# AiryDisk2D¶

class astropy.modeling.functional_models.AiryDisk2D(amplitude=1, x_0=0, y_0=0, radius=1, **kwargs)[source] [edit on github]

Two dimensional Airy disk model.

Parameters: Other 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). 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 [R12] for more details about the Airy disk.

References

 [R12] (1, 2) http://en.wikipedia.org/wiki/Airy_disk

Attributes Summary

Methods Summary

 evaluate(x, y, amplitude, x_0, y_0, radius) Two dimensional Airy model function

Attributes Documentation

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

Methods Documentation

classmethod evaluate(x, y, amplitude, x_0, y_0, radius)[source] [edit on github]

Two dimensional Airy model function