Signal transfer function

The signal transfer function (SiTF) is a measure of the signal output versus the signal input of a system such as an infrared system or sensor. [cite book | title = The Optical Transfer Function of Imaging Systems | author = Tom L. Williams | publication = CRC Press | year = 1998 | isbn = 0750305991 | url = http://books.google.com/books?id=-luzt97NKLEC&pg=PA247&dq=SiTF+signal-transfer-function+input-and-output&as_brr=3&ei=aW_tSMW0LY32sgPz_Y2YBw&sig=ACfU3U2RiRXiIsqTURSS6Uo-qUm2ACGKrA ]

SiTF evaluation

In evaluating the SiTF curve, the signal input and signal output are measured differentially; meaning, the differential of the input signal and differential of the output signal are calculated and plotted against each other. An operator, using computer software, defines an arbitrary area, with a given set of data points, within the signal and background regions of the output image of the infrared sensor, i.e. of the Unit Under Test (UUT), (see "Half Moon" image below). The average signal and background are calculated by averaging the data of each arbitrarily defined region. A second order polynomial curve is fitted to the data of each line. Then, the polynomial is subtracted from the average signal and background data to yield the new signal and background. The difference of the new signal and background data is taken to yield the net signal. Finally, the net signal is plotted versus the signal input. The signal input of the UUT is within its own spectral response. (e.g. color-correlated temperature, pixel intensity, etc.). The slope of the linear portion of this curve is then found using the method of least squares. [Electro Optical Industries, Inc.(2005). EO TestLab Methodology. In "Education/Ref". http://www.electro-optical.com/html/toplevel/educationref.asp.]

SiTF calculations

The average signal and background are calculated by the following equations:

:$mu,Sig\_\{ave\}\; =\; frac\{sum\_\{i=o\}^n\; X\_i\}\{n\}\; qquad\; qquad\; mu,Background\_\{ave\}\; =\; frac\{sum\_\{i=0\}^p\; Y\_i\}\{p\}$

:where :$n,$ = the number of lines in the target area $X,$ or $Y,$:$p,$ = the horizontal pixel resolution in the target area $X,$ or $Y,$:$i,$ = the $i,$^th line or horizontal pixel resolution in the target area $X,$ or $Y,$:$X,$ = an arbitrarily defined area in the illuminated portion of the image (signal region).:$Y,$ = an arbitrarily defined area in the non-illuminated portion of the image (background region).

A second order polynomial is calculated using a double summation:

:$f(X)\_i\; =\; sum\_\{j=0\}^m\; sum\_\{i=0\}^n\; a\_j\; X\_i^j\; qquad\; qquad\; f(Y)\_i\; =\; sum\_\{j=0\}^m\; sum\_\{i=0\}^n\; a\_j\; Y\_i^j$:$f,$ = the output sequence best fit:$X,$ = the input sequence (signal region):$Y,$ = the input sequence (background region):$a,$ = the polynomial fit coefficient:$m,$ = the polynomial order

The second order polynomial is subtracted from the original data and the mean is taken:

:$mu,Sig\; =\; mu,Sig\_\{ave\}\; -\; f(X)\_i\; qquad\; qquad\; mu,Background\; =\; mu,Background\_\{ave\}\; -\; f(Y)\_i$

Then, the net signal is calculated:

:$Signal\; =\; mu,Sig\; -\; mu,Background$

SiTF curve

The SiTF curve is then given by the signal output data, (net signal data), plotted against the signal input data (see graph of SiTF to the right). All the data points in the linear region of the SiTF curve can be used in the method of least squares to find a linear approximation. Given $n,$ data points $(x\_i,,y\_i,)$ a best fit line parameterized as $y\; =\; mx\; +\; b,$ is given by: [Aboufadel, E.F., Goldberg, J.L., Potter, M.C. (2005)."Advanced Engineering Mathematics (3rd ed.)."New York, New York: Oxford University Press]

:$m\; =\; frac\{frac\{sum\; x\_iy\_i\}\{n\}\; -\; frac\{sum\; x\_i\}\{n\}\; frac\{sum\; y\_i\}\{n\{frac\{sum\; x\_i^2\}\{n\}-(frac\{sum\; x\_i\}\{n\})^2\}\; qquad\; qquad\; b\; =\; frac\{sum\; y\_i\}\{n\}\; -\; m\; frac\{sum\; x\_i\}\{n\}$

See also

* Optical transfer function
* Signal-to-noise ratio
* Distortion
* Minimum resolvable temperature difference
* Noise equivalent temperature difference
* Power spectral density
* Minimum resolvable contrast
* Signal to noise ratio (image processing)

References

External links

* http://www.electro-optical.com/html/