Eyepieces for fast f/2.8 telescopes

[Michael Koch]

Hello all,

I have tested a few TeleVue Ethos eyepieces with a Zygo interferometer at a very fast f/2.8 light cone (tested with a f/1.9 transmission sphere, and aperture limited in software to 67.9%).
Three tested eyepieces have quite different amounts of spherical aberration:
21mm Ethos Z8 = 0.80 waves (undercorrected)
13mm Ethos Z8 = 0.33 waves (undercorrected)
8mm Ethos Z8 = -0.48 waves (overcorrected)

Now let's compare two cases:
Case 1: A f/2.8 paraboloid mirror is perfect, and the eyepiece has 1 wave of spherical aberration.
Case 2: A paraboloid mirror has 1 wave of spherical aberration, and the eyepiece is perfect.
When we make a star test with these two telescopes, will we see the same error in both cases? Or can we argue that the error in the eyepiece is less severe, because it occurs closer to the observer's eye?

The backgound of my question is that a friend of me has figured a 14" f/2.8 mirror, and we think the mirror is quite good, verified by two independant tests.
However when making the star test the mirror isn't as good as expected. We are trying to figure out what's going on.

Thanks,
Michael

[Phil Hobbs]

Post by Michael Koch
Hello all,
I have tested a few TeleVue Ethos eyepieces with a Zygo interferometer at a very fast f/2.8 light cone (tested with a f/1.9 transmission sphere, and aperture limited in software to 67.9%).
21mm Ethos Z8 = 0.80 waves (undercorrected)
13mm Ethos Z8 = 0.33 waves (undercorrected)
8mm Ethos Z8 = -0.48 waves (overcorrected)
Case 1: A f/2.8 paraboloid mirror is perfect, and the eyepiece has 1 wave of spherical aberration.
Case 2: A paraboloid mirror has 1 wave of spherical aberration, and the eyepiece is perfect.
When we make a star test with these two telescopes, will we see the same error in both cases? Or can we argue that the error in the eyepiece is less severe, because it occurs closer to the observer's eye?
The backgound of my question is that a friend of me has figured a 14" f/2.8 mirror, and we think the mirror is quite good, verified by two independant tests.
However when making the star test the mirror isn't as good as expected. We are trying to figure out what's going on.

The pupil of the eye will be the limiting aperture if the system is
designed for comfort, but it may or may not be in a test setup.

In the absence of vignetting, I think they'll be pretty similar since
both are basically occurring in the pupil (of the telescope). If the
eyepiece were optically closer to the image, the effect would be less,
because the phase errors would have mainly a local effect, and of course
right at the image, it would hardly do anything except change the FOV.
(It would be a field lens and not an eyepiece.)

Cheers

Phil Hobbs

[Michael Koch]

Post by Phil Hobbs
The pupil of the eye will be the limiting aperture if the system is
designed for comfort, but it may or may not be in a test setup.

Let's assume that in a star test we use high magnification, so that the exit pupil is smaller than the eye pupil. No vignetting.

Post by Phil Hobbs
In the absence of vignetting, I think they'll be pretty similar since
both are basically occurring in the pupil (of the telescope). If the
eyepiece were optically closer to the image, the effect would be less,
because the phase errors would have mainly a local effect, and of course
right at the image, it would hardly do anything except change the FOV.
(It would be a field lens and not an eyepiece.)

That makes things complicated, because the Ethos eyepiece is a complex design and at least one (field-)lens is in front of the image plane. As far as I know, the optical layout hasn't yet been published. I tested the eyepiece as a black box and I don't know if the spherical aberration originates near the focal plane or near the exit pupil.

Some pictures of the 21mm Ethos test setup:
https://www.facebook.com/astroelectronic/posts/428917360903364

Michael

[Phil Hobbs]

Post by Michael Koch

Post by Phil Hobbs
The pupil of the eye will be the limiting aperture if the system is
designed for comfort, but it may or may not be in a test setup.

Let's assume that in a star test we use high magnification, so that the exit pupil is smaller than the eye pupil. No vignetting.

Post by Phil Hobbs
In the absence of vignetting, I think they'll be pretty similar since
both are basically occurring in the pupil (of the telescope). If the
eyepiece were optically closer to the image, the effect would be less,
because the phase errors would have mainly a local effect, and of course
right at the image, it would hardly do anything except change the FOV.
(It would be a field lens and not an eyepiece.)

That makes things complicated, because the Ethos eyepiece is a complex design and at least one (field-)lens is in front of the image plane. As far as I know, the optical layout hasn't yet been published. I tested the eyepiece as a black box and I don't know if the spherical aberration originates near the focal plane or near the exit pupil.
https://www.facebook.com/astroelectronic/posts/428917360903364
Michael

Well, you could do a Foucault knife-edge test. Not as easy as a star
test, of course, but you don't need additional optics.

