.. _photutils-aperture:

Aperture Photometry (`photutils.aperture`)
==========================================

Introduction
------------

The :func:`~photutils.aperture.aperture_photometry` function and the
:class:`~photutils.aperture.ApertureStats` class are the main tools to
perform aperture photometry on an astronomical image for a given set of
apertures.


.. _photutils-apertures:

Apertures
---------

Photutils provides several apertures defined in pixel or sky
coordinates.  The aperture classes that are defined in pixel
coordinates are:

* `~photutils.aperture.CircularAperture`
* `~photutils.aperture.CircularAnnulus`
* `~photutils.aperture.EllipticalAperture`
* `~photutils.aperture.EllipticalAnnulus`
* `~photutils.aperture.RectangularAperture`
* `~photutils.aperture.RectangularAnnulus`

Each of these classes has a corresponding variant defined in sky
coordinates:

* `~photutils.aperture.SkyCircularAperture`
* `~photutils.aperture.SkyCircularAnnulus`
* `~photutils.aperture.SkyEllipticalAperture`
* `~photutils.aperture.SkyEllipticalAnnulus`
* `~photutils.aperture.SkyRectangularAperture`
* `~photutils.aperture.SkyRectangularAnnulus`

To perform aperture photometry with sky-based apertures, one will need
to specify a WCS transformation.

The :func:`~photutils.aperture.aperture_photometry` function
and the :class:`~photutils.aperture.ApertureStats` class both
accept `~photutils.aperture.Aperture` objects. They can also
accept a supported `regions.Region` object, i.e. a region
that corresponds to the above aperture classes, as input. The
:func:`~photutils.aperture.aperture_photometry` function also accepts a
list of `~photutils.aperture.Aperture` or `regions.Region` objects if
each aperture/region has identical positions.

The :func:`~photutils.aperture.region_to_aperture` convenience
function can also be used to convert a `regions.Region` object to a
`~photutils.aperture.Aperture` object.

Users can also create their own custom apertures (see
:ref:`custom-apertures`).


.. _creating-aperture-objects:

Creating Aperture Objects
-------------------------

The first step in performing aperture photometry is to create an
aperture object.  An aperture object is defined by a position (or a
list of positions) and parameters that define its size and possibly,
orientation (e.g., an elliptical aperture).

We start with an example of creating a circular aperture in pixel
coordinates using the :class:`~photutils.aperture.CircularAperture`
class::

    >>> from photutils.aperture import CircularAperture
    >>> positions = [(30.0, 30.0), (40.0, 40.0)]
    >>> aperture = CircularAperture(positions, r=3.0)

The positions should be either a single tuple of ``(x, y)``, a list of
``(x, y)`` tuples, or an array with shape ``Nx2``, where ``N`` is the
number of positions.  The above example defines two circular apertures
located at pixel coordinates ``(30, 30)`` and ``(40, 40)`` with a
radius of 3 pixels.

Creating an aperture object in sky coordinates is similar.  One first
uses the :class:`~astropy.coordinates.SkyCoord` class to define sky
coordinates and then the
:class:`~photutils.aperture.SkyCircularAperture` class to define the
aperture object::

    >>> from astropy import units as u
    >>> from astropy.coordinates import SkyCoord
    >>> from photutils.aperture import SkyCircularAperture
    >>> positions = SkyCoord(l=[1.2, 2.3] * u.deg, b=[0.1, 0.2] * u.deg,
    ...                      frame='galactic')
    >>> aperture = SkyCircularAperture(positions, r=4.0 * u.arcsec)

.. note::
    Sky apertures are not defined completely in sky coordinates. They
    simply use sky coordinates to define the central position, and the
    remaining parameters are converted to pixels using the pixel scale
    of the image at the central position. Projection distortions are
    not taken into account. They are **not** defined as apertures on
    the celestial sphere, but rather are meant to represent aperture
    shapes on an image. If the apertures were defined completely in sky
    coordinates, their shapes would not be preserved when converting to
    or from pixel coordinates.


Converting Between Pixel and Sky Apertures
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

The pixel apertures can be converted to sky apertures, and
vice versa, given a WCS object. To accomplish this, use the
:meth:`~photutils.aperture.PixelAperture.to_sky` method for pixel
apertures. For this example, we'll use a sample WCS object::

    >>> from photutils.datasets import make_wcs
    >>> wcs = make_wcs((100, 100))
    >>> aperture = CircularAperture((10, 20), r=4.0)
    >>> sky_aperture = aperture.to_sky(wcs)
    >>> sky_aperture  # doctest: +FLOAT_CMP
    <SkyCircularAperture(<SkyCoord (ICRS): (ra, dec) in deg
        (197.89234399, -1.36689653)>, r=0.39999999985539925 arcsec)>

and the :meth:`~photutils.aperture.SkyAperture.to_pixel` method for
sky apertures, e.g.,::

