Observing Emission Lines With 3D Printed Spectrometer

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Observing Emission Lines with 3D Printed SpectrometerHelena Gien, David PearsonDepartment of Physics and AstronomyThe University of Georgia, Athens, Georgia 30602(Dated: December 5, 2016)We designed a 3D printed a spectrometer using an iPhone 6S as the image capturing platform.With our device, we hoped to demonstrate the physics of spectrometry, and therebyhighlighting the underling optical principles. By careful analysis of the principles of diffractionand interference we could design an apparatus that would attach to an iPhone allowing thecamera to detect the spectrum produced by various light sources. The design would allow thespectrometer to be transferrable between iPhones. Our goal with our spectrometer is todemonstrate the physics of spectrometry by collecting the light spectrum from Hydrogen,Helium, Neon, Sodium, and incandescent lamps. Through comparison between our images andthe actual emission lines for each source, we verified the resolution of our spectrometer towithin 9nm. We successfully measured a distinction between Helium lines separated by 9nm,however we could not distinguish Sodium lines separated by approximately 0.6nm.I. SPECTROMETERSOur goal directs us into the field of spectroscopy, thestudy of interactions between light and matter.1Joseph von Fraunhofer pioneered many of thequantitative aspects of the field through his inventionof the spectroscope.2 The original design employedthe use of a telescope adapted to mount a diffractionslit and prism which greatly increased the viewer’sability to observe solar absorption lines andaccurately record data.3 In time, further designmodifications introduced the first spectrometers,utilizing a camera in place of an optical viewing tube.3Modern day spectrometers yield far greaterresolution by means of highly refined collimating and1Skoog, Douglas A., F. James. Holler, and Stanley R.Crouch. Instrumental Analysis. Austrailia: ThomsonBrooks/Cole, 2007. Print.focusing lenses to first form the incident rays intoparallel lines, then after passing through a diffractingmedium, focusing and separating light by wavelengthonto the detecting device. Our device requires threecomponents to operate correctly: light reducing slit,diffraction grating, and iPhone camera. An openingslit, which reduces and aligns the light so that it maybe focused on a diffraction grating. The diffractiongrating is a sheet of transparent plastic withthousands of small slits on one face. The incominglight refracts due to the change of refraction indexfrom air to plastic. The light then interacts with themany slits causing interference. Similar wavelengthsconstructively and destructively interact causinginterference patterns. Over the entire face of the2Peatross, Justin, and Michael Ware. Physics of Light andOptics. Provo, UT: Brigham Young U, Dept. of Physics,2015. PDF.3Brand, John. Lines of Light: The Sources of DispersiveSpectroscopy. N.p.: Gordon and Breach, 1995. Print.

