AiryDisk2D¶

class astropy.modeling.functional_models.AiryDisk2D(amplitude, x_0, y_0, radius, **kwargs)[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 the fixed 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 the tied property of a parameter may be used.

bounds : dict

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

eqcons : list

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

ineqcons : list

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

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`
`input_names`	list() -> new empty list
`param_names`	list() -> new empty list
`radius`
`x_0`
`y_0`

Methods Summary

`eval`(args, *kwargs)	Deprecated since version 1.0.
`evaluate`(x, y, amplitude, x_0, y_0, radius)	Two dimensional Airy model function

Attributes Documentation

amplitude¶

input_names = ['x', 'y']¶

param_names = ['amplitude', 'x_0', 'y_0', 'radius']¶

radius¶

x_0¶

y_0¶

Methods Documentation

classmethod eval(*args, **kwargs) [edit on github]¶: Deprecated since version 1.0: The eval method is deprecated and may be removed in a future version. Use AiryDisk2D.evaluate instead.

Two dimensional Airy model function

classmethod evaluate(x, y, amplitude, x_0, y_0, radius)[source] [edit on github]¶: Two dimensional Airy model function

Navigation

AiryDisk2D¶

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