AiryDisk2D

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

Bases: Fittable2DModel

Two dimensional Airy disk model.

Parameters:

amplitudepython:float

Amplitude of the Airy function.

x_0python:float

x position of the maximum of the Airy function.

y_0python:float

y position of the maximum of the Airy function.

radiuspython:float

The radius of the Airy disk (radius of the first zero).

Other Parameters:

fixeda python: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.

tiedpython: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.

boundspython: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.

eqconspython:list, optional

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

ineqconspython: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]

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	Names of the parameters that describe models of this type.
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

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

Names of the parameters that describe models of this type.

The parameters in this tuple are in the same order they should be passed in when initializing a model of a specific type. Some types of models, such as polynomial models, have a different number of parameters depending on some other property of the model, such as the degree.

When defining a custom model class the value of this attribute is automatically set by the Parameter attributes defined in the class body.

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