This is the project report for my internship at HBCSE-TIFR. The project describes a low-cost method for analysing the spectrum of LEDs and determining the wavelength.

1. Low-cost method of determination of wavelength using Tracker
Contributed by:
1) Radhika Prasad
Affiliation: Miranda House, University of Delhi
Email id: radhika.prasad@mirandahouse.ac.in
Phone number: 9910673723
2) Anuradha Gupta
Affiliation: St. Xavier’s College, Kolkata
Email id: anu.gupta.1903@gmail.com
Phone number: 9163522916
Name of Mentor: Dr. Rajesh B. Khaparde
Affiliation: HBCSE-TIFR, Mumbai
Email id: rajeshkhaparde@gmail.com
Phone number: 9892355422
Abstract
Spectroscopy is used to characterise various sources of light. Typical spectroscopy techniques involve the
use of sophisticated spectrometers and software which prove to be expensive. In this article, we present
a low-cost and easy to implement setup for analysing the spectra of LEDs which have not been as widely
explored as that of gas discharge lamps. The apparatus includes LEDs, a sodium vapour lamp, an ordinarily
available transmission grating, a simple digital camera and Tracker software which is a freeware. We
determine the characteristic peak wavelength of various LEDs using this arrangement. The results turned
out to be accurate up to the order of 1% thus this method is both accurate and cheap. This makes it ideal
for implementing at the school and undergraduate level and will enable students to gain insight about
spectrum analysis.

2. Sources of Light
Light is essential for life. Our primary source of light and energy is the sun. Apart from the natural sources
of light (the stars), humans have developed various artificial sources including incandescent light bulbs,
compact fluorescent lamps (CFLs), sodium vapour lamp, mercury vapour lamp, light emitting diodes
(LEDs), lasers and many more. These have varied applications in various fields, for example, incandescent
light bulbs have largely been used for lighting purposes in buildings (offices and homes) which have been
replaced by CFLs, and more recently, LEDs, due to their exceptionally high energy efficiency. LED is a
semiconductor device, a p-n junction diode, which emits light when a suitable potential is applied to it.[1]
Mercury vapour and low-pressure sodium vapour lamps are gas discharge lamps which use vapourised
metals to produce light. Low-pressure sodium vapour lamp is a low intensity and nearly monochromatic
lamp with an average wavelength of 589.3 nm (two spectral lines at 589.0 nm and 589.6 nm) ie, a bright
yellow colour.[2]
Lasers are also monochromatic sources of light (with a spread of about a few nm) but
they are extremely intense and emit light coherently and have almost negligible divergence. Their
applications range from laser surgery, laser printing to cutting and welding metals amongst others.
Sources of light are characterised by their optical spectra- the wavelengths which compose the light and
their spectral intensity. With the wide variety of light sources available currently (with LEDs being a recent
addition), spectroscopy analysis has become increasingly important. Students in schools and
undergraduate colleges should be aware of its significance and applications.
Spectroscopy: The Art of Analysing Spectrum
Spectrum can be analysed with the help of a spectrometer. Spectrometers can be of two types. The first
one is where light from the source passes through a collimator and is captured by a telescope, both of
which are fixed to a turntable, which has a grating table attached to it so that a grating can be placed in
between the collimator and the telescope. The turntable is graduated in degrees and the telescope can
be moved around it in order to capture the various spectral lines. With this method, the wavelength of
spectral lines can be determined but not the intensity profile.
Figure 1: Spectrometer; image adapted from
https://www.colorado.edu/physics/phys1020/phys1020_sp05/labs/Lab3_lightcoloratom.html


