1. 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/m 2 Column density = volume density (moles/m 3 ) * Distance (meters) At Paranal, air is about 31.5 moles/m 3 (calibratable to about 10 -3 if temperature is known to within.3 o Thus 100 meters of air is ~= 3150. moles/m 2 1 airmass ~= 350,000 moles/m 2 H 2 O is typically.05 –.3 moles/m 3 depending on humidity: At 15 o and 20% RH, density =.14 moles/m 3, thus 100 meters of such air is 14. moles/m 2, =.25 mm PWV

2. Achromatic differential delay Phase delay same for all optical frequencies Phase at each frequency:  2  (where  is phase delay)

3. Non-achromatic delay from water vapor exhibiting First Order Dispersion Phase delay at each optical frequency proportional to refractivity at that wavelength

4. Viewed at phase of center frequency, envelope (“group delay”) shifts w/r/t phase Non-achromatic delay from water vapor exhibiting First Order Dispersion

5. 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

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

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

8. Refractive index of water vapor (Computed by Richard Mathar)

10. 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)

11. …. 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) R esiduals 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   

12. Now, Water Vapor dispersion (Gets worse at longer wavelengths) Recall that atmospheric fluctuations are around.5 – 1 moles/m 2 rms

13. 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)

14. Water Vapor dispersion, with phase-tracking at K band 0 – 5 moles/m^2 (typical p-p value due to atmosphere)

16. The end