    >>> position = SkyCoord(197.893, -1.366, unit='deg', frame='icrs')
    >>> aperture = SkyCircularAperture(position, r=0.4 * u.arcsec)
    >>> pix_aperture = aperture.to_pixel(wcs)
    >>> pix_aperture  # doctest: +FLOAT_CMP
    <CircularAperture([26.14628817, 56.58410628], r=4.000000000439743)>

Performing Aperture Photometry
------------------------------

After the aperture object is created, we can then perform the photometry
using the :func:`~photutils.aperture.aperture_photometry` function. We
start by defining the aperture (at two positions) as described above::

    >>> positions = [(30.0, 30.0), (40.0, 40.0)]
    >>> aperture = CircularAperture(positions, r=3.0)

We then call the :func:`~photutils.aperture.aperture_photometry`
function with the data and the apertures. Note that
:func:`~photutils.aperture.aperture_photometry` assumes that the input
data have been background subtracted. For simplicity, we define the data
here as an array of all ones::

    >>> import numpy as np
    >>> from photutils.aperture import aperture_photometry
    >>> data = np.ones((100, 100))
    >>> phot_table = aperture_photometry(data, aperture)
    >>> phot_table['aperture_sum'].info.format = '%.8g'  # for consistent table output
    >>> print(phot_table)
     id xcenter ycenter aperture_sum
    --- ------- ------- ------------
      1    30.0    30.0    28.274334
      2    40.0    40.0    28.274334

This function returns the results of the photometry in an Astropy
`~astropy.table.QTable`.  In this example, the table has four columns,
named ``'id'``, ``'xcenter'``, ``'ycenter'``, and ``'aperture_sum'``.

Since all the data values are 1.0, the aperture sums are equal to the
area of a circle with a radius of 3::

    >>> print(np.pi * 3.0 ** 2)  # doctest: +FLOAT_CMP
    28.2743338823


.. _photutils-aperture-overlap:

Aperture and Pixel Overlap
--------------------------

The overlap of the aperture with the data pixels can be handled in
different ways.  The default method (``method='exact'``) calculates the
exact intersection of the aperture with each pixel.  The
other options, ``'center'`` and ``'subpixel'``, are faster, but with
the expense of less precision.  With ``'center'``, a pixel is
considered to be entirely in or out of the aperture depending on
whether its center is in or out of the aperture.  With ``'subpixel'``,
pixels are divided into a number of subpixels, which are in or out of
the aperture based on their centers.  For this method, the number of
subpixels needs to be set with the ``subpixels`` keyword.

This example uses the ``'subpixel'`` method where pixels are resampled
by a factor of 5 (``subpixels=5``) in each dimension::

    >>> phot_table = aperture_photometry(data, aperture, method='subpixel',
    ...                                  subpixels=5)
    >>> print(phot_table)  # doctest: +SKIP
     id xcenter ycenter aperture_sum
    --- ------- ------- ------------
      1    30.0    30.0        27.96
      2    40.0    40.0        27.96

Note that the results differ from the exact value of 28.274333 (see
above).

For the ``'subpixel'`` method, the default value is ``subpixels=5``,
meaning that each pixel is equally divided into 25 smaller pixels
(this is the method and subsampling factor used in `SourceExtractor
<https://sextractor.readthedocs.io/en/latest/>`_).

The precision can be increased by increasing ``subpixels``, but note
that computation time will be increased.


Aperture Photometry with Multiple Apertures at Each Position
------------------------------------------------------------

While the `~photutils.aperture.Aperture` objects support multiple
positions, they must have a fixed size and shape (e.g., radius and
orientation).

To perform photometry in multiple apertures at each position, one may
input a list of aperture objects to the
:func:`~photutils.aperture.aperture_photometry` function.  In this
case, the apertures must all have identical position(s).

Suppose that we wish to use three circular apertures, with radii of 3,
4, and 5 pixels, on each source::

    >>> radii = [3.0, 4.0, 5.0]
    >>> apertures = [CircularAperture(positions, r=r) for r in radii]
    >>> phot_table = aperture_photometry(data, apertures)
    >>> for col in phot_table.colnames:
    ...     phot_table[col].info.format = '%.8g'  # for consistent table output
    >>> print(phot_table)
     id xcenter ycenter aperture_sum_0 aperture_sum_1 aperture_sum_2
    --- ------- ------- -------------- -------------- --------------
      1      30      30      28.274334      50.265482      78.539816
      2      40      40      28.274334      50.265482      78.539816

For multiple apertures, the output table column names are appended
with the ``positions`` index.