grating, this operation takes place thousands of timeseffectively separating each wavelength andprojecting them at a different angle. The longer thewavelength, the greater the angle. This operation canbe seen by the following formula.(1)Eq.1. Diffraction grating equation. Variable Index: angle of displacement from the incident plane.m order number of maxima. wavelength of light.a grating spacing in meters.FIG.1. Diagram of the diffraction grating equation.Note: angle of incoming light with respect to thegrating.Each wavelength is separated into individualcategories of their respective maxima order number.When incident light is comprised of several sources,these maxima align in staggered positioningdependent upon wavelength. Therefore, an imagemay be captured on the camera of each wavelength’ssimilar order of maxima adjacent to the correspondingmaxima of all other wavelengths. However complex orsimple the device used, the operator may observeabsorption or emission lines from the incoming light.II. EMISSION LINESOur focus is in the capturing of emission lines fromdifferent substances allowing the observation ofspecific wavelengths of the emitted light, and thecorrelation with observed color. Objects absorb andreflect light based upon their composition, and thecolors we see are a direct result of the wavelengthsof light from the visible spectrum reflected to oureyes. A red apple absorbs the visible light except forwavelengths close to 700nm, which are reflected toour eyes, and our brains interpret this signal as thecolor red. A spectrometer acts as our eye bygathering incoming light and separating it bywavelength so that we may see a red band of colorcaptured in our photo. Other objects emit light whenstimulated by an external source. This stimulationcan come from any sort of electromagnetic radiationincident upon the substance. Most of the radiationfails to fully interact with the medium. However,under certain circumstances, electrons in themedium receive the precise amount of energyneeded to excite to a higher energy level. Theelectrons always tend to return to equilibrium, and todo so, they must release a photon. It is preciselythese photons in which we hope to capture. Thisprocess may occur for matter in any state; solid,liquid, gas, or plasma. Fluorescent lighting uses thisprinciple of stimulated emission in two stages. First, acurrent is passed through a mercury vapor enclosedin a low‐pressure housing. The current stimulates theelectrons to the next energy level, and to return theyrelease an ultraviolet photon. This photon thenstrikes a phosphor coating on the walls of thehousing, thereby stimulating the phosphor to anexcited state. The phosphor then in turn emits thevisible photon that we see. Each emitted photon is ofa particular wavelength which, if in the visiblespectrum, corresponds to a particular color. Whenmulticolored light enters the opening slit of thespectrometer, it will then pass through a diffractiongrating causing the incident light to bend and interactwith itself creating observable phenomena. Whenlight waves constructively interfere with one anotherthe captured image will display a band of light ofgreater intensity known as an emission line.

scope features a flat end, to which we have affixedthe slit, and the opposing end with an approximate31 sloped face. The sloped face glues to a mountingring that is seated just inside the diameter of the casecutout. Inside the scope a 1cm square diffractiongrating (1000/mm) is suspended just north of centerby thick black cardstock.FIG. 2. Carbon as seen through a spectrometer. Thebands of increased intensity exemplify constructiveinterference.These emission lines act as an object’s fingerprint,allowing for the detection of certain materials bycharacteristic emission lines. Depending upon thesource of light incident upon the object, it may ormay not display the entire visible spectrum.FIG. 3. Two separate light sources as seen from thespectrometer. The top bar displays solar light, versusthe compact fluorescent light on the bottom.III. DESIGNWe designed our spectrometer using 123D Designand printed each component with a Lulzbot Mini. Thedimensions used were formatted to fit an AppleiPhone 6S. The entire design includes fivecomponents, three of which utilized the 3D printer.The three main components included the phonecase, scope and mounting ring. The case attached onall sides of the phone and we used rounded edgeswith a wrap‐around design to seat the phone in thecase. See Appendix. The case is approximately 7.1cmwide, 14.1cm long to the highest point, and 1cmdeep. It features a 3cm circular cutout 0.5cm fromthe leftmost edge in the upper left hand corner whenfacing downward.The scope is 6.5cm at the longest tip to tip with a3cm diameter barrel, 2.5cm internal diameter. TheOur initial intentions were to print out the slit wewould use to align and reduce the incoming lightfrom the source. However, we encounter difficulty inrendering a uniform sub‐millimeter slit. Instead, weused black cardstock and a hobby razor to create aslit of approximately 0.5mm.IV. CALIBRATIONTo calibrate our machine, we needed to make severalsmall modifications to the angle of the scopeattachment and the best slit size and placement toachieve the greatest image. To appraise the initialvalue parameters of our spectrometer we must firstfind a full spectrum light source. We obtained a fullvisible spectrum flashlight and began takingphotographs to calibrate.The initial test we performed was to see if thediffraction grating had been properly aligned for theslits to be parallel with the slit opening. With animproperly aligned grating, we received the imageseen in Fig. 4.FIG. 4. Improperly aligned diffraction grating. Whenthis occurs, the bands of color are compressed onone another resulting in an image that will not yieldclearly defined emission lines.

