Aperture Photometry

Counting a star’s photons

A star, no matter how nearby or distant, is a point source: its light falls onto a detector spread out only by the blurring of Earth’s atmosphere and the telescope optics. That blurred blob — the point spread function (PSF) — typically spans a few arcseconds from the ground, sampled across maybe a dozen pixels on a CCD. To measure how bright the star is, you simply need to add up all the light in that blob. Aperture photometry does exactly that: draw a circle (the aperture) around the star and sum every pixel value inside it.

The catch is that the pixels inside the aperture do not record only starlight. The night sky itself glows — from atmospheric airglow, scattered moonlight, zodiacal light, and the unresolved haze of faint distant stars and galaxies — and the detector adds its own bias and dark current. Every pixel in your aperture therefore contains a baseline of sky background that must be removed before the number means anything.

The annulus: measuring what to subtract

To estimate that background, aperture photometry samples the sky in a concentric ring called the annulus (or sky annulus), drawn well outside the star’s light profile — far enough that the wings of the PSF no longer contribute. Within the annulus you compute a robust per-pixel sky value, and crucially you take the median rather than the mean. The median rejects outliers: a cosmic ray hit, a faint neighboring star, or a hot pixel will skew an average but barely move a median. That per-pixel sky level is then multiplied by the number of pixels in the aperture and subtracted:

net_flux = Σ(pixels in aperture) − N_aperture × sky_per_pixel

A typical configuration on a well-sampled image might use an aperture radius of 4 pixels, an inner annulus radius of 8 pixels, and an outer radius of 12 pixels. The annulus is deliberately set a few pixels beyond where the star’s light fades into the noise, so it samples genuinely empty sky.

Choosing the radius: a noise trade-off

How big should the aperture be? This is the central judgment call, and it is a genuine trade-off:

• Too small, and you clip the wings of the PSF, throwing away real starlight and producing a systematically faint, scatter-prone measurement.
• Too large, and although you capture essentially all the star’s light, you also enclose far more sky pixels — and each one contributes shot noise. For a faint star, the noise from a huge aperture full of sky can swamp the tiny signal you are trying to measure.

The signal-to-noise ratio peaks at an intermediate radius. For faint, background-limited sources this optimum sits at roughly 1 to 1.5 times the FWHM of the PSF. For bright, photon-limited stars where the star’s own shot noise dominates, a larger aperture of 3–5 FWHM is better because it captures nearly all the flux with little noise penalty. Observers often build a curve of growth — measured flux versus aperture radius — to find where the flux plateaus and choose the radius accordingly.

Aperture radius trade-off for a point source (illustrative)

Aperture radius	Fraction of light captured	Sky pixels enclosed	Best for
0.7 × FWHM	~60–70%	Few	Very faint, crowded
1.0 × FWHM	~80%	Moderate	Faint sources (max S/N)
1.5 × FWHM	~90%	More	Typical faint targets
3 × FWHM	~99%	Many	Bright, photon-limited
5 × FWHM	~100%	Very many	Aperture-correction reference

From flux to magnitude

The net flux, divided by the exposure time, gives an instrumental magnitude:

m_inst = −2.5 × log10(net_flux / exposure_time)

The factor of 2.5 and the logarithm come from the Pogson definition of the magnitude scale, fixed in 1856 to match the ancient naked-eye system: a difference of exactly 5 magnitudes corresponds to a factor of 100 in flux, so each single magnitude is a factor of 100^1/5 ≈ 2.512. A brighter star has a smaller magnitude — a quirk inherited from Hipparchus ranking the brightest stars as "first magnitude."

To turn the instrumental magnitude into a calibrated magnitude on a standard system, you add a zero point measured from standard stars of known brightness, correct for atmospheric extinction (which grows with airmass as light passes through more atmosphere near the horizon), and apply small color terms that account for filter mismatch:

m_cal = m_inst + ZP − k × airmass + color_term

Finally, because any finite aperture misses a little light in the PSF wings, an aperture correction is applied: the offset between the small working aperture and a very large reference aperture, measured on bright isolated stars. This recovers the total magnitude while keeping the favorable noise of the small radius.

Where it works and where it breaks

Aperture photometry is the default for measuring stars in uncrowded fields: variable stars, exoplanet transits, asteroids, supernova light curves. Space missions exploit it ruthlessly — Kepler measured transiting planets to about 0.1 millimagnitude precision on quiet stars by summing pixels in carefully chosen apertures with no atmosphere to blur the PSF.

It breaks down when sources overlap. In the core of a globular cluster, stars are packed so tightly that any aperture encloses several of them, and even the sky annulus is contaminated by neighbors — there is no empty sky to sample. Extended objects like galaxies present a similar problem: their light spills past any reasonable circle. In these regimes astronomers turn to PSF-fitting photometry (the classic DAOPHOT approach), which models the shape of the point spread function and fits it to every star simultaneously, deblending overlapping sources that a simple circle cannot separate.

Aperture photometry vs. PSF-fitting photometry

Aspect	Aperture photometry	PSF-fitting photometry
Best field	Sparse, uncrowded	Crowded, blended sources
Sky handling	Annulus median subtraction	Fit as part of the model
Assumptions	Isolated point source	Known/modeled PSF shape
Speed & simplicity	Fast, transparent	Heavier, model-dependent
Typical tool	photutils, SExtractor	DAOPHOT, ALLSTAR