Other apertures have multiple parameters specifying the aperture size
and orientation.  For example, for elliptical apertures, one must
specify ``a``, ``b``, and ``theta``::

    >>> from astropy.coordinates import Angle
    >>> from photutils.aperture import EllipticalAperture
    >>> a = 5.0
    >>> b = 3.0
    >>> theta = Angle(45, 'deg')
    >>> apertures = EllipticalAperture(positions, a, b, theta)
    >>> phot_table = aperture_photometry(data, apertures)
    >>> for col in phot_table.colnames:
    ...     phot_table[col].info.format = '%.8g'  # for consistent table output
    >>> print(phot_table)
     id xcenter ycenter aperture_sum
    --- ------- ------- ------------
      1      30      30     47.12389
      2      40      40     47.12389

Again, for multiple apertures one should input a list of aperture
objects, each with identical positions::

    >>> a = [5.0, 6.0, 7.0]
    >>> b = [3.0, 4.0, 5.0]
    >>> theta = Angle(45, 'deg')
    >>> apertures = [EllipticalAperture(positions, a=ai, b=bi, theta=theta)
    ...              for (ai, bi) in zip(a, b)]
    >>> phot_table = aperture_photometry(data, apertures)
    >>> for col in phot_table.colnames:
    ...     phot_table[col].info.format = '%.8g'  # for consistent table output
    >>> print(phot_table)
     id xcenter ycenter aperture_sum_0 aperture_sum_1 aperture_sum_2
    --- ------- ------- -------------- -------------- --------------
      1      30      30       47.12389      75.398224      109.95574
      2      40      40       47.12389      75.398224      109.95574


.. _photutils-aperture-stats:

Aperture Statistics
-------------------

The :class:`~photutils.aperture.ApertureStats` class can be
used to create a catalog of statistics and properties for
pixels within an aperture, including aperture photometry.
It can calculate many properties, including statistics
like :attr:`~photutils.aperture.ApertureStats.min`,
:attr:`~photutils.aperture.ApertureStats.max`,
:attr:`~photutils.aperture.ApertureStats.mean`,
:attr:`~photutils.aperture.ApertureStats.median`,
:attr:`~photutils.aperture.ApertureStats.std`,
:attr:`~photutils.aperture.ApertureStats.sum_aper_area`,
and :attr:`~photutils.aperture.ApertureStats.sum`. It
also can be used to calculate morphological properties
like :attr:`~photutils.aperture.ApertureStats.centroid`,
:attr:`~photutils.aperture.ApertureStats.fwhm`,
:attr:`~photutils.aperture.ApertureStats.semimajor_sigma`,
:attr:`~photutils.aperture.ApertureStats.semiminor_sigma`,
:attr:`~photutils.aperture.ApertureStats.orientation`, and
:attr:`~photutils.aperture.ApertureStats.eccentricity`. Please see
:class:`~photutils.aperture.ApertureStats` for the complete
list of properties that can be calculated. The properties can be
accessed using `~photutils.aperture.ApertureStats` attributes
or output to an Astropy `~astropy.table.QTable` using the
:meth:`~photutils.aperture.ApertureStats.to_table` method.

Most of the source properties are calculated using the "center"
:ref:`aperture-mask method <photutils-aperture-overlap>`, which gives
aperture weights of 0 or 1. This avoids the need to compute weighted
statistics --- the ``data`` pixel values are directly used.

The ``sum_method`` and ``subpixels`` keywords are used to determine
the aperture-mask method when calculating the sum-related properties:
``sum``, ``sum_error``, ``sum_aper_area``, ``data_sumcutout``, and
``error_sumcutout``. The default is ``sum_method='exact'``, which
produces exact aperture-weighted photometry.

The optional ``local_bkg`` keyword can be used to input the per-pixel
local background of each source, which will be subtracted before
computing the aperture statistics.

The optional ``sigma_clip`` keyword can be used to sigma clip the pixel
values before computing the source properties. This keyword could be
used, for example, to compute a sigma-clipped median of pixels in an
annulus aperture to estimate the local background level.

Here is a simple example using a circular aperture at one position.
Note that like :func:`~photutils.aperture.aperture_photometry`,
:class:`~photutils.aperture.ApertureStats` expects the input data to
be background subtracted. For simplicity, here we roughly estimate the
background as the sigma-clipped median value::

    >>> from astropy.stats import sigma_clipped_stats
    >>> from photutils.aperture import ApertureStats, CircularAperture
    >>> from photutils.datasets import make_4gaussians_image