A properly aligned grating will yield an image as seenin Fig. 5.FIG. 5. Notice the bands of color are no longercollapsed into a small band. This greatly enhances thepotential to visualize emission lines of smallerwavelength ranges. With a calibrated spectrometer,such as this, we can now begin experimentation.This processes calibrated our spectrometer two‐fold.It not only verifies the proper orientation betweenour slit and grating, but also shows that we haveindeed captured the first maxima of eachwavelength. The visible spectrum progresses fromviolet to red (390nm – 700nm) an incompletespectrum would indicate a discrepancy betweenangle of incident light and camera orientation. Inaccordance with Eq.1, we would need an angle ofapproximately 35 to capture the longest visiblewavelengths of 700nm. Through calibration, wefound an angle of 31 to yield the best results. Theprecision of our equipment, coupled with thenecessary eradication of all other sources of light,including reflective distortion inside the scope, allplay a factor in the final resolution of ourspectrometer. To calculate our theoretical value ofresolution, we employ the following formula: The resolution factor ( ) is a valued calculated fromthe groove density on the grating, and slit width. It iscalculated by considering the total number ofdiffraction grating slits struck by the light. The greaterthe number of slits employed, the greater theresolution of the spectrometer. With a slit width ofapproximately 0.5mm and a distance to grating ofapproximately 5.5cm, we calculated a span ofincident light to be 0.17mm. This value is determinedusing Eq. 3 with 390 and 700nm. The span of0.17mm multiplied by 1000 lines per mm yields aresolution factor of 170.(3)Eq. 3. Equation for the approximation ofdisplacement y for light incident upon a diffractiongrating. Variable Index: y displacement of light. m Order of maxima. Wavelength of light. D distance from slit to grating. d slit separation. For adiffraction grating of 1000 lines per millimeter, slitseparation d 1 m.Given the range of our spectrometer will be limitedto the visible spectrum, our values for eachparameter are determined by the technicalspecifications of the iPhone 6S 12 mega pixel camera.Resolution Factor: RF170Slit Width: WS0.5mmRange: 310nmPixel Width: WP1.4 mNumber of Pixels:12x106Spectrometer Resolution 1.56nm(2)Eq. 2. Calculation for spectrometer resolution.Variable index: resolution factor, range ofspectrometer, slit width, number of pixels, width of pixels.FIG. 6. Our theoretical values for the spectrometerresolution. Note: The resolution factor wasapproximated from values achieved byspectrometers with smaller slit widths.

It is of importance to note these values are onlyapproximations to the theoretical values of ourequipment. The iPhone 6S camera contains a fargreater quantity of pixels of a much smaller size thanmost spectrometers. This theoretically increases theresolution dramatically. However, with smaller pixelsand tight pixel spacing, we encounter a decrease inthe amount of light that may be incident upon thecamera lens. This requires the incident light to be ofhigh intensity, and our environment to be as dark aspossible. These necessary conditions led the testingof our resolution potential to be conducted withlamps of differing elements in a dark room.FIG. 7. Standard gas discharge lamp schematics. Weimplemented a lamp of this type for each of thegases we tested.4The apparatus was pointed directly at the lightemitted from the gas discharge lamp in an otherwisecompletely dark lab room. The following images werecollected for each gas. They are shown below (left)next to images taken with a commercial spectrograph(right).V. EXPERIMENTATIONThe goal of this experiment was then to test theapparatus against lamps with known emissionspectra. Hydrogen, Helium, Neon, and Sodium lampswere used to collect images with our spectroscope. Inaddition, the full visible spectrum was observed withan incandescent bulb for comparison.A gas discharge lamp was used to observe each of thegasses listed above. In this setup, each element isisolated in a glass tube. A power supply is used toapply a 115V potential difference across the gas. Ascurrent flows through the tube, electrons are excitedto different energy levels and as they return to theirground states they emit photons with discretewavelengths.FIG. 8. Side by side comparison of our spectral imagesversus a computer rendering of the actual spectrallines given for each gas. Our photos are hosted onthe left, and the renderings are on the right.To further examine the resolution achieved by ourapparatus, each image was scaled to the fullspectrum image taken using an incandescent bulb.The full spectrum was estimated to be 300nm inlength (from 400nm to 700nm) and each image wasscaled to 300px in width (1 pixel per nanometer).A python program was written to sum the pixels ineach of these 300 columns. This was used todetermine the relative “intensity” of each band at itslocation on the visible spectrum. The results of thisinvestigation are shown below using helium as anexample.4Miller, Samuel C., and Donald G. Fink. Neon Signs;Manufacture--installation--maintenance. New York:McGraw-Hill, 1935. Print.

