The first working hypothesis to explain the wavelength variation of the calibration of the IVM was not really viable because the 2 paths through the instrument that it envisioned would never be in focus and coaligned. Here we try again.
At normal incidence, a Fabry-Perot etalon transmits a given wavelength when the plate spacing is (P + e + 1/2) times that wavelength, where (2P+1) is the integer order and e the difference of the phase shift at a reflection from half-wave.
The IVM etalon has reflectors that are thin film stacks. For a reflection finesse of 50, as we measure for the IVM etalon, the reflectance must be about 94%. Using a simple quarter wave stack to achieve this reflectance would require of order 10 layers, for a total thickness of 2.5 wavelengths. The reflected wave is a sum over all the various interface reflections, and comes from some effective distance into the coating.
Many of the materials used in thin film coatings are semicrystalline; in a pure state they may be birefringent, and in a thin film may develop as columnar structures.
The second working hypothesis for the cause of the variation of the IVM calibration with wavelength is as follows:
1) One of more of the layers in the thin film reflectors in the etalon is slightly birefringent.
2) The slight difference in index of refraction causes the effective depth of reflection from the reflectors and/or the phase change at reflection to vary slightly with input polarization.
3) The passband shifts and the FWHM of the passband varies because the effective plate separation is a function of polarization state.
The passband of the etalon is observed to shift with input modulation state, by about +/-0.2 scan steps, or about +/-4.8 mA, when the system is fed with a pure polarization state.
The polarization variation of the passband central wavelength and FWHM would be unobservable in the continuum where the normal calibration observations are made. They would only show up when the etalon is scanned into a spectrum line, and would generate crosstalk terms that look like the first and second derivatives of the intensity.
The shift in effective spacing would be uniform over the field, as is observed.
A change in plate spacing of 1/2 wave shifts the passband by 1 order. A change in plate spacing of 1/(2*finesse) wave shifts the passband by 1 FWHM. We measure a total shift of (9.6 mA / 72 mA) or 0.13 FWHM. This corresponds to a spacing shift of 0.13 / (2*finesse) wave = 0.0013 wave = 8 Angstroms.
Alternately, the value of the phase shift defect e could change by a similar amount. A passband shift of 0.001 wave would correspond to a phase shift change of 0.006 radians.
The IVM etalon coatings are broadband and therefore complex. A simple coating was modeled to estimate the magnitude of possible effects. The coating has 9 quarter-wave layers, alternately tantalum pentoxide and silicon dioxide. The peak reflectance is 93%, close to the IVM value.
The phase shift has some variation.
The index of tantalum pentoxide is 2.1 at the design wavelength near 6303A. As a test, the index of refraction of the tantalum pentoxide was decreased by 0.01. The peak reflectance decreased by 0.3%, corresponding to a decrease in finesse from 44.8 to 42.8 and an increase in FWHM by a factor of 1.05.
Taking the Fourier transform of the reflectance, we can estimate the change in depth of reflection. The amplitude of the transform decays roughly exponentially over the first 8 time steps. The mean time was about 1.76 time steps; each time step is about 1/2.5 wave periods. Therefore the mean depth of reflection is about 0.7 waves into the film. When the index is changed, the depth decreases by 0.005 time steps, or about 0.002 waves. This is comparable to the estimate above from the observed shifts, and suggests that small index of refraction variations could be important.
The change in phase shift is plotted below. Changes of order 0.005 radians are possible, again in the range estimated above from the observed shifts.
The smaller amplitude of the crosstalk inferred in the old configuration, when the modulator was followed by a polarizer, suggests that limiting the polarization states on the etalon did help. However, the polarizer was oriented at 45 degrees to the Rochon, to permit light in both the Data and Geometry cameras, therefore some crosstalk was still possible and present.
This model has several problems.
Because the passband variations are polarization dependent, a simple shift of the spectra for each modulation state will not work; that would be appropriate only if the shifts were seen for unpolarized input light. Further, because the polarization amplitude of the solar spectra variations not only spatially but also spectrally, no simple solution is obvious. It appears that the present scheme of fitting the crosstalk in terms of the spectral intensity gradients is the most useful.
The time variation requires that a day be devoted to running the IVM through the Cal optics.
Last modified: Wed Jun 25 17:49:28 HST 2003