    >>> data = make_4gaussians_image()
    >>> _, median, _ = sigma_clipped_stats(data, sigma=3.0)
    >>> data -= median  # subtract background from the data
    >>> aper = CircularAperture((150, 25), 8)
    >>> aperstats = ApertureStats(data, aper)  # doctest: +FLOAT_CMP
    >>> print(aperstats.xcentroid)  # doctest: +FLOAT_CMP
    149.98963482915323
    >>> print(aperstats.ycentroid)  # doctest: +FLOAT_CMP
    24.97165265459083
    >>> print(aperstats.centroid)  # doctest: +FLOAT_CMP
    [149.98963483  24.97165265]

    >>> print(aperstats.mean, aperstats.median, aperstats.std)  # doctest: +FLOAT_CMP
    42.38192194155781 26.53270189818481 39.19365538349298

    >>> print(aperstats.sum)  # doctest: +FLOAT_CMP
    8204.777345704442

Similar to `~photutils.aperture.aperture_photometry`, the input aperture
can have multiple positions::

    >>> aper2 = CircularAperture(((150, 25), (90, 60)), 10)
    >>> aperstats2 = ApertureStats(data, aper2)
    >>> print(aperstats2.xcentroid)  # doctest: +FLOAT_CMP
    [149.98175939  89.97793821]
    >>> print(aperstats2.sum)  # doctest: +FLOAT_CMP
    [ 8487.10695247 34963.45850824]
    >>> columns = ('id', 'mean', 'median', 'std', 'var', 'sum')
    >>> stats_table = aperstats2.to_table(columns)
    >>> for col in stats_table.colnames:
    ...     stats_table[col].info.format = '%.8g'  # for consistent table output

    >>> print(stats_table)  # doctest: +FLOAT_CMP
     id    mean     median     std       var       sum
    --- --------- --------- --------- --------- ---------
      1 27.915818 12.582676 36.628464 1341.6444  8487.107
      2 113.18737 112.11505 49.756626 2475.7218 34963.459

Each row of the table corresponds to a single aperture position (i.e., a
single source).


Background Subtraction
----------------------

Global Background Subtraction
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

:func:`~photutils.aperture.aperture_photometry` and
:class:`~photutils.aperture.ApertureStats` assume that the input data
have been background-subtracted. If ``bkg`` is a float value or an
array representing the background of the data (e.g., determined by
`~photutils.background.Background2D` or an external function), simply
subtract the background from the data::

    >>> phot_table = aperture_photometry(data - bkg, aperture)  # doctest: +SKIP

In the case of a constant global background, you can pass in the background
value using ``local_bkg`` in :class:`~photutils.aperture.ApertureStats`.
This would avoid reading an entire memory-mapped array into memory
beforehand, as would happen if you manually subtract the background as
shown above. So instead you could do this::

    >>> aperstats = ApertureStats(data, aperture, local_bkg=bkg)  # doctest: +SKIP

Local Background Subtraction
^^^^^^^^^^^^^^^^^^^^^^^^^^^^

One often wants to also estimate the local background around
each source using a nearby aperture or annulus aperture
surrounding each source. A simple method for doing this is to
use the :class:`~photutils.aperture.ApertureStats` class (see
:ref:`photutils-aperture-stats`) to compute the mean background level
within the background aperture. This class can also be used to calculate
more advanced statistics (e.g., a sigma-clipped median) within the
background aperture (e.g., a circular annulus). We show examples of both
below.

Let's start by generating a more realistic example dataset::

>>> from photutils.datasets import make_100gaussians_image
>>> data = make_100gaussians_image()

This artificial image has a known constant background level of 5. In the
following examples, we'll leave this global background in the image to
be estimated using local backgrounds.

For this example we perform the photometry for three sources in a
circular aperture with a radius of 5 pixels. The local background level
around each source is estimated using a circular annulus of inner radius
10 pixels and outer radius 15 pixels. Let's define the apertures::

    >>> from photutils.aperture import CircularAnnulus, CircularAperture
    >>> positions = [(145.1, 168.3), (84.5, 224.1), (48.3, 200.3)]
    >>> aperture = CircularAperture(positions, r=5)
    >>> annulus_aperture = CircularAnnulus(positions, r_in=10, r_out=15)

Now let's plot the circular apertures (white) and circular annulus
apertures (red) on a cutout from the image containing the three sources:

.. plot::

    import matplotlib.pyplot as plt
    from astropy.visualization import simple_norm
    from photutils.aperture import CircularAnnulus, CircularAperture
    from photutils.datasets import make_100gaussians_image

    data = make_100gaussians_image()
    positions = [(145.1, 168.3), (84.5, 224.1), (48.3, 200.3)]
    aperture = CircularAperture(positions, r=5)
    annulus_aperture = CircularAnnulus(positions, r_in=10, r_out=15)

    norm = simple_norm(data, 'sqrt', percent=99)
    plt.imshow(data, norm=norm, interpolation='nearest')
    plt.xlim(0, 170)
    plt.ylim(130, 250)

    ap_patches = aperture.plot(color='white', lw=2,
                               label='Photometry aperture')
    ann_patches = annulus_aperture.plot(color='red', lw=2,
                                        label='Background annulus')
    handles = (ap_patches[0], ann_patches[0])
    plt.legend(loc=(0.17, 0.05), facecolor='#458989', labelcolor='white',
               handles=handles, prop={'weight': 'bold', 'size': 11})


