Convert Two Intensity Images into one Temperature Image

I have two intensity images from two different wave lengths sensors, and want to convert into one temperature image.

In order to avoid the emissivity dependence, the relation must be a ratio between the intensities. However when I try to do the ratio between them, all the picture have almost the same value and the result is not trustworthy. I wonder how I could do this conversion to obtain the temperature regardless the emissivity value and without so much background noise.

The calibration is being done using a filament bulb and the relation between the two images are based on the ratio of the peak intensities in each picture, related to the temperature.

The sensors have an offset difference of 2 X-axis pixel and 19 Y-axis pixel.

[DGM]

We don't know anything about these images, how they're scaled, or what calculations you're trying to perform.

All I see is two images which appear to be presumed uint12-scale. Without any other context, that doesn't tell me anything about physical quantities.

Interesting, though.

[matheus]

The images are measuring the radiance of a filament with known temperatures, to then be transformed to a temperature measurement. The calculation I am trying to do is transforming the intensity level of two camera in two different wave lengths, to a temperature image.

[Image Analyst]

Not sure I know what you want to measure the temperature OF. You know the temperature of the filament - you say it's known. However to get a scale we'd need to know the temperature of something else - something not hot, like the background. Of course the background and filament most likely have different emissivities, which will be a problem. What wavelength are the two cameras at? Are they both thermal cameras in the thermal range, or are they in the optical range. FLIR says:

"Most gas detection cameras (such as propane, methane, and butane detectors) are midwave cameras, meaning they have a spectral range of 3µm to 5µm. Almost all other thermal cameras are longwave, and have a spectral range of 8µm to 14µm."\

The filament seems to have a variety of temperatures in it - it doesn't appear to be a single temperature. Do you know the range of temperatures in it?

Again,

1. Other than the filament, which has known temperature, what else in the scene do you want to measure the temperature of?
2. What are the wavelength ranges of your cameras?

When you divide the images, make sure they're both double, otherwise you will have quantization.

[matheus]

1. Other than the filament, which has known temperature, what else in the scene do you want to measure the temperature of?

• I used many temperatures of the filament, and using the peak intensity I found a exponential relation between the ratio of the peak intensity in each picture and the temperature expected. it was a relation T = alfa*exp((Short_int/Long_int)*beta). And then applied it pixel-by-pixel in the other images.

1. What are the wavelength ranges of your cameras?

• 7µm-8.5µm

[Image Analyst]

So you have an image and you only want temperatures of the filament, and nothing else in the scene, right? And somehow, by some other trusted method, you've determined the "true" temperature of the filament precisely at the peak/brightest locations only. And you want to calibrate the gray levels of the camera image with the "true", trusted temperatures from your other trusted method. What is this other method that you determined the true temperatures with?

What is Short_int and Long_int? Are they short integer and long integer images? Like one is an 8 bit integer and one is a 16 bit integer? Why are they not the same bit length? Or is one the image from one camera and one the image from the other camera, but they are both integer valued, like uint16 images?

If Short_int and Long_int are both integer images you will need to cast them both to double before dividing: double(Short_int) ./ double(Long_int)

Are both cameras mid-wave IR cameras (rather than thermal cameras) and both in the same mid-wave wavelength range (7-8.5 µm), or do you have some kind of IR filter in front of the lenses to pick out a more narrow range of temperatures for each, like one is sensitive to 7 to 7.5 microns and one is senstive to 8 to 8.5 µm?

Do you have a reference to some web page where it says that theory says you are supposed to use that formula to compute the temperature from the gray values?

[matheus]

The method is controlling the voltage and tension of the filament, and knowing the temperature of it.

The ratio is the shorter wave length intensity divided by the longer intensity value.

The calculation is based on wiens approximation of the plancks law for dual wavelength sensors.