Determination of atmospheric ozone content through absorption of red and green light

__MATHJAX_DOLLAR__ Research Group: Evan Anders, Nick Brunner, James Giltz, and Alden Welsch

Launch: Whitworth Fall 2012

An integrating sphere was constructed from two half wiffle balls with a pair of LEDs (green and red) and a pair of accompanying wavelength-selective photodiodes. It was assumed that, as the molecular components of the interior of the integrating sphere changed, the measured photodiode voltages would change. Our purpose was to determine the atmospheric ozone concentration at increasing elevations through analysis of the measured voltage readings of the photodiodes. The integrating sphere ascended to high levels of the trophosphere, and data was recorded during its ascent and fall; unfortunately, significant design problems distorted data during the descent, and introduced an astounding amount of noise throughout the entirety of the flight. Although not performed before launch, calibration attempts were made after the experimental apparatus was recovered. Unstable calibration apparatus damaged the circuit beyond repair, and minimal meaningful data was gathered. A discussion of experimental theory and methods follows.

Importance of Ozone in the Atmosphere
Earth’s atmosphere is mostly contained within 11 km (36,000 ft) of the surface. Most of human activity takes place in the troposphere, the lowest of the layers of the atmosphere, beginning at the surface and ending around 9 km (30,000 ft), depending on geography and weather. The atmosphere extends through the stratosphere (up to 51 km, 170,000 ft), the mesosphere (up to 85 km, 280,000), the thermosphere (up to 380 km, 240 mi), and the exosphere (not easily defined). A variety of gases fill this space, including nitrogen (N2), oxygen (O2), argon (Ar), carbon dioxide (CO2), neon (Ne), helium (He), hydrogen (H2), and ozone (O3). Although ozone only makes up about 0.07 ppmv (parts per million by volume) or 7 x 10-6 % of the total material in the atmosphere, ozone is important for the absorption of ultraviolet (UV) light from the sun, which is harmful to life on Earth. This makes the detection and measurement of ozone important those studying the environment and the impact it has on the ecology of life on Earth. The ozone layer is located inside the stratosphere and upper regions of the troposphere and the concentration of ozone in this layer is 2 to 8 ppm. Weather balloons often fly to heights in the stratosphere, so the amount of ozone in this layer can be fairly easily measured. Ozone absorbs light in the UV spectrum, as well as in the visible spectrum of light. The amount of ozone, then, can be detected by measuring the amount of light that is absorbed by the ozone.

This experiment sought to measure the amount of green and red light (wavelengths of 632 nm, and 523 nm) absorbed by ozone in the stratosphere. Light-emitting diodes of each wavelength and photo-diode detection circuits were encapsulated in a space to allow for fluctuation in absorbed light to be detected.

Experimental Theory


A substance's absorption cross section, $$\sigma$$, can be expressed in terms of

$$ \epsilon = \sigma/$$ln 10,

where $$ \epsilon $$ is the molar absorptivity coefficient, and both $$\epsilon$$ and $$\sigma$$ are in units of M-1 cm-1. Rearranging and converting molarity (mol/L) into units of (1/cm^3) through multiplication by a factor of 1000 and division by Avogadro's number, we can obtain the substance's absorptivity in terms of its cross section in the widely used units of cm2, such that

$$ \epsilon = \sigma/(3.82 \times 10^{-21}) $$.

Utilizing this relation alongside the Beer-Lambert Law ,

$$ T = 10^{-\epsilon c l}$$ ,

we can measure the transmissivity, $$T$$, of the light as it travels over a path of length $$l$$ through some concentration of the substance in question.

