Blackbodies
(TOC)
Solids and liquids
radiate visible light at temperatures of 500°C and above.3 A surface
which absorbed all incident radiant energy would appear black. Such a surface
would also be a complete radiator. Such idealized surfaces are called blackbodies.
A practical incandescent radiator will exhibit behavior similar to that of
a blackbody (e.g. a tungsten incandescent bulb). The nature of the radiation
from blackbodies was analyzed in some detail by Max Planck.4 He
found that the energy radiated by complete radiators is distributed over a
range of wavelengths in a mathematically predictable pattern. As the temperature
of the body is altered, the distribution of energy is also altered. For example,
the wavelength an electric stove emits keeps changing with variation in temperature.
Figure 2.1 illustrates the distribution of energy from a blackbody as a function
of wavelength at a fixed temperature.
Figure .1 Distribution of energy from a blackbody as a function of wavelength.
This graph can be thought of as a relative plot of energy at each wavelength. It is this information about blackbodies that will be used to help calibrate the MISI. If the temperature of the blackbody is known, the spectral exitance at a particular wavelength can be calculated using the following relationship developed by Max Planck:
(2.1)
Background on the MISI (TOC)
The MISI is an internal R&D activity within the lab to design, assemble and fly an imaging system collecting in 70 spectral channels covering the range from 0.4 to 14 microns with a spatial resolution down to one foot over a 90° field-of-view.1 As mentioned before, the MISI is also capable of sampling data in vis-near infrared (VIS-NIR), short-wave (SWIR), mid-wave (MWIR) and long-wave (LWIR) infrared regions of the electromagnetic spectrum. It is the calibration of the MISI in the thermal region which provokes this research.
The Digital Imaging and Remote Sensing (DIRS) laboratory of the Rochester Institute of Technology’s Center for Imaging Science has operated airborne electro-optical imaging systems for over a decade.1 Recently, it has become evident that there is a need to develop a new airborne electro-optical imaging system. This proposed system should be capable of collecting data in many spectral bands at high resolution while maintaining high radiometric fidelity. The system under construction is a Modular Imaging Spectrometer Instrument (MISI) which is a vast improvement over past electro-optical airborne imaging systems. This is because it will be able to meet current demands as well as be able to adapt easily (hence Modular) to future improvements or concepts.
The need to calibrate
Absolute calibration is essential for a variety of scientific studies and image analysis applications. For example, the removal of atmospheric effects for building heat loss and water quality studies require absolute radiometric data. To extend signatures extracted from a particular scene to data collected in different scenes or at different times under different atmospheric conditions, or even to data collected by different sensors, requires both an absolute measure of radiance and correction for atmospheric effects.1 For example, a main problem encountered in radiometric calibration of satellite image data is correction for atmospheric effects. Without this correction, an image digital number cannot be converted to a surface reflectance value.2 This type of calibration is essential to the MISI in both the visible and thermal regions of the spectrum.
The objective of this research is to devise, construct and implement a means of calibration for the MISI using onboard blackbody radiators. This task will be divided up into three sections. The first being the construction of a radiation source and design of a feedback control system. Second is the evaluation of the source in terms of its uniformity and control. And lastly, if time permits, will be the implementation of the source(s) into the MISI system.
There are existing systems/blackbodies that can be thermally controlled from -10°C to 100°C and have an absolute temperature calibration accuracy of 0.01°C, but these systems will not physically fit into the MISI. Furthermore, these systems are very expensive. Controllable blackbodies of this type are usually used in a laboratory settings where size and convenience is not an issue.
Calibration contribution to the MISI
Though the calibration of a line scanner is not a new concept, it is important to the integrity of the MISI at RIT. If the calibration system devised in this research proves to be successful, the MISI would be able to be used for a multitude of applications with the assurance that the data collected was radiometrically correct. This calibration contribution to the MISI would enable it to serve as;
--an airborne laboratory for earth observation research.
--a high resolution under flight system for high altitude aircraft and satellite sensor performance evaluation.
--a versatile data collection platform for acquiring imagery to be used in algorithm development and evaluation for reconnaissance and environmental applications.
