Image from a mirror not flat at the relevant wavelength

[Thomas Womack]

Suppose you have a telescope designed for the thermal infra-red, so
surfaces machined to about 2.5um accuracy.

If you use a dichroic mirror rather than a long-pass filter at the IR
detector, it's clearly possible to direct the visible light to a focus
on a second detector. Do you get any form of image at that point
given that the mirror accuracy is 5-lambda?

And, if so, assuming that everything is rigid and correctly aligned
for perfect images on the IR detector, is the _centroid_ of the image
at the visible detector going to be reasonably well-defined? Can this
be used at least to help out the orientation-determination system?

Thanks in advance for any help you can offer

Tom (wishing he had checked that the university had Zemax licenses
before taking on an MSc project involving optic design ...)

[Phil Hobbs]

Post by Thomas Womack
Suppose you have a telescope designed for the thermal infra-red, so
surfaces machined to about 2.5um accuracy.
If you use a dichroic mirror rather than a long-pass filter at the IR
detector, it's clearly possible to direct the visible light to a focus
on a second detector. Do you get any form of image at that point
given that the mirror accuracy is 5-lambda?
And, if so, assuming that everything is rigid and correctly aligned
for perfect images on the IR detector, is the _centroid_ of the image
at the visible detector going to be reasonably well-defined? Can this
be used at least to help out the orientation-determination system?
Thanks in advance for any help you can offer
Tom (wishing he had checked that the university had Zemax licenses
before taking on an MSc project involving optic design ...)

Depends sensitively on the details. If the surface is pretty smooth on
a 100-nm length scale, but not shaped too accurately, you'll get some
sort of visible image, as you do with a magnifying glass or a
searchlight mirror, which are similarly inaccurate but smooth.

If the surface errors come from coarse diamond turning, you'll get all
sorts of diffraction effects, and there may not be much of an optical
image at all. The surface will consist of a series of concentric
grooves that don't tilt as you go further out from the axis, so in the
short-wavelength limit (ray optics) it's probably not a focusing surface.

If it's random surface roughness, the reflection will be diffuse, so you
won't get a visible image at all.

(BTW Zemax has a student version.)

Cheers

Phil Hobbs

[Thomas Womack]

Post by Phil Hobbs

Post by Thomas Womack
Suppose you have a telescope designed for the thermal infra-red, so
surfaces machined to about 2.5um accuracy.
If you use a dichroic mirror rather than a long-pass filter at the IR
detector, it's clearly possible to direct the visible light to a focus
on a second detector. Do you get any form of image at that point
given that the mirror accuracy is 5-lambda?
And, if so, assuming that everything is rigid and correctly aligned
for perfect images on the IR detector, is the _centroid_ of the image
at the visible detector going to be reasonably well-defined? Can this
be used at least to help out the orientation-determination system?
Thanks in advance for any help you can offer
Tom (wishing he had checked that the university had Zemax licenses
before taking on an MSc project involving optic design ...)

Depends sensitively on the details. If the surface is pretty smooth on
a 100-nm length scale, but not shaped too accurately, you'll get some
sort of visible image, as you do with a magnifying glass or a
searchlight mirror, which are similarly inaccurate but smooth.
If the surface errors come from coarse diamond turning, you'll get all
sorts of diffraction effects, and there may not be much of an optical
image at all. The surface will consist of a series of concentric
grooves that don't tilt as you go further out from the axis, so in the
short-wavelength limit (ray optics) it's probably not a focusing surface.
If it's random surface roughness, the reflection will be diffuse, so you
won't get a visible image at all.

Thank you, that's extremely useful and clarifies things I wasn't even
aware I didn't know. There's an unreasonably tight hypothetical
budget and I was hoping that 2.5um surface accuracy for working in the
thermal IR meant the optical surfaces could just be diamond-turned; I
hadn't thought about the tilting of the grooves.

I will tell the AOCS people that they still need a high resolution
star tracker ...

Post by Phil Hobbs
(BTW Zemax has a student version.)

Unfortunately only available to explicitly participating institutions
of which Cranfield isn't one :(

Tom

[Phil Hobbs]

Post by Thomas Womack

Post by Phil Hobbs

Post by Thomas Womack
Suppose you have a telescope designed for the thermal infra-red, so
surfaces machined to about 2.5um accuracy.
If you use a dichroic mirror rather than a long-pass filter at the IR
detector, it's clearly possible to direct the visible light to a focus
on a second detector. Do you get any form of image at that point
given that the mirror accuracy is 5-lambda?
And, if so, assuming that everything is rigid and correctly aligned
for perfect images on the IR detector, is the _centroid_ of the image
at the visible detector going to be reasonably well-defined? Can this
be used at least to help out the orientation-determination system?
Thanks in advance for any help you can offer
Tom (wishing he had checked that the university had Zemax licenses
before taking on an MSc project involving optic design ...)

Depends sensitively on the details. If the surface is pretty smooth on
a 100-nm length scale, but not shaped too accurately, you'll get some
sort of visible image, as you do with a magnifying glass or a
searchlight mirror, which are similarly inaccurate but smooth.
If the surface errors come from coarse diamond turning, you'll get all
sorts of diffraction effects, and there may not be much of an optical
image at all. The surface will consist of a series of concentric
grooves that don't tilt as you go further out from the axis, so in the
short-wavelength limit (ray optics) it's probably not a focusing surface.
If it's random surface roughness, the reflection will be diffuse, so you
won't get a visible image at all.

Thank you, that's extremely useful and clarifies things I wasn't even
aware I didn't know. There's an unreasonably tight hypothetical
budget and I was hoping that 2.5um surface accuracy for working in the
thermal IR meant the optical surfaces could just be diamond-turned; I
hadn't thought about the tilting of the grooves.

Folks often do a quick polish of a diamond-turned surface to reduce the
scatter and other artifacts. If that's been done, the surface will
focus visible light at some level.

Post by Thomas Womack
I will tell the AOCS people that they still need a high resolution
star tracker ...

Post by Phil Hobbs
(BTW Zemax has a student version.)

Unfortunately only available to explicitly participating institutions
of which Cranfield isn't one :(
Tom

There are also some very decent free packages. Beam Four is now free at
<https://www.stellarsoftware.com>, and our erstwhile regular poster Jim
Klein has a pretty powerful lens design program KDP-2, which you can get
at <http://www.ecalculations.com> (password is avon1). He worked on it
for a good 20 years, and it can apparently do just about anything.

KDP2 is actually open source, but (a) it's in Fortran, and (b) it relies
on some proprietary graphics framework whose name I forget.

Cheers

Phil Hobbs