FIG. 9. Graphical rendering of our spectral image ofHelium emissions. Note: the two wavelength peaks atapproximately 492nm and 501nm are distinctlyseparated indicating our resolution to be capable ofdistinguishing 9nm.FIG. 10. Actual emissions of Helium gas with indiceson the 492nm and 501nm wavelengths.The closest distinguishable peaks on our graphcorrespond to the 492nm and 501nm known heliumemission lines. Thus, we can confidently say ourapparatus can resolve peaks within 9nm of oneanother.VI. SUMMARY AND CONCLUSIONWhen light interacts with a diffraction grating we seethe physical expression of the principle ofinterference. The light waves strike each slit anddiffract by an angle that corresponds to the incidentwavelength. The similar wavelengths interfere withthe light emitted from each of the thousands of slitscausing the observable phenomenon of interference.For each maxima, we are witnessing the constructiveinterference pattern, and the distance between eachmaxima is due to the destructive interference. Thenet result is the separation and organization of themaxima of each wavelength of light. When thispattern is focused on our camera, we can capture animage of the emission spectra for a given lightsource. Our goal was to observe this phenomenon bycreating a 3D printed spectrometer by which wecould integrate an iPhone 6S and capture spectralimages.After designing and printing the components for ourspectrometer, we calibrated the equipment byorienting the slit with the diffraction grating until wehad a satisfactory image of a full spectrum ofincandescent light. Once calibrated, we tookmeasurements of our final dimensions andproceeded to calculate a theoretical value ofresolution. We then proceeded to capture images ofHydrogen, Helium, Neon, and Sodium gas lamps andused these images to test our theoretical values ofresolution.Our apparatus produces results nearly identical tothose found with a commercial spectrometer. Wewere able to view a range of about 400nm‐700nm ofwavelengths in the visible spectrum. Some of thesewavelengths (like the 520nm faint green in the neonand sodium) were almost too dim to appear, but theyare usually not even included in the standardemission spectra for these elements. Through meansdiscussed in the previous section, we definitivelydetermined our apparatus could resolve emissionbands within 9nm of one another.

VII. APPENDIXFIG. A1. Case body with the internal cutout facingobserver. The circular cutout for the camera is in thetop right corner.FIG. A3. Scope attachment. Angled side attaches tomounting ring so that scope creates a 31 betweenthe camera lens and diffraction grating. This is apositive angle taken from the horizontal.FIG. A4. Scope attachment positioned so that thediffraction grating is visible. It is suspended andpositioned to be aligned with the camera just northof center. It is held in place by black cardstock.FIG. A5. Our captured image of Hydrogen.FIG. A2. Mounting ring, by which the scopeattaches to the case. The scope is glued to this ring,which fits inside the circular cutout on the case.FIG. A6. Graphical rendering of the emission lines ofour Hydrogen image.

FIG. A10. Graphical rendering of the emission lines ofour Sodium vapor image.FIG. A7. Captured image of Neon gas.FIG. A11. Captured image of Helium gas.FIG. A8. Graphical rendering of the emission lines ofNeon gas.FIG. A12. Graphical rendering of our Helium gasimage.FIG. A9. Our captured image of Sodium vapor.

absorption or emission lines from the incoming light. II. EMISSION LINES Our focus is in the capturing of emission lines from different substances allowing the observation of specific wavelengths of the emitted light, an

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