Gaussian2D

class prose.blocks.psf.Gaussian2D(**kwargs)

Fit an elliptical 2D Gaussian model to an image effective PSF

To be used after a PSF building block

read Image.psf

write

• Image.psf_models_params

• Image.psf_model

• Image.fwhmx

• Image.fwhm

• Image.psf_model_block

PSF model is

\[f(x, y|A, x_0, y_0, \sigma_x, \sigma_y, \theta, b) = - A \exp\left(\frac{(x'-x'_0)^2}{2\sigma_x^2} \frac{(y'-y'_0)^2}{2\sigma_y^2}\right) + b\]

\[\begin{split}\text{with}\quad \begin{gather*} x' = xcos(\theta) + ysin(\theta) \\ y' = -xsin(\theta) + ycos(\theta) \end{gather*}\end{split}\]

is fitted from an effective psf. scipy.optimize.minimize is used to minimize \(\chi ^2\) from data. Initial parameters are found using the moments of the effective psf. This method is 4 times faster than photutils.centroids.fit_2dgaussian and lead to similar results.

Example

We start by loading an example image and buidling its median psf

from prose import blocks, Sequence
from prose.tutorials import example_image

# our example image
image = example_image()

# Sequence to build image PSF
sequence = Sequence([
    blocks.SegmentedPeaks(),  # stars detection
    blocks.Cutouts(),
    blocks.MedianPSF(),       # building PSF
])

sequence.run([image])

INFO telescope A not found - using default

INFO telescope A not found - using default

We can now apply the Gaussian2D block to the image in order to model its PSF

import matplotlib.pyplot as plt

block = blocks.psf.Gaussian2D()
image = block(image)

INFO telescope A not found - using default

and vizualise the result

from prose import viz

print(f"model: {image.psf_model_block}")
print("fwhmx, fwhmy, theta: " + ", ".join([f"{p:.2f}" for p in block.fwhm(image.psf_models_params)]))

plt.figure(figsize=(12, 5))

plt.subplot(131)
plt.imshow(image.psf)
plt.title("PSF")

plt.subplot(132)
plt.imshow(image.psf_model)
plt.title(f"PSF model ({image.psf_model_block})")

plt.subplot(133)
residuals = image.psf - image.psf_model
ax = plt.imshow(residuals)
plt.title("residuals")
viz.add_colorbar(ax)

plt.tight_layout()

model: Gaussian2D
fwhmx, fwhmy, theta: 3.78, 3.61, -1.02