peak in pixels, and convert to radians. Calculate the wavelength. You can also measure the angles with angular vernier of spectrometer. Is it more accurate than the digital measurement? (11) Use a sodium lamp as light source to observe the doublet in its spectrum. You are supposed to see two overlapped lines in the first order diffraction pattern and two separated lines in the second order. Calculate the wavelength splitting of doublet to check if it is around 0.597nm. Use ImageJ to get the intensity ratio of the doublet. The line at around 589.0nm is supposed to have twice the intensity of the line at around nm. You may not be able to image the pattern using the same magnification you used for the mercury lamp. (Recommend to use maximum optical zoom.) If you change the zoom at any point during the alignment, just recalibrate the camera. You can also measure the angles with angular vernier. 2.2 Calibration Here are three possible methods to calibrate your system and convert the pixels to radians. (1) The following approximate conversion will be good if you set the Canon Optura40 digital camera to minimal zoom (both optical and digital zoom off): θ(radians) = pixeldif mm 4.8mm,Where 3.21 mm is the CCD width and 4.8 mm is focal length of the camera at min optical zoom( This convert ion works only for min zoom). If you set the camera to maximal optical zoom (digital zoom off): θ(radians) = pixeldif mm 67.2mm. (2) Pick one of the maxima (e.g. the zeroth order fringe). Swing the edge of the camera a couple degrees past the maximum and then return (to minimize backlash) so that it is at the edge of the field of view. Record the angular position. Continuing in the same direction, 4

5 sweep back across the field of view until the maximum is aligned with the opposite edge of the screen. Record the angular position and calculate the number of degrees in one view. Divide this number by 720 pixels and convert to radians to find the number of radians per pixel. (3) If we involve the true values of wavelength of mercury spectrums, we can calibrate the system and determine the wavelength of other spectrums( e.g. hydrogen). Get the distance between each peak and the zeroth peak in pixels with ImageJ. Also calculate the angles in radians between lines with true values of mercury emission line spectrum (404.7nm for violet line, 435.8nm for blue, 546.1nm for green and 578.2nm for yellow). Divide the angles by number of pixels to obtain the convertion factor. Then keep everything the same and replace the mercury tube with hydrogen tube. Do not change the zoom. Now you can do the measurement of hydrogen. 2.3 More experiment options: Different light source can be used for the same apparatus. (1) Could you measure different wavelengths of colored LEDs? With the same apparatus, replace the mercury lamp with an LED board. There are multiple colored LEDs per board so you can measure multiple wavelengths. You may not be able to image the pattern using the same magnification you used for the mercury lamp. If you change the zoom at any point during the alignment, just recalibrate the camera. You are supposed to see at least the zeroth order and first order diffraction patterns. (2) Another experiment option is to distinguish the spectrum of helium and deuterium. Use helium and deuterium lamps as light sources and the locations of first order diffraction fringes should have a tiny difference. This part needs extremely perfect alignment and calibration, otherwise the spectrum shift will be much smaller than the equipment errors. Again, you will probably have to adjust the zoom and radian/pixel calibration. Note: The apparatus source is prone to focusing error so make sure the camera is focused at infinity. Could you think of ways to improve the apparatus and enhance the accuracy? (3) pick up an unknown tube and measure the wavelengths of its spectral lines. Could you identify it with its spectrum? 3 Appendix Video Capture Instructions: A. To capture video open VirtualDub.exe 5

6 i. Click: file>capture avi ii. Click: file>set capture file (remember where you put it) iii. Click: audio>uncheck enable audio capture (Dont forget to do this!) iv. Click: capture>capture video v. After 5-8 second, hit sec to end the capture. You should have captured around 200 frames and the audio size should be 0 bytes. vi. Click: file>exit capture mode vii. Click: file>open video file (open your file) viii. Click: file>save as avi ix. Change the name of the file and save it x. Exit VirtualDub B. To obtain data from the image open WCIF ImageJ i. Click: file>open (open the one with the new name) ii. Click: image>stacks >Z-Projector iii. Leave group size alone, but change projection type to average intensity. iv. The program will process and eventually open the averaged image. The image quality should be much sharper which will make measurement easier. v. With the mouse draw a thin horizontal box across the center of the image. The height should be small enough to minimize the effect of the curvature and the length should be long enough to include the fringes. vi. Click: analyze>plot profile Sample images and data Note that the data shown here do not have the same calibration. 6

7 Figure 3: The first order lines of sodium doublet Figure 4: The intensity of first order lines of sodium doublet 7

8 Figure 5: The second order lines of sodium doublet Figure 6: The intensity of second order lines of sodium doublet 8

9 Figure 7: Hydrogen spectrum: On the left is the zeroth order, on the right are the first order lines of cyan and red. 9