# Creating a simulated starfield image and performing photometry using webbpsf and photutils.GriddedPSFModel¶

## Imports¶

• matplotlib inline for creating non-interactive plots
• numpy for numerical computations
• astropy.io.fits for accessing FITS files
• astropy.stats.gaussian_sigma_to_fwhm for converting $\sigma$ to FWHM
• astropy.table.Table for constructing Astropy table
• astropy.utils.misc.NumpyRNGContext for reproducible random result
• astropy.visualization for normalized image display
• photutils for photometry related classes and functions
• webbpsf for JWST PSF related functions
In [1]:
%matplotlib inline

import numpy as np
import matplotlib.pyplot as plt
from astropy.io import fits
from astropy.stats import gaussian_sigma_to_fwhm
from astropy.table import Table
from astropy.utils.misc import NumpyRNGContext
from astropy.visualization import imshow_norm, PercentileInterval, SqrtStretch
from photutils import BasicPSFPhotometry
from photutils import DBSCANGroup, MMMBackground
from photutils.datasets import make_noise_image
from webbpsf.gridded_library import display_psf_grid
from webbpsf.utils import to_griddedpsfmodel


ValueErrorTraceback (most recent call last)
<ipython-input-1-c9861cb722ec> in <module>
8 from astropy.utils.misc import NumpyRNGContext
9 from astropy.visualization import imshow_norm, PercentileInterval, SqrtStretch
---> 10 from photutils import BasicPSFPhotometry
11 from photutils import DBSCANGroup, MMMBackground
12 from photutils.datasets import make_noise_image

/opt/conda/envs/notebooks_env/lib/python3.6/site-packages/photutils/__init__.py in <module>
17
18 if not _ASTROPY_SETUP_:  # noqa
---> 19     from .aperture import *  # noqa
20     from .background import *  # noqa
21     from .centroids import *  # noqa

/opt/conda/envs/notebooks_env/lib/python3.6/site-packages/photutils/aperture/__init__.py in <module>
5
6 from .bounding_box import *  # noqa
----> 7 from .circle import *  # noqa
8 from .core import *  # noqa
9 from .ellipse import *  # noqa

/opt/conda/envs/notebooks_env/lib/python3.6/site-packages/photutils/aperture/circle.py in <module>
13 from .core import PixelAperture, SkyAperture
---> 15 from ..geometry import circular_overlap_grid
16
17 __all__ = ['CircularMaskMixin', 'CircularAperture', 'CircularAnnulus',

/opt/conda/envs/notebooks_env/lib/python3.6/site-packages/photutils/geometry/__init__.py in <module>
4 """
5
----> 6 from .circular_overlap import *  # noqa
7 from .elliptical_overlap import *  # noqa
8 from .rectangular_overlap import *  # noqa

__init__.pxd in init photutils.geometry.circular_overlap()

ValueError: numpy.ufunc size changed, may indicate binary incompatibility. Expected 216 from C header, got 192 from PyObject

## Introduction¶

The simulated image will be made using a spatially-dependent JWST PSF generated by webbpsf. photutils will be then used to perform PSF-fitting photometry on the simulated JWST NIRCam image.

The intended audience are astronomers already familiar with PSF photometry, the FITS file format, and basic Python usage. In-depth scientific and technical backgrounds will not be discussed nor taught in this notebook.

Background on JWST PSF simulation: https://jwst.stsci.edu/science-planning/proposal-planning-toolbox/psf-simulation-tool-webbpsf

Background on PSF photometry: https://photutils.readthedocs.io/en/stable/psf.html

Some notes about the file: It is pre-generated grid of JWST PSFs for NIRCam A1 detector in F090W filter. The file is hosted on STScI Box file sharing system.

Defining some terms:

We start by loading into FITS HDU a pre-generated grid of JWST PSFs for NIRCam A1 detector in F090W filter.

In [ ]:
url = 'https://stsci.box.com/shared/static/6h8wsr2ts0t24s79cxmnyk8bldt0vv3i.fits'
hdu = fits.open(url)


## File information¶

In [ ]:
hdu.info()


Astropy has saved a cached copy of this file under your local cache directory for Astropy; default is ~/.astropy/cache/download.

This file only has a single extension that holds a data cube. The cube consists of 16 PSF images, each with dimension of 404 by 404 pixels. Each PSF is oversampled by a factor of 4, so the actual detector pixel dimension covered by the PSF is 101 by 101.

Now, let's look at the first PSF in the cube.

In [ ]:
data = hdu[0].data[0]
plt.figure(figsize=(9, 9))
imshow_norm(data, interval=PercentileInterval(99.), stretch=SqrtStretch())


## Creating a PSF model¶

We now create a photutils.GriddedPSFModel from the FITS HDU.

In [ ]:
psfmodel = to_griddedpsfmodel(hdu, ext=0)

In [ ]:
psfmodel


psfmodel is an instance of a photutils.GriddedPSFModel. Let's view some of it's attributes.

The oversampled PSF grid is stored internally as a 3D numpy.ndarray. The first axis represents the number of PSFs, while the second and third axes represent the (ny, nx) shape of the 2D PSFs.

