AtmosphericModel/scripts/ADC_instruction.ipynb

Atmospheric Dispersion Corrector model

This notebook explains how you can use the ADC.py analytic ADC model for some quick simulations. For the model to be representative, the following assumptions must apply:

• The ADC consists of two amici prisms, totaling 4 glass prisms in total
• The ADC is located in the pupil plane of the instrument (or very close to it)
• The rotation of the prisms is defined as follows: for \theta=0 the ADC is in it's maximum dispersive configuration. For any other rotation angle, the top prism set rotates by \theta degrees and the bottom prism set also rotates by \theta degrees in opposite direction. The total relative angle is thus 2\theta. From this also follows that the minimum dispersion magnitude is reached at \theta=90 degrees.

The ADC.py model is really not made for very general use, so it will likely require some editing in the source code by the user to make it work for a different instrument than MICADO.

We first start by importing the necessary files. Here we'll use the AstroAtmosphere package to calculate the atmospheric dispersion, but a manual input is also possible.

In [5]:

import numpy as np
import ADC
import AstroAtmosphere

Then we calculate the atmospheric dispersion for a given set of conditions.

In [6]:

# Atmospheric conditions
T   = 288.15 	# k
P   = 101325  	# Pa
H   = 0.3
xc  = 400   	# ppm
lat = -25 		# degrees
h   = 2500  	# m
l1  = 1.49 		# micron, start H-band
l2  = 1.78 		# micron, end H-band
zenith = 30 	# degrees

# Initializing dispersion model
at  = AstroAtmosphere.Observatory()
rho = at.rho(p=P, T=T, RH=H, xc=xc)
disp = AstroAtmosphere.dispersion(lat, h)
disp.setReducedHeight(P, rho)

# Calculation of indices of refraction at l1 and l2
n1 = at.n_tph(l=l1, T=T, p=P, RH=H, xc=xc)
n2 = at.n_tph(l=l2, T=T, p=P, RH=H, xc=xc)

# Calculation of atmospheric dispersion in milli arc sec
dispersion = disp.cassini(n1, n2, zenith)*3.6e6

Now, we initialize the ADC class. We can calculate the dispersion in sky angles, i.e. in terms of the Field of View of the telescope, for a given rotation of the ADC prisms. In this case, if we set \theta=30 degrees, we find that the ADC produces 58 milli arc seconds of dispersion in H-band.

In [7]:

# Initialize ADC object
adc = ADC.ADC()

# Calculate the dispersion for a given rotation
theta = 30 # degrees
adc.setOrientation(theta)
adcDispersion = adc.calculateDispersion(l1,l2)[1]
print(
    'The dispersion of the ADC for {:.0f} degrees of rotation: {:.3f} mas'\
    .format(theta, adcDispersion))

The dispersion of the ADC for 30 degrees of rotation: 58.011 mas

Of course, we're often much more interested in the optimum positioning of the ADC given an amount of atmospheric dispersion. This is done as follows.

In [8]:

# Optimize for atmospheric dispersion, given wavelength range {l1,l2}
adcOptimumAngle = adc.optimize(dispersion, l1, l2) 
adcDispersionOptimized = adc.calculateDispersion(l1,l2)[1]

print('The atmospheric dispersion: {:.3f} mas'.format(dispersion) )
print('The optimum ADC angle in this case: {:.1f} degrees'.format(adcOptimumAngle))
print('The residual dispersion: {:.3f} mas'.format(dispersion - adcDispersionOptimized))

The atmospheric dispersion: 24.771 mas
The optimum ADC angle in this case: 68.1 degrees
The residual dispersion: 0.000 mas