This is my first post here. For one of my projects I need to do a temperature compensation according to the distance, browsing I found an article called "High precision infrared temperature measurement system based on dsitance compensation" that does exactly what I need. I have tried to replicate with their data the methodology they propose but I am unable to obtain the same result.
According to the article, a relationship is made between the distance and an adjustment parameter called Y (equation 1 in the image), my problem is not how to solve the ecucations presented in order to obtain the parameters $a_0, a_1, a_2$ shown in equation 4.
Article capture
Data
Thank you very much to whoever can help me.
You are correct : there is a problem somewhere.
If we use the data $$\left( \begin{array}{cc} d & T \\ 0 & 33.37 \\ 10 & 33.11 \\ 20 & 32.87 \\ 30 & 32.70 \\ 40 & 32.32 \\ 50 & 31.82 \\ 60 & 31.32 \end{array} \right)$$ and the model is either
$$\frac T {T_0}=b_0+b_1\,d +b_2\,d^2$$ the exact results are $$b_0=\frac{34988}{34965}\approx 1.0006578$$ $$b_1=-\frac{43}{116550}\approx -0.00036894037$$ $$b_2=-\frac{73}{6993000}\approx -0.000010439010$$ which differ from the numbers they give.
If, as it seems, they fit $$\frac {T_0}T=c_0+c_1\,d +c_2\,d^2$$ the exact results are $$c_0=\frac{11681771821960765499}{11687496483739052592}\approx 0.99951019$$ $$c_1=\frac{50500159478371189}{155833286449854034560}\approx 0.00032406529$$ $$c_2=\frac{2449273119119}{201708529727558400}\approx 0.000012142635$$ which also differ from the numbers they give.