IVM Variable Retarders

Reflections and Fringes

This page is to describe effects due to multiple reflections from the internal surfaces of the substrates of the variable retarders. The reflections are quite small, but since they depend on retarder tuning a small instrumental polarization may be introduced.

Because the liquid crystal has a different index than the substrate, reflections can occur at the interface. It's best to think of these devices as a low-finesse etalon, where the finesse is controlled by the reflection due to index mismatch and varies with the applied voltage. Since we don't know the exact cell thickness or what phase shifts occur at the interface, we can't model the exact wavelength dependence of the transmission variation, but we can get the free spectral range and amplitudes for various retardance settings.

Last updated:Wed Aug 30 17:28:49 HST 2000
Donald L. Mickey

LVR A

The modulation sequence for the first retarder is [.625, .875, .625, .375] wave. At 630 nm wavelength, this requires

that the variable index (for horizontal polarization, since the fast axis is in the vertical direction) is [1.55646 1.57104 1.55646 1.54188].This figure shows the transmission for vertical polarization (cyan), and for horizontal polarization at 3/8 wave (green), 5/8 wave (red) and 7/8 wave (yellow). The free spectral range is about 12 nm. So if we happened to hit the wavelength where the yellow curve has a minimum, we could get a transmission of 0.997 or so and a polarizance of about 0.002 (-Q) at the second modulation state.

LVR B

The fast axis of the second retarder is at +45 degrees from vertical. Its retardance settings are

[0.347957 0.152043 0.652043 0.152043] wave. At 630 nm, the variable index must then be [1.54654 1.52596 1.57846 1.52596]. This figure shows the transmission for +45 degree polarization in cyan, and for -45 degree polarization at .152 wave (green), .348 wave (red) and .652 wave (yellow). Again, the worst transmission is about 0.997. Since this device has its principal axis at 45 degrees to that of the analyzer, only the average transmission matters here.

Conclusions

We should expect to see intensity differences between the modulation states amounting to as much as perhaps 0.5% if we hit a bad wavelength in the fringe spectrum.
The polarization effect in LVR A means that the spurious modulation will be different for the Data and Geometry cameras, probably not in a predictable way.
LVR B affects both cameras the same. Its retardance removes about half the Q polarization created in LVR A, thus reducing the difference between the two cameras.
The fringe spacing is around 12 nm for LVR A and 22 nm for LVR B. This means the variation over the typical 72 pm IVM wavelength scan will be pretty small, below the 10^-4 level.
These effects will be primarily to introduce a spurious instrumental polarization, somewhere around the 0.1% level. It ought to be pretty stable since it depends mostly on the retardance settings, which we evaluate frequently in CALRTD.
These calculations assume normal incidence. The fact that the actual retarders integrate over a range of angles will change things, but I'm not sure just how.
The actual reflectance at the substrate might be more than calculated for the e-wave, since the LC molecules right next to the alignment layer don't tilt much in response to applied voltage. It's hard to guess just what this would do; maybe increase the overall fringe amplitude but reduce the dependence on applied voltage.

If you have comments or suggestions, email me at Don Mickey

Last modified: Wed Jun 25 17:45:46 HST 2003