Topic 6: Thermal Sensing Topic 6: THERMAL SENSINGceeserver.cee.cornell.edu/wdp2/cee6100/6100 Topics/Topic06_Fa15… · Blackbody Radiation. Planck's Formula. describes the magnitude

CEE 6100 / CSS 6600 Remote Sensing Fundamentals 1 Topic 6: Thermal Sensing

Topic 6: THERMAL SENSING • Thermal infrared sensing directly detects radiative (apparent) temperature • The data are normally used to determine absolute or relative temperatures from a distance

after correction for emissivity and/or atmospheric correction. • An excellent web site describing the physics, history and sensing technology underlying

thermal imaging: http://www.omega.com/literature/transactions/volume1/trantocvol1.html

Blackbody Radiation Planck's Formula describes the magnitude and spectral distribution of radiation emitted by a blackbody source.

𝑀𝑀𝜆𝜆 =2𝜋𝜋ℎ𝑐𝑐2

𝜆𝜆5 �(𝑒𝑒𝑒𝑒𝑒𝑒) ℎ𝑐𝑐𝜆𝜆𝜆𝜆𝜆𝜆 − 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 108m/sec k = Boltzmann's constant = 1.38 x 10-23 J/°K T = absolute temperature in degrees Kelvin

Wien's Displacement Law If Planck's Equation is differentiated with respect to wavelength and set equal to 0 to find the peak of the emission curve, one arrives at Wien's Displacement Law

λmax = C3 / T

where: λmax = wavelength at which exitance is maximum C3 = hc/(4.965°K) = 2.898 x 10-3 m-K = 2898 µ-K

http://www.omega.com/literature/transactions/volume1/trantocvol1.html

CEE 6100 / CSS 6600 Remote Sensing Fundamentals 2 Topic 6: Thermal Sensing Stefan-Boltzmann Law If Planck's formula is integrated with respect to wavelength, the result is the Stefan-Boltzmann Law:

� 𝑀𝑀𝜆𝜆𝑑𝑑𝜆𝜆 = 𝑀𝑀𝑡𝑡𝑡𝑡𝑡𝑡 = 𝜎𝜎𝜆𝜆4∞

𝜆𝜆=0

where σ = Stefan-Boltzmann constant = 5.67 x 10-8 w m-2 K-4 The total exitance from a blackbody at any temperature thus corresponds to the total area under the particular curve for that temperature. Terrestrial emission vs. reflected solar radiation The solar emission spectrum extends out beyond the SWIR and into the thermal infrared (TIR) range; however, the amount of solar radiation reflected from the earth's surface decreases rapidly beyond the SWIR. The graph shows the solar emittance (RH scale) and earth emittance (LH scale) adjusted to show the approximate relationship for an earth-viewing system. Reflected solar radiation is significant up to about 5 µm,, but is negligible beyond that. The gray portions of the graph are the wavebands typically used by thermal sensing systems. Atmospheric windows The Stefan-Boltzmann Law is derived assuming that observations are made at all wavelengths. It is not feasible to make observations over all wavelengths, or even the wavelength range over which the bulk of emission from the earth occurs because of limits in atmospheric transmission. Remote instruments view the earth's emission through the atmosphere which is highly absorbing over wide spectral ranges. The atmospheric absorption is illustrated in the plat of the spectral bands selected for the Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER). There are broad absorption bands at 2.5-3.0 µm, 4.2-4.6 µm, and 5.5-8.0 µm, restricting observations to the zones of transmission.

https://asterweb.jpl.nasa.gov/instrument.asp

https://asterweb.jpl.nasa.gov/instrument.asp

CEE 6100 / CSS 6600 Remote Sensing Fundamentals 3 Topic 6: Thermal Sensing Observations are possible in the 3-5 µm range, but during daylight hours, thermal emission from the earth (which is already rather weak) competes with reflected solar radiation. In the 8-14 µm range, on the other hand, thermal emission peaks near 10 µm, transmission is generally good in that wavelength range, and there is little interference from reflected sunlight. Note that, while transmission is generally good in the 8-14µm range, there is still significant absorption, especially by carbon dioxide and ozone. Detection over a limited spectral range Because of the limited spectral range, an object's temperature cannot be calculated directly from the remotely sensed radiative emittance using the Stefan-Boltzmann Law

𝑀𝑀𝜆𝜆1−𝜆𝜆2 = � 𝑀𝑀𝜆𝜆𝑑𝑑𝜆𝜆 ≠

𝜆𝜆2

𝜆𝜆1

� 𝑀𝑀𝜆𝜆𝑑𝑑𝜆𝜆 = 𝜎𝜎𝜆𝜆4∞

𝜆𝜆=0

Rather, the amount of radiation emitted by an object over a band of wavelengths is only a fraction of the total. This fraction can be defined:

𝐹𝐹𝜆𝜆1−𝜆𝜆2 =𝑀𝑀𝜆𝜆1−𝜆𝜆2𝑀𝑀𝑡𝑡𝑡𝑡𝑡𝑡

=1𝜎𝜎𝜆𝜆4

� 𝑀𝑀𝜆𝜆𝑑𝑑𝜆𝜆

𝜆𝜆2

𝜆𝜆1

There are two general approaches to determine radiometric temperature.

a. Use a single reference source at a known temperature (close to the target temperature)

b. Use two reference sources at known temperatures. (Ideally, spanning the range of the target temperatures.)

CEE 6100 / CSS 6600 Remote Sensing Fundamentals 4 Topic 6: Thermal Sensing a) Sensing radiometric temperature using a single reference source

• Simultaneously measure Tref and Tu. • Choose a reference s.t. Tref ≈ Tu

Then the relationship between the levels of exitance from the "unknown" object and the reference source is:

𝑀𝑀𝑢𝑢

𝑀𝑀𝑟𝑟= �

𝐹𝐹𝑢𝑢𝐹𝐹𝑟𝑟𝜎𝜎𝜆𝜆𝑢𝑢4

𝜎𝜎𝜆𝜆𝑟𝑟4�

Where: Mu, Mr = exitance from the unknown and reference

Fu, Fr = corresponding fractions of radiation received over wavelengths sensed Tu, Tr = temperatures of unknown and reference

Solving for the temperature of the unknown: 𝜆𝜆𝑢𝑢 = �𝑀𝑀𝑢𝑢𝑀𝑀𝑟𝑟

𝐹𝐹𝑢𝑢𝐹𝐹𝑟𝑟𝜆𝜆𝑟𝑟4�

1 4⁄= 𝜆𝜆𝑟𝑟 �

𝑀𝑀𝑢𝑢𝑀𝑀𝑟𝑟�1/4

If Tr ≈ Tu then Fr ≈ Fu , 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. • The reference source can be an integral

part of the sensor, itself. • This approach is convenient in those

radiometers where a rotating "chopper" is used to interrupt the radiation received from the unknown.

b. Using two reference sources at known

temperatures • The reference sources are preset at temperatures which encompass the range of

temperatures of the unknowns. • The procedure is simply to interpolate between the signals received from the

references to determine the radiometric temperatures of the unknowns. • Temperature dependence is assumed to be linear.

M1,bb

T14 T2

4

M2,bb blackbody, ε=1.0

ε<1.0

Tu4

Mu,bbεMu,bb

Ta4

Exitt

ance

wavelength

Tu

Tr

λ1 λ2

detecto

radiation from unknown source

shaft for rotating chopper

CHOPPER

referenc

radiation from reference source

mirrors on back surface of chopper vanes

CEE 6100 / CSS 6600 Remote Sensing Fundamentals 5 Topic 6: Thermal Sensing Emissivity Emissivity, ε, is a measure of how efficiently an object emits radiation as compared to a blackbody, i.e., M = ε Mbb = σεT4 or, in terms of the apparent temperature, 𝑻𝑻𝒂𝒂 = 𝜺𝜺𝟏𝟏 𝟒𝟒⁄ 𝑻𝑻𝒃𝒃𝒃𝒃.

Note: the apparent temperature is directly dependent on the actual temperature and is relatively weakly dependent on the emissivity

Since emissivity, like exitance, is a spectral quantity,

Mλ = ελ Mbbλ

and 2

1 2

1

bbM M dλ

λ −λ λ λ

λ

= ε λ∫

• The emissivity will be different for different materials • Emissivity of the same material can vary with:

- direction - surface roughness - temperature - moisture content

• Emissivity is a spectral quantity:

Average emissivities of metals Typical average values: Metals: ε < 0.5 - emissivity increases with increasing temperature - increases substantially with the formation of an oxide layer. ==> @ 100°C aluminum, polishedε ≈ 0.05 anodizedε ≈ 0.55

brass polished ε ≈ 0.03 anodized ε ≈ 0.61

Average emissivities of non-metals Typical average values:non-metals in the 10-14µ range: ε > 0.8 - emissivity decreases with increasing temperature

Material ε Material ε concrete ~ 0.95 water (distilled) ~ 0.98 sand ~ 0.90 wood (oak) ~ 0.90 soil, dry 0.92-0.94 wet snow ~ 0.98 sat. 0.95-0.98 dry snow 0.85-0.90 vegetation ~ 0.98 dry ~ 0.88-0.94

Snow: Note that ε cannot be estimated by visual appearance. Reflectance is high in visible ==> low absorption in vis. Emissivity is high in TIR ==> high absorption

wavelength

ε

0.8

1

selective emitter

graybody blackbody

CEE 6100 / CSS 6600 Remote Sensing Fundamentals 6 Topic 6: Thermal Sensing An observed radiometric temperature difference might be caused by a difference in actual temperatures or by a difference in emissivities.

• In order to retrieve absolute temperatures, a correction must be made for any difference in emissivity between the unknown objects and the references.

• For relative temperatures of multiple unknowns, corrections must be applied to account for any differences in the objects' emissivities.

Spectral Emissivity 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 level, and it must get rid of energy (by emitting some light) to move to a lower level. Gustav Kirchoff described the processes in 1860 as follows: I. A dense object will produce a continuous spectrum when heated (blackbody radiation;

Planck's formula). II. A low-density, gas that is excited (meaning that the atoms have electrons in higher levels

than normal) will produce an emission-line spectrum. III. If a source emitting a continuous spectrum is observed through a cooler, low-density gas,

an absorption-line spectrum will result. A blackbody produces a continuous spectrum. This is in agreement with Kirchoff's first law. When the light from this blackbody passes through a cloud of cooler gas, certain wavelengths are absorbed by the atoms in that gas. This produces an absorption spectrum according to Kichoff's third law. However, if you observe the cloud of gas from a different angle, so you cannot see the blackbody, you will see the light emitted from the atoms when the excited electrons move to lower levels. This is the emission spectrum described by Kirchoff's second law. Thus, by Kirchoff's Law: absorptivity + reflectivity + transmissivity = 1 or: α (λ) + ρ (λ) + τ (λ) = 1.0 For opaque materials, τ = 0.0, therefore α (λ) + ρ (λ) = 1.0 Given that emissivity is simply the reverse of absorption1, then: ε (λ) + ρ (λ) = 1.0

Spectral Emissivity: water, ice and snow; ε ≈ 0.94 to 0.99 for 3 µ < l < 14 µ. Snow is unusual in that it has a high reflectance in the solar (visible) region where most of the downwelling energy is during the day, and a very high emissivity in the thermal region.

Spectral emissivity: Green vegetation Green vegetation typically has a very high emissivity because it contains water. Senescent (dry) vegetation has a more variable emissivity, especially in the 3 to 5 region, which depends on the type and structure of the cover type, the dryness, and so forth. 1 This relationship is strictly true only for bodies in thermal equilibrium. SEE: http://ieeexplore.ieee.org/stamp/stamp.jsp?arnumber=01265348 and http://www.lprl.org/resources/Kirchhoffs_law.pdf

http://ieeexplore.ieee.org/stamp/stamp.jsp?arnumber=01265348

http://www.lprl.org/resources/Kirchhoffs_law.pdf


Spectral emissivity: soil and minerals • ε ≈ 0.84 - 0.9 @ 3-5 µ ≈ 0.96 - 0.98 @ 8 - 14 µ • Emissivity in the 3 to 5 region depends strongly

on the water and organic content. • The "restrahlen" bands of quartz sand cause strong spectral features between 8 and 10 microns that depend on the grain size.

Water, ice, and snow: ε ≈ 0.94 to 0.99 for 3 µ < l < 14 µ. Snow is unusual in that it has a high reflectance in the solar (visible) region where most of the downwelling energy is during the day, and a very high emissivity in the thermal region.

Spectral Emissivity

Spectral emissivities measured on the ground (curves) and derived from ASTER observations (boxes). From: http://eospso.gsfc.nasa.gov/ftp_ATBD/REVIEW/ASTER/ATBD-AST-03/atbd-ast-03.pdf



Sensing Radiometric Temperature • Manmade materials have among the lowest emissivity values. • The emissivity of polished metals can be made less than 0.01 (better than 99% reflecting)

and are good for use in thermal infrared optical systems. • Rough dielectric materials such as asphalt and brick are in the same range as natural

materials, approximately 0.90 to 0.98.

Apparent vs. true temperature • Need to collect information that can be related to the temperature of an object. • We measure radiometric/apparent temperature not contact, thermometric or kinetic

temperature. • Remember Kirchoff's law for opaque objects:

α + ρ = ε + ρ = 1 i.e., if an object (at thermal equilibrium) is not emitting, it is reflecting.

• The total exitance detected from a real object is thus: 𝑀𝑀𝑑𝑑𝑑𝑑𝑡𝑡 = 𝑀𝑀𝑑𝑑𝑒𝑒𝑒𝑒𝑡𝑡 + 𝑀𝑀𝑟𝑟𝑑𝑑𝑟𝑟𝜎𝜎𝜎𝜎𝜆𝜆4 + 𝜌𝜌𝜌𝜌 - note: the importance of ε, λ, E and T - note: if ε = 0.8, ρ = 0.2

Important points: • For typical earth temperatures

for λ < 3 µ , Memit < Mrefl (solar radiation)

for 3 µ < λ < 5 µ , Memit ~ Mrefl

for 5 µ < λ Memit > Mrefl • Thermal sensing is often conducted at night (especially during predawn hours) but may

also be done during the day. The goal may be to – determine absolute or relative temperature, – observe temperature change, or – maximize the contrast of thermal targets.

• Atmospheric effects - atmospheric windows @ 3-5 µ, 8-14 µ - thermal IR will not penetrate fog or rain - thermal IR will sense through dry smoke (forest fires) - apparent temp. is affected by winds over ~ 10 knots

Sensitivity: • Sensitivity is defined in terms the Noise-Equivalent change in Temperature, NEΔT • Satellite systems have been designed with a NEΔT ≈ 0.1K • Typical thermal targets include:

• cloud top temperatures (as low as 100K for high altitude clouds) • sea-surface temperatures (only -2 K to 30K but needing high radiometric precision) • land temperatures (as high as 350K for equatorial desert in summer)

• Need 0.1K over a 250K range 10-12 bit quantization


Thermal Imaging Radiometer Why doesn't the detector sense the temperature of the casing, the mirrors or it's own temperature rather than that of the point on the ground?

Thermal Radiometers

• non-imaging instruments • generally used to collect TIR radiation along a

nadir track • often used to calibrate scanner data

Thermal Scanners • imaging instruments • primary purpose is to provide a thermal image (scene variability) • typically not as well calibrated as a radiometer

GOES (Geostationary Operational Environmental Satellite)

Focal plane array for the GOES–12 to 15 imager. The squares represent the size of the individual detectors for each band.

http://rsd.gsfc.nasa.gov/goes/text/databook/section03.pd

CHANNEL 1 2 3 4 5 center wavelength (µ) 0.65 3.9 6.75 10.7 12.0 detector Si InSb HgCdTe HgCdTe HgCdTe IFOV (µrad) 28 112 224 112 112 GIFOV (km) 1 4 8 4 4 vis shortwave moisture longwave 1 longwave 2


Detector Response

Visible shortwave (Mid-IR) moisture

visible thermal

CEE 6100 / CSS 6600 Remote Sensing Fundamentals 12 Topic 6: Thermal Sensing AVHRR (Advanced Very High Resolution Radiometer)

Swath = 2500 km

ASTER (Advanced Spaceborne Thermal Emission and Reflection Radiometer )

Newtonian catadiotropic Telescope

Scanning mirror • scanning • pointing • calibration

Blackbody source • viewed before/after each observation • periodically heated through a range of temperatures to

provide gain and offset calibration

Cryocooler for HgCdTe detectors


ASTER (cont'd)

Braidwood Nuclear power plant in Illinois, located about 75 km southwest of Chicago Braidwood Nuclear can be seen in the VNIR image (top) as the bright blue-white pixels just above the large cooling pond used to discharge heated effluent water. In the bottom image, a single ASTER Thermal Infrared band was color coded to represent heat emitted from the surface. The warmest areas are white; progressively cooler areas are colored red, orange, yellow, green, blue, and black for the coolest. Note the bright white plume of hot water discharged from the power plant. The water grows progressively cooler as it circulates around the pond.

NOAA AVHRR : Sea Surface Temperature (Rutgers)

http://marine.rutgers.edu/cool/sat_data/?product=sst&region=nybight&nothumbs=0


Other Examples

Car and people • Car engine is warm indicating that it has been running recently. • The outer edges of the wheels are warm indicating that the car was recently moving long enough to heat up the tires. • Pavement under the car is warmed slightly, indicating that the car has not sat at this location very long.

Pick-up truck • Wheels, both the outer edges and the sides, are quite warm, as are the wheel wells indicating that the car has been in motion long enough to heat them up. • Ground appears to have been warmed up substantially indicating that the truck has been sitting there for more than a few minutes. • Front window is cold, back window is warm (?)

Thermal history

• Bodies have warmed up the couch and the heat pattern remains even after the people have moved.

Thermal Reflection and thermal history

• Note the thermal history of hand print on the car door. • Note the thermal reflection of the man's head in the car window. Note also, the shadow of the crowbar. Glass is moderately reflective in the thermal. • The background glass (away from the reflection) is dark indicating that the glass itself is relatively cold.

Thermal Shadow • Note the thermal shadow of the helicopters on the ground. The tarmac outside of the shadow has been warmed by the sun. • The relatively cold shadow remains for a time after a helicopter has been moved.

CEE 6100 / CSS 6600 Remote Sensing Fundamentals 15 Topic 6: Thermal Sensing Water damage – change in emissivity

• Water seepage and leaks have changed the emissivity of the surface, making the damaged areas appear significantly warmer than the undamaged areas.

Water damage – rooftop • Red = “hot”, Blue/Violet = “cold”. • The water-damaged areas appear warmer due to the altered emissivity

Steam line leaks • A pre-dawn image of the main Cornell Campus. • Underground steam lines are visible because they have heated the surface. • Leaks, like the one near Schoellkopf stadium, heat up the surface excessively. • Structures that are at the same temperature (grass and walks) appear different due to emissivity differences. • Water is both warmer and more emissive than land.

Oil slick The lower emissivity of the oil makes it appear much cooler than the surrounding water.

CEE 6100 / CSS 6600 Remote Sensing Fundamentals 16 Topic 6: Thermal Sensing Urban Heat Island Pilot Project

• In 1998, EPA launched the Urban Heat Island Pilot Project (UHIPP). The purpose of UHIPP is to:

– Assist cities in efforts to adopt and evaluate heat island reduction strategies and programs;

– Encourage research, education, and communication; – Demonstrate and document successful heat island reduction projects that may

be adopted in other communities; and – Build community support and understanding of heat island reduction

measures. • Factors affecting the magnitude of heat islands are prevailing climate, topography,

and urbanization in a given geographical location. As a result, the benefits of using heat island reduction measures depend on local conditions.

Thermally Sensed Image of Houston (http://www.epa.gov/heatisland/pilot/houston.html)

• Red and white areas indicate hot spots and generally correspond with roads and roofs. • Blue, green, and purple areas are cool and indicate water and vegetation. • The temperature ranges from approximately 149° F (65° C) for the hot spots and 77° F (35° C) for the cooler areas. Panchromatic Thermal

Campfire detection Response of the Thermal Imaging Radiometer at a wavelength of 8.1- to 12.4-µm to a small campfire at a distance of 2 km. The fire-containing pixel had a digital number of 40,135 ± 10. The nearby background average digital number was 39,914 ± 10

http://www.epa.gov/heatisland/pilot/houston.html

CEE 6100 / CSS 6600 Remote Sensing Fundamentals 17 Topic 6: Thermal Sensing Multispectral thermal sensing Forest fire monitoring

NASA's Ikhana UAV flew over Southern California wildfires Wednesday, Oct. 24, 2007 with thermal-infrared imaging equipment peering through smoke and haze to record high-quality imagery of the hot spots. The images were taken at 10:21 a.m. PDT over the Harris Fire in San Diego County, looking west and then overlain on the topography in Google Earth to produce the 3-D image at the left. The hot spots (in yellow) are concentrated on the ridgeline in the left center of the photo. The Autonomous Modular Scanner (AMS) Wildfire sensor has recently been flown to monitor and map the wildfires in California. Designed by scientists from NASA Ames, the system scans 12 spectral channels ranging from the visible

bands through reflective, mid- and thermal infrared. Unlike body-heat-sensing equipment typically used by security professionals, the device is calibrated to observe fires and other high-temperature sources, discriminating 0.5 °C increments up to 1000 °C. At 20,000 ft and 2.5 mrad, spatial resolution is 50 ft. Still, because fire is so much hotter than the surrounding area, the system can detect even a small campfire from high altitudes. In a 16.5-h flight over Idaho, Montana and Wyoming, the scientists collected 15 GB of raw data and 131 processed images over six wildfires. Snow Cover

Topic 6: Thermal Sensing Topic 6: THERMAL SENSINGceeserver.cee.cornell.edu/wdp2/cee6100/6100 Topics/Topic06_Fa15… · Blackbody Radiation. Planck's Formula. describes the magnitude

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