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# Wavefront Error vs Lens Temperature Shift Question

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### #1 AXAF

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Posted 01 May 2021 - 09:18 AM

If a 2-inch lens (a triplet, to be exact) is subjected to a 1 degree Celsius temperature change,

would this noticeably alter the wavefront error of light passing through it? Would a larger

temperature shift be required? Asking in relationship to a project at work.

Thanks.

### #2 Steve Dodds

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Posted 01 May 2021 - 09:28 AM

Theoretically yes, but in practice you are going to need 20-30 degrees to change it even a 1/4 wave.

### #3 MitchAlsup

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Posted 01 May 2021 - 09:55 AM

Wavefront error: Only during the time the temperature change is diffusing through the glass.

If the lens is used at stable Temperature[1] and is properly focused, it will have wavefront error[1].

If this lens is then used at stable temperature[2] and is properly focused, it will have the same wavefront error.

{Optical Scaling Principle}

### #4 Steve Dodds

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Posted 01 May 2021 - 10:28 AM

Wavefront error: Only during the time the temperature change is diffusing through the glass.

If the lens is used at stable Temperature[1] and is properly focused, it will have wavefront error[1].

If this lens is then used at stable temperature[2] and is properly focused, it will have the same wavefront error.

{Optical Scaling Principle}

No it won't because there is a difference in thickness in the elements, so the center is going to contract more than the edge, causing SA, Not much but a little

### #5 dan chaffee

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Posted 01 May 2021 - 11:51 AM

No it won't because there is a difference in thickness in the elements, so the center is going to contract more than the edge, causing SA, Not much but a little

If that was significant enough to be noticeable with in focus images, doublets and triplets would be

less than superb performers, once stabilized.  Keeping things in perspective is a good idea, much

like saying a drop of dew on an objective will increase diffraction by an amount of no consquence

to image quality.

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### #6 MKV

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Posted 01 May 2021 - 12:25 PM

No it won't because there is a difference in thickness in the elements, so the center is going to contract more than the edge, causing SA, Not much but a little

It's best to make a point using actual numbers. Raytrace analysis can easily provide them.

Edited by MKV, 01 May 2021 - 12:26 PM.

### #7 MitchAlsup

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Posted 01 May 2021 - 01:28 PM

No it won't because there is a difference in thickness in the elements, so the center is going to contract more than the edge, causing SA, Not much but a little

But a coefficient of thermal expansion is uniform through a glass lens. So while a lens is thicker/thinner in the middle (positive/negative power lens), the edge and the center (and diameter) expand/contract proportionally the same over any given temperature change.

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### #8 Steve Dodds

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Posted 01 May 2021 - 03:10 PM

But a coefficient of thermal expansion is uniform through a glass lens. So while a lens is thicker/thinner in the middle (positive/negative power lens), the edge and the center (and diameter) expand/contract proportionally the same over any given temperature change.

If it's thicker it expands more, if it's thin it expands very little.  Basic physics guys.

### #9 davidc135

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Posted 01 May 2021 - 06:05 PM

It'll just be scaled up or down- dimensions and proportions, focal length and any existing aberrations.

But if the c.t.e of the differing glasses vary significantly that might potentially complicate things. If cemented, of sizeable aperture and with a high temperature difference

If the glasses expand by less than 10 x 10^-6 per *C that's a wavelength across 2''

David

Edited by davidc135, 01 May 2021 - 06:21 PM.

### #10 BGRE

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Posted 01 May 2021 - 06:06 PM

Wavefront error: Only during the time the temperature change is diffusing through the glass.

If the lens is used at stable Temperature[1] and is properly focused, it will have wavefront error[1].

If this lens is then used at stable temperature[2] and is properly focused, it will have the same wavefront error.

{Optical Scaling Principle}

Not true.

This is only approximately correct if the temperature coefficient of the refractive indices of the various lenses were zero.

If a system is scaled (in the with no change in refractive index ) the residual aberrations are multiplied by the scaling factor.

