# What is the relationship between lens f-number and camera performance or NEdT?

In general, uncooled thermal imagers require relatively fast optics for best performance. The most common figure of merit used to describe how well a thermal imager performs is referred to as Noise Equivalent Temperature Difference, or NEdT. The units of NEdT are milli-Kelvins, or mK (thousandths of a degree). The lower the NEdT value of a system, the better the performance. Because the f/number of a lens has an effect on how well the system will perform, and in order to be able to fairly compare the performance between thermal imaging systems, the specification for NEdT is often referred, or normalized, to f/1.0.

A simple formula can be used to calculate how the NEdT of a thermal imager will be affected by changing the f/number. The formula involves 3 variables:

1) the f/number of the optic being used on the camera;

2) the NEdT that is typical of the camera with that optic; and

3) the f/number to which the camera performance is to be normalized (usually f/1.0).

By assigning a value of X to variable 1, and Y to the NEdT value of the camera using optic X, the normalized value (to f/1.0) can be calculated as:  (1.0÷X)² x Y.

As an example, assume a thermal imager with an NEdT of 87mK using an f/1.6 lens. To normalize its performance to f/1.0, the calculation is:  (1.0÷1.6)² x 0.087; or (0.625)² x 0.087; or 0.3906 x 0.087; equals 0.03398; which is 34.0mK. This means that a camera with an f/1.6 optic has about 2.5 times less thermal sensitivity than the same camera with an f/1.0 lens.

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