Simple mean within a circular annulus
"""""""""""""""""""""""""""""""""""""

We can use the :class:`~photutils.aperture.ApertureStats` class to
compute the mean background level within the annulus aperture at each
position::

    >>> from photutils.aperture import ApertureStats
    >>> aperstats = ApertureStats(data, annulus_aperture)
    >>> bkg_mean = aperstats.mean
    >>> print(bkg_mean)  # doctest: +FLOAT_CMP
    [4.99411764 5.1349344  4.86894665]

Now let's use :func:`~photutils.aperture.aperture_photometry` to perform
the photometry in the circular aperture (in the next example, we'll use
:class:`~photutils.aperture.ApertureStats` to perform the photometry)::

    >>> from photutils.aperture import aperture_photometry
    >>> phot_table = aperture_photometry(data, aperture)
    >>> for col in phot_table.colnames:
    ...     phot_table[col].info.format = '%.8g'  # for consistent table output
    >>> print(phot_table)
     id xcenter ycenter aperture_sum
    --- ------- ------- ------------
      1   145.1   168.3    1128.1245
      2    84.5   224.1      735.739
      3    48.3   200.3    1299.6341

The total background within the circular aperture is the mean local
per-pixel background times the circular aperture area. If you are
using the default "exact" aperture (see :ref:`aperture-mask methods
<photutils-aperture-overlap>`) and there are no masked pixels, the exact
analytical aperture area can be accessed via the aperture ``area``
attribute::

    >>> aperture.area  # doctest: +FLOAT_CMP
    78.53981633974483

However, in general you should use the
:meth:`photutils.aperture.PixelAperture.area_overlap` method where
a ``mask`` keyword can be input. This ensures you are using the
same area over which the photometry was performed. If using a
:class:`~photutils.aperture.SkyAperture`, you will first need to convert
it to a :class:`~photutils.aperture.PixelAperture`. Since we are not
using a mask, the results are identical::

    >>> aperture_area = aperture.area_overlap(data)
    >>> print(aperture_area)  # doctest: +FLOAT_CMP
    [78.53981634 78.53981634 78.53981634]

The total background within the circular aperture is then::

    >>> total_bkg = bkg_mean * aperture_area
    >>> print(total_bkg)  # doctest: +FLOAT_CMP
    [392.23708187 403.29680431 382.40617574]

Thus, the background-subtracted photometry is::

    >>> phot_bkgsub = phot_table['aperture_sum'] - total_bkg

Finally, let's add these as columns to the photometry table::

    >>> phot_table['total_bkg'] = total_bkg
    >>> phot_table['aperture_sum_bkgsub'] = phot_bkgsub
    >>> for col in phot_table.colnames:
    ...     phot_table[col].info.format = '%.8g'  # for consistent table output
    >>> print(phot_table)
     id xcenter ycenter aperture_sum total_bkg aperture_sum_bkgsub
    --- ------- ------- ------------ --------- -------------------
      1   145.1   168.3    1128.1245 392.23708           735.88739
      2    84.5   224.1      735.739  403.2968           332.44219
      3    48.3   200.3    1299.6341 382.40618           917.22792

Sigma-clipped median within a circular annulus
""""""""""""""""""""""""""""""""""""""""""""""

For this example, the local background level around each source is
estimated as the sigma-clipped median value within the circular annulus.
We'll use the :class:`~photutils.aperture.ApertureStats` class to
compute both the photometry (aperture sum) and the background level::

    >>> from astropy.stats import SigmaClip
    >>> sigclip = SigmaClip(sigma=3.0, maxiters=10)
    >>> aper_stats = ApertureStats(data, aperture, sigma_clip=None)
    >>> bkg_stats = ApertureStats(data, annulus_aperture, sigma_clip=sigclip)

The sigma-clipped median values in the background annulus apertures
are::

    >>> print(bkg_stats.median)  # doctest: +FLOAT_CMP
    [4.89374178 5.05655328 4.83268958]

The total background within the circular apertures is then the per-pixel
background level multiplied by the circular-aperture areas::

    >>> total_bkg = bkg_stats.median * aper_stats.sum_aper_area.value
    >>> print(total_bkg)  # doctest: +FLOAT_CMP
    [384.35358069 397.14076611 379.5585524 ]

Finally, the local background-subtracted sum within the circular
apertures is::

    >>> apersum_bkgsub = aper_stats.sum - total_bkg
    >>> print(apersum_bkgsub)  # doctest: +FLOAT_CMP
    [743.77088731 338.59823118 920.07553956]

Note that if you want to compute all the source properties (i.e., in
addition to only :attr:`~photutils.aperture.ApertureStats.sum`) on the
local-background-subtracted data, you may input the *per-pixel* local
background values to :class:`~photutils.aperture.ApertureStats` via the
``local_bkg`` keyword::

    >>> aper_stats_bkgsub = ApertureStats(data, aperture,
    ...                                   local_bkg=bkg_stats.median)
    >>> print(aper_stats_bkgsub.sum)  # doctest: +FLOAT_CMP
    [743.77088731 338.59823118 920.07553956]

Note these background-subtracted values are the same as those above.


.. _error_estimation:

Aperture Photometry Error Estimation
------------------------------------

If and only if the ``error`` keyword is input to
:func:`~photutils.aperture.aperture_photometry`, the returned table
will include a ``'aperture_sum_err'`` column in addition to
``'aperture_sum'``.  ``'aperture_sum_err'`` provides the propagated
uncertainty associated with ``'aperture_sum'``.

For example, suppose we have previously calculated the error on each
pixel value and saved it in the array ``error``::

    >>> positions = [(30.0, 30.0), (40.0, 40.0)]
    >>> aperture = CircularAperture(positions, r=3.0)
    >>> data = np.ones((100, 100))
    >>> error = 0.1 * data

    >>> phot_table = aperture_photometry(data, aperture, error=error)
    >>> for col in phot_table.colnames:
    ...     phot_table[col].info.format = '%.8g'  # for consistent table output
    >>> print(phot_table)
     id xcenter ycenter aperture_sum aperture_sum_err
    --- ------- ------- ------------ ----------------
      1      30      30    28.274334       0.53173616
      2      40      40    28.274334       0.53173616

``'aperture_sum_err'`` values are given by:

.. math:: \Delta F = \sqrt{\sum_{i \in A}
          \sigma_{\mathrm{tot}, i}^2}

where :math:`A` are the non-masked pixels in the aperture, and
:math:`\sigma_{\mathrm{tot}, i}` is the input ``error`` array.

In the example above, it is assumed that the ``error`` keyword
specifies the *total* error --- either it includes Poisson noise
due to individual sources or such noise is irrelevant. However, it
is often the case that one has calculated a smooth "background-only
error" array, which by design doesn't include increased noise on bright
pixels. To include Poisson noise from the sources, we can use the
:func:`~photutils.utils.calc_total_error` function.

Let's assume we have a background-only image called ``bkg_error``.
If our data are in units of electrons/s, we would use the exposure
time as the effective gain::

    >>> from photutils.utils import calc_total_error
    >>> effective_gain = 500  # seconds
    >>> error = calc_total_error(data, bkg_error, effective_gain)  # doctest: +SKIP
    >>> phot_table = aperture_photometry(data - bkg, aperture, error=error)  # doctest: +SKIP


Aperture Photometry with Pixel Masking
--------------------------------------

Pixels can be ignored/excluded (e.g., bad pixels) from the aperture
photometry by providing an image mask via the ``mask`` keyword::

    >>> data = np.ones((5, 5))
    >>> aperture = CircularAperture((2, 2), 2.0)
    >>> mask = np.zeros(data.shape, dtype=bool)
    >>> data[2, 2] = 100.0  # bad pixel
    >>> mask[2, 2] = True
    >>> t1 = aperture_photometry(data, aperture, mask=mask)
    >>> t1['aperture_sum'].info.format = '%.8g'  # for consistent table output
    >>> print(t1['aperture_sum'])
    aperture_sum
    ------------
       11.566371

The result is very different if a ``mask`` image is not provided::

    >>> t2 = aperture_photometry(data, aperture)
    >>> t2['aperture_sum'].info.format = '%.8g'  # for consistent table output
    >>> print(t2['aperture_sum'])
    aperture_sum
    ------------
       111.56637


Aperture Photometry Using Sky Coordinates
-----------------------------------------

As mentioned in :ref:`creating-aperture-objects`, performing
photometry using apertures defined in sky coordinates simply requires
defining a "sky" aperture at positions defined by a
:class:`~astropy.coordinates.SkyCoord` object.  Here we show an
example of photometry on real data using a
`~photutils.aperture.SkyCircularAperture`.

