AiryDisk2D¶
-
class
astropy.modeling.functional_models.
AiryDisk2D
(amplitude=1, x_0=0, y_0=0, radius=1, **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, optional
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, 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 thetied
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, themin
andmax
properties of a parameter may be used.- eqcons : list, optional
A list of functions of length
n
such thateqcons[j](x0,*args) == 0.0
in a successfully optimized problem.- ineqcons : list, optional
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 [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
¶
-
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
¶
-
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