AiryDisk2D¶
-
class
astropy.modeling.functional_models.
AiryDisk2D
(amplitude=1, x_0=0, y_0=0, radius=1, **kwargs)[source]¶ Bases:
astropy.modeling.Fittable2DModel
Two dimensional Airy disk model.
- Parameters
- amplitudefloat
Amplitude of the Airy function.
- x_0float
x position of the maximum of the Airy function.
- y_0float
y position of the maximum of the Airy function.
- radiusfloat
The radius of the Airy disk (radius of the first zero).
- Other Parameters
- fixeda 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.- tieddict, 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.- boundsdict, 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.- eqconslist, optional
A list of functions of length
n
such thateqcons[j](x0,*args) == 0.0
in a successfully optimized problem.- ineqconslist, 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
Attributes Summary
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).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')¶
-
radius
= Parameter('radius', value=1.0)¶
-
x_0
= Parameter('x_0', value=0.0)¶
-
y_0
= Parameter('y_0', value=0.0)¶
Methods Documentation