Thin Film Literature Review

[Jashcraf]

I'd like to try to do a literature review entirely in github issues. Maybe each comment is a different paper?

[Jashcraf]

Sabatke et al 2018 "Polarization ray tracing and polarization aberration compensation in reflective, astronomical telescopes"

This seems very much in line with what we expect to do. In this study the author's aims were to:

• parameterize the polarization aberrations of surfaces in terms of impact on diattenuation, retardance
• Evaluate Jones pupils of a LUVOIR-type design
• Design coatings on secondary to mitigate the aberration

They cite the method in Macleod to determine the coating coefficients, that's good! Poke has the same method.

They approximate the orientation and retardance as quadratic terms with ad-hoc coefficients. I don't really think this is necessary because Poke can do these directly and quite fast. Maybe they do some fitting?

Methods

They do ray tracing in code v with rsi and mine the data with Mathematica to do the polarization math. An obscured 15m and unobscured 8m telescope are tested. 1.6nm rms polarization aberrations are shown, which is "concerning" for coronagraphy. Note that they don't propagate through a rigorous physical optics model of ECLIPS.

Results

They characterize the PSF via the MTF along x- and y- slices. I guess this makes the most sense for the incoherent combination of the PSF's. They compute the MTF's of the XX and XY terms separately and then normalize the off-diagonal to the on-diagonal. I'd be curious to see how this relates to the diffraction limit, but this isn't plotted.

They construct a hybrid model where the ray tracing and coating results are "interpolated" to make the design space easier to explore.

They imply that the jones matrix is constructed from 4-layer coatings typically. They also claim to cross-check their parametric model against the real model of the ray trace and coating, but don't say by how much the models deviate from one another.

Ah in Fig. 7 they show that the Jones pupils have good agreement.

As they vary the ad-hoc coefficients they can find a minimum in the RMS WFE for the pupil element they care about. So that's how the design space is probed. How then is that translated to a coating design?

It appears that they start with a recipe of LiF over Al, and vary the thicknesses to get the ad-hoc coefficients they want. They get their desired ad-hoc coating, but don't actually evaluate the final jones pupil with this coating.

[Jashcraf]

Miller et al "Birefringent coating to remove polarization aberrations"

Hey it's Sawyer I kind of know him. In any case these authors propose a design methodology where they design birefringent coatings to mitigate polarization aberrations. Practically I'm not sure that these work on a large scale, but it'd be interesting to see if these work as compensator plates.

In the abstract high-contrast imaging is called out directly. They claim to optimize the polarization aberrations over a 170nm bandwidth.

The paper covers a lot of cases, so I'm going to jump to section 2.4 with a Compensator design for reflection off of a Al-coated mirror.

They express the thin-film effect of a coating consisting of

• an AR coating
• a C-plate

• The mirror substrate

  and perform an SVD on this matrix, the polarization aberrations can be computed as a function of wavelength and AOI.

  The merit function is a sum over wavelength and angle of the square root of the sum of the squared polarization aberration.

I'm not terribly familiar with C-plates, but those can be determined by the following:

They specify that a negative C-plate is most suitable to reflection from an Aluminum mirror. They optimize with the above merit function while varying the thickness of the C-plate. The result is very close to an identity matrix, but they only do this for discrete AOI without consideration for the point-spread function.

I think I still don't totally get how to describe a Jones matrix given this information. Maybe reaching out to Sawyer would be worth doing.

[Jashcraf]

Wu et al, "Fundamentals of Liquid Crystal Devices"

c-plates are either positive or negative, and are of the uniaxial variety

This is a pretty useful figure

[Jashcraf]

Balasubramanian et al "Deep UV to NIR space telescopes and exoplanet coronagraphs: a trade study on throughput, polarizationm mirror coating options, and requirements"

Problem statement: 10^-10 Contrast at 2-10 L/D. This is, in part, limited by polarization aberrations. Most of the paper is focused on throughput which we care less about for now. But, it's important to note that a reference telescope architecture was proposed in 2011 by Shaklan et al "Stability error budget for an aggressive coronagraph on a 3.8m telescope".

5. Pupil fields with different coatings on the mirrors.

It opens with

which is a typo. All of the fields are not coherent with eachother. There should be a |Axx + axy|^2 + |Ayy + Ayx|^2 instead.

Ex 5.1 starts off with this statement

Which feels backwards to me. Specifically "The cross polarization term Exy, i.e. the x field induced by the incident y field will be incoherent with Exx, though both may pass unattenuated through a polarizer aligned to xx"

I don't understand why the Exy light would be incoherent? It's been rotated into the x-plane, so the electric field vectors are parallel and should interfere. I'm gonna skip past this for now and just move on to the results.

They show that the contrast degrades to just below the 10^-10 level, which might just be a prominent noise source. Note that they don't switch to a Mueller PSM. The remainder of the results are tables of the achievable contrast in a dark region.

Conclusions

• Two coronagraphs are needed for the two orthogonal polarizations
• One polarization channel cannot have a 2L/D dark hole
• Al + MgF2 is the best direct term and worst cross term. Further optimization may be feasible.