Calculate Telescope properties

telescope_resolution

import scipy as S

import pylab

#My Cheap Telescope
APPERTURE = 0.114
FOCAL_LENGTH= 0.910

#http://en.wikipedia.org/wiki/Visible_spectrum
min_visible = 380e-9
max_visible = 750e-9

#http://en.wikipedia.org/wiki/Luminosity_function
SCOTOPIC_PEAK = 507e-9 #The peak of the low-light luminosity function. Usually you use this if you are looking in a telescope
PHOTOPIC_PEAK = 555e-9 #The peak of the daylight luminosity function.


def plank_law(L,T):
        """
        Plank's Law for the radiation density of a black-body or cavity radiator.
        L because Lambda is a reserved word in Python
        T for temperature in Kelvins
        
        http://en.wikipedia.org/wiki/Planck%27s_law
        http://en.wikipedia.org/wiki/Stefan%E2%80%93Boltzmann_law
        """
        h = 6.62606957e-34#Plank's Constant
        k = 1.3806488e-23#Boltzmann's Constant
        c = 299792458.0 #Speed of light in a vacuum
        
        density = (8.0*S.pi*h*c)*S.power(L,-5.0) * S.power(S.exp(h*c*S.power(L*k*T,-1.0))-1.0, -1.0)

        return density

def myarange(start,stop, numstep=100):
        return S.arange(start, stop, stop/numstep)

def angular_resolution_at_wavelength(aperture, L):
        """
        Calculates the best theoretical angular resolution for a given aperture and wavelength (L).

        http://en.wikipedia.org/wiki/Angular_resolution
        """
        return S.arcsin(1.220*L*S.power(aperture, -1.0))

def rad_to_deg(R):
        return R*180.0*S.power(S.pi,-1.0)

temps = [3000,4000,5778, 6000]



#fig = pylab.figure()
#x = myarange(0.0, 3e-6,100)[1:]
#for T in temps:
#       pylab.plot(x,plank_law(x,T))
#pylab.show()

#realy, the arcsin here is just for the principle of the thing. At this tiny angles, the sin is roughly the angle(in radians)
fig = pylab.figure()
x_vis = myarange(min_visible, max_visible,100)
y_arcsec = rad_to_deg((angular_resolution_at_wavelength(APPERTURE, x_vis)))*60.0*60.0
pylab.plot(x_vis, y_arcsec)
pylab.axvline(SCOTOPIC_PEAK)
pylab.axvline(PHOTOPIC_PEAK)
pylab.show()

Rayleigh_Limit = rad_to_deg((angular_resolution_at_wavelength(APPERTURE, SCOTOPIC_PEAK)))*60.0*60.0

print "Theoretical Resolution (Rayleigh): %f\"" % Rayleigh_Limit