Digital Aperture Photometry

ASTR 3010

Lecture 10

Textbook 9.5

Photometry• How bright is the object?

• In an object frame…

measured brightness = source + background

background (or “sky”) : all unwanted light not originated from the source foreground + background scattered light glow of the atmosphere radiation from the telescope, etc.

In this lecture, we will focus only on the tasks of separating signals from background and getting uncertainty of the measurement.

Digital Apertures• Aperture : a circular area centered on the centroid of the object

Three computations in the aperture photometry:1. Add up all pixