Optics Part 2 – The Coefficient of Thermal Defocus on Real Materials

Learn how temperature changes affect the focal length of a lens, and how specific material temperature changes can be calculated.

Transcript Below

Understanding how material properties and coefficient of thermal defocus change focal length

Looking at this very simple example – again this is just for a thin lens – so it’s a very simple example, but it can demonstrate how these material properties can influence the coefficient of thermal defocus [α] which then influences the change in focal length [Δf]. If you look at different lens materials, you can start to see kind of different classifications. If you compare their thermal expansion coefficient, their change in index of refraction with temperature, [than] you can start to understand how they will affect your δ [coefficient of thermal defocus].

Infrared Materials

For example, infrared optic materials like chalcogenide glasses, as well as germanium and silicon, the thermal expansion coefficient [α] is positive and has a small magnitude. But the change in index of refraction [dn/dT] with temperature is very large and it is also positive. If you look at – let’s not leave out the index of a fraction [nabs]. Typically, the index of refraction [nabs], well it will always will be positive, but it’ll be fairly small in comparison. This term will be quite small, it’s a fraction essentially. So if you have a small thermal expansion coefficient [α] that’s positive minus a large change in index of refraction with temperature [dn/dT] that is positive, δ tends to be negative. And because the dn/dT is so big – it’s so much bigger than this thermal expansion coefficient [α] for infrared optic materials – this can be quite large. Now for chalcogenide glasses, for example this will be smaller because the dn/dT will be smaller, but for silicon and germanium this is quite large.


If you compare that to polymers, you’ll have a very large and positive coefficient of thermal expansion [α], and then you’ll have a fairly medium to large negative dn/dT [change of index of refraction with change in temperature] which can create a very large positive [coefficient of thermal defocus δ] – oh whoops very large positive let’s erase this um – so this [nabs­] will actually be positive, but small as well. You’ll have a very large positive δ [coefficient of thermal defocus] because a positive thermal expansion coefficient [α] that’s large minus a negative dn/dT makes this term positive. So for polymers this [coefficient of thermal defocus δ]  is going to be a very large number.


Then for different glasses, actually using this term you can take a look this is for different materials, nbk7 for example very very common material, its thermal expansion coefficient [α] is small positive and quite small at 7.1 ppm/°C, its dn/dT is very small and positive at 1.1 ppm/°C, and its index of refraction [nabs] is positive and it is 1.5168. So your δ [coefficient of thermal defocus] is actually going to be for nbk7 [glass] is going to be, I believe it’s going to be positive, and it’s going to be small. That’s one of the advantages of this material. Other glasses you can do the same type of just eyeballing will this material react to temperature drastically just based off of this very simple equation

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