AiryDisk2D¶
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class
astropy.modeling.functional_models.
AiryDisk2D
[source] [edit on github]¶ Bases:
astropy.modeling.Fittable2DModel
Two dimensional Airy disk model.
Parameters: amplitude : float
Amplitude of the Airy function.
x_0 : float
x position of the maximum of the Airy function.
y_0 : float
y position of the maximum of the Airy function.
radius : float
The radius of the Airy disk (radius of the first zero).
Other Parameters: fixed : a dict
A dictionary
{parameter_name: boolean}
of parameters to not be varied during fitting. True means the parameter is held fixed. Alternatively thefixed
property of a parameter may be used.tied : dict
A dictionary
{parameter_name: callable}
of parameters which are linked to some other parameter. The dictionary values are callables providing the linking relationship. Alternatively thetied
property of a parameter may be used.bounds : dict
eqcons : list
A list of functions of length
n
such thateqcons[j](x0,*args) == 0.0
in a successfully optimized problem.ineqcons : list
A list of functions of length
n
such thatieqcons[j](x0,*args) >= 0.0
is a successfully optimized problem.See also
Notes
Model formula:
\[f(r) = A \left[\frac{2 J_1(\frac{\pi r}{R/R_z})}{\frac{\pi r}{R/R_z}}\right]^2\]Where \(J_1\) is the first order Bessel function of the first kind, \(r\) is radial distance from the maximum of the Airy function (\(r = \sqrt{(x - x_0)^2 + (y - y_0)^2}\)), \(R\) is the input
radius
parameter, and \(R_z = 1.2196698912665045\)).For an optical system, the radius of the first zero represents the limiting angular resolution and is approximately 1.22 * lambda / D, where lambda is the wavelength of the light and D is the diameter of the aperture.
See [R5] for more details about the Airy disk.
References
[R5] (1, 2) http://en.wikipedia.org/wiki/Airy_disk Attributes Summary
amplitude
param_names
radius
x_0
y_0
Methods Summary
evaluate
(x, y, amplitude, x_0, y_0, radius)Two dimensional Airy model function Attributes Documentation
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amplitude
¶
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param_names
= ('amplitude', 'x_0', 'y_0', 'radius')¶
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radius
¶
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x_0
¶
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y_0
¶
Methods Documentation
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classmethod
evaluate
(x, y, amplitude, x_0, y_0, radius)[source] [edit on github]¶ Two dimensional Airy model function
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