3. The second type is one in which grating and collimating lens are placed in a small box which contains a
detector as well. Light enters the device through an optical fibre and then passes through a slit. These are
sophisticated devices with exceptionally high levels of accuracy since much of the human error is reduced.
Companies manufacturing these spectrometers provide software with the help of which the spectral
intensity can be analysed (plot of intensity vs wavelength). We used the Ocean Optics HR4000
spectrometer (together with SpectraSuite software accompanying it) to provide a standard against which
we compared our experimental results. The HR4000 spectrometer is responsive within the wavelength
range 200nm to 1100nm.[3]
Figure 2: Ocean Optics Spectrometer; image at https://oceanoptics.com/product/hr4000-custom/
Both these equipment are quite expensive and difficult to set up for schools and various undergraduate
labs. We have experimented with a low-cost setup where Tracker software has been used for spectral
analysis. This setup can easily be implemented in schools and students will gain a hands-on experience in
spectroscopy.
What is Tracker?
Tracker is an open source software (freeware) created by Douglas Brown and is built on the Open Source
Physics Java Framework, hosted by the comPADRE Digital Library, a collection of open source resources
for Physics.[4]
Although it is primarily a video analysis tool, used in motion studies and tracking in
kinematics and dynamics, it can also be used as a photo analysis tool.[5][6]
The RGB profiles and intensity
profiles of the images can be analysed with the help of “RGB Region” and “Line Profile” tools respectively.
In the Line Profile tool, there is also an option of visualizing the contribution of the red (R), green (G) and
blue (B) colours separately. The Line Profile tool measures the intensity of image pixels along a user-
defined straight line. A “spread” value can be set which determines the number of pixels to be considered
above and below the line for averaging out the intensity. This helps in reducing noise in the images.

4. A Brief Theory of Optical Diffraction
The theory of optical diffraction can be found in all books of general physics and optics at the
undergraduate level.[7][8]
We discuss it cursorily over here.
Figure 3: Arrangement for producing Young’s interference pattern (image adapted from Optics by Ajoy Ghatak)
Consider a source of light at S and two slits S1 and S2 a distance d apart (d should be comparable to the
wavelength of light source used). Consider a screen at a far away distance (Fraunhofer regime); this
ensures that we can consider the rays from S1 and S2 as nearly parallel. The rays meeting P (on the screen)
are said to be diffracted at an angle . The path difference between the two rays meeting at P is 𝑑𝑠𝑖𝑛𝜃.
For constructive interference, we have:
𝑑𝑠𝑖𝑛𝜃 = 𝑛𝜆 (1)
For first order maximum, 𝑛 = 1.
Since OP (xn) is small, we have from small angle approximation:
𝑠𝑖𝑛𝜃 ≈ 𝜃 ≈ 𝑡𝑎𝑛𝜃 = (2)
From (1) and (2) we obtain:
𝜆 = (for first order maximum) (3)
This theory for “Young’s double slit experiment” can be easily extended to gratings. For gratings, d is the
grating element, ie, the spacing between adjacent rulings on the grating. This can be easily found using
grating specifications. For example, in a 7500 LPI (lines per inch) grating (the one used in our experiments),
the value of d will be 1 inch/7500.
The resolution of a grating depends on the number of rulings; a higher number of lines per inch would
increase the resolution but at the same time, it would also increase the diffracting angle.
xn


