AiryDisk2D

class astropy.modeling.functional_models.AiryDisk2D(amplitude=1, x_0=0, y_0=0, radius=1, **kwargs)

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, optional

A dictionary {parameter_name: boolean} of parameters to not be varied during fitting. True means the parameter is held fixed. Alternatively the fixed property of a parameter may be used.

tied : dict, optional

A dictionary {parameter_name: callable} of parameters which are linked to some other parameter. The dictionary values are callables providing the linking relationship. Alternatively the tied property of a parameter may be used.

bounds : dict, optional

A dictionary {parameter_name: value} of lower and upper bounds of parameters. Keys are parameter names. Values are a list or a tuple of length 2 giving the desired range for the parameter. Alternatively, the min and max properties of a parameter may be used.

eqcons : list, optional

A list of functions of length n such that eqcons[j](x0,*args) == 0.0 in a successfully optimized problem.

ineqcons : list, optional

A list of functions of length n such that ieqcons[j](x0,*args) >= 0.0 is a successfully optimized problem.

See also

Box2D, TrapezoidDisk2D, Gaussian2D

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 [1] for more details about the Airy disk.

References

[1]	(1, 2) https://en.wikipedia.org/wiki/Airy_disk

Attributes Summary

amplitude
input_units	This property is used to indicate what units or sets of units the evaluate method expects, and returns a dictionary mapping inputs to units (or None if any units are accepted).
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

amplitude = Parameter('amplitude', value=1.0)

input_units

This property is used to indicate what units or sets of units the evaluate method expects, and returns a dictionary mapping inputs to units (or None if any units are accepted).

Model sub-classes can also use function annotations in evaluate to indicate valid input units, in which case this property should not be overridden since it will return the input units based on the annotations.

param_names = ('amplitude', 'x_0', 'y_0', 'radius')

radius = Parameter('radius', value=1.0)

x_0 = Parameter('x_0', value=0.0)

y_0 = Parameter('y_0', value=0.0)

Methods Documentation

classmethod evaluate(x, y, amplitude, x_0, y_0, radius)

Two dimensional Airy model function