Philpot & Philipson: Remote Sensing Fundamentals Thermal Sensing 9.1 W.D. Philpot, Cornell University, Fall 2016

THERMAL INFRARED SENSING 9.1 Blackbody Radiation revisited Thermal infrared sensing is normally applied to determine absolute or relative temperatures from a distance. The ultimate purpose may vary from characterizing rooftop insulation or power plant effluents to detecting forest fires, leaking reservoirs or leachate from a landfill. At global and regional scales thermal images are used to map the sea surface temperature. The basic process is the same in all cases: to use radiometers, scanners or thermal television devices to sense radiation that is related to heat and relatable to temperature. This may involve several assumptions or estimations regarding the emissive properties of the object or phenomenon under study. The basic relationships were presented in Section 2.11 and begin with Planck's formula:

( )

2

52 hcM

exp hc / kt 1λπ

=λ λ −

(9.1)

where: Mλ = exitance at wavelength λ h = Planck's constant = 6.625 x 10-34 J-sec c = speed of light in a vacuum = 2.997 x 108 m/sec k = Boltzmann's constant = 1.38 x 10-23 J/K T = absolute temperature in degrees Kelvin If this equation is differentiated with respect to wavelength and set equal to 0, one arrives at Wien's Displacement Law which defines the wavelength of maximum exitance:

λmax T = C3 (9.2)

where: λmax = wavelength at which exitance is maximum C3 = 2.898 x 10-3 m K In accordance with Wien's Displacement Law, as the temperature of a blackbody increases, the wavelength of maximum radiation decreases. Objects at temperatures generally encountered on the earth's surface (approx. 300 K) emit peak radiation at a wavelength of approximately 10 µm and emission drops off rapidly at shorter wavelengths. At wavelengths shorter than 3 to 4 µm, in fact, although the reflectivity of a blackbody at earth temperatures is zero, real objects (ε < 1.0) generally emit less radiation than they reflect during daylight periods. Reviewing from Section 2.11, if Planck's formula is integrated with respect to wavelength, the result is the Stefan-Boltzmann Law:

4tot

0

M d M T∞

λ

λ=

λ = = σ∫ (9.3)

where σ = Stefan-Boltzmann constant = 5.67 x 10-8 w/m2K4. The Stefan-Boltzmann Law is basic to thermal sensing. In the simplest case, if the total exitance of an object were measured, one could simply compute the temperature of the object, presuming that the object was identical to a blackbody in its emissive characteristics. This temperature would be referred to as the "blackbody, "radiometric" or "apparent" temperature.

Philpot & Philipson: Remote Sensing Fundamentals Thermal Sensing 9.2 W.D. Philpot, Cornell University, Fall 2016

9.2 Total Versus Spectral Radiation The Stefan-Boltzmann Law cannot be implemented directly in remote sensing applications in part because the atmosphere absorbs over significant wavelength ranges, and in part because emission from the earth is masked by reflected radiation (at least during the day) and radiation emitted from the atmosphere. In practice, emitted radiation is collected only over a band of wavelengths defined by the detector. This may be rather small part of the blackbody emission spectrum. For example, a mercury-cadmium-telluride (HgCdTe) detector, which is commonly employed for thermal sensing, is sensitive over wavelengths from approximately 8 to 14 µm. Although this band encompasses the wavelengths of maximum emission from blackbodies and nearly all real objects, and matches a range of good atmospheric transmission, it does not encompass all wavelengths of emission. Over the 3 to 5 µm range, corresponding to another atmospheric transmission window, indium-antimony (InSb) detectors are commonly used. The blackbody curves spanning typical temperatures at the earth’s surface are shown in Figure 9.1 with the two standard wavebands used for remote sensing shown in gray. Also shown in Figure 9.1 is an approximation of the solar radiation available for reflection during daylight hours. In the 3 to 5 µm range, the reflected radiation can be roughly equivalent to the emitted radiation.1 In this wavelength range reflected radiation can seriously complicate the interpretation of the detected daytime radiation.

Figure 9.1: Blackbody curves for typical Earth temperatures. The wavebands used for

remote sensing of the earth in the thermal range are shown in gray. Also shown (in red) is an approximation of the direct solar radiation from 3-4µ.

Within these limited wavebands, an object's temperature cannot be calculated directly from the Stefan-Boltzmann Law since the amount of radiation emitted by an object over a band of wavelengths is only a fraction of the total.

1 The solar radiation is the direct solar radiation plus the forward scattered light coming from a small annulus around the solar disk, generally called direct + circumsolar radiation. The values were taken from the ASTM tables for solar spectral irradiance for an air mass of 1.5, http://rredc.nrel.gov/solar/spectra/am1.5/.

Philpot & Philipson: Remote Sensing Fundamentals Thermal Sensing 9.3 W.D. Philpot, Cornell University, Fall 2016

2

1 2

1

4totM M d M T

λ

λ −λ λ

λ

= λ = σ∫ ≠ (9.4)

This fraction can be defined:

2

1 21 2

1

4tot

M 1P M dM T

λλ −λ

λ −λ λ

λ

= = λσ ∫ (9.5)

Unfortunately, numerical values of this fraction vary with temperature (i.e., the fraction varies with the specific blackbody curve). Since temperature is normally the quantity sought by thermal remote sensing, it is not possible to define the temperature, blackbody curve, or fraction beforehand.

9.3 Sensing Radiometric Temperature There are two general approaches to determine radiometric temperature. Both use reference temperature sources for calibration.

a. Use a single reference source at a known temperature The first approach to determining radiometric temperatures is to measure radiation from a single reference source at the same time that radiation is measured from the object whose temperature is being sought. With the reference source set at a predetermined temperature, the relationship between the levels of exitance from the "unknown" object and the reference source is, as follows:

4

u u u4

r r r

M F TM F T

σ=

σ (9.6)

where: Mu, Mr = levels of exitance from the unknown and reference Fu, Fr = fractions of radiation received over wavelengths being sensed Tu, Tr = temperatures of unknown and reference

This relation can be rearranged to solve for the temperature of the unknown:

1/4

4u uu r

r r

M FT TM F

= (9.7)

If the temperatures of the unknown and reference source are relatively close (T1 ≤ Tu ≤ T2), the fractions of radiation received will be approximately equal (Figure 9.2). That is, the blackbody curves may differ, but the fractions of the total radiation will be close. All other quantities in the equation are known or measured. This approach is sometimes taken with radiometers in which the reference source can be an integral part of the sensor, itself. It is especially convenient in those radiometers where a rotating "chopper" is used to interrupt the radiation received from the unknown. The primary purpose of the chopper is to convert the incoming signal from a direct to an alternating current. However, when the detector is not receiving radiation from the unknown target, it can receive radiation from the reference. One configuration is shown in Figure 0.3, where the backside of the chopper is coated with a mirror, which reflects radiation from the reference to the detector.

Philpot & Philipson: Remote Sensing Fundamentals Thermal Sensing 9.4 W.D. Philpot, Cornell University, Fall 2016

Figure 9.2: Radiation emitted by an unknown at temperature Tu, and by a reference source at

temperature Tr. The approximation will only be valid over the range [T1,T2]

Figure 0.3: Operation of a typical chopper.

b. Use two reference sources at known temperatures. An extension of the first approach to sensing radiometric temperatures is to use two references instead of one. These reference sources are preset at temperatures that bound the range of temperatures of the unknowns. Insofar as the levels of radiation received from the unknowns are within the range of those levels received from the references, the procedure is simply to interpolate between the signals received from the references to determine the radiometric temperatures of the unknowns (Figure 9.4). Some degree of extrapolation is also possible. With this approach, the two reference sources may be internal or external to the sensor. For example, a hot and cold reference could be built into a scanner that operates with a rotating mirror. When the mirror is not reflecting radiation from the ground (i.e., unknown targets), it could be reflecting radiation from the hot and cold references. Alternatively, or in addition, the contact temperatures of selected ground objects could be measured at the time of sensing. These can provide reference temperatures if they can be discriminated in the scanner data and if their temperatures encompass the temperatures of targets of interest. One major concern with either of these approaches is correcting for emissivity. Without correcting for the emissivity of the target, the best that one can retrieve from the remotely sensed data is the "radiometric" temperature or "apparent" temperature.

Philpot & Philipson: Remote Sensing Fundamentals Thermal Sensing 9.5 W.D. Philpot, Cornell University, Fall 2016

M1,bb

T14 T2

4

M2,bb blackbody, ε=1.0

ε<1.0

Tu4

Mu,bbεMu,bb

Ta4

a. b.

Figure 9.4: Radiation emitted by an unknown and two reference sources: a) blackbody curves for the two calibration sources bound the curve for the unknown blackbody emitter; b) linear interpolation (solid line) to find target temperature, Tu, based on the observed blackbody emittance, Mu,bb (solid line), and the apparent temperature, Ta, of a non-blackbody source (ε < 1, dotted line) at the same real temperature, Tu, based on its emittance, εMu,bb.

9.4 Emissivity Revisited As described in Section 2.11, emissivity is a measure of how efficiently an object emits radiation as compared to a blackbody. The total exitance from a real object at temperature T is thus some proportion of the total exitance from a blackbody at the same temperature – and the proportionality factor is the emissivity:

M = ε Mbb = εσT4 (9.8)

or, in terms of the apparent temperature:

1/4aT = Tε (9.9)

That is, the apparent temperature is strongly dependent on the actual temperature and is relatively weakly dependent on the emissivity.

Since emissivity, like exitance, is a spectral quantity,

Mλ = ελ Mbbλ (9.10)

and 2

1 2

1

bbM M dλ

λ −λ λ λ

λ

= ε λ∫ (9.11)

Different materials have different emissivities. Moreover, the emissivity of the same material will vary with direction or with changes in the material's surface, temperatures, moisture content or related property. For metals, emissivity is relatively low, often below 0.5. This value generally increases with temperature, and it increases substantially with the formation of an oxide layer. For example, the emissivity of polished aluminum at 100°C is 0.05, while that of anodized aluminum at the same temperature is 0.55. Comparable values for polished and anodized brass are 0.03 and 0.61. These values refer to the emissivity over all wavelengths, in a direction which is normal to the surface.

Exitt

ance

wavelength

Tu

Tcool

Thot

Philpot & Philipson: Remote Sensing Fundamentals Thermal Sensing 9.6 W.D. Philpot, Cornell University, Fall 2016

In contrast to metals, the emissivity of non-metals tends to be relatively high – often over 0.8 – and it decreases with increasing temperature. Representative emissivities (total, normal) at 20°C are: distilled water, 0.96; sand; 0.90; dry soil, 0.92; saturated soil, 0.95; wood (planed oak), 0.90; concrete, 0.92. It is very important to remember that radiation is from the surface of the material and may not be representative of the temperature of the volume of the material. As an example, a 55 gallon drum filled with water at 30°C may have a skin temperature that is significantly different if there is a breeze blowing over the drum or if the drum is wet. A painted drum will also register a different apparent temperature than an unpainted drum. Also, recall that emissivity is related to absorptivity through Kirchoff's Law which states that the proportions of radiation reflected, transmitted and absorbed must sum to 1.0. For an opaque medium, the transmissivity is zero and, if the material is in thermal equilibrium, the radiation emitted must equal the radiation absorbed. (One must, of course, also assume that energy is not being conducted to or from the target material and that convective gains/losses are negligible. Conductive gains/losses are generally negligible, but any appreciable wind will alter the surface temperature.) If these conditions are met, then the emissivity of the material, ε, is equal to one minus the reflectivity, ρ, of the material:

ε = 1 − ρ (9.12) Thus, materials that are highly reflective will have a very low emissivity, and materials that are highly absorbing will have a high emissivity.

9.5 Spectral Emissivity In the discussion above we have treated emissivity only as an average value over the waveband of interest whereas it is actually a spectral quantity. The emission process is basically the reverse of the absorption process. An electron must acquire energy (by absorbing some light) to move to a higher energy level, and it must get rid of energy (by emitting some light) to move to a lower level. Introducing spectral dependence into Kirchoff’s Law, we have:

α (λ) + ρ (λ) + τ (λ) = 1.0 (9.13)

For opaque materials, τ (λ) = 0.0, therefore;

α (λ) + ρ (λ) = 1.0 (9.14) Given that emissivity is simply the reverse of absorption, then:

ε (λ) + ρ (λ) = 1.0 (9.15) This is exciting because the spectral emissivity appears to provide a great deal of target specificity that is not available in other spectral regions. As an example, consider Figure 9.5, emissivity spectra collected in the laboratory. The vegetation spectra are very similar, but significantly different in the 8-14 µ range. In contrast, there are marked differences between the brown, sandy loam and the CaCO3. Systems have been designed to exploit the spectral specificity of thermal emission. One notable example is the Advanced Spaceborne Thermal Emission and Reflectance Radiometer (ASTER), launched in 1999, which has 5 bands in the 8-14 µ range. The spectral variability observed for an individual target will be due only to the emissivity of that material; the temperature

Philpot & Philipson: Remote Sensing Fundamentals Thermal Sensing 9.7 W.D. Philpot, Cornell University, Fall 2016

is constant. If the spectral emissivity is characteristic of the material, it can be identified and the absolute emissivity will be known within some uncertainty. The absolute temperature can then be determined. This is illustrated below in the plot of spectral emissivity of water and playa determined both in the field and derived from ASTER observations.

Figure 9.5: Spectral emissivities of various materials measured in the laboratory. The

wavelength ranges used in remote sensing are marked by dotted lines: red for the 3-5µ range, green for the 8-14µ range. (Adapted from: http://imkisysweb.fzk.de/isys-public/datasets/geo/spectra-aster/examples_for_spectra.htm)

Figure 9.6: Spectral emissivities measured on the ground (curves) and derived from ASTER

observations (boxes). (From:

Philpot & Philipson: Remote Sensing Fundamentals Thermal Sensing 9.8 W.D. Philpot, Cornell University, Fall 2016

http://eospso.gsfc.nasa.gov/ftp_ATBD/REVIEW/ASTER/ATBD-AST-03/atbd-ast-03.pdf)

It is worth noting that even calibration sources may exhibit spectral variability in their emissivity (Figure 9.7). Properly, an exact temperature cannot be computed without including the spectral emissivity of the target together with the spectral responsivity of the detector over its active spectral range. In practice, if there is only a single thermal channel, an average emissivity is often used to estimate the temperature. With spectral radiance measurements, it is becoming feasible to extract emissivity information as well as temperature data.

Figure 9.7: Spectral emissivity measured at 7 different points on blackbody 1 of the ASTER

radiometer. ASTER bands are illustrated in gray.

9.6 The Importance of Emissivity and Atmosphere Variation in emissivity has a pronounced effect on the results obtained with either of the two approaches for determining temperatures. If absolute temperatures are being sought with either a one- or two-reference source instrument, a correction must be made for any difference in emissivity between the unknown objects and the references. If relative temperatures of several unknowns are being sought, corrections must be applied to account for any differences in the objects' emissivities. In essence, an observed radiometric temperature difference might be caused by a difference in actual temperatures or by a difference in emissivities. The importance of real objects having emissivities less than 1.0 is not limited to correcting for emissivity before temperatures can be determined from emitted radiation. Remembering Kirchoff's law for opaque objects, α + ρ = ε + ρ = 1, it should be clear that, if an object is not emitting, it is reflecting. If ε is less than 1.0, the radiation measured from an object will be only partly determined by the object's temperature. The remainder is determined by the object’s reflectivity and by the amount of radiation available for reflection. The total exitance from a real object is thus:

M = Memit + Mref = ε σ T4 + ρ E (9.16)

where E is the total irradiance on the radiation object. One can take steps to minimize ρE during a thermal sensing mission. For example, sensing in the 8 to 14 µm wavelengths minimizes solar irradiance. Further, acquiring thermal infrared data during non-daylight hours eliminates solar irradiation. Depending on the desired thermal contrasts, the data might be acquired just after sunset, in the middle of the might, or just before sunrise (pre-dawn).

Philpot & Philipson: Remote Sensing Fundamentals Thermal Sensing 9.9 W.D. Philpot, Cornell University, Fall 2016

Lastly, the effects of sensing through the atmosphere should be recognized. There are atmospheric windows in the infrared spectrum (e.g., 3-5 µm and 8–14µm), yet some absorption normally occurs. In addition, while infrared radiation is not affected by a dry smoke, (e.g., forest fire), it is attenuated by moisture; thermal sensing cannot "penetrate" a rainfall or fog. Similarly, although wind will not effect infrared radiation per se, it can affect the measured temperature by increasing evaporative losses, thereby altering an object's surface temperature.

9.7 Resolution

9.7.1 Spatial Resolution Spatial resolution of remote thermal imaging systems is generally substantially poorer than that of VNIR systems. One reason for this is that the energy of a single photon in the thermal region is significantly less than that of a photon in the VNIR region, a fact that complicates the development of suitable photodiodes. The standard material for thermal detectors is Mercury-Cadmium-Teluride (HgCdTe). A second reason for the relatively poor spatial resolution is that the total energy emitted by bodies at earth temperatures (~300°K) is low, and increasing the IFOV of the detector is one way to compensate for this.

9.7.2 Radiometric Resolution The spatial resolution is, in part driven by the need for relatively high radiometric resolution and precision. The detector must be designed to collect enough photons to register relatively small changes in temperature. Radiometric resolution is expressed in terms of a noise equivalent change in temperature, NE∆T, i.e., a change in temperature that is equivalent to the background noise. Satellite and aircraft thermal radiometers and imaging systems have an NE∆T that is typically on the order of 0.1°K in order to resolve meaningful temperature differences. This level of sensitivity requires that the sensor be cooled to reduce the internal noise. (The detector must also be shielded from from emission from other components.)

At the same time, the system must be designed for temperatures ranging from ~100°K to observe cloud top temperatures of high-altitude clouds, to ~350°K for summertime desert temperatures. To span a range of 250°K and a resolution of 0.1°K, the instrument must be able to represent 2,500 distinct values. Thus, thermal remote sensing imaging systems typically digitize data to 10 or 12 bits (1024 or 4096 gray values) rather than the 8-bits (256 gray values) common with VNIR systems.

9.8 Examples of Instruments

9.8.1 Geostationary Environmental Operational Satellite (GOES) GOES satellites are geostationary (i.e., they fly at 36,000 km above the earth's surface) and provide the full earth hemisphere views that are a mainstay of meteorological observation. This series of satellites have been flying since 1975. The early systems were stabilized by the spinning of the satellite and used the spinning to provide the scanning motion for the imaging system (a spin-scan radiometer). The more recent systems use a Cassegrain telescope (all-reflective optics) to collect the radiation and a scanning mirror to perform the imaging tasks.

Philpot & Philipson: Remote Sensing Fundamentals Thermal Sensing 9.10 W.D. Philpot, Cornell University, Fall 2016

The most recent system (GOES 12) includes an a 5-channel scanner (Table 0.1). The input optics consists of a Cassegrain telescope which uses entirely reflective optics. The telescope directs the radiation to an array of detectors in the focal plane. The system boasts an absolute accuracy of 1°K and a relative accuracy within one channel of ~0.3°K. This is typical of satellite systems. Higher relative accuracy is possible, but not usually required for earth resource applications.

Imager Instrument Characteristics (GOES I-M)

Channel number: 1 (Visible)

2 (Shortwave)

3 (Moisture)

4 (IR-1)

5 (IR-2)

Wavelength range (µ) 0.55 - 0.75 3.80 - 4.00 6.50 - 7.00 10.20 - 11.20 11.50 - 12.50

Instantaneous nadir GFOV 1 km 4 km 8 km 4 km 4 km

Detector type: Silicon InSb HgCdTe HgCdTe HgCdTe

System absolute accuracy IR channels: less than or equal to 1 K

Visible channel: 5% of maximum scene irradiance

Imaging rate Full earth disc, less than or equal to 26 minutes

Table 0.1: Characteristics of the GOES imaging system.

Figure 0.8: Focal plane array for the GOES–12 imager. The squares represent the size of the

individual detectors for each band. (Adapted from http://goes.gsfc.nasa.gov/text/databook/section03.pdf )

9.8.2 Advanced Very High Resolution Radiometer (AVHRR) The AVHRR is a broad-band, four or five channel (depending on the model) scanner, sensing in the visible, near-infrared, and thermal infrared portions of the electromagnetic spectrum. The AVHRR series began with the first system flown on TIROS-N which was launched in 1978. The most recent version of this sensor , AVHRR/3, is carried on NOAA's Polar Orbiting Environmental Satellites (POES), beginning with TIROS-N in 1978.

Philpot & Philipson: Remote Sensing Fundamentals Thermal Sensing 9.11 W.D. Philpot, Cornell University, Fall 2016

Channel Spectral Bandpass (µ) GIFOV at nadir (km) Signal to Noise (S/N) (NEΔT)

1 (Visible) 0.580 - 0.68 1.1 9:1 at 0.5% Albedo

2 (Near IR) 0.725 - 1.00 1.1 9:1 at 0.5% Albedo

3A (Near IR) 1.580 - 1.64 1.1 20:1 at 0.5% Albedo

3B (IR-Window) 3.550 - 3.93 1.1 0.12 K at 300 K

4 (IR-Window) 10.300 - 11.3 1.1 0.12 K at 300 K

5 (IR-Window) 11.500 - 12.5 1.1 0.12 K at 300 K

Table 0.2: Characteristics of the AVHRR/3 channels

9.8.3 Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) ASTER, a cooperative venture between NASA two Japanese agencies, is an imaging instrument that is flying on the Terra satellite launched in December 1999 as part of NASA's Earth Observing System (EOS). The ASTER radiometers include 3 bands in the VNIR (15 m GIFOV) and 6 spectral bands in the SWIR (30 m GIFOV), however, the major interest in this system is its thermal sensor radiometer which has 5 bands in the 8-12 µ range with 90 m GIFOV. A diagram of the thermal sensor system is shown in Figure 0.9. There are 10 detectors for each of the 5 thermal channels, so the instrument collects 10 scan lines on each mirror pass. These detectors are cooled to 80°K to insure that the detectors are not detecting noise from themselves or from the walls of the container. The telescope design (Figure 0.10) is notable in that is it catadioptric, i.e., it uses both reflective and refractive components. It uses an aspheric primary mirror and lens for aberration correction.

There is a single blackbody reference source, but it consists of a plat that is heated through a range of temperatures, providing a series of reference temperatures that can be used to calibrate for the instrument gain and offset. The mirror performs as the chopper in addition to controlling scanning and pointing for the system.

Philpot & Philipson: Remote Sensing Fundamentals Thermal Sensing 9.12 W.D. Philpot, Cornell University, Fall 2016

Figure 0.9: Diagram of the ASTER Thermal Scanning Radiometer (Adapted from the

ASTER website: http://asterweb.jpl.nasa.gov/tir.asp )

Figure 0.10: Newtonian catadioptric telescope design.