5. Descriptive Method
We now discuss the procedure in detail which we employed for studying the spectra of various LEDs using
a low-cost setup.
Experimental Setup:
The setup consisted of an LED mounted on a stand which was connected to a low power voltage source
via a 100 resistor in series (to limit the current passing through the LED). A pinhole was mounted right
in front of the LED (to obtain a thinner and sharper spectrum). This acted as the source of light. The light
then fell on a grating (7500 LPI in our case)) and the spectrum was captured using an ordinary digital
camera (Nikon D5300 with a lens of 35mm and Canon Powershot SX40HS in our case) placed right after
the grating. For the calibration, a sodium vapour lamp was used in place of the LED. The experiment was
performed in a dark room. The ideal photography settings were determined after a few trials. High-
intensity photographs (slow shutter speed and wide aperture) create bright spectra but it is somewhat
blurred whereas low-intensity photographs might prevent certain faint spectral lines from being captured.
When colour is not so important, it helps if images are captured in black and white mode. This eliminates
some minor colour-dependent intensity enhancement which might have been introduced by the
camera.[9]
Once the camera is set, the settings and the setup should not be disturbed throughout the
course of the experiment. The experimental setup is depicted below:
Figure 4: Experimental Setup
The spectrum is actually formed (virtually) in the plane of the pinhole, ie, in the plane of the source of
light.
Calibration
Tracker measures distances in terms of pixels. Thus, in order to increase the accuracy, the distance D
between the grating and the spectrum formed should also be calibrated in pixels instead of a hand-held
measuring tape. For this purpose, a lamp of known wavelength (sodium vapour lamp in our case) was
used as the source of light.[10]
Since the wavelength  of the light source is known, the grating element d
is known and the distance x1 of the central spot from the first order maximum of the spectrum can be
light
source
pinhole
gratingcamera
spectral
line
D

6. measured from Tracker, we can use (3) to calculate D in pixels. The conversion from pixels back to
wavelength in nm can be achieved by using the same formula again once D is calibrated in pixels.
For the grating we used (7500 LPI), 𝑑 = = 3386.67 𝑛𝑚 (4)
Figure 5: Sodium vapour lamp spectrum for calibration (faint first order maximum can be seen on either side of the
central spot)
The spectrum was loaded into the Tracker tab (if memory ran out, then the memory size allocated to
Tracker was increased by clicking the box in top right corner titled “memory in use”). Coordinate axes
(present under the “Track” menu) were set with the x-axis along the spectrum and origin at the central
spot. For intensity analysis, an intensity vs position (along x-axis) graph is plotted with the help of “Line
Profile” tool (present under the “track” menu).[11]
Then, a line is drawn across the region which is to be
examined (the spectral spots) by holding the shift and left mouse keys simultaneously. The distance from
the origin to the first order maxima are measured in pixels with the help of “Tape Measure” tool (under
“Measuring Tools” in “Track” menu). The average distance was found out to be 1479.5 pixels.
Figure 6: calibration of D in pixels using sodium vapour lamp and Tracker software (the intensity vs wavelength
graph is on the right)

7. The wavelength lambda of sodium vapour lamp is 589.3 nm (average), hence the value of D in pixels from
(1) is:
𝐷 =
. ( )∙ . ( )
. ( )
= 8502.59 𝑝𝑖𝑥𝑒𝑙𝑠 (5)
The conversion from pixels back to wavelength in nm is thus given by:
𝜆 =
( )∙ ( )
( )
= 0.3983 ∙ 𝑥 (𝑛𝑚) (6)
The wavelength can be calculated separately in excel or the conversion formula from pixels to nm can be
fed into Tracker itself with the help of the “Data Builder” tool. This appears on clicking the x-axis of the
intensity plot and then clicking “Define” which helps in setting a user-defined function.
Figure 7: Data Builder Tool in Tracker for scaling the x-axis according to a user-defined function
Spectrum Analysis
After the calibration was done, we could move on to the spectrum analysis part. The sodium vapour lamp
was replaced with various LEDs and photographs of the resulting spectra were captured (without
disturbing the setup).[12]
The photographs were then loaded into Tracker and the intensity profiles were
plotted as described above. The characteristic peak wavelength was read off directly from the plot (since
the x-axis had been calibrated into nm with the help of “Data Builder” tool as described above).
Figure 8: Blue LED Spectrum

8. Figure 9: Blue LED spectrum shot in monochrome (black and white); the spectrum is faint to the eye but strong
enough to be picked up by Tracker
Figure 10: Tracker Analysis of Blue LED Spectrum

9. Figure 11: Zoomed-in version of blue LED spectrum intensity vs wavelength plot obtained by Tracker
Comparing with Ocean Optics Spectrometer
After performing the entire experiment, we compared our results with those obtained from Ocean Optics.
The LED was connected to the power supply and placed in an “Integrating Sphere” which was connected
to the Ocean Optics spectrometer (HR4000 in our case). The SpectraSuite software was launched on the
laptop to which the spectrometer was connected. The plot of intensity vs wavelength was obtained in the
SpectraSuite tab.
Figure 12: Blue LED spectrum analysis with Ocean Optics SpectraSuite

10. Experimental Data and Result
d = 3386.67 nm
D = 8502.59 nm
COLOUR
CHARACTERISTIC PEAK WAVELENGTH (nm)
PERCENTAGE ERROR
EXPERIMENTAL VALUE
VALUE FROM OCEAN
OPTICS
Blue 459.78 460.70 0.20
Bright Green 519.73 521.64 0.37
Green 510.95 510.89 0.01
Parrot Green 574.60 572.00 0.45
Orange 593.50 591.66 0.31
Yellow 603.30 605.00 0.28
Red 634.40 640.00 0.87
Conclusions
We have presented a low-cost method in this work which helps in analysing the spectra of various LEDs
and determining their characteristic peak wavelengths. The error in the experimentally determined values
is very small, of the order of 1%. This suggests the high degree of accuracy involved. Thus, the low-cost
setup is easy to implement at the undergraduate and school level, as well as accurate. If sodium vapour
lamp is unavailable, then commercially available laser pointers can be used but care should be taken that
laser light should not directly fall on the camera lens as it might get damaged due to the extremely high
intensity, instead, it can be taken on a white sheet of paper. Students will be exposed to various
experimental (setting up the apparatus, capturing photographs) and computational (use of software for
analysis) techniques with the help of this experiment.
Acknowledgements
This undergraduate student project was carried out under the National Initiative on Undergraduate
Science (NIUS) programme at Homi Bhabha Centre for Science Education-Tata Institute of Fundamental
Research (HBCSE-TIFR), Mumbai. The authors express their gratitude to the HBCSE authorities and the
staff at NIUS optics laboratory for their constant help and support during the study.
References
[1] Wikipedia, “Light-emitting diode”, https://en.wikipedia.org/wiki/Light-emitting_diode
[2] Wikipedia, “Sodium-vapor lamp”, https://en.wikipedia.org/wiki/Sodium-vapor_lamp
[3] Ocean Optics, product description of HR4000, https://oceanoptics.com/product/hr4000-custom/
[4] Tracker software, https://physlets.org/tracker/
[5] Douglas Brown and Anne J Cox, “Innovative Uses of Video Analysis”, The Physics Teacher, 47, 145
(2009)

11. [6] M Rodrigues and P Simeão Carvalho, “Teaching optical phenomena with Tracker”, Physics Education,
49, 671 (2014)
[7] Ajoy Ghatak, Optics, 5th
ed, McGraw Hill Education (India) Pvt. Ltd., New Delhi (2012)
[8] Eugene Hecht, Optics, 2nd
ed, Addison-Wesley Publishing Co., New York (1987)
[9] Douglas Brown, “Spectroscopy Using the Tracker Video Analysis Program”, AAPT (2005),
https://physlets.org/tracker/download/AAPT_spectroscopy_poster.pdf
[10] M Rodrigues, M B Marques and P Simeão Carvalho, “Measuring and teaching light spectrum using
Tracker as a spectrometer”, Proc. SPIE 9793, 97931L (8 October 2015); doi: 10.1117/12.2223120
[11] YouTube, “spectrum analysis”, A tutorial on using Tracker for spectroscopy,
https://www.youtube.com/watch?v=UCCPkJpUQEw
[12] The photographs of the LED spectra and their corresponding intensity profiles obtained from Ocean
Optics SpectraSuite can be viewed at the following links:
https://drive.google.com/drive/folders/1SLgocTTX_6d_7DqSL-vBdxcnH8yp6S3n
https://drive.google.com/drive/folders/0B_FPp3wuZ1qqTHNSbDFCN0liSXM