`webbpsf`

and `photutils.GriddedPSFModel`

¶*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
```

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:**

**F090W:**A NIRCam filter**FITS:**Flexible Image Transport System (https://fits.gsfc.nasa.gov/fits_primer.html)**HDU:**Header/Data Unit in a FITS file**JWST:**James Webb Space Telescope**NIRCam:**Near-Infrared Camera on JWST (https://jwst.stsci.edu/instrumentation/nircam)**NRCA1:**NIRCam A1 detector**PSF:**Point-spread function

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)
```

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())
```

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)
```

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())
```

`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,
aperture_radius=3.)
```

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.

**Author:** Data Analysis Tools Branch, STScI

**Updated on:** Consult GitHub repository for edit history