We start by loading a Spitzer 4.5 micron image of a region of the
Galactic plane::

    >>> import astropy.units as u
    >>> from astropy.wcs import WCS
    >>> from photutils.datasets import load_spitzer_catalog, load_spitzer_image
    >>> hdu = load_spitzer_image()  # doctest: +REMOTE_DATA
    >>> data = u.Quantity(hdu.data, unit=hdu.header['BUNIT'])  # doctest: +REMOTE_DATA
    >>> wcs = WCS(hdu.header)  # doctest: +REMOTE_DATA
    >>> catalog = load_spitzer_catalog()  # doctest: +REMOTE_DATA

The catalog contains (among other things) the Galactic coordinates of
the sources in the image as well as the PSF-fitted fluxes from the
official Spitzer data reduction.  We define the apertures positions
based on the existing catalog positions::

    >>> positions = SkyCoord(catalog['l'], catalog['b'], frame='galactic')  # doctest: +REMOTE_DATA
    >>> aperture = SkyCircularAperture(positions, r=4.8 * u.arcsec)  # doctest: +REMOTE_DATA

Now perform the photometry in these apertures on the ``data``.  The
``wcs`` object contains the WCS transformation of the image obtained
from the FITS header.  It includes the coordinate frame of the image
and the projection from sky to pixel coordinates.  The
`~photutils.aperture.aperture_photometry` function uses the WCS
information to automatically convert the apertures defined in sky
coordinates into pixel coordinates::

    >>> phot_table = aperture_photometry(data, aperture, wcs=wcs)  # doctest: +REMOTE_DATA

The Spitzer catalog also contains the official fluxes for the sources,
so we can compare to our fluxes.  Because the Spitzer catalog fluxes
are in units of mJy and the data are in units of MJy/sr, we need to
convert units before comparing the results.  The image data have a
pixel scale of 1.2 arcsec/pixel.

    >>> import astropy.units as u
    >>> factor = (1.2 * u.arcsec) ** 2 / u.pixel
    >>> fluxes_catalog = catalog['f4_5']  # doctest: +REMOTE_DATA
    >>> converted_aperture_sum = (phot_table['aperture_sum'] *
    ...                           factor).to(u.mJy / u.pixel)  # doctest: +REMOTE_DATA

Finally, we can plot the comparison of the photometry:

.. doctest-skip::

    >>> import matplotlib.pyplot as plt
    >>> plt.scatter(fluxes_catalog, converted_aperture_sum.value)
    >>> plt.xlabel('Spitzer catalog PSF-fit fluxes ')
    >>> plt.ylabel('Aperture photometry fluxes')

.. plot::

    import matplotlib.pyplot as plt
    from astropy import units as u
    from astropy.coordinates import SkyCoord
    from astropy.wcs import WCS
    from photutils.aperture import SkyCircularAperture, aperture_photometry
    from photutils.datasets import load_spitzer_catalog, load_spitzer_image

    # Load dataset
    hdu = load_spitzer_image()
    data = u.Quantity(hdu.data, unit=hdu.header['BUNIT'])
    wcs = WCS(hdu.header)
    catalog = load_spitzer_catalog()

    # Set up apertures
    positions = SkyCoord(catalog['l'], catalog['b'], frame='galactic')
    aperture = SkyCircularAperture(positions, r=4.8 * u.arcsec)
    phot_table = aperture_photometry(data, aperture, wcs=wcs)

    # Convert to correct units
    factor = (1.2 * u.arcsec) ** 2 / u.pixel
    fluxes_catalog = catalog['f4_5']
    converted_aperture_sum = (phot_table['aperture_sum']
                              * factor).to(u.mJy / u.pixel)

    # Plot
    plt.scatter(fluxes_catalog, converted_aperture_sum.value)
    plt.xlabel('Spitzer catalog PSF-fit fluxes ')
    plt.ylabel('Aperture photometry fluxes')
    plt.plot([40, 100, 450], [40, 100, 450], color='black', lw=2)

Despite using different methods, the two catalogs are in good
agreement.  The aperture photometry fluxes are based on a circular
aperture with a radius of 4.8 arcsec.  The Spitzer catalog fluxes were
computed using PSF photometry.  Therefore, differences are expected
between the two measurements.


Aperture Masks
--------------

All `~photutils.aperture.PixelAperture` objects have a
:meth:`~photutils.aperture.PixelAperture.to_mask` method that returns
a `~photutils.aperture.ApertureMask` object (for a single aperture
position) or a list of `~photutils.aperture.ApertureMask` objects, one
for each aperture position. The `~photutils.aperture.ApertureMask`
object contains a cutout of the aperture mask weights and a
`~photutils.aperture.BoundingBox` object that provides the bounding box
where the mask is to be applied.