--and as a survey instrument for demonstration and proof-of-concept studies of image analysis methods in areas such as energy conservation, water quality assessment, and hazardous waste site management.1
How the Blackbodies will be used to Calibrate the MISI (TOC)
One of the most important issues concerning the calibration of the MISI in the thermal regions of the EM spectrum is the issue of detector drift. It would be nice if the detectors in the MISI were "ideal detectors" in that the radiance signal that came out was truly the radiance that fell upon them (or irradiance). Most detectors that are used for thermal data acquisition are susceptible to low frequency drift, meaning they have a tendency to drift around the actual value they are trying to record. This may be due to a variety of reasons. The liquid nitrogen used to cool the detectors may be moving around causing non uniformities in cooling. There may also be a loss of vacuum in the detector thus increasing the potential for atmospheric conduction through the metal casing of the detector. So it is with utmost importance that the thermal detector shift be accounted for in the MISI.
A way to account for the detector shift is to find a relationship between the measured radiance from the detector and the known, or calculated, radiance of the blackbodies. That is where this research gains its importance. In order to correct the radiance shift due to the detector, the blackbody temperature must be known accurately to minimize errors. This temperature value, recorded by the monitoring circuit, will be converted to a radiance value and used to generate a look up table to account for the detector shift on a scan-line by scan-line basis. Since two blackbodies are used, both the gain and offset of each channel are calibrated for every scan line.
We can see this approach if we first take a look at a hypothetical sample scan line generated by the MISI as shown in Figure 2.2.
Figure .2 Sample scan line generated by MISI. This is one revolution of the scan mirror.
First we must quantize the measured radiance values. This will be done with a 12bit A to D conversion. With 12bit resolution, a radiance value can take on a value from 0 to 4095. After this stage, the radiance is considered a digital count (LDCmeasured). There will be approximately 1570 samples for the ground data and 20 samples for each of the blackbodies for a total of 1590 samples.
When sampling the radiance data for the blackbodies, it is important to generate a representative value of the radiance in that region. It would be ideal if the detector was able to read the radiance of the blackbody instantaneously. In other words have an instantaneous on time. In reality, though, this is not the case. There is usually some integration time associated with the detector that can be modeled by the convolution of two RECT functions. This results in the function shown in Figure 2.3.
Figure .3 Convolution of two RECT functions. This is used to simulate the integration time associated with the radiance being measured by the detectors.
When sampling the radiance in the blackbody region, one hopes to see a flat region in which to obtain the representative radiance value. If there is no flat region, which is most likely to occur, the radiance value will have to be an average of x number of pixels in the flat region. But how many pixels does one average? This can found by fixing the number of pixels to be averaged, running multiple scans to average out the noise (temporal averaging) and then compare the radiance values obtained to the actual radiance calculated for the blackbodies.
Each temperature, one from each blackbody, needs to be converted to an equivalent radiance value. This is accomplished through the use of the Planckian equation (Eq 2.1).
The radiance equivalent of the blackbody temperature values can be denoted as such:
LBB1actual
LBB2actual
One assumption that will be made is the fact that there is a linear relationship between the measured radiance values and the actual blackbody radiance values determined from the Planckian equation. In other words, we are assuming that the detectors, though noisy, exhibit some linearity in their behavior. With this assumption of linearity, we can derive a relationship using the well know slope-intercept form of an equation of a line with slope m and y-intercept b.
y = mx + b (2.2)
The slope factor m in the equation will be representative of the gain inherent in the detectors while the y-intercept factor b will characterize the bias of the detectors. With this knowledge the gain and bias factors can be represented as the following:
(2.3)
(2.4)
Substitution and simplification yields:
(2.5)
If:
We can establish a relationship between the measured radiance (y) LDCmeasured, and the corrected radiance (x) LDCcorrected. With these parameters the equation for the corrected radiance becomes:
(2.6)
Though radiometricaly correct, the equation does not account for the detector spectral responsivity (b). The responsivity depends on the spectral characteristics of the source and sensor. Generally the responsivity is given with reference to a source with a known blackbody distribution temperature. This sensor effect can be accounted for by factoring in a responsivity term into the measured radiance values. With this factor equation 2.6 becomes:
(2.7)
A typical plot of this look up table (LUT) might look like Figure 2.4.
Figure .4 Possible LUT of corrected radiance values v.s. measured radiance values for a single scan line generated by the MISI.
Here a linear relationship is shown between the corrected radiance values and the measured values, as mentioned before this is assumed. With this linear relationship, it is now possible to extrapolate corrected radiance values from measured radiance values for every scan line.
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