In an experimental setup utilizing an LED and a photodiode, data will be obtained as some voltage, not some transmissivity. The LED outputs light of a number of wavelengths, all at a number of different intensities, with the peak wavelength being the most intense. Additionally, a wavelength-selective photodiode has a responsivity curve, detecting each wavelength of light with a varying sensitivity. The detection of the photodiode is translated by its circuit into a voltage by some proportionality factor. Utilizing the absorption cross section definition, the Beer-Lambert law, and the physical properties of this experimental setup, it is determinable that

$$ V_{\lambda} = k I_\lambda d_\lambda 10^{\alpha \left(\sigma_\lambda c\right)} $$,

where for some wavelength, $$\lambda$$, $$V_\lambda$$ is the voltage of detected, $$I_\lambda$$ is the intensity of emitted light, $$d_\lambda$$ is the detector responsivity, $$k$$ is an unknown constant determined by the photodiode circuit, and $$\alpha$$ is an unknown constant which includes the path length. Unfortunately, this is an over-simplified model, which assumes the light is passing through only one substance. This is not the case; in reality, light passes through air as well as ozone. As such, the equation can be modified to include both of these things, such that

$$ V_\lambda = kI_\lambda d_\lambda 10^{-\alpha\left( \sigma_{\lambda, ozone} c_{ozone} + \sigma_{\lambda, air} c_{air} \right)} $$.

At this point, it is necessary to take note of some of the elements of properties of air which further complicate our procedure. Air is composed of a number of different molecules, the concentrations of which change individually as altitude increases, according to the barometric formula ,

$$ c = c_0e^{-\frac{Mgh}{RT}} $$

where $$c$$ is the atmospheric concentration at a certain altitude $$h$$, $$c_0$$ is the atmospheric concentration at sea level, $$g$$ is gravity's acceleration, $$T$$ is temperature, $$R$$ is the universal gas constant, and $$M$$ is the molar mass of the molecule in question.

Not only does each constituent of air have its own variable concentration, but their cross sections vary as well. Our once-simpler expression now becomes

$$ \sigma_{\lambda, air}c_{air} = \displaystyle\sum_{j}\left(\sigma_{\lambda, j}c_j\right) $$

for each $$j$$ particle which significantly contributes to air. At this point, we can return to our expression for the photodiode's voltage, now modified such that

$$ V_\lambda = kI_\lambda d_\lambda 10^{-\alpha\left( \sigma_{\lambda, ozone} c_{ozone} + \displaystyle\sum_{j}\left(\sigma_{\lambda, j}c_j\right) \right)} $$.

Unfortunately, this is but one wavelength. In reality, an LED of a specific color emits a number of wavelengths, so the total voltage recorded by the selective photodiode is really a summation of all of the voltage contributions of individual wavelengths, such that

$$ V_{color} = k_{color}\displaystyle\sum_{i} I_i d_i 10^{-\alpha \left( \sigma_{i, ozone} c_{ozone} + \displaystyle\sum_{j}\left(\sigma_{i, j}c_j\right) \right)} $$.

Where $$V_{color}$$ is the voltage of one wavelength selective photodiode, and a different--yet linearly proportional--spectrum must be obtained for each of the voltages. In our experiment, we utilized an integrating sphere with two LEDs: red and green, as well as two matching wavelength selective photodiodes. The emissivity spectra of our LEDs is shown in figures 1.2 and 1.3.

After gathering known information for absorption cross sections and calculating concentrations, two unknown constants remain in our equation relating voltage and ozone concentration, $$k$$ and $$\alpha$$. The constant $$k$$ is determined based on circuitry, while the constant $$\sigma$$ depends on the dimensions of the integrating sphere. A test utilizing a constant ozone concentration and a test using a known concentration of ozone can be used to produce a system of equations to calculate these unknowns. Upon the determination of these constants, the concentration of ozone can be measured through the absorption of light.

We were able to obtain an O3 cross section for relevant wavelengths (see Fig 1.1) as well as a partial O2 cross section, but research efforts did not succeed in obtaining further cross section data in the visible spectrum. Raw cross section data and calculated emissivity information for our LEDs are attached:.

Mechanical




Diagrams
Figures 2.1-2.4 show the physical specifications of our experimental apparatus.