Let's start by creating a circular-annulus aperture::

    >>> from photutils.aperture import CircularAnnulus
    >>> from photutils.datasets import make_100gaussians_image
    >>> data = make_100gaussians_image()
    >>> positions = [(145.1, 168.3), (84.5, 224.1), (48.3, 200.3)]
    >>> aperture = CircularAnnulus(positions, r_in=10, r_out=15)

Now let's create a list of `~photutils.aperture.ApertureMask` objects
using the :meth:`~photutils.aperture.PixelAperture.to_mask` method using
the aperture mask "exact" method::

    >>> masks = aperture.to_mask(method='exact')

Let's plot the first aperture mask:

.. doctest-skip::

    >>> import matplotlib.pyplot as plt
    >>> plt.imshow(masks[0])

.. plot::

    import matplotlib.pyplot as plt
    from photutils.aperture import CircularAnnulus, CircularAperture
    from photutils.datasets import make_100gaussians_image

    data = make_100gaussians_image()
    positions = [(145.1, 168.3), (84.5, 224.1), (48.3, 200.3)]
    aperture = CircularAperture(positions, r=5)
    annulus_aperture = CircularAnnulus(positions, r_in=10, r_out=15)
    masks = annulus_aperture.to_mask(method='exact')
    plt.imshow(masks[0])

Let's now use the "center" aperture mask method and plot the resulting
aperture mask:

.. doctest-skip::

    >>> masks2 = aperture.to_mask(method='center')
    >>> plt.imshow(masks2[0])

.. plot::

    import matplotlib.pyplot as plt
    from photutils.aperture import CircularAnnulus, CircularAperture
    from photutils.datasets import make_100gaussians_image

    data = make_100gaussians_image()
    positions = [(145.1, 168.3), (84.5, 224.1), (48.3, 200.3)]
    aperture = CircularAperture(positions, r=5)
    annulus_aperture = CircularAnnulus(positions, r_in=10, r_out=15)
    masks2 = annulus_aperture.to_mask(method='center')
    plt.imshow(masks2[0])

We can also create an aperture mask-weighted cutout from the data,
properly handling the cases of partial or no overlap of the aperture
mask with the data. Let's plot the aperture mask weights (using the mask
generated above with the "exact" method) multiplied with the data:

.. doctest-skip::

    >>> data_weighted = masks[0].multiply(data)
    >>> plt.imshow(data_weighted)

.. plot::

    import matplotlib.pyplot as plt
    from photutils.aperture import CircularAnnulus, CircularAperture
    from photutils.datasets import make_100gaussians_image

    data = make_100gaussians_image()
    positions = [(145.1, 168.3), (84.5, 224.1), (48.3, 200.3)]
    aperture = CircularAperture(positions, r=5)
    annulus_aperture = CircularAnnulus(positions, r_in=10, r_out=15)
    masks = annulus_aperture.to_mask(method='exact')
    plt.imshow(masks[0].multiply(data))

To get a 1D `~numpy.ndarray` of the non-zero weighted data values, use
the :meth:`~photutils.aperture.ApertureMask.get_values` method:

.. doctest-skip::

    >>> data_weighted_1d = masks[0].get_values(data)

The :class:`~photutils.aperture.ApertureMask` class also provides a
:meth:`~photutils.aperture.ApertureMask.to_image` method to obtain
an image of the aperture mask in a 2D array of the given shape and a
:meth:`~photutils.aperture.ApertureMask.cutout` method to create a
cutout from the input data over the aperture mask bounding box. Both of
these methods properly handle the cases of partial or no overlap of the
aperture mask with the data.


.. _custom-apertures:

Defining Your Own Custom Apertures
----------------------------------

The :func:`~photutils.aperture.aperture_photometry` function can
perform aperture photometry in arbitrary apertures.  This function
accepts any `~photutils.aperture.Aperture`-derived objects, such as
`~photutils.aperture.CircularAperture`.  This makes it simple to
extend functionality: a new type of aperture photometry simply
requires the definition of a new `~photutils.aperture.Aperture`
subclass.

All `~photutils.aperture.PixelAperture` subclasses must define
a ``bounding_boxes`` property and ``to_mask()`` and ``plot()``
methods. They may also optionally define an ``area`` property. All
`~photutils.aperture.SkyAperture` subclasses must only implement a
``to_pixel()`` method.

* ``bounding_boxes``:  The minimal bounding box for the aperture.
  If the aperture is scalar, then a single
  `~photutils.aperture.BoundingBox` is returned. Otherwise, a list of
  `~photutils.aperture.BoundingBox` is returned.

* ``area``: An optional property defining the exact analytical
  area (in pixels**2) of the aperture.

* ``to_mask()``: Return a mask for the aperture. If the aperture is
  scalar, then a single `~photutils.aperture.ApertureMask` is returned.
  Otherwise, a list of `~photutils.aperture.ApertureMask` is returned.

* ``plot()``: A method to plot the aperture on a `matplotlib.axes.Axes`
  instance.


API Reference
-------------

:doc:`../reference/aperture_api`
