Abstract
The concept of emissivity has been with the scientific and engineering world since Planck formulated his blackbody radiation law more than a century ago. Nevertheless， emissivity is an elusive concept even for experts. It is a vague and fuzzy concept for the wider community of engineers. The importance of remote sensing of temperature by measuring IR radiation has been recognized in a wide range of industrial， medical， and environmental uses. One of the major sources of errors in IR radiometry is the emissivity of the surface being measured. In real experiments， emissivity may be influenced by many factors： surface texture， spectral properties， oxidation， and aging of surfaces. While commercial blackbodies are prevalent， the much-needed grey bodies with a known emissivity， are unavailable. This study describes how to achieve a calibrated and stable emissivity with a blackbody， a perforated screen， and a reliable and linear novel IR thermal sensor， 18 dubbed TMOS. The Digital TMOS is now a low-cost commercial product， it requires low power， and it has a small form factor. The methodology is based on two-color measurements， with two different optical filters， with selected wavelengths conforming to the grey body definition of the use case under study. With a photochemically etched perforated screen， the effective emissivity of the screen is simply the hole density area of the surface area that emits according to the blackbody temperature radiation. The concept is illustrated with ray tracing simulations， which demonstrate the approach. Measured results are reported.
What is emissivity and who needs measurements of emissivit
As a fundamental principle of physics， all materials emit electromagnetic radiation. The intensity of this radiation， measured in terms of power， is directly influenced by the material's temperature and its emissivity. Emissivity is a property that quantifies a material's ability to emit thermal radiation relative to a perfect black body.
More than a century ago， Planck formulated his radiation law， expressing the power emitted by a model body named “blackbody”， as a function of temperature and wavelength.
Planck’s radiation law is a mathematical model describing the amount of radiation from a closed metallic furnace held at a well-controlled temperature. The model body has become known as a blackbody.
Every material radiates power， but real materials are not perfect blackbodies. Emissivity is a material's ability to radiate a fraction of the power that a perfect blackbody would radiate at a given temperature. Thus， the amount of radiated power is dependent on the material’s temperature and the material’s emissivity.
IR thermometers take advantage of this. They measure the amount of power exiting an object in an infrared band. They calculate the temperature based on this measured power and the material’s emissivity.
Accordingly， accurate temperature measurements cannot be obtained without measuring simultaneously the emissivity. The errors introduced by non-accurate emis-sivity value are significant and increase with object temperature.
Fig. 1 Planck’s radiation law is a theoretical physical concept. Left side： the parameters de-scribing the ideal blackbody. Right side： the parameters describing the ideal grey body
Every material radiates energy. As discussed above， emissivity is a factor between 0 and 1， which multiplies Plank’s radiation law. It is the ratio of the radiation emitted from the surface of a body to the theoretical emission of an ideal blackbody of the same size and shape according to Planck’s Law.
The amount of radiated power is dependent on the material’s temperature and the material’s emissivity. The emissivity may vary with wavelength and temperature. A grey body has constant emissivity within the measurement IR optical bandpass filter. While the ideal blackbody has an emissivity = 1， the grey body emits a constant fraction of the radiation， which is termed emissivity. Thus， a grey body is a surface whose emissivity is constant regardless of wavelength.
For calibration and simulation of remote temperature systems， a “grey body” with a variable emissivity down to low emissivity in the range of 0–0.98， is required.
Blackbody manufacturers strive to provide a near-ideal blackbody with an emissivity as close to 1 as possible， which is theoretically not achievable because such an ideal blackbody does not emit. State-of-the-art blackbody manufacturers provide blackbodies with an emissivity of 0.98 ± 0.02. A commercial grey body with well-calibrated emissivity is not available， since in real experiments， emissivity may be influenced by many factors： surface texture， spectral properties， oxidation， and aging of surfaces. This is why emissivity measurements are challenging， as further explained below.
There are two types of blackbodies： cavity and extended area， as illustrated in
Fig. 2 There are 2 types of commercial black bodies. On the left： image of extended area blackbody for calibration. On the right： an image of cavity blackbody. Images from Ref.［
Extended area blackbodies are made of a heated， high-conductivity metallic plate， which is covered by black paint. A calibrated Resistance Temperature Detector （RTD） made of platinum controls the temperature of the metallic plate.
In theory， an extended area blackbody may provide a good calibration. In practice， there are several issues. The emissivity of the metal layer is anywhere from 0.02 to 0.50 depending on the metal. Furthermore， most metals oxidize. This does increase the emissivity， up to 0.80， but it also results in a very large uncertainty due to the time-dependent variance in the emissivity of oxides. To get around these problems with metals， the surface is painted with black paint. In the 8 – 14 µm bandwidth， special paints are available that have an average emissivity of 0.96 to 0.98. However， the black paint also oxidizes during operation， and its emissivity changes.
Industrial factories monitor the manufacturing process with remote temperature sensing using black tape on the monitored surface. The black tape is calibrated， and its emissivity is measured to be ~0.95. However， tapes with well-calibrated emissivity in a wide range of values are not available. Military equipment suppliers provide low-emissivity tape， lower than 0.3， to camouflage military systems and equipment in the dark. Such tapes are not available for everyone.
To summarize， in real experiments， emissivity may be influenced by many factors： surface texture， spectral properties， oxidation， and aging of surfaces. Hence， it is essential to measure simultaneously both temperature as well as emissivity.
There are no blackbody manufacturers that provide a “grey body” with known lower surface emissivity. This raises the question of how to test， calibrate， and measure remote temperature device performance with a target that has unknown emissivity.
Below， in
Fig. 3 The new grey body is based on a high-quality extended area blackbody, a perforated screen, and a high-performance IR uncooled thermal sensor. The metallic screen transmits only a fraction of the blackbody radiation, depending on the density of the holes. Accordingly, a set of perforated screens transform the blackbody into a grey body, as explained in the text below
We prepare a set of perforated screens with varying fractions of holes relative to the overall area. With a perforated screen， the effective emissivity of the surface is simply the hole density area of the surface area that emits according to the blackbody temperature radiation. The remaining density area of the screen， which is metallic and highly reflective， reflects radiation according to the ambient temperature. If the screen temperature is equal to the ambient temperature， the emissivity of the screen is not relevant since what is emitted by the screen is compensated by what is reflected from the screen.
As illustrated in
Fig. 4 Illustration of the sensor field of view facing an extended area black body with a perforated screen
To mitigate this effect， it is beneficial to maintain the screen's temperature in thermal equilibrium with the ambient environment. This ensures that the emitted radiation from the screen closely matches the reflected ambient radiation， minimizing any potential impact on the measurement results.
Thus， a perforated screen with a controlled hole density， held at the ambient temperature， allows us to control the emissivity of a commercial blackbody.
The perforated holes are designed with the following rules： to be uniformly distributed， and the hole diameter is designed to be small and with an adequate number of holes within the field of view of the sensor. By applying Far Field Approximation to the measurements， we aim to neglect diffraction effect
In IR thermography， we focus the main wavelength of IR radiation are around 10 µm， and therefore holes around 1 mm in diameter are adequate. We refer to the above setup （
| , | (1) |
where is the detector signal measured facing the screen between the blackbody， as shown in
The signal from the screen is equal to the ratio of the holes of the perforated screen to the total area if the screen and ambient air are at the same temperature. To achieve that， the screen is “soaked” in the ambient temperature （~20 °C）， and the measurement is applied rapidly （10 s or less）. Thus， the screen with a known percentage of holes can “transform” a near ideal extended area blackbody to a practical grey body with a known emissivity.
Photochemically etched perforated screens provide a precise， robust， and repeatable solutio
With photochemical etching， perforated screens are manufactured from a single piece of metal， including thicknesses down to 100-micron foil. Finally， the screens are packaged in a frame. This gives them greater strength and integrity as well as a more vertical etching profile.
We have designed a screen made of 0.1 mm stainless steel with holes with a radius of 1 mm and a pitch between the center of the holes of 2.15 mm. The spec for the product is +/-0.05 mm. The perforated screen provides a ratio of between the holes area to the whole plate.
The measurement setup is described in
The “screen approach” is based on the following assumptions： thermal equilibrium； conservation of energy； Kirchhoff Law； an opaque blackbody； a reflecting plate； and a perforated screen. It is discussed in detail at Ref.［
In specific optical band pass regions， the error in temperature may be related to the emissivity by simulations. For the sake of simplicity， we discuss this issue for monochromatic radiation.
Monochromatic Planck’s radiation law：
| . | (2) |
The relation between emissivity differentiation to temperature differentiation for monochromatic radiation：
| . | (3) |
To show the impact of uncertainty in emissivity evaluation on the calculated temperature from the radiation it can be inferred for example with expression （3） for monochromatic radiation λ=10 µm， object emissivity of 0.98 and object temperature of 310 K， an in-accuracy of Δε=0.01， introduces temperature in-accuracy of 0.6862℃. The uncertainty caused by emissivity increases with the wavelength （） as well as temperature （
The TMOS is a novel micromachined n-MOS CMOS transistor operating at subthreshold and performing as a thermal IR uncooled sensor. The TMOS stands for thermal MOS. It was originally invented at Technion， and a patent was filed and granted in 2003.
The development was funded by TODOS Technologies
The TMOS Uncooled thermal sensor has the following advantages： small form factor， lightweight， low-power， low-cost and high performance tailored for the specific use case of the grey body discussed in this work. An important feature of the Digital TMOS is the linearity with emissivity. A circuit implemented on the Digital TMOS， known as PTAT- Proportional to Absolute Temperature， measures the sensor physical temperature， which is determined by the ambient temperature and the measurement conditions.
Fig.5 Image of commercial Digital-TMOS
Sensing specifications：
⋅ IR sensitivity： 2000 LSB/℃
⋅ RMS noise： 25 LSBrms
⋅ Operating wavelength： 5 µm to 20 µm
⋅ Local temperature sensor accuracy： ±0.3 ℃
| . | (4) |
Based on the upgraded RMS noise of 25 LSB （RMS）， the resolution is therefore NETD ~12 mK. The TMOS has emerged in the last decade as a preferred uncooled IR thermal sensor， since it features low fabrication cost， typical of CMOS thermopiles， and high performance， typical of bolometers
The unique feature of this device is that it simultaneously employs two sensors with different optical bandpass filters. Accordingly， the measurement yields two power equations with two unknowns： the temperature and the emissivity. By solving these two equations， the effective emissivity is derived. This approach enabled us to measure remotely and accurately the forehead temperature and emissivity
Fig. 6 The front side of the watch-like prototype for measuring wrist temperature
Fig. 7 The backside of the watch-like prototype for measuring wrist temperature. Two TMOS sensors with modified filters sense the skin temperature and emissivity with great accuracy
Fig. 8 The emissivity of the human skin as a function of wavelength， in comparison to water. Based on Ref.［
In an earlier pape
Ray tracing simulation
In order to avoid a full 3D ray tracing simulation， which is both time and resource-consuming， the semi-azimuthal symmetry of the problem was used， with ray tracing performed on 2D cross-sections rather than the entire 3D problem. For each such cross-section， the ratio between the number of rays emitted from the source and rays reaching the detector was calculated， as well as the length ratio between the holes’ total length and the mask’s diameter. The effective emissivity of each 2D cross-section is taken as the ratio between detected and emitted rays， and is expected to equal the hole-mask length ratio.
Fig. 9 （a） The complete 3D model of the simulation. a 2D cross-section is marked as a yellow place intersecting the detector， mask and source； （b） example of a ray tracing simulation done on a single 2D cross-section
As the hole mask does not have complete azimuthal symmetry， several 2D cross-sections were used. The overall mask’s emissivity is taken as the average of all 2D emissivity and the overall mask’s hole area to mask area ratio is taken as the average of all 2D length ratios. The two sizes are expected to be equal， proving the validity of a blackbody source with a hole mask acting as an effective grey body.
Fig. 10 Two cross-sections of the hole mask and their respective ray tracing simulations. The resulting ray tracing pattern is different due to the different mask cross-section for each axis
Infrared The radius of the holes in the mask was taken as 1mm. Two-hole spacings were simulated： 2.15 mm and 2.5 mm. The simulation demonstrated a good match between the length ratios and ray ratios， showing that for each cross-section， the effective emissivity matches the mask’s hole to diameter ratio. The averaged emissivity and averaged hole to mask area ratio also demonstrated a good match， indicating that the hole mask， combined with the blackbody source， form an effective grey body.
Fig. 11 Two cross-sections of the hole mask and their respective ray tracing simulations. The resulting ray tracing pattern is different due to the different mask cross-section for each axis
For the 2.15 mm-spaced mask， the emissivity obtained from the ray tracing simulation was 0.7793±0.0278 and the emissivity obtained from the geometric hole to mask area ratio was 0.7838±0.0141. For the 2.5 mm-spaced mask， the emissivity obtained from the ray tracing simulation was 0.5851±0.0313 and the emissivity obtained from the geometric hole to mask area ratio was 0.5811±0.0278. For both spacings， we can see that the obtained geometric and ray-tracing emissivity closely match. The difference can be attributed to the accuracy of the ray-tracing simulation. A more accurate simulation requires additional rays and is thus more time and resource consuming. The variance in emissivity is a result of the different mask 2D cross-sections at each angle. The variance is expected to decrease for a more refined mask with smaller holes and smaller spacings， resulting in a smoother intensity profile for the graybody source.
Infrared （IR） radiometry is a very useful form of temperature measurement in industrial， scientific， and medical applications. The unique advantages of radiometry are quick response times and that is a remote sensing approach. Namely， it does not have to be in contact with the area being measured. The major drawback is that IR radiometer accuracy depends on calibration.
Calibration requires a well-calibrated blackbody as well as determination of the emissivity of the surface being measured. Emissivity is a physically well-defined parameter but in real experiments， it may be influenced by many factors： surface texture， spectral properties， oxidation， and aging of surfaces.
This work describes a methodology for how to calibrate radiometers in the lab or in the factory or FAB， using the “screen approach” and the novel thermal sensor dubbed Digital TMOS.
In summary， we cannot measure temperature correctly by remote sensing unless we take into consideration the emissivity.
The industry tends to ignore this fact since the emissivity of materials is unknown and hard to assess. We have invented and developed a grey body， which enables us to use it as a reference for emissivity to validate the TODOS remote temperature measurements.
The TODOS Digital TMOS with our algorithm measures the temperature of people’s forehead temperature， regardless of the presence of varying layers of cosmetics or sun lotions. Commercial remote temperature systems cannot achieve that.
The interested markets should be manufacturers of mobile phones who want to integrate remote temperature applications； Health industry for Hospitals： not requiring patient collaboration， avoiding contamination， reducing nurses’ workload， saving costs associated with biomedical thresh； Agriculture Industry for farm animals， pets， and more.
Acknowledgements
The authors express their sincere gratitude to the reviewers and the editor for their constructive criticism and insightful suggestions， which have contributed to a substantial enhancement of this paper's clarity and comprehensibility.
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