Disussion of dispersion etc. (especially between wavelength bands) and fringe-tracking - Jeff Meisner

A note on units:

Column densities of air or water vapor are in: moles/m2

Column density = volume density (moles/m3) * Distance (meters)

At Paranal, air is about 31.5 moles/m3

(calibratable to about 10-3 if temperature is known to within .3o Thus 100 meters of air is ~= 3150. moles/m2

1 airmass ~= 350,000 moles/m2

H2O is typically .05 – .3 moles/m3 depending on humidity:At 15o and 20% RH, density = .14 moles/m3, thus 100 meters of such air is 14. moles/m2, = .25 mm PWV

• Achromatic differential delay• Phase delay same for all

optical frequencies

• Phase at each frequency:2(where is phase delay)

• Non-achromatic delay from water vapor exhibiting First Order Dispersion

• Phase delay at each optical frequency proportional to refractivity at that wavelength

• Viewed at phase of center frequency, envelope (“group delay”) shifts w/r/t phase

• Non-achromatic delay from water vapor exhibiting First Order Dispersion

• Tracking the “group delay” we see the fringe phase go from 0 to 2 and repeat!

• Non-achromatic delay from water vapor exhibiting First Order Dispersion

MIDI observation, tracking atmospheric (?) OPD and water vapor

Matching of dispersion variations in N-band vs. optical frequency with theoretical curve (from Richard Mathar)(2 free parameters fitted: offset & scale)

SNR

Refractive index of water vapor (Computed by Richard Mathar)

Dispersive effect between (and within) bands due to 0 – 600 mole/m^2 of additional dry air. (= 20 meter delay-line offset)Note that dispersion from dry air increases rapidly at short wavelengths

(Tracking at the group-delay in K band)

….

Delay line offset, meters-8 -6 -4 -2 0

2

Fitting first order dispersion due to dry air vs. differential delay-line air column (from VINCI)Residuals from fit place upper limit on atmospheric water-vapor at low temporal frequencies (< .01 Hz since ~100 second observations) of < .3 mole/m^2

D

Now, Water Vapor dispersion(Gets worse at longer wavelengths)

Recall that atmospheric fluctuations are around .5 – 1 moles/m2 rms

Phase referencing at K band, phase error at other wavelengths due to 1 mole/m^2 of differential water vapor:Is worst at long N band (22 THz)

Water Vapor dispersion, with phase-tracking at K band0 – 5 moles/m^2 (typical p-p value due to atmosphere)

Water Vapor dispersion, with phase-tracking at K band0 – 5 moles/m^2 (typical p-p value due to atmosphere)

The end