Cheers

Phil Hobbs
--
Dr Philip C D Hobbs
Principal Consultant
ElectroOptical Innovations LLC
Optics, Electro-optics, Photonics, Analog Electronics

160 North State Road #203
Briarcliff Manor NY 10510

hobbs at electrooptical dot net
http://electrooptical.net

[Michael Koch]

Post by Phil Hobbs
Well, you could do a Foucault knife-edge test. Not as easy as a star
test, of course, but you don't need additional optics.

My friend tested the mirror with a Bath interferometer from the center of curvature. Spherical aberration was subtracted in software. I don't remember if he also made a Foucault test.
I tested the same mirror with a Zygo interferometer in autocollimation against a calibrated reference flat. Both results are in good agreement. We are quite sure that the mirror is good.
The problem is that in the star test some eyepieces show overcorrection and some show undercorrection.

Michael

[Phil Hobbs]

Post by Michael Koch

Post by Phil Hobbs
Well, you could do a Foucault knife-edge test. Not as easy as a star
test, of course, but you don't need additional optics.

My friend tested the mirror with a Bath interferometer from the center of curvature. Spherical aberration was subtracted in software. I don't remember if he also made a Foucault test.
I tested the same mirror with a Zygo interferometer in autocollimation against a calibrated reference flat. Both results are in good agreement. We are quite sure that the mirror is good.
The problem is that in the star test some eyepieces show overcorrection and some show undercorrection.
Michael

Ah, I see. Sure sounds like the eyepiece, then, unless the mirror is
too thin and you're supporting it differently in the two tests. A bit
of mirror sag would turn into spherical.

Hadn't heard of a Bath interferometer before. One popular scheme for
centre-of-curvature testing is the Smartt interferometer.

Cheers

Phil Hobbs
--
Dr Philip C D Hobbs
Principal Consultant
ElectroOptical Innovations LLC
Optics, Electro-optics, Photonics, Analog Electronics

160 North State Road #203
Briarcliff Manor NY 10510

hobbs at electrooptical dot net
http://electrooptical.net

[Michael Koch]

Post by Phil Hobbs
Hadn't heard of a Bath interferometer before.

It's quite popular among amateur mirror makers. Many informations about the Bath interferometer can be found here:
https://groups.io/g/Interferometry/wiki/home

Michael

[Phil Hobbs]

Post by Michael Koch

Post by Phil Hobbs
Hadn't heard of a Bath interferometer before.

https://groups.io/g/Interferometry/wiki/home
Michael

Interesting, thanks.

Cheers

Phil Hobbs
--
Dr Philip C D Hobbs
Principal Consultant
ElectroOptical Innovations LLC
Optics, Electro-optics, Photonics, Analog Electronics

160 North State Road #203
Briarcliff Manor NY 10510

hobbs at electrooptical dot net
http://electrooptical.net

[Michael Koch]

Phil,

I'm not sure if I have understood all this correctly. Let's use another example:

We are star testing a lens with 10cm diameter and 100cm focal length.

Case 1: The lens has 10 waves of astigmatism (over the full 10cm aperture). The spot size in the best focal plane will be much larger than the Airy disk.

Case 2: The lens is perfect, but we put an astigmatic window exactly in the middle between the lens and the focal plane. The window introduces 10 waves of astigmatism (over 5cm aperture) into the light cone.

In both cases the light cone has 10 waves of astigmatism when it arrives at the focal plane.
But I think case 2 will have a smaller spot size than case 1. Do you agree?

Case 3: Let's assume the astigmatic window is placed at distance x in front of the perfect lens. In this case the spot size is independant of distance x, right?

Are there any general rules how to estimate the spot size, depending on the position along the light path where the aberration is introduced?

Thanks,
Michael

[Phil Hobbs]

Post by Michael Koch
Phil,
We are star testing a lens with 10cm diameter and 100cm focal length.
Case 1: The lens has 10 waves of astigmatism (over the full 10cm aperture). The spot size in the best focal plane will be much larger than the Airy disk.
Case 2: The lens is perfect, but we put an astigmatic window exactly in the middle between the lens and the focal plane. The window introduces 10 waves of astigmatism (over 5cm aperture) into the light cone.
In both cases the light cone has 10 waves of astigmatism when it arrives at the focal plane.
But I think case 2 will have a smaller spot size than case 1. Do you agree?

Sure. If you put it right at the image, it wouldn't aberrate the spot
at all. The spatial frequency of the ripples corresponds to the angle
at which the aberrated component is spreading out, so the less distance
it has to propagate, the less the spot spreads out.

In this example, the aberrator isn't in the pupil, so the two cases
aren't equivalent.

Post by Michael Koch
Case 3: Let's assume the astigmatic window is placed at distance x in front of the perfect lens. In this case the spot size is independant of distance x, right?

Not exactly. If it's far enough away, some of the aberrated components
will get vignetted, so the spot will actually improve. And if it's far
from the pupil as it was in Case 2, the effects will be different.
Right at the lens it doesn't matter which side you put the aberrator,
provided that both are sufficiently thin. (It would matter for, say, a
100x microscope objective, because the working distance is much smaller
than the focal length.)

Post by Michael Koch
Are there any general rules how to estimate the spot size, depending on the position along the light path where the aberration is introduced?

As a SWAG, it'll go linearly with propagation distance, because spatial
frequencies in the aberrated wavefront have a 1:1 correspondence with
plane waves propagating off axis.

There are important modifications to this, e.g. our earlier discussion
of over- vs under-corrected spherical. The local intensity in the spot
goes as the modulus squared of the E field, which sounds simple but has
a lot of nontrivial consequences.

One is that aberrated components cause the biggest nuisance when they're
interfering with the unaberrated part of the beam, i.e. when they cross
the axis. The fringe amplitude goes as

ripple = Re{E_aberr E_stig*}

where E_aberr and E_stig are the electric fields of the aberrated and
stigmatic (unaberrated) components. For reasonable-quality beams,
E_stig is larger, so the fringes are worst when the two are both large,
which is when the major aberrated components cross the axis.

That means that undercorrected spherical looks nastiest just inside
focus, and overcorrected looks worst just outside focus.

Cheers

Phil Hobbs

[Phil Hobbs]

Post by Phil Hobbs

Post by Michael Koch
Phil,
We are star testing a lens with 10cm diameter and 100cm focal length.
Case 1: The lens has 10 waves of astigmatism (over the full 10cm aperture). The spot size in the best focal plane will be much larger than the Airy disk.
Case 2: The lens is perfect, but we put an astigmatic window exactly in the middle between the lens and the focal plane. The window introduces 10 waves of astigmatism (over 5cm aperture) into the light cone.
In both cases the light cone has 10 waves of astigmatism when it arrives at the focal plane.
But I think case 2 will have a smaller spot size than case 1. Do you agree?

Sure. If you put it right at the image, it wouldn't aberrate the spot
at all. The spatial frequency of the ripples corresponds to the angle
at which the aberrated component is spreading out, so the less distance
it has to propagate, the less the spot spreads out.
In this example, the aberrator isn't in the pupil, so the two cases
aren't equivalent.

Post by Michael Koch
Case 3: Let's assume the astigmatic window is placed at distance x in front of the perfect lens. In this case the spot size is independant of distance x, right?

Not exactly. If it's far enough away, some of the aberrated components
will get vignetted, so the spot will actually improve. And if it's far
from the pupil as it was in Case 2, the effects will be different.
Right at the lens it doesn't matter which side you put the aberrator,
provided that both are sufficiently thin. (It would matter for, say, a
100x microscope objective, because the working distance is much smaller
than the focal length.)

I should add that in the special case of an astronomical telescope, the
depth of focus at the pupil is effectively infinite, which is why
atmospheric aberrations can be modelled as a stochastic phase screen
without worrying much about what fluctuations occur at what distance.
Also, the incoming wavefront is essentially infinitely wide, so the
effects of vignetting are much reduced--for every ray that misses due to
aberration, another one gets in that would have missed.
So in that special case, it's pretty well independent of axial
position, as you say.

Fun--I haven't thought about this stuff for awhile, and here I am with
an astronomy undergrad degree. ;)

Cheers

Phil Hobbs

[Michael Koch]

Phil,

I did make some raytracing simulations and came to the conclusion that it doesn't care on which surface an aberration is produced. The result in the focal plane is always the same. One wave of spherical aberration in the eyepiece gives the same result as one wave of spherical aberration in the telescope mirror. One wave of astigmatism produced near the secondary in a Newton telescope gives the same result as one wave of astigmatism in the primary mirror.
Under the assumption that the Zernike polynomial is defined over the acutal diameter of the light cone at that surface.
http://www.astro-electronic.de/Zernike_in_Systems.pdf

Michael

[Phil Hobbs]

Post by Michael Koch
Phil,
I did make some raytracing simulations and came to the conclusion that it doesn't care on which surface an aberration is produced. The result in the focal plane is always the same. One wave of spherical aberration in the eyepiece gives the same result as one wave of spherical aberration in the telescope mirror. One wave of astigmatism produced near the secondary in a Newton telescope gives the same result as one wave of astigmatism in the primary mirror.
Under the assumption that the Zernike polynomial is defined over the acutal diameter of the light cone at that surface.
http://www.astro-electronic.de/Zernike_in_Systems.pdf
Michael

Wow, Beam4--there's a blast from the past. I used to like it a lot back
in the DOS days.

Cheers

Phil Hobbs

[Michael Koch]

Phil,

Yes, BEAM4 is a very nice program from the past and since a few years it's available as freeware. I began wo work with BEAM2 back in 1994 or so.

There is also an easy expanation for this result. The lateral error in the focal plane depends on two things:
1. The distance from the plane where the error is produced to the focal plane. Smaller distance means smaller lateral error.
2. The angular deviation of a beam at the surface where the error is produced. This depends on the wavefront error and the diameter of the light cone at that plane. A 1 wave error over 40mm diameter will produce a larger angular error than 1 wave over 200mm diameter.
These two effects compensate each other, so that the result in the focal plane is always the same, regardless on which surface the wavefront error is produced.
Always under the assumption that we define the Zernike polynomial over the actual diameter of the light cone at that surface.

Michael