Changing the temperature doesn't result in a the various elements and spaces changing dimensions by the same factor unless the thermal expansion tempcos are identical for all materials used.

Unless the aberrations of the individual elements are large the variation of residual aberrations with temperature will be small unless materials with larget thermal expansion coefficients and/or large refractive index tempco are used, Raytracing can be used to evaluate the variation of residual aberrations with temperature if the various tempcos are known.

### #11 MitchAlsup

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Posted 01 May 2021 - 07:11 PM

If it's thicker it expands more, if it's thin it expands very little.  Basic physics guys.

Lets say the outer edge of a lens is 2mm and the center is 4mm and the lens is 100mm in diameter and has a focal length of 1000mm at temperature 1.

Now, over at temperature 2, the outer edge is 2.001mm the center is 4.002 and the diameter is 100.050 and now has a focal length of 1000.500mm.

If you look the scale of everything in the lens has changed by exactly the same proportion, and the change in FL is what required the phrase "properly focused" for the statement to be correct.

So, yes the thicker stuff expands more, but the proportionality remains constant at any stable temperature. This is known as optical scaling, more generally applied to medium to large changes in the scale of the device but it still applies in the micro scaling of an optical device.

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### #12 KBHornblower

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Posted 01 May 2021 - 07:23 PM

The trouble happens when the lens or mirror is still cooling, and is warmer inside than at the surface.  This can cause stresses that deform the figure.

### #13 Steve Dodds

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Posted 01 May 2021 - 07:44 PM

Lets say the outer edge of a lens is 2mm and the center is 4mm and the lens is 100mm in diameter and has a focal length of 1000mm at temperature 1.

Now, over at temperature 2, the outer edge is 2.001mm the center is 4.002 and the diameter is 100.050 and now has a focal length of 1000.500mm.

If you look the scale of everything in the lens has changed by exactly the same proportion, and the change in FL is what required the phrase "properly focused" for the statement to be correct.

So, yes the thicker stuff expands more, but the proportionality remains constant at any stable temperature. This is known as optical scaling, more generally applied to medium to large changes in the scale of the device but it still applies in the micro scaling of an optical device.

I'll give you that with refractors, but it's not the case with reflectors, with a large temp change they will change minutely, I've seen it in the shop, dropping the temp to 50 and a perfectly corrected 20" was slightly undercorrected at 50 degrees.

### #14 BGRE

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Posted 02 May 2021 - 03:45 AM

https://wp.optics.ar...mieson-1981.pdf

Gives some examples of how aberrations of a lens can vary significantly with temperature.

Although the dominant effect due to temperature changes is defocus, an inappropriate choice of glass types means that even a 10C change in temperature can have also have significant effect on transverse aberrations.

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### #15 Mike I. Jones

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Posted 02 May 2021 - 04:54 AM

I wrote this article for everyone on Cloudynights years ago that addresses this very topic.  Hope it helps you.  Mike

https://www.cloudyni...al-design-r2948

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### #16 dan chaffee

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Posted 02 May 2021 - 11:42 AM

I would expect to refocus *any* telescope if the temperature of the preceding session was

significantly different than the last, even if it was just a function of the tube or trusses shortening

or lengthening, regardless of what happens to the glass...unless it's made of something with

near zero CTE.

### #17 MitchAlsup

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Posted 02 May 2021 - 02:42 PM

I wrote this article for everyone on Cloudynights years ago that addresses this very topic.  Hope it helps you.  Mike

https://www.cloudyni...al-design-r2948

How skilled would an observer have to be to see (using his own eyes) the kinds of aberrations illustrated in Figure 7 ?

### #18 Mike I. Jones

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Posted 02 May 2021 - 09:21 PM

Once you refocus to the sharpest image at any temperature that has been more or less steady after a while, it would be tough to see such small image errors.  That's the point of athermalization: to give good image quality over a temperature range.  There might be a little change in the through-focus chromatic behavior at different temperatures, but at best focus, change in image quality should be nearly zero.

