Bases: astropy.modeling.core.Parametric2DModel
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).
|
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 [R4] for more details about the Airy disk.
References
- 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.
Attributes Summary
Methods Summary
eval(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 eval(x, y, amplitude, x_0, y_0, radius)[source] [edit on github]
Two dimensional Airy model function