Thermal Calibration of MISI

As the years pass by the world has become more dependent on information. The growing need of information has caused the rate at which we get it to be increasingly important. As the population keeps rising, the question becomes can this world handle the ever escalating demand on the earth’s resources. One solution to a small aspect of this problem is through the use of remote sensing.

Remote sensing can give information over large remote areas very quickly. These areas especially include those that may be hard to reach because of rough terrain or the region is sparsely populated. After the data is sensed, it's processed by many different algorithms and information is derived for a wide range of people. Since this technology is so new, a problem arises because many people are skeptical to trust the information. Remotely sensed data relies on the satellites and air-borne sensors to work with a great deal of accuracy. Therefore, in order to prove this data is trustworthy and valid, we must constantly check the sensors. Many different calibration techniques exist as a way of verifying the sensors. These ensure they are working properly. This is the reason that this research has been conducted.

The main goal of this research is to use the results to calibrate NASA’s Landsat 7 ETM + (Enhanced Thematic Mapper Plus) satellite within 0.5 K. This satellite orbits the earth continually taking data of the earth without constant check-ups of its sensors that make sure its on-board calibration is correct. To calibrate this sensor on the ground is not that easy or cheap. To trust the validity of Landsat 7’s data, we can use different calibration techniques that can calibrate while Landsat 7 is in orbit. The sensor used in this research does this by utilizing an under-flight method. This entails using a separate sensor that flies directly under Landsat 7 at the same time, to confirm the data values it receives from the earth.

In this research the sensor that will be used for the under-flight technique is called Modular Imaging Spectrometer Instrument (MISI). An image of MISI is shown below. It was invented at Rochester Institute of Technology (RIT), to take information of the earth in the visible, near and long-wave infrared portions of the spectrum. MISI currently has an on-board calibration system used to check that the temperature is correct after each line scan. Even though this feature exists on MISI, we must make sure the on-board calibration system is properly working. This confirmation occurs when the blackbodies correctly track the temperature of the earth’s surface. The blackbodies are used as MISI’s own calibration system, approximating perfect blackbodies. Therefore their characteristics and radiance values can be easily figured out by using Plank’s equation. After MISI is calibration in the laboratory, we must also verify the sensors work with actual data. We can check this by using atmospheric correction techniques.

There are a few atmospheric correction techniques that use MISI's data to extract information about the impact of the atmosphere on observed radiance. This is a reverse engineering technique that is most commonly used when verifying sensor data to actual data. We assume that the sensor provides accurate radiance values and then work backward to extract the actual ground radiance tracked by MISI. The forward engineering application uses the ground truth as a basis, and applies atmospheric correction techniques to the data to yield the radiance values that should be seen by the sensor. These methods include the multi-band, multi-angle, and multi-altitude. Again, this is done to verify the calibration of MISI. Once it confirms the data is valid, we can then use a radiative transfer code to transfer the data values of the radiance to space. Using this code can give us an accurate radiance value that should match Landsat’s radiance value. If these values are equal, we can verify that Landsat is properly working.

For this research, I will be basing my operation on previous procedures that test the calibration of MISI. This process has been established by Chapter X: Calibration of Thermal Infrared (TIR) Sensor by Dr. Schott, Scott Brown, and J. Barsi which will be appearing in a book written by D.A. Quattrochi and J.C. Luvall called Thermal Remote Sensing in Land Surface Processes (1). Another paper used for its calibration procedures was the article given at the London conference, “Calibration Procedures for Evaluation of In-Flight Radiometry Performance of Thermal Infrared Satellite Sensors”, by Dr. Schott, Timothy Gallagher, and Julia Barsi (2).

The basic goal of instrument calibration is to relate the instrument measurements to the instrument reaching radiance. If this can be done with a high degree of certainty, then the data can be used accurately for other research. The known radiance, taken from blackbody standards, will be sensed by the instrument used (MISI). There are two processes that must take place: radiometric calibration and spectral calibration. Radiometric calibration is necessary to verify the instrument's ability to correctly measure the magnitude of the incident radiation, while spectral calibration is necessary to verify the instrument’s ability to notice spectral distribution of incident radiation. The digital counts of an image are then converted to observed radiance levels over that spectral channel. The calibration relies on the use of radiation source standards. We will use blackbodies as a source. They approximate perfect radiators with emissivities equal to one, and spectral radiance described by the Plankian function. With this, if we known one temperature of the blackbodies, we know their spectral radiance.