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### #19 jimhoward999

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Posted 03 May 2021 - 04:15 PM

The temperature sensitivity depends on the details of the optical design.

It matters whether one is talking about a thermal soak or a gradient.   I have never seen an optical design where a uniform 1°C change in temperature had a measurable effect on wavefront error after refocus.  Usually it takes 5-10°C or more, assuming a refocus.

Optical designs containing CaF2 or Fluorite glasses tend to have less thermal sensitivity than other designs  (with respect to thermal focus only...thermal shock is another matter entirely).    The reason is that those materials have negative dn/dT and a high CTE.   That means the focal length increases at high temperature, which tends to cancel what others lens elements do and the mount does, at least with respect to thermal defocus.  But that is a gross generalization that may not be true for a particular design.

Not sure what materials are in the triplet in question.

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### #20 AXAF

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Posted 04 May 2021 - 01:09 PM

Thanks, all, for this discussion. It gives me something to think about as I try to understand my data.

The triplet lens in question serves to collimate the light coming out of an LED light source. The development

of this stellar source was long ago in the past, so am not sure of the glass type. I do know that this lens

has been measured on a Zygo interferometer to have a wavefront error of 0.010 RMS, well within the requirement of 0.050 RMS. No attempts are ever made to adjust the focus, which would simply amount to repositioning the light source with respect to the collimation lens via a translation stage. The stage maintains its position to within 2 microns.

This beam of collimated light is collected/focused onto a sensor. We first sum up 120 frames of

data to form a pixel response function (PRF) from the individual PSFs. I wonder if a barely perceptible

temperature-induced error for a single image frame (i.e. PSF) might become more noticeable at the level

of the PRF.

The hardware that generates this collimated light is capable of producing a log file, not that it was

generated in this test case. The log file would include the temperature of the collimation lens. I suppose

the best thing to do is to see if there is a correlation between the collimation lens temperature

and the shape of the PRF, if I can ever convince the test group to rerun the experiment.

Sorry that I cannot be any more specific than this, as the work is proprietary. Regardless, this

-Gary

Edited by AXAF, 04 May 2021 - 01:10 PM.

### #21 jimhoward999

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Posted 04 May 2021 - 07:24 PM

Thanks, all, for this discussion. It gives me something to think about as I try to understand my data.

The triplet lens in question serves to collimate the light coming out of an LED light source. The development

of this stellar source was long ago in the past, so am not sure of the glass type. I do know that this lens

has been measured on a Zygo interferometer to have a wavefront error of 0.010 RMS, well within the requirement of 0.050 RMS. No attempts are ever made to adjust the focus, which would simply amount to repositioning the light source with respect to the collimation lens via a translation stage. The stage maintains its position to within 2 microns.

This beam of collimated light is collected/focused onto a sensor. We first sum up 120 frames of

data to form a pixel response function (PRF) from the individual PSFs. I wonder if a barely perceptible

temperature-induced error for a single image frame (i.e. PSF) might become more noticeable at the level

of the PRF.

The hardware that generates this collimated light is capable of producing a log file, not that it was

generated in this test case. The log file would include the temperature of the collimation lens. I suppose

the best thing to do is to see if there is a correlation between the collimation lens temperature

and the shape of the PRF, if I can ever convince the test group to rerun the experiment.

Sorry that I cannot be any more specific than this, as the work is proprietary. Regardless, this

-Gary

one question that comes to mind is: where did this collimating triplet come from?    It is understood that it is ancient, but was it custom designed for this purpose or was it a COTS purchased item?    That matters, because if it was custom designed, and has no thermal focus adjustment then very likely the temperature environment would have been considered.

One other factor, that probably was considered, but you never know, is the wavelength variation of the LED with temperature.    Sometimes people design LED collimators and forget to consider that the LED emission wavelength shifts with temperature and this can itself cause a focus shift.

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