Construction Notes
The pod was constructed out of five pieces of foam. A current of greater than 2 A was run through the nichrome wire, producing significant heat such that the wire could melt and carve the foam. The pod's top and bottom were cut from 1 in thick foam with dimensions of 15.5 cm on each side. The three body sections were cut from 2 inch thick foam, with a square interior removed. The exterior body section dimensions are 15.5cm x 15.5cm and the interior body section dimensions are roughly 11cm x 11cm.

Once the foam pieces of the pod were cut, epoxy was prepared and used to attach the three middle sections together; the base was attached to the end of this structure using epoxy, while the top plate was left separate.

We then cut two 22 cm sections of a thin, hollow, hard plastic tube and placed them at opposite (diagonal) corners of the box, with their ends extending roughly 1 cm out of the bottom surface of the box. We pushed the lid of the box onto the hollow tubes to open a space for them to pace through in the foam of the lid. At this point, the lid was removed such that the tubes could be epoxied into the box, securing them firmly in place.

In order to fit the fan in the side of the pod, we cut a square hole in its middle body section and measured it to be slightly larger than the fan itself. The fan was then placed in this opening and hot glued into it. Special care was taken to not allow glue to touch the fan blades.

When the materials were all constructed, we hollowed out the lid of the pod with the soldering iron such that there would be enough room for the transmitter to fit in the roof of the pod. As a note to future groups, it is unwise to hollow out any part of the box with a soldering iron, as it is detrimental to the soldering iron and the air quality of the room--a different means should be discovered.

After constructing the pod, we set about constructing the circuits for the photodiodes, LEDs, and fan (see Electrical section). We soldered these circuits together and then hot glued the connections to make them more durable. Additionally, we salvaged the ozone sensor circuit utilized two years ago and attached it to our +/- 9V rails and our ground.

After creating these circuits, we turned our attention towards the integrating sphere. Our integrating sphere was constructed of epoxy and two half 9cm-diameter wiffle balls. Two large holes were placed along the axis of the sphere for air input and ouput, and four small holes were created (in sets of two, with a 90 degree arc between the sets) for the circuit elements. After the integrating sphere was connected, it was surrounded in aluminum foil to significantly reduce the quantity of light which escaped the sphere. After the sphere was constructed, LEDs and photodiodes were hot glued into appropriate holes.

Once all of this was complete, we placed the ozone sensor at the bottom of our pod, and placed our photodiode/LED/fan circuit along one wall of the box. The integrating sphere was placed such that one of its circulation holes faced the input fan, and all of these elements were secured using hot glue and duct tape. Finally, when the balloon was launched, the batteries were secured to the sides of the pod using duct tape.

Special Structural Purchases
 * Wiffle Ball x 2

Electrical






Figures 3.1-3.3 display all circuits implemented in the construction of our pod.

To acquire data, the quantity of emitted light which was detected after traveling throughout the integrating sphere had to be measured. Wavelength-selective photodiodes for both color ranges were used to measure the amount of light in the integrating sphere. As a means of validation (to determine if decreases in detected light intensity related to increasing ozone contents or some other factor) an ozone sensor was placed inside of the apparatus.

Circuits used include two photodiode detector circuits, a circuit used to power both LEDs and the fan, and an additional circuit which was used to supply power to and amplify voltages from an ozone sensor. Outputs of all circuits connected to a master radio transmitter (DAQ), and all circuits were powered by Li-ion 9 V batteries.

The photodiode circuit consists of three parts: a light detector, an inverting amplifier, and a voltage divider. The light detector utilized an LM741 op amp and a selective photodiode, producing a negative voltage when appropriate wavelengths of light are detected. This negative voltage was then run through the inverting amplifier to turn it into a positive voltage (as only voltages in the range of 0-5 V could be sent through the DAQ) and to magnify it. During final circuit tests, it was discovered that our inverting amplifier produced a voltage over 5 V in some cases; for this reason, we added a voltage divider at the end of both of our circuits to ensure that damage would not be done to the DAQ. Had the circuit been fully tested prior to construction, the inverting amplifier resistor values would have changed and the voltage divider would be removed from both circuits.