Spectral standards are used to perform wavelength calibration using well-known narrow-line structures, such as lasers. In addition, we can use filters to selectively pass narrow wavelength ranges from broadband sources. Source standards are then used to verify/update the calibration of the infrared monochrometers used in combination with broadband sources to generate the spectral radiance of a sensor.

For the calibration of the field and in-flight sensors, the radiance from each blackbody must be known and a count versus radiance calibration can be performed for each detector in every band. The empirical fit used for digital count shown below is found in the Chapter X (1) paper used in this research:

A collimator may be used with a small blackbody to fill the entrance aperture with known radiance levels leaving the overall linear calibration response to be equal to the empirical fit. (1)

The onboard calibration monitoring involves periodic end to end testing, because there is drift in the instrument over time. This explains why there is a need to calibrate the instruments. One way to assess the end to end performance of the satellite system is with ground truth data and under-flight estimates. The onboard calibration can be done with thermistors and multiple monitoring probes. The thermistors are imbedded/attached to the surface of each blackbody and used to approximate the kinetic temperature that leads to the systems radiance. The multiple monitoring probes simply provide a redundant check throughout the mission. (1)

The main purpose of this experiment is to reduce residual errors in the calibration process of MISI. This is needed to compare the surface temperatures estimated by the space-based sensor to measrurements made by aircraft sensors. One way this can be done is by measuring the temperature and emissivity (one minus the reflection) of a target, and then to estimate the radiance from that target that is reaching the spacecraft using a radiative transfer equation from the earth to the satellite. An alternative choice, which is the way proposed in this research, is to measure the radiant temperature of the surface using a calibrated airborne imaging system flown under the satellite. This avoids errors of estimating effects of most of the atmosphere because MISI under-flies the satellite over much of the atmosphere.

The use of under-flights for post launch sensor calibration verification is applicable to provide another check with the propagation models. The airborne sensor can be calibrated in the laboratory immediately before or after a flight, and often employs multiple full aperture blackbody calibrators. It does this under the satellite and over most of the atmosphere. The key factor is to choose uniform targets whose ground temperatures are assumed identical, and whose radiance can be measured at the aircraft and the satellite altitudes. Four things that must hold true are: the temperature must be constant between the two acquisition times, the radiance are observed from the same target, the emissivity of targets must be the same, and the airborne and satellite sensors must have the same spectral response. (2)

There are many reasons why a sensor can get off track. Being off can cause a tremendous amount of error in calculations that use the data. That is why it is necessary to validate Landsat’s temperature to this desired degree of accuracy. Due to this constraint it is necessary to trust MISI’s data to 0.3 K. The need for this amount of accuracy stems from an easy calculation that takes into affect the Landsat 7 error allowance, and the estimated error of the radiative transfer model from the satellite to the airborne sensor. The radiative transfer code used is called MODTRAN. A certain amount of error is inherent in this code, and by subtracting this error from the Landsat 7 error allowance we then have an acceptable error for MISI’s tracking system.

The method used in this research is based off of previous procedures conducted here at RIT. We wanted to modify the procedure to see if using oil bath blackbodies instead of water baths would improve calibration performance. We also wanted to change the procedure so it could be utilized outside of the laboratory. While making these changes, it was still important to maintain the confidence of the experiment. When MISI was tested, it was important to ask ourselves, does the radiance predicted by the thermistors on the blackbodies actually equal the real radiance of the targets being used?

My hypothesis stated that it is possible to calibrate MISI’s blackbodies to within an error of 0.3 K. In order to prove this hypothesis is true, we tested MISI using a calibration procedure. An earlier procedure, which had used a water bath technique, was maintained for this research as source data. For the water bath procedure, we start using two water baths, one of hot temperature and one of cool temperature, using a digital thermometer we continually check the temperature of both baths. We want to use these two temperatures as “known data” to calibrate the onboard MISI blackbodies. To match a blackbody to a certain temperature, of the water baths, we can vary the input signal given to the blackbodies and trace it using the thermistors. A thermistor is simply a temperature sensor that is used on MISI.

Environment is critical to calibration. The outputs given by MISI are a function of their environment and, if wrong, they may cause cascading errors in other instruments depending on the data. For example, if the environment is too cold, the blackbodies may sweat, causing errors in the readings. This in turn will cause the margin of error in the Landsat calibration data to increase. It is known, from previous studies, that the temperature MISI can read is about eight degrees below ambient temperature (temperature in the plane). Here ambient summer temperature is in the range of 18 to 25 Celsius.

