Infrared thermometer working principle

[misterwicked]

So, as far as I understand IR thermometer works by measuring light irradiance coming from an object (in the IR spectrum) and then calculating the object temperature using Stefan's law. Since the irradiance falls like 1/r² with distance, I am wondering how it takes distance into consideration.

I would appreciate some useful answers.

 

[DrClaude]

It's not Stefan's law that comes into play, but Wien's displacement aw (or, more generally, Planck's law), see https://en.wikipedia.org/wiki/Black-body_radiation#Equations

 

[misterwicked]

You're saying the IR thermometer measures peak wavelength and not the irradiance?

 

[DrClaude]

You're saying the IR thermometer measures peak wavelength and not the irradiance?

Yes. As you figured out yourself, irradiance will depend on the distance to the object. Also, irradiance is much more affected by the fact that actual objects are not perfect black bodies than peak wavelength.

 

[misterwicked]

This sounds sensible to me. Except I can't imagine how then one of those things can cost only a couple of $.

Additionaly, in this datasheet it is stated that "As the temperature of the body rises, the
intensity of this infrared energy increases. The temperature of the body can therefore
be determined by measuring the intensity of this infrared energy."

 

[DrClaude]

Some IR thermometers might work on a different principle. We'll have to let people more knowledgeable than me chime in.

 

[Lord Jestocost]

This sounds sensible to me. Except I can't imagine how then one of those things can cost only a couple of $.

Additionaly, in this datasheet it is stated that "As the temperature of the body rises, the
intensity of this infrared energy increases. The temperature of the body can therefore
be determined by measuring the intensity of this infrared energy."

Simple infrared non-contact thermometers are generally total radiation pyrometers. The optical system of such infrared thermometer determines a circular measurement spot and the target must completely fill out this spot. Thus, the radius of the measured spot on the target has to scale with the distance. See, for example, Fig. 11 and 12 in [PDF]Principles of Non-Contact Temperature Measurement.

 

[Charles Link]

These IR thermometers either assume an emissivity of unity, or , in some cases, will allow you to input an emissivity. They will read (inaccurately) very low in the case of a metal that is reflective in the IR and thereby has very low emissivity there. If they use a pyroelectric detector, (pyroelectrics can be made to respond to virtually all wavelengths=it depends on the coating they have that absorbs the incident radiation), they essentially work from Stefan's Law. If they use a photodiode that responds in the IR, the item of interest is the Planck blackbody function over the wavelengths for which the photodiode responds.

 

[OmCheeto]

Simple infrared non-contact thermometers are generally total radiation pyrometers. The optical system of such infrared thermometer determines a circular measurement spot and the target must completely fill out this spot. Thus, the radius of the measured spot on the target has to scale with the distance. See, for example, Fig. 11 and 12 in [PDF]Principles of Non-Contact Temperature Measurement.

So, the answer to misterwicked's question:

Since the irradiance falls like 1/r² with distance, I am wondering how it takes distance into consideration.

would be: The irradiance does not fall like 1/r², as you are measuring the irradiance from a plane, and not a point, if you are using the device correctly, and therefore, distance is irrelevant.

Yes?

ps. This gives me a grand idea for a new experiment. I've had an infrared thermometer for several years, and it works great for measuring the temperature of big things, like my wood stove, the side of my house, etc. But it's pretty much useless for measuring small or odd shaped things, like candle flames or electric stove top heating elements. Although those two examples are thermally outside the range of my device, I'm wondering if I could use the 1/r² law, and some maths, to semi-accurately measure their temperatures.

pps. Thank you, @misterwicked , for asking a good question.

 

[Charles Link]

It is possible to calibrate a pyroelectric detector (which will give a voltage proportional to the incident power) using the Stefan-Boltzmann law, along with the inverse square law, and using a commercially available blackbody source (they can be somewhat expensive), and measure the temperature of other sources with it, with the assumption that the source being measured has emissivity $\epsilon=1.0$. $\\$ For small sources of known geometry, the inverse square law will apply. The equation of interest is the power incident on the detector, (using the inverse square law), $P= \frac{L \, A_s \, A_d}{s^2}$, where $L=\frac{\sigma \, T^4}{\pi}$. The $\pi$ is kind of an odd factor, but arises because the intensity $I(\theta)=I_o \cos(\theta)$ for a Lambertian source, and the radiated power is $P=\iint I(\theta, \phi) \, d \Omega=\int\limits_{0}^{2 \pi} \int\limits_{0}^{\frac{\pi}{2}} I(\theta) \, \sin(\theta) \, d \theta \, d \phi =I_o \, \pi=\sigma \, T^4 \, A_s$ over a hemisphere. Thereby the on-axis intensity $I_o=L \, A_s=\frac{\sigma \, T^4}{\pi} \, A_s$

 

[misterwicked]

The irradiance does not fall like 1/r², as you are measuring the irradiance from a plane, and not a point, if you are using the device correctly, and therefore, distance is irrelevant.

If irradiance is constant with distance and the device measures incident radiation from a cone, then a signal coming from larger distance should be larger since the spot diameter is larger there. What am I missing?

 

[Asymptotic]

If irradiance is constant with distance and the device measures incident radiation from a cone, then a signal coming from larger distance should be larger since the spot diameter is larger there. What am I missing?

View attachment 214248

Measured temperature is an average of whatever is radiating within the cone. With this camera, displayed temperature is averaged within the center circle (white arrow), and measures a relatively hot area. Consider what happens while pulling back ...in this case, progressively larger, cooler areas on the right hand, cooling fan side of the motor lie within the cone, and displayed average temperature will decrease.

IR thermometers (particularly the better ones) usually have an option to switch between displaying the average, maximum, or minimum temperature measured within the spot diameter.

 

[misterwicked]

Measured temperature is an average of whatever is radiating within the cone. With this camera, displayed temperature is averaged within the center circle (white arrow), and measures a relatively hot area. Consider what happens while pulling back ...in this case, progressively larger, cooler areas on the right hand, cooling fan side of the motor lie within the cone, and displayed temperature average will decrease.

Let's assume you have an infinite plane with uniform temperature. The irradiance is constant with distance from this plane. However, when the device is closer it will get signal from a smaller spot, than when you move further away from the plane. Following this logic it should measure hotter and hotter temperature as you are going further away, since it would get signal from larger and larger spots. The measurement is however, distance independent.

 

[Asymptotic]

Following this logic it should measure hotter and hotter temperature as you are going further away

I don't follow that logic.

 

[Lord Jestocost]

If irradiance is constant with distance and the device measures incident radiation from a cone, then a signal coming from larger distance should be larger since the spot diameter is larger there. What am I missing?

View attachment 214248

The intensity (or irradiance) of infrared light radiating from every point source on the observed spot is inversely proportional to the square of the distance from the source. On the other hand, the area of the observed spot scales with the square of the distance.

 

[misterwicked]

The intensity (or irradiance) of infrared light radiating from every point source on the observed spot is inversely proportional to the square of the distance from the source. On the other hand, the area of the observed spot scales with the square of the distance.

Ok, so this is the key to understanding why measurement is distance independent. Irradiance falls by 1/r² with distance and this is exactly compensated by larger spot sizes, which scale up by the same amount by which the irradiance decreases with distance. Thanks!

 

[OmCheeto]

I'm wondering if I could use the 1/r² law, and some maths, to semi-accurately measure their temperatures.

The test results do not look promising...

It is possible to calibrate a pyroelectric detector...

Just not by me.

Oh, my, god...

It's no wonder people* hate science. This is impossibly hard!

================

*young and impatient, and old and senile.

 

[Charles Link]

The test results do not look promising...

View attachment 214404
Just not by me.

Oh, my, god...

It's no wonder people* hate science. This is impossibly hard!

================

*young and impatient, and old and senile.

It's not likely to work with a flame. In general, you just don't have the emissivity from the gaseous state (i.e. the emissivity will be much much less than 1.0), particularly when it is not a plasma. I think most of the light output from a candle flame is the result of atomic and molecular transitions. It does not behave like a blackbody, and there will be little correlation between what you measure (under the assumption that it is a blackbody) and the actual temperature. Any correlations that you would get between the radiated power and the actual temperature would be somewhat coincidental.