How much does a drop in temperature affect focus?

Question

In an answer to question "What lens characteristics are important in astrophotography?" there was mentioned "If the temperature changes drastically, you may need to refocus as different materials in the lens will expand and contract at different rates." But the accepted answer to "How does one focus in very dark conditions?" suggests a tape marking on lens, and wouldn't that turn out to be useless when temperature drops at night?

Is it possible to estimate the focus shift beforehand, when focus was first found in 5 Celsius degrees in the evening and then at night the temperature drops to -10 Celsius degrees? How would I calculate, or estimate, the focus shift between these temperatures?

On the other hand, is it likely that 15 Celsius degrees (27 F) change in temperature really does shift focus so much that I'd need to re-focus? How drastic change in temperature makes refocusing typically necessary?

In my case it is a small size dslr-like camera with a 14mm lens that has somewhat large front element and the lens weighs more than the camera body. And focus would be at infinity for stars.

Answer 1

From my reading, the amount materials within a "handheld" lens expand / contract over, for example, 15C is so minimal it's not worth thinking about.

However this really becomes an issue on large telescopes, both refracting and reflecting (even more so).

Why?

As a (rough) example, let's imagine a large reflecting telescope which has a body length of 3m, and is constructed from tubular aluminium. Pure aluminium pure has a linear thermal expansion rate of 0.0000222m/m/K, which means it gets longer / shorter by 0.0222mm per degree Kelvin (or C) per meter of its length.

Therefore the telescope would shorten by 0.0222mm × 3m × 15C = 0.999mm as the temperature drops 15C. This coupled with the magnification at the secondary mirror leads to a dramatic focus shift.

Answer 2

I think you can do some experiment on your own. I would take several snapshots (with camera,settings, focus and light blocked to the same values) and with different temperatures of a slanted edge standard and measure the MTF with ImageJ and MTF plugin or with Imatest. Then you can plot the MTF graph with different temperatures and see the result.

I think the different expansion coefficients aren't the only causes of this change, materials have different refractive index with different temperatures and I think you should take in account that if your lens become very cold condensation could be formed in the optics because inside your camera is warmer than outside.

Answer 3

Focal length rises about 0.7 promille in the temperature range -10 to 20C, and the day vs night / temperature focus position in Hubble is carefully modeled (and they are not simple relations "focus vs Temp") and is in the range of 5-7 microns. But still the deviation of those models are pretty large. One thing is temperature, another is temperature changes, and the spreading of that change into the components over time, and then there's extended exposure to those temperatures.

check this out and this and this

Answer 4

Each lens design will react to temperature changes differently. I generally check focus several times during an astrophotography session as much to be sure that I haven't accidentally changed focus as for any other reason.

A tape marking gets you close enough to start the process. When focusing on dim point sources of light such as stars, nothing shows up in the viewfinder or even via Live View until focus is almost achieved because the miniscule amount of light is spread out too far to be detectable when the lens is too far out of focus. Until you are fairly close to infinity focus you can pan the entire night sky and not see anything to focus on (unless the moon is visible). Once you are close, as you would be if you were properly focused before a change in temperature, it is relatively easy to turn on LV, zoom in on a medium star, check the focus, and correct slightly if necessary. A lot depends on just how in focus you want your stars to be. Sometimes slightly out-of-focus looks more realistic as the brighter stars look larger to our eyes.

The physical amounts of contraction/expansion in the lens due to temperature changes within the range of your question are very small. But the effect those amounts have can be significant. If a camera's mounting flange is off by even as little as 50µm (50 microns or 0.05mm) from one side to the other it will make the camera unusable for any type of critical focus work at large apertures. And the effects can be seen with as little as 20µm of error. Astrophotography, where you have extremely small point sources of light across the entire field of view is often the most focus critical work many photographers ever do.