Testing


Of the two tests required for meaningful interpretation of data mentioned in our Introduction, we were only able to successfully complete one. As such, we do not have the required data to produce an accurate relationship between altitude and atmospheric ozone content. Additionally, no testing occurred until after our balloon launch; as such, our circuit was damaged and recorded voltages were consistently lower than before the launch. Recognizing this, even if we had successfully completed both required tests after the flight, our results would have been off by some constant. Regardless, discussion of conducted tests follows.

Test 1: Constant Concentration of Ozone
We powered our pod with three Li-ion 9 V batteries and attached the probes of a Fluke 199 Scopemeter Oscilloscope to the red photodiode output and green photodiode outputs of our pod. In a laboratory with a constant concentration of ozone (essentially zero), we collected data for roughly two hours, results of which can be seen in the attached figures and datasheets. After an initial drop in voltage, the batteries began to supply power consistently and the voltage reading of the photodiode circuits was constant for the next hour and a half. At this point in time, someone opened the lab door and it slammed closed, which put causing vibrations in the room and resulted in a significant amount of noise in the readings. After a minute or two, the readings stabilized to a constant value. After approximately fifteen more minutes, the door was once again opened and slammed shut, which sent an even greater degree of noise into the circuit, from which it took roughly five minutes to calm down to normal values.

This test supported two conclusions:

  The light detected by our photodiodes does not change in the presence of a constant concentration of ozone.  Vibrations in the environment introduce a large degree of noise into our circuit (an unfortunate result for a circuit meant to collect data during a flight of constant buffeting).



Raw data from these tests is attached and shown in figures 4.1 and 4.2:





Test 2: Unknown Concentration of Ozone Greater than Background Concentration
Despite the fact that we knew that our photodiode circuits did not output decreasing voltages in the presence of a constant ozone concentration, we still needed to learn whether or not our circuit would output decreased voltages in the presence of increased ozone concentration. As such, we set out to obtain an unknown concentration of ozone greater than that of air's. We obtained an Ealing Timing Pulse and Spark Source (model 33-026) as well a 6.5 inch tall, 3.0 inch outer diameter glass jar and a large plastic bag. We powered our pod with three 9 V Li-ion batteries, and we sparked the leads of the Ealing spark source inside of the glass jar for thirty seconds with the plastic bag over the apparatus. After turning off the spark machine and removing the leads from the jar, we placed it over the fan of our pod with our pod lid secured (as it was during the launch, without an output hole) and saw no change in voltage. We conducted a similar test with the lid off of the pod and viewed a similar lack of results. The same insignificant results were seen for tests utilizing 1 minute of sparking and 1.5 minutes of sparking. After two minutes of sparking, the ozone in the jar managed to produce a slight change in the measured voltage of one photodiode, but results were still minimal and likely caused by the decreasing strength of the batteries (which we detached and found to be delivering below 9 V.

After this discouraging lack of results, we chose to spark inside of our integrating sphere to create ozone directly in the light's path. Due to the decreased power output of the batteries we had been using and the utter lack of other batteries nearby, we used an Elenco XP-760 power supply to power our circuit with rails of +/- 9 V. We turned on the Ealing sparker, immediately saw a back emf of 130 V measured by the Elenco power supply, and saw one of our photodiode's readings drop to zero. Although the sparker was quickly turned off, the damage was done and testing efforts were concluded.

It has been determined that sparking and creating an inconclusive concentration of ozone is not an effective way to test our experimental apparatus, and that it is in fact a dangerous means of testing for the circuitry. If time and budget permit, a known, concentration of ozone should be obtained from an outside source, into which the integrating sphere should be placed. Refer to our Error Discussion and Suggestions for Future Work section for further details.

Gathered Data
Data gathered came from two sources: our specific experiment pod and the balloon command module.