Here there are 16 PSFs (from a 4x4 reference grid) and the shape of each is 404x404 pixels.

In [ ]:
psfmodel.data.shape


The oversampling attribute is the PSF oversampling factor.

In [ ]:
psfmodel.oversampling


The grid_xypos attribute contains a list of the (x, y) positions of reference PSFs. The PSF at an arbitrary (x, y) position is interpolated from the grid of reference PSFs.

In [ ]:
psfmodel.grid_xypos


This model contains a 4x4 grid of reference PSFs.

In [ ]:
len(psfmodel.grid_xypos)


The meta attribute is dictionary holding detailed information how the PSF model grid was generated by webbpsf. For example, psfmodel.meta['fovpixel'] would indicate that "field of view in pixels (full array)" is 101 pixels.

In [ ]:
psfmodel.meta

In [ ]:
fovpixel = psfmodel.meta['fovpixel']
print(fovpixel[1], 'is', fovpixel[0])


We can use the webbpsf.gridded_library.display_psf_grid function to visualize the PSF grid.

In [ ]:
display_psf_grid(psfmodel)


## Creating simulated starfield¶

Now let's use the psfmodel grid to create a simulated starfield image. First, we'll define 25 stars with random positions and fluxes. We are using a small image with limited number of stars for faster computation; feel free to use a larger image and/or more stars when you run this notebook locally, if desired.

In [ ]:
shape = (512, 512)
data = np.zeros(shape)
nstars = 25
flux_max = 200000.

with NumpyRNGContext(12345):  # Seed for repeatability
xx = np.random.uniform(low=0, high=shape[1], size=nstars)
yy = np.random.uniform(low=0, high=shape[0], size=nstars)
zz = np.random.uniform(low=0, high=flux_max, size=nstars)


Now we'll evaluate the model at these positions and fluxes.

In [ ]:
eval_xshape = np.int(np.ceil(psfmodel.data.shape[2] / psfmodel.oversampling))
eval_yshape = np.int(np.ceil(psfmodel.data.shape[1] / psfmodel.oversampling))

for xxi, yyi, zzi in zip(xx, yy, zz):
x0 = np.int(np.floor(xxi - (eval_xshape - 1) / 2.))
y0 = np.int(np.floor(yyi - (eval_yshape - 1) / 2.))
x1 = x0 + eval_xshape
y1 = y0 + eval_yshape

if x0 < 0:
x0 = 0
if y0 < 0:
y0 = 0
if x1 > shape[1]:
x1 = shape[1]
if y1 > shape[0]:
y1 = shape[0]

y, x = np.mgrid[y0:y1, x0:x1]
data[y, x] += psfmodel.evaluate(x=x, y=y, flux=zzi, x_0=xxi, y_0=yyi)


Let's add some noise to the image.

In [ ]:
noise = make_noise_image(data.shape, 'gaussian', mean=0, stddev=2, random_state=123)
data += noise


Let's display the simulated JWST NIRCam A1 detector image in F090W filter.

In [ ]:
plt.figure(figsize=(9, 9))
imshow_norm(data, interval=PercentileInterval(99.), stretch=SqrtStretch())


## Performing PSF-fitting photometry with GriddPSFModel¶

We can also use GriddedPSFModel to perform PSF-fitting photometry.

For this simple example, we'll use photutils.BasicPSFPhotometry to perform the photometry. Here we're inputting a table of the initial positions (instead of inputting a star finder object).

First, we'll create an Astropy table defining the initial guesses of star positions.

In [ ]:
init_tbl = Table()
init_tbl['x_0'] = xx.astype(int)
init_tbl['y_0'] = yy.astype(int)
init_tbl['flux_0'] = zz.astype(int)


Then, we define the parameters to initialize a BasicPSFPhotometry instance.

In [ ]:
sigma_psf = 3.
daogroup = DBSCANGroup(2.0 * sigma_psf * gaussian_sigma_to_fwhm)
mmm_bkg = MMMBackground()
fit_shape = (eval_yshape, eval_xshape)
phot = BasicPSFPhotometry(daogroup, mmm_bkg, psfmodel, fit_shape, finder=None,


Now, we call the instance on the data. This step might take a few seconds. See https://github.com/astropy/photutils/issues/631 for more information.

In [ ]:
tbl = phot(data, init_guesses=init_tbl)


The result is an Astropy table containing the initial and fitted values of the star positions and fluxes. We can format the displayed values by setting table[column_name].format.

In [ ]:
tbl['x_fit'].format = '%.1f'
tbl['y_fit'].format = '%.1f'
tbl['flux_fit'].format = '%.4e'
tbl['flux_unc'].format = '%.4e'
tbl['x_0_unc'].format = '%.4e'
tbl['y_0_unc'].format = '%.4e'

In [ ]:
tbl


We can also view the residual image of the best-fit model PSF image subtracted from the data.

In [ ]:
diff = phot.get_residual_image()

In [ ]:
plt.figure(figsize=(9, 9))
imshow_norm(diff, interval=PercentileInterval(99.), stretch=SqrtStretch())
plt.colorbar()


The residual image is essentially noise, indicating good PSF model fits to the data.