Parametric PSF Formula

[darkownt]

Hi All:

I am sure this information is buried somewhere on the forum or in the documentation but I can't seem to find it.

What is the formula used in generating the parametric PSF, the one used in deconvolution, restoration, and convolution, and having four parameters StdDev, Shape, Aspect ratio, and Rotation?

I'd greatly appreciate it!

Colin

[Raymond]

Hi Colin
Did you have a look at the documentation of the Dynamic PSF process? Maybe it answers your questions.

[darkownt]

The formulas documented in DynamicPSF are of the seperate gaussian and moffat functions, I need the single funtion that generates the Parametric PSF mentioned above.

cheers
Colin

[Juan Conejero]

Hi Colin,

The parametric PSF is a variable shape function defined as:



where the parameters are:

B: Local background.
A: Amplitude, which is the maximum value of the function, and also the function's value at the centroid coordinates.
x₀, y₀: Centroid coordinates in pixel units. This is the position of the center of symmetry of the function.
sigma_x, sigma_y: Standard deviation of the function's distribution on the horizontal and vertical axes, measured in pixels.

As implemented in tools such as Convolution and Deconvolution, the following parameters have fixed values: B=0, A=1, x₀=y₀=0.

The parameter k > 0 is the shape parameter. When k = 2, the function is Gaussian; when k < 2 the function is leptokurtic (peaked profile), and when k > 2 it is platykurtic (flat profile). The variable shape function is useful because one can fine tune the PSF's profile with a single parameter, taking a Gaussian profile as reference.

[darkownt]

Thanks Juan! 

That's exactly what I needed!!!