Experiment Pod Data
Plots of raw data collected by our experiment pod can be seen both with respect to altitude and time in figures 5.1-5.3 (to the right). A decrease in photodiode voltage and ozone sensor voltage can be seen with respect to time, but there is no obvious correlation between altitude and voltage. Additionally, there is an exceptional amount of noise in data collected by the photodiodes, making it impossible to analyze. Essentially, the data collected by our pod cannot be analyzed to obtain any sort of meaningful relationship between ozone concentration and height, and is therefore useless. A discussion of these poor results follows below.

Raw data points are available:.

Command Module Data
Temperature and altitude data were gathered by the command module and were used to find the concentrations of the constituents of air on our launch day. Utilizing percentage-by-volume information on the constituents of air at sea level along with the ideal gas law,

$$ PV = nRT $$,

it was possible to determine the concentration of air at sea level in terms of moles per liter.

Utilizing the barometric formula (as displayed in our Experimental Theory section), we were able to obtain atmospheric concentration values for all constituents of air at all heights which our balloon reached. Graphs of concentration with respect to altitude can be seen in figures 5.4-5.11.

Raw concentration data points are available:.

Error Discussion and Suggestions for Future Work
As mentioned, our collected data was essentially meaningless; in an effort to guide future research groups to greater success, we have isolated specific reasons for our poor results.

Excessive Noise
The first major issue that we confronted with our collected data is that of significant noise, which can be seen throughout all data collected by our photodiodes over the duration of the balloon's flight. Our constant level of ozone test (see section on Testing) also showed that our circuit became less stable as time passed. While somewhat susceptible to outside vibrations affecting circuit results after first being powered, our results became increasingly more affected by outside movements as our circuit was powered for longer. Although we are uncertain of exactly why our circuit became less stable over time, we do understand what the major cause of this excessive noise was: poor circuit construction. Our suggestion for avoiding this significant noise is to take care while constructing all aspects of the circuit. This means that it is necessary to ensure that all wires are as short as possible and as flush with the circuit board or integrating sphere as possible. Our wires haphazardly bended every which way in our pod and were likely jarred by batteries, the integrating sphere, or other circuits every time our pod was buffeted. Each of these jars likely affected the electrical connections of our circuits, causing significant noise.

Lesson learned: Design and validate the circuit far in advance. Allow ample time for precise, clean circuit construction.

Ozone Concentration Decreased With Respect to Time, Not Height
The second and more startling issue displayed by our results was that ozone concentration and light intensity decreased over time rather than with increasing height. Luckily, this problem proved to have a very obvious cause: we failed to create an output vent for our pod. Although we created an input vent with a fan to draw air in from outside of the pod, we failed to create an output through which air and ozone could pass out of our pod. Essentially, air was sucked into our pod and had trouble escaping. This problem is easy to fix: add an output vent, which can either mean adding another hole with a fan to pull air out of the pod or leaving an open hole outside of the input hole to allow air to pass through.

Lesson learned: Design experimental apparatus wisely. When trying to create increased air flow, create a path for air to flow through.

Improper Testing and Calibration
We largely failed to plan ahead throughout the construction of our pod. Although we consistently validated that it functioned, we did not check for valid results (which led to the addition of a voltage divider after our inverting amplifier to ensure that no damage was done to our radio transmitter). This same trend happened with calibration; although we constructed a circuit which measured ozone concentrations, we did not calibrate it as outlined in our testing section.

In addition to carefully constructing circuits, it is important that circuits be calibrated such that their flight data can be interpreted into meaningful, significant data. In order to properly calibrate an ozone-measuring integrating sphere, it must be subject to two known concentrations of ozone: background ozone concentration and a greater, known concentration of ozone. No safe way to produce a known concentration of ozone is available at Whitworth, but there are companies which distribute known concentrations of gases such as ozone. It is imperative that future researchers never conduct tests using an Ealing 33-036 spark source or similar spark source to obtain an unknown concentration of ozone due to its danger to both human health and the functionality of electronics.

Lesson learned: Calibration is essential in order to achieve any meaningful experimental results. Additionally, it is important to carefully plan calibration efforts and to implement appropriate lab safety techniques.