This topic is dedicated to the modelisation of the targets in the future ASPRO.

Note : this is related to the ModelFitting (LITpro) software for both LITpro gui and yorick model fitting.

Context

Target models are elaborated from elementary analytical models.

ASPRO models

In ASPRO, the user can define a single target model from 1 up to 6 elementary models (functions).

Here is the list of supported functions with their parameters :

Model Description Parameters
POINT Point source Offset R.A., Offset Dec, Flux
C_DISK Circular Disk Offset R.A., Offset Dec, Flux, Diameter
E_DISK Elliptical Disk (inclined) Offset R.A., Offset Dec, Flux, Maj. diam., Min. diam, Pos Ang
U_RING Unresoved Ring Offset R.A., Offset Dec, Flux, Diameter
RING Annulus (Resolved Ring) Offset R.A., Offset Dec, Flux, Inner Diameter, Outer Diameter
C_GAUSS Circular Gaussian source Offset R.A., Offset Dec, Flux, Diameter
E_GAUSS Elliptical Gaussian source Offset R.A., Offset Dec, Flux, Maj. diam., Min. diam, Pos Ang
EXPO Exponential brightness Offset R.A., Offset Dec, Flux, Diameter
POWER-2 B = 1/r^2 Offset R.A., Offset Dec, Flux, Diameter
POWER-3 B = 1/r^3 Offset R.A., Offset Dec, Flux, Diameter
LD_DISK Limb-Darkened Disk (quadratic) Offset R.A., Offset Dec, Flux, Diameter, a , b
where a and b are the first and 2nd order parameters for a quadratic limb-darkening where I(m)=T(0)(1-a(1-m)-b(1-m^2)) (a=0, b=0: uniform disk)(see, e.g., Claret et al, 1995, Astron. Astrophys. Suppl. Ser, 114, 247)
BINARY Binary (flux ratio, separation, angle) Offset R.A., Offset Dec, Flux, Flux Ratio, Rho, Theta

Notes :

  1. that the model uses Fluxes, so that the output values will be Correlated Fluxes and not Visibilities.
    By insuring that the flux (or the sum of fluxes when 2 or more functions are added) is ONE, correlated fluxes and normalized visibilities will be equivalent.
  2. Spatial coordinates (offsets, diameter, etc...) are in arc second.
    Offsets are in arc second on the tangential plane at the center of field of view, positive towards West (RA axis) and North (DEC axis).
    Position Angles are in degrees, East Of North.

LITpro models

In LITpro, the user can build one target model per target (present in the OIFits file) with an unbounded list of elementary models with their parameters.
An XML schema defines the current data model for the target models and such XML documents are exchanged between the GUI (java based) and the LITpro server (yorick).

Here is the list of supported yoga functions with their parameters :

Model Description Parameters Function description
punct Point source flux_weight x y lpb_punct(ufreq, vfreq, flux_weight, x, y)
disk Circular Disk flux_weight x y diameter lpb_disk(ufreq, vfreq, flux_weight, x, y, diameter)
elong_disk Elliptical Disk (inclined) flux_weight x y minor_axis_diameter elong_ratio major_axis_pos_angle lpb_elong_disk(ufreq, vfreq, flux_weight, x, y, minor_axis_diameter, elong_ratio, major_axis_pos_angle)
ELONG_RATIO = major_axis / minor_axis
flatten_disk Elliptical Disk (inclined) flux_weight x y major_axis_diameter flatten_ratio minor_axis_pos_angle lpb_flatten_disk(ufreq, vfreq, flux_weight, x, y, major_axis_diameter, flatten_ratio, minor_axis_pos_angle)
FLATTEN_RATIO = major_axis / minor_axis
circle Unresoved Ring flux_weight x y diameter lpb_circle_diameter(ufreq, vfreq, flux_weight, x, y, diameter)
ring Annulus (Resolved Ring) flux_weight x y diameter width lpb_ring(ufreq, vfreq, flux_weight, x, y, diameter, width)
elong_ring Elliptical ring flux_weight x y minor_internal_diameter elong_ratio width major_axis_pos_angle lpb_elong_ring(ufreq, vfreq, flux_weight, x, y, minor_internal_diameter, elong_ratio, width, major_axis_pos_angle)
ELONG_RATIO = MAJOR_INTERNAL_DIAMETER / MINOR_INTERNAL_DIAMETER
flatten_ring Elliptical ring flux_weight x y major_internal_diameter flatten_ratio width minor_axis_pos_angle lpb_flatten_ring(ufreq, vfreq, flux_weight, x, y, major_internal_diameter, flatten_ratio, width, minor_axis_pos_angle)
FLATTEN_RATIO = MAJOR_INTERNAL_DIAMETER / MINOR_INTERNAL_DIAMETER
gaussian Circular Gaussian source flux_weight x y fwhm lpb_gaussian(ufreq, vfreq, flux_weight, x, y, fwhm)
elong_gaussian Elliptical Gaussian source flux_weight x y minor_axis_fwhm elong_ratio major_axis_pos_angle lpb_elong_gaussian(ufreq, vfreq, flux_weight, x, y, minor_axis_fwhm, elong_ratio, major_axis_pos_angle)
ELONG_RATIO = MAJOR_AXIS_FWHM / MINOR_AXIS_FWHM
flatten_gaussian Elliptical Gaussian source flux_weight x y major_axis_fwhm flatten_ratio minor_axis_pos_angle lpb_flatten_gaussian(ufreq, vfreq, flux_weight, x, y, major_axis_fwhm, flatten_ratio, minor_axis_pos_angle)
FLATTEN_RATIO = MAJOR_AXIS_FWHM / MINOR_AXIS_FWHM
limb_linear Limb-Darkened Disk (linear) flux_weight x y diameter a1_coeff DOCUMENT lpb_limb_linear(ufreq, vfreq, flux_weight, x, y, diameter, a1_coeff)
o(mu) = 1 - A1_COEFF(1-mu)
limb_power Limb-Darkened Disk (power) flux_weight x y diameter power lpb_limb_power(ufreq, vfreq, flux_weight, x, y, diameter, power)
o(mu) = mu^POWER
limb_quadratic Limb-Darkened Disk (quadratic) flux_weight x y diameter a1_coeff a2_coeff lpb_limb_quadratic(ufreq, vfreq, flux_weight, x, y, diameter, a1_coeff, a2_coeff)
A1_COEFF, A2_COEFF ([-1,1])
o(mu) = 1 - A1_COEFF(1-mu) - A2_COEFF(1-mu)^2
limb_sqrt Limb-Darkened Disk (square root) flux_weight x y diameter a1_coeff a2_coeff lpb_limb_sqrt(ufreq, vfreq, flux_weight, x, y, diameter, a1_coeff, a2_coeff)
o(mu) = 1 -A1_COEFF(1-mu) - A2_COEFF(1-sqrt(mu))