The correction of the onboard blackbodies also needs to address the background effects. The spectral radiance from the blackbodies is computed using Plank’s equation, and the kinetic temperature is recorded (every line for MISI) from the blackbody. One thing that must be taken into account is that the full aperture blackbody is not nearly as “black” as the blackbody standards. The spectral emissivity of the onboard blackbodies must be well known (0.95 to 0.97), and the background temperature must be monitored and taken into account to minimizes errors.

There are some emissivity issues that must be taken into account. The target selected for calibration is required to have a large uniform radiance value to minimize errors due to registration. Ideally the radiance must have uniform emissivity values over large areas. Emissivity values are well known and are ideally high and spectrally flat. Water is an attractive target from the emissivity standpoint. It has large uniform areas, high emissivity, and angular variation is quite small to angles exceeding forty-five degrees.

The main goal in our theory is to try to eliminate all the errors we can. Therefore, we try to take in account as much information about the environment that will affect MISI as is possible. When troubleshooting to reduce the error, this information of the surround can be a key player.

MISI has been an ongoing project within the Digital Imaging and Remote Sensing (DIRS) group at the College of Imaging Science (CIS). Initially, to calibrate MISI, the blackbodies were disconnected from MISI and taken into the calibration lab. When MISI is not connected to the thermistors, the read out loadings were changed. The approach used was highly dependent on consecutive observations (runs) of oil bath blackbodies followed by MISI blackbodies. A run is defined as testing the blackbodies at various temperatures throughout a given temperature range. There are usually about ten different temperatures taken per run. For this method, the oil baths calibrated the observing radiometer and this radiometer in turn is used to calibrate the MISI blackbody temperatures.

After using the oil bath approach, the idea to use water baths was conceived. To simulate the oil-bath blackbodies, we made two water baths, one hot and one cold to use as a reference. They are regulated and well mixed to make sure the temperature is uniform over the entire area. Then the data is sensed by MISI as a system, and processed as if it were flight data. For this approach, the MISI long-wave infrared detectors became the observing radiometers. The two water baths were positioned close to the sensor so that each scanline was covered from the beginning to the end. They were also very close to each other so that they met in the middle under the scanner at 90° below MISI. The baths were well mixed and the temperatures recorded so that they were “knowns” within the calculations used to manipulate the data.

The two things we assumed were that since the water baths were directly below MISI the emissivity of the water baths was at normal (90°) viewing angle. This assumption was used to predict the amount of radiance produced by the water baths.

First we start by converting the temperatures of the known water baths into blackbody radiances. This is done using a look-up-table (LUT) using the Plankian equation. This Plankian look-up table can change radiance to temperature. We assume that the blackbodies on MISI are ideal in that they use the Plankian relation. A perfect blackbody is described by Plank’s equation.

L_BB(T) is the spectral radiance of blackbody as a function of temperature.
c is the speed of light, 3.0x10⁸m/s. lis the wavelength (mm).

is the wavelength (mm).
h is plank’s constant, 6.626x10^-34joule-seconds.
k is the Boltzmann gas constant, 1.38x10^-23 joules/Kelvin.
T is the temperature in Kelvin.

If the relation was not assumed to be ideal, we could use the relation below which weights the blackbody radiance by the emissivity. This is a more practical view of the blackbodies, and would be used for those who do not want to assume their blackbodies are ideal.

(T) is the spectral radiance as a function of temperature.

(

) is the emissivity as a function of wavelength.
L_BB(T) is the spectral radiance of the blackbody as a function of temperature.

The relationship below is a linear equation that is used to plot DC vs. radiance for each detector and each run. The slopes (m) and intercepts (b') can be derived from the equations to be used in the calculation to get the value for the radiance of the blackbodies.

DC_wb is the digital count taken by the MISI sensor of the water bath.
DC_bb is the digital count taken by the MISI sensor of the blackbody.
L_Twb is the spectral radiance as a function of temperature of the water baths.
L_Tbb is the spectral radiance as a function of temperature of the blackbodies.
m_wb is the slope of the line made by the two points of the graph of radiance vs. DC of the water baths.
m_bb is the slope of the line made by the two points of the graph of radiance vs. DC of the blackbodies.
b'_wb is the y-intercept of the line made on the graph of radiance vs. DC of the water baths.
b'_bbis the y-intercept of the line made on the graph of radiance vs. DC of the blackbodies.

Next we want to use these slopes in a ratio, multiplied by the emissivity of the blackbodies to get the emissivities of the water baths.

The emissivities of the blackbodies are estimated using the graphs below. Each detector has different responses. This can be seen on the graph below of Detector response of Emissivity vs. wavelength.

Figure 2. A plot to show each detectors sensitivity to certain wavelengths.

Figure 3. A plot to show the MISI blackbodies sensitivity to ceratain emissivities.

The emissivity of the blackbody is estimated from the graph above for each detector.

Using the detector response wavelengths we weight the spectral emissivity curve to obtain the emissivity values for the detectors. Emissivity depends on the radiation property of the target under investigation (water). This indicates how efficiently the surface emits radiation compared to ideal radiation.

Then we went to calculate the background radiance, that is seen by the equation below. This equation was used to calculate the radiance of the blackbodies on MISI and then compared with the measured water bath radiance.

Key approximations include the blackbody emissivity, e_bb, done above, and the radiance of the water bath background, L_WBbg. The radiance of the water bath background is assumed to be ambient. This is approximately 18 – 25 C. Therefore, upon calculate we did a high and low value with these corresponding minimum and maximum. Then once we know the radiance of the blackbody background we can convert it to an effective background temperature using the Plankian LUT as used before.

After completing this calibration, and assuring that MISI works correctly, MISI can then be set up in an airplane and take data. This happens simultaneously to the flight of Landsat 7 above the ground, and the gathering of ground truth data below. The DIRS team takes the ground truth in various places that MISI flies over.

Figure 4. An example of the blackbody and water bath plot of digital count versus radiance.

This graph is a sample of a DC vs. radiance plot. As you can see the two points represent the two targets for water baths and two for blackbodies. Each has one of hot and cold temperature. By fitting the linear curve, we can get an equation for the line that gives us slope and intercept values that are used in the blackbody radiance calculation. These graphs exist for each detector run with each detector.

The results obtained from this experiment were not taken from the water bath method. It was discovered that while doing this experiment, the water bath method was successful only if a few circumstances were carefully watched. That is that the positioning of the water baths below the sensor is very important. Specifically, the emissivity of water changes. We assumed that emissivity was the same over the entire bath and didn’t change from run to run. This is only true if you carefully position the baths in the same place for every run. Even though these requirements are tricky, they can be done. Therefore the water bath method can be done if more care is taken in controlling and monitoring the view angles. We did not watch this for the trials we had done. We did however, monitor the whole time with a thermistor on the blackbodies to make sure the blackbodies were working correctly. Using the independently monitored thermistor we could estimate the blackbody temperatures and calibrate the instrument.

Figure 5. A plot of the MISI blackbody response dependent on the varying temeperature.

The graph shows a relationship between YSI thermistor temperature and MISI thermistor voltage. The significance of this graph shows that the MISI thermistor is tracking correctly if there is a linear relationship between the YSI thermistor temperature and the MISI thermistor voltage. As we plotted the data and fit a linear relationship to each line, we can see that the blackbodies are not exactly the same. The R-squared value for blackbody two has a linear relationship of 0.9998 with one being a one to one relationship. Blackbody one has a linear relationship 0.9979. As can be interpreted this is almost exactly what we want. From these results we see that blackbody two more closely tracks the correct temperature than blackbody one. The root means squared error was calculated for both of these with results of 0.3 and 0.1 K error.

RMS is calculated by first squaring the values, then taking the mean of it and then the square root of it. This was used on the data to compute the error in the apparent radiance to the real radiance. Here these values were calculated to be 0.3K and 0.1K. This was just used to show the error in the fit of the data with the linear relationship. Basically, this tells us how well we know the blackbody temperatures of the ground using MISI.

After trying this water bath method we discovered a few problems. When plotting the digital counts (DC) vs. the temperature (Celsius), we discovered that the MISI blackbody slope was steeper than the water bath slope. To us, this means that MISI’s blackbodies generate more change in radiance than water baths for a given change in temperature. Therefore, the blackbodies have a greater emissivity than the water baths. An ideal emissivity is at one. The blackbodies emissivities are known because they were measured from a piece a material that was painted the same time it was painted and sent to a laboratory to be measured. It is close to one. The water bath emissivity is therefore lower than expected at less than one. It has to be low enough from the blackbodies that it is noticeable. Water emissivity at nadir is expected to be approximately 0.98, which is less than one.

The emissivities for the water baths are highly dependent on angles. If they are not positioned directly below, the viewing angle causes the emissivity to change enough that we cannot assume we know the emissivity. If the angle is at 90° then the emissivity is approximately the emissivity of the blackbodies. If the angle is less than 90°, then the emissivity starts to deviate from the blackbodies, continually getting worse the smaller the angle gets. The emissivity becomes less than that of the blackbodies.

After completing the research it also became apparent that another vital piece of information was needed to aid in reducing the amount of error that we calculated regarding the correct tracking of temperature. This information was the background temperature. When conducting this experiment, we did not record the temperature of the room MISI was in precisely or sometimes not at all. We assumed it was in a general range, which was pretty much the same for each run. This range was at ambient temperature of 18 to 25 Celsius.

The results we achieved did support my hypothesis. One blackbody tracked to 0.3K and the other 0.1 K. My hypothesis just stated it was possible to calibrate the sensor to 0.3K.These results advance the knowledge of the field in that it made even more evident the importance of meticulousness that is key to making the water bath work to the best of the its ability. It is hypothesized that this method would work, but is not optimal for our purposes in the trail and error in calibrating sensors. This method was not retested because we checked the calibration of the blackbodies using the thermistors without using the water baths at all. It is speculated that the water bath method could be used under a few conditions. These conditions were not thoroughly tested at this time due to the urgency of getting the machine in the aircraft. Since it was discovered that the sensors worked by using the extra thermistors directly, we did not test the other method again. Overall, using the thermistors to track the correct temperature is strongly recommended because it is much easier and faster, and can occur with less error than using the water bath method.

A likely sources of error using the water bath method was due to the angular dependency the emissivity had as the water baths got moved underneath of the sensor due to bumping or different placement of the baths for each run. Also it is important to get the background temperature of MISI. This is used in the equation to calculate the radiance and temperature of the blackbodies. We were estimating before, which added to the error, but we didn’t go back and prove this because of time constraints. Since the thermistor method worked, we finished using that technique. It is also inherent in using the whole system to test the blackbodies that error will occur. As with any machinery there is errors that occur as the information travels through the equipment. This is acceptable for our purposes, because we have gotten results that were within an acceptable range. This method is utilized because we do not have any other alternative methods that work with this degree of accuracy.

In conclusion, I recommend that the thermistors be used directly to check the blackbody thermistors directly. It is easier, faster, and depends on a significantly less amount of outside data that could have extreme effects on accuracy when trying for specific amount of validity within a certain degree of error. The other method is speculated to work, with the proper care and instruction, though it was not tested. Due to time constraints this was not possible at this time, but in the future I suggest you heed those precautions.

One thing we must take into consideration upon doing the calibration of MISI is cost. In terms of instruments, manpower, and the fact that time increases significantly if very small temperature error exist, cost must be considered. These facts make us reconsider what degree of calibration is necessary; therefore, this study had been reduced from 0.1K originally to 0.3K. The time and energy costs of using the thermistors are minimal in many ways. Not only in time and dependence on a number of outside factors, it has a minimal amount of errors inherent in using them directly because it is singular piece of equipment that can directly check MISI’s thermistors. This is exactly what is wanted in a quick and easy world that we live in.

Now that MISI is effectively calibrated it can be used to collect data. This has not happened yet due to bad weather, a lack of help and due to waiting for Landsat 7 to fly overhead at the same time. This takes a lot of good luck and planning. This is exaggerated by sharing a plane and plane time, which has caused some dilemmas in flying MISI this year. Not only is sharing a problem, it is expensive. Other people can bid for the plane too. A few times some activities were scheduled this year, but it has not worked out. Once this does happen we can check Landsat 7. It is also difficult to coordinate a group of people to collect ground truth data collectively. An image taken by MISI is shown below. The top portion is in the visible portion of the electromagnetic spectrum. The bottom portion is in the infrared (thermal) portion of the spectrum.

Figure 6. An example of an image taken from MISI in the visible and infrared portions of the spectrum.

The multi-altitude technique flies MISI at different altitudes over the same strip of land. The targets used have a range of radiance values and are identified, with their radiance measured, at each altitude from the flight altitude down to the lowest practical point. The radiances are plotted as a function of altitude and extrapolated to zero altitude. The data taken is nearly vertical, and since this technique has a functional dependence on the altitude and viewing angle, we take note of the dependencies but assume linearity.

This project finished by verifying the results that were hypothesized in the proposal. The blackbodies on MISI are calibrated, and MISI is now ready for her flight season. She is mainly used to detect the data of earth’s radiance. When using the data from MISI to calibrate Landsat 7, we are now positive that the calibration results will be correct to within a certain degree. We expect to confidently determine that Landsat 7 is correctly tracking the earth's radiance within an error of 0.5K.