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A simple spectrophotometer using common materials and a digital camera

This article has been downloaded from IOPscience. Please scroll down to see the full text article. 2011 Phys. Educ. 46 332 (http://iopscience.iop.org/0031-9120/46/3/014) View the table of contents for this issue, or go to the journal homepage for more

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A simple spectrophotometer using common materials and a digital camera Eko Widiatmoko, Widayani, Maman Budiman, Mikrajuddin Abdullah and Khairurrijal1 Department of Physics, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Jalan Ganesa 10, Bandung 40132, Indonesia E-mail: [email protected]

Abstract A simple spectrophotometer was designed using cardboard, a DVD, a pocket digital camera, a tripod and a computer. The DVD was used as a diffraction grating and the camera as a light sensor. The spectrophotometer was calibrated using a reference light prior to use. The spectrophotometer was capable of measuring optical wavelengths with a theoretical accuracy as high as 0.2 nm. Using this spectrophotometer, wavelengths are determined via image processing.

Introduction In the present day, spectrophotometry is known as a well-established method both in physical and chemical quantities measurements. For example, spectrophotometry has been used in determining absorbance, film thickness and semiconductor band gap [1–3]. Unfortunately, standard spectrophotometers are expensive and they have complex instrumentation too. Their use is also limited to researchers in universities and research institutions. Those reasons have led to the design of a simple and lowcost spectrophotometer, which can be built and operated by students in classrooms as well as ordinary people. Several simple spectrophotometers have been designed using easily obtained materials such as cardboard and gratings made from digital versatile discs (DVDs) [4–6]. In addition, they are mainly 1 Author to whom any correspondence should be addressed.

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46 (3)

intended for direct visual observations, in which wavelengths can be obtained by looking at a scale which could be linear or angular. The ability of a digital camera to record spectra would be a great advantage in designing a simple spectroscope. The images could be saved, manipulated, and displayed on a computer. This approach has been reported previously in [7], where the spectrum image was printed and measured manually. However, with fully digital methods, wavelength measurement can be more precise and faint spectral lines can be detected. In this article, we describe a spectroscope design intended to be used with a digital camera. The spectroscope is made of cardboard and a DVD grating. The spectroscope is mounted on an adjustable support, also made of cardboard, to align its position relative to the camera and tripod. We also demonstrate that the spectroscope can be calibrated and, in turn, can be used as a spectrophotometer.

0031-9120/11/030332+08$33.00 © 2011 IOP Publishing Ltd


45 º 3 cm

slit 20 cm (a)

grating

(b)

Figure 1. (a) Schematic diagram and (b) photograph of the designed spectroscope with a circular hood to block stray light.

The spectrophotometer can be used in introducing the light spectrum and spectrophotometry in classrooms because the cardboard structures are light and portable. It means that the simple and low-cost design spectrophotometer may replace ‘real’ spectrophotometers for that purpose. Another advantage is that the simple spectrophotometer is easy to operate and students, therefore, can conduct experiments without demanding any assistance.

Spectrophotometer design The first part of a spectrophotometer system is a spectroscope box. As illustrated in figure 1(a), the spectroscope consists of a long cardboard box with two ends. One end of the long cardboard box has an entrance slit that allows light to enter the spectroscope and the other end has a window covered by a grating. A photograph of the designed spectroscope is shown in figure 1(b) with the grating situated at the right side. The spectroscope box was made from six separated pieces of cardboard. The first piece is a long box without lids at its ends. The second is a 3 cm × 3 cm square piece with a 1.5 cm × 1.5 cm square hole in the middle that serves as a slit holder. The slit itself was made from two rectangles of 1 cm × 2 cm cardboard, May 2011

Figure 2. Grating extraction from a DVD.

which were cut carefully in order to make straight edges. Then, these two pieces were placed and glued at the hole to form a 0.5 mm width slit, as recommended in [8]. This method eliminates the difficulty of cutting a thin slit directly in cardboard. On the other side of the long box, the grating was mounted in a similar way to the slit. A rectangular cardboard window was made to hold the grating. The last part is a circular hood to block stray light, as shown in figure 1(b). The diameter was adjusted to accommodate the camera lens. The grating was made from a DVD. Noting that the recording tracks are circles equally spaced by 0.74 μm, the grating has about 1350 lines mm−1 [9]. A rectangular piece of 1 cm × 2 cm in size was cut from the DVD as shown in figure 2. The segment was then sliced by a knife to separate the bottom layer from the upper. The remaining reflective coating on the bottom layer was peeled off using sticky tape [10]. The transparent bottom layer, which is now ready to use as a transmission grating, was placed on the end of the box, with the ruled side facing inwards to avoid damage from accidental touches. The grating is placed at a specific angle so that the first-order diffracted rays will come out roughly perpendicular to the grating. Applying the grating equation [11]

D(sin θd − sin θi ) = mλ,

(1)

where θd is the angle of diffracted rays, θi is the incident angle to the grating normal (45◦ ), D is the grating length constant, m = −1, and λ is set to visible light (400–700 nm), this makes the first-order diffraction pattern come out at 9.6◦ to −13.8◦ from the grating normal. The grating is placed very close to the camera lens so that a small grating could provide a large angle of view. PHYSICS EDUCATION

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(a)

(b)

Figure 3. Overall spectroscope construction.

To mount the spectroscope to the camera, a set of support structures is placed to adjust the box position relative to the camera in three axes. The structures can be fixed between the camera and the tripod. The overall construction is shown in figure 3 and more detailed pictures are shown in appendix A. All the structures were made of cardboard. Without support structures, the spectroscope can also be used for direct visual observations.

(c)

Figure 4. Spectral images taken with a Fujifilm A100 pocket digital camera with an image size of 5 megapixels: (a) philips TLD10W/54 fluorescent lamp, (b) cadmium discharge lamp, (c) helium discharge lamp (images were resized and cropped).

Si

Results and discussion

A

Spectral images It was found that placing a second slit near the grating makes images become sharper but more difficult to see and to record. Not only does the image get fainter, but also the viewing position must be more precise. The recorded image contains only a part of the spectrum. Therefore, the spectroscope design does not use a second slit. Typical spectral images with one slit are shown in figure 4. The length of the spectroscope box affects spectrum viewing as follows. During visual observations with various box lengths, the eye must focus to different distances to see sharp images. Figure 5 shows image construction for a particular wavelength. In Fraunhofer diffraction, the light rays coming to the slit are parallel, and the diffraction pattern is formed far away from the grating. However, in this arrangement the light ray direction is more like that of a pinhole camera with finite hole (slit) width. The effect of the slit width will be discussed later in this text. The finite angle of incoming light rays means that the 334

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L

B

R

Figure 5. Image construction diagram. For details, see text.

diffraction pattern is located somewhere in front of the grating. If the incident angle difference of two incoming monochromatic light rays A and B is dθ , then the first-order diffracted rays will also differ by dθ . It is seen in figure 5 that the distance between the points where those rays strike the grating is R dθ L= . (2) cos θi Therefore, the image distance from the grating can be written as

si =

R cos θd L cos θd = . dθ cos θi

(3)

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(a)

(b)

(c)

Figure 6. Spectral images with a box length of (a) 10 cm, (b) 20 cm, (c) 30 cm, with the camera focus set to infinity (‘fireworks’ mode).

Because θi = 45◦ and cos θd is in the range of 0.97–1, the spectroscope box requires the eye, or the camera, to focus at a distance that is roughly 1.4 times the box length. However, most pocket digital camera models have only an automatic focus system. Some cameras even cannot focus because of the darkness. Another option is ‘fireworks’ mode, which sets the focus to infinity and the exposure time adjustable. A longer box makes more distant spectrum images, which is more comfortable to the eye. When the camera focus is set to infinity, the longer box will give sharper images, as demonstrated in figure 6. But a box longer than 30 cm is impractical to build and use. However, if the camera can be focused, a 20 cm box could make good pictures. Converting to wavelength Converting the spectral image into wavelength information is independent of the imaging method. Any spectral picture can be converted if the relation between pixel position and wavelength is known. To obtain this relation, the observer must first take a spectrum with known wavelengths and calibrate the pixel scale into wavelength. If the position of the grating from the camera is constant, the spectral image position will also be constant. Calibration must be done right after assembling the system. The configuration may be different for each assembly, but must be constant May 2011

Figure 7. Incandescent lamp spectrum image (above) and the corresponding pixel intensity curve (below).

for one measurement batch. The light source used for calibration may be a fluorescent lamp, which can be found anywhere, or a discharge lamp (hydrogen, helium, cadmium, mercury, etc), which are usually found in laboratories. When observing pixel values, it is found that spectral line brightness cannot be measured correctly. A spectrum of an incandescent light bulb, which is like a blackbody radiation spectrum, is shown in figure 7. The greyscale pixel value graph differs greatly from that of a blackbody. It seems that the camera’s red, green and blue filters are blocking certain wavelengths. Besides, when one points the spectroscope to different parts of the light source, a portion of the spectrum can change in brightness. This is because of the absence of a collimator. The bandwidth of the spectrometer can be calculated from the graph in figure 7. The edges of the spectral image represent the bandwidth, which is in the range of 415–660 nm. This limitation is certainly set by the camera filter and not by geometry such as lens diameter and sensor chip size, because the spectral image only occupies a small region roughly in the middle of the overall image. When the camera position is adjusted slightly, the position of the spectrum changes but the spectral pattern is the same. When using larger image sizes, the wavelength resolution also increases. The value of wavelength difference per pixel (inverse of the coefficient of p in the calibration function) increases linearly with image width in pixels. When compared with image megapixel numbers, this value was roughly proportional to (megapixels)1/2 . This relationship is given in figure 8. Here we give an example of a calibration result. With an image PHYSICS EDUCATION

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Table 1. Calculated wavelengths from figure 10 and the related reference wavelength. Pixel

Measured ˚ wavelength (A)

Wavelength of mercury ˚ from [12] (A)

1504 2045

4360.0 5465.2

4358.335 5460.75

size of 10 megapixels and no camera zoom, the calibration function obtained is ˚ ). λ = 2.043 p + 1287.6 (A

(4)

This equation is related with the graph in figure 9. This corresponds to a resolution limit of 0.2 nm/pixel. As another example, the spectrum of a fluorescent tube lamp was taken and is shown in figure 10, and the wavelengths were calculated with equation (4). Mercury spectral lines from NIST data were used as reference. As shown in table 1, the accuracy is 0.5 nm. Resolving power and errors The slit width limits the resolving power. A wider slit produces a larger angular size of the spectral 336

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lines. For example, when the slit width is 0.15 mm (measured by a feeler gauge) and the box length is 20 cm, the angular size of the slit as seen from the grating is 0.75 mrad. The angular size of the spectral line images is the same as this value. From the grating equation in equation (1), this angle corresponds to 0.55 nm in wavelength difference. The helium spectrum in figure 9(a ) is magnified at the brightest peak at 501.5 nm, which is shown in figure 11. The full width at half maximum (FWHM) of this peak is 3 pixels. This corresponds to 0.6 nm, which agrees with the prediction before. May 2011


Figure 10. Fluorescent lamp spectrum (above) and pixel intensity graph (below). Figure 11. Magnification of the He spectral line (above) at 501.5 nm and its FWHM (below).

The errors in wavelength measurements came mainly from the error of spectroscope positioning relative to the camera. When measuring the same light spectrum multiple times, the accuracy obtained was 0.5 nm. But when other light sources are used, the spectroscope assembly may misalign, which results in errors in the next measurements. Errors can also come from the grating. If the grating is not carefully cut from the DVD, the lines may be tilted. Misalignment during spectroscope construction can also tilt the grating and this causes the spectral image to tilt. The spectra in figure 4 are slightly tilted clockwise. Furthermore, the curved nature of the tracks in a DVD makes the spectral lines also curve. These errors make the spectral line positions uncertain. However, this uncertainty can be minimized by taking lines from the same y -coordinate for every image. Use of a camera’s optical zoom improves wavelength resolution, but the spectrum became harder to record properly. For example, when the mercury spectrum was zoomed, the middle of the image was featureless—only a smooth, continuous spectrum on which our camera could not focus.

Discussion The spectroscope is easy to use. With a tripod and camera, it requires only a few minutes to assemble and to take a single spectrum. The longest part of the measurement process is the alignment of the spectroscope with the light source. Spectral image analysis can be carried out with or without a special computer program. Without it, the experimenter should open the image in any available image viewing program, May 2011

such as Microsoft Paint, point at the spectral lines one by one, and write down the pixel positions. The pixel data are then compared with a reference to obtain a calibration function that relates a pixel to a wavelength. We wrote a program in Visual Basic to partly automate the calibration and image conversion. The user opens a calibration image file, points at the spectral lines, selects known wavelengths, and presses a button to do the mathematics. Once a calibration function from pixel to wavelength is known, other images with unknown wavelengths can be identified. The program can also analyse a horizontal line across an image and plot pixel greyscale values along that line. The flowchart of the program is shown in appendix B. For use in the classroom, the spectrophotometer can be used to introduce the light spectrum and spectrometry to students. The simple and lowcost design can replace ‘real’ spectrophotometers for this purpose because the cardboard structures are light and portable. The advantages of this spectrophotometer design are as follows. The spectroscope can and should be connected with a digital camera. The spectroscope is easy to build, although it needs some handicraft experience, and the materials are common. The spectrophotometer must be calibrated prior to measuring wavelengths. A known problem in using the spectroscope is alignment of the light source, because one must look in a direction that is different from the light source direction, and some people have difficulty in finding the right position to see the spectrum. We asked 25 students to use this spectrophotometer and we received positive responses. The PHYSICS EDUCATION

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E Widiatmoko et al students were able to carry out the experiment themselves after being given a short training session of 15 min. Senior high school students, who had a little or no knowledge about the spectrophotometer principle, and undergraduate students, who had the knowledge, agreed that the instrument helps in understanding the concept of the light spectrum and spectrometry (80%); that it is easy to use (68%); and that they were willing to do further experiments to increase their understanding (96%).

Appendix B

calibration

obtaining the wavelength

open image file containing known wavelengths

open image file

user selects a pixel row

user selects a pixel row

display pixel greyscale value graph

display pixel greyscale value graph

user selects a spectral line

user points at a pixel of interest

line position (pixel)

pixel x-position

repeat for other pixels

repeat for other pixels

Conclusions A simple spectrophotometer design using cardboard, a DVD, a pocket digital camera, a tripod and a computer has been discussed and tested. The advantages of the spectrophotometer are that it is easy to construct and is inexpensive. The theoretical accuracy of the spectrophotometer depends on the image size of the digital camera, for example 0.2 nm for 10 megapixels. The images taken with the camera need to be calibrated for each measurement batch and then converted into wavelength. Spectral line brightness measurement using the spectrophotometer was unreliable.

Appendix A

select wavelengths from reference

make calibration function

end

known wavelength list

calibration function

convert pixel position to wavelength

wavelength data

end

Figure B.1. Flowcharts for the spectrum reading program. Received 10 November 2010, in final form 9 February 2011 doi:10.1088/0031-9120/46/3/014

References

Figure A.1. Detailed spectroscope assembly pictures. 338

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[1] Evdokimov I N and Losev A P 2007 Potential of UV–visible absorption spectroscopy for characterizing crude petroleum oils Oil Gas Bus. 1–21 www.ogbus.ru/eng/authors/ Evdokimov/Evdokimov 1e.pdf [2] Huibers P D T and Shah D O 1997 Multispectral determination of soap film thickness Langmuir 13 5995–8 [3] Abdullah M, Khairurrijal, Iskandar F and Okuyama K 2006 Nanocrystalline Materials: Their Synthesis–Structure–Property Relationships ed S C Tjong (New York: Elsevier Science) chapter 9 (Semiconductor Nanoparticle–Polymer Nanocomposites) pp 275–310 [4] Edwards R K, Brandt W W and Companion A L 1962 A simple and inexpensive student spectroscope J. Chem. Educ. 39 147–8 [5] Thompson K 1996 An easy-to-build spectroscope Phys. Educ. 31 382–5 [6] Wakabayashi F 2008 Resolving spectral lines with a periscope-type DVD spectroscope J. Chem. Educ. 85 849–53 [7] Wahab M F 2009 Estimating the wavelength of sodium emission in flame—the easy way Phys. Teach. 47 367 May 2011

A simple spectrophotometer using common materials and a digital camera [8] Wakabayashi F and Hamada K 2006 A DVD spectroscope: a simple, high-resolution classroom spectroscope J. Chem. Educ. 83 56–8 [9] Vollmer M 2005 Diffraction revisited: position of diffraction spots upon rotation of a transmission grating Phys. Educ. 40 562–5 [10] http://ioannis.virtualcomposer2000.com/ spectroscope/toyspectroscope.html; electronics.howstuffworks.com/dvd2.htm [11] Giancoli D C 2009 The wave nature of light Physics: Principles with Applications 6th edn (New York: Addison-Wesley) ch 24 [12] Ralchenko Yu, Kramida A E, Reader J and NIST ASD Team 2008 NIST Atomic Spectra Database (Version 3.1.5) (online) available at http://physics.nist.gov/asd3 (10 December 2009), National Institute of Standards and Technology, Gaithersburg, MD Eko Widiatmoko received a BSc in physics with Cum Laude from Institut Teknologi Bandung (ITB), Indonesia in 2008. At present, he is studying for an MSc in physics at the same university and is a physics laboratory instructor at a private senior high school. He is also an instructor at a private learning centre on robotics. His works are mainly about basic physics and electronics. He is also interested in cardboard constructions. Widayani received BSc and MSc degrees in physics from Institut Teknologi Bandung in 1984 and 1991, respectively, and a PhD in polymer science from The University of Manchester Institute of Science and Technology (UMIST), Manchester, UK in 2003. In 1990 she joined the Faculty of Mathematics and Natural Sciences, ITB and is currently an associate professor of polymer physics. She is involved in research on natural-fibre polymer composite. In recent years, she has also been interested in physics teaching and education.

May 2011

Maman Budiman received a BSc in physics from Institut Teknologi Bandung in 1989 and MEng and PhD degrees in physical electronics from Tokyo Institute of Technology, Japan in 1995 and 1998, respectively. He joined the Faculty of Mathematics and Natural Sciences, ITB in 1991 and is currently an assistant professor. He research is in optoelectronic materials and devices as well as embedded systems and instrumentation. He is also interested in physics teaching and education.

Mikrajuddin Abdullah obtained BSc and MSc degrees in physics from Institut Teknologi Bandung in 1992 and 1996, respectively, and a DEng in chemical engineering from Hiroshima University, Japan in 2002. In 1994 he entered the Faculty of Mathematics and Natural Sciences, ITB, where he is currently a professor of physics of nanomaterials. His research topics include nanomaterials and nanodevices, as well as electronics and instrumentation. He is also interested in physics education.

Khairurrijal received BSc and MSc degrees in physics from Institut Teknologi Bandung in 1989 and 1993, respectively, and a DEng from Hiroshima University, Japan in 2000. He joined the Faculty of Mathematics and Natural Sciences, ITB in 1991 and is currently a professor of physics of materials and instrumentation. He is extensively involved in research on electronic materials and devices as well as electronics and instrumentation. He is also interested in physics education.

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