Notes :

  1. Like ASPRO, the user can choose to normalize or not the flux (Section Fitter options / Checkbox Normalize total flux) and the POS_ANGLE is measured in degrees, from the positive vertical semi-axis (i.e. North direction) towards to the positive
  2. In contrary to ASPRO, spatial coordinates (offsets, diameter, etc...) are in milli arc second


Elliptical models are defined twice for disk, ring and gaussian models (flattened or elongated) whereas ASPRO simply gives both axis diameters.
TODO : choose how to express those parameters in an uniform way i.e. keep a single model with minor and major axis diameters but the GUI could propose several modes (both axis diameters, minor_axis_diameter + elong_ratio, major_axis_diameter + flatten_ratio)


In LITpro, a parameter can be shared between several models i.e. different elementary model can use the same parameter value and the fit will consider those parameters as linked.

Hierarchical & composite models

In both ASPRO and LITpro, the user must define each model and each parameter with their values i.e. there is no specific rule or wizard to adjust the positions (offset ra / dec in ASPRO or x,y in LITpro) or the flux weight considering the list of elementary models.

Binary Models

Binary models (2 puncts for example) are missing in LITpro expressed with specific parameters distance (rho) and angle (theta) and a flux ratio between the two models.

ASPRO has a specific binary model (rho, theta, flux ratio) made of two punct models punct1 (x1, y1, flux1) and punct2 (x2, y2, flux2)
rho = sqrt (x2^2 + y2^2)
theta = arctan2 (y2, x2)
flux ratio = flux2 / flux1
where x1 = y1 = 0 because the first component of the binary must be at the center.

Moreover, this could be generalized to any elementary model (punct, disk, ellipse, limb-darkened disk ...) => Composite model needed to define custom or derived parameters.

Model Group

A Model Group can be introduced to represent such binary or more complex models with common parameters (x, y, flux) and optional parameters like (rho, theta, flux ratio) for binary models (2 child models) ... It is a new elementary model to group other elementary models to form a model hierarchy.

TBC

Multi wave length target models

For now, both ASPRO and LITpro are not supporting multichromatic models (i.e. multiple wave lengths).
Such models are called monochromatic models ('gray')

A major evolution will be to enhance the current target modeling to take into account the wavelength impact on model parameters i.e. paramX = f(lambda) and for LITpro on fitting such complex parameters too.

The main problems resides in the way to express such wave length dependency (functions or array values) ...

TBC

New ASPRO / LITpro Models

The work on target models for the new ASPRO is the good time to define a shared target model component (java gui and xml based) that reuses the LITpro model description (xml schema) and enhances it for both ASPRO (first) and LITpro (next).

TODO :

  • Choose and give priorities to models to implement among LITpro models
  • Define precisely how to express elliptical parameters
  • Define the interaction rules between the model group and child models

Rules

  1. Coordinates/ Angles are defined in milli arc second (mas) unit.
  2. Stay compatible with the LITpro software as much as possible !

Other ideas

  • Custom user analytical models : Could the user provide a custom analytical model giving an xml description containing a script (to be defined) in order to easily enhance the finite list of supported models ?
    That could be a 'simple way' to define a binary model made of two punct models providing the parameter function mapping between rho / theta / flux ratio and the punct model parameters punct1 (x1, y1, flux1) and punct2 (x2, y2, flux2)
  • Gui :
    • By default the new ASPRO will not have any default target model at startup. However, the user can define a default target model in the user preferences
    • A single target model can be applied to several targets (shared model) and later, every target can have its specific target model.

-- LaurentBourges - 10 Feb 2010

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Topic revision: r2 - 2010-02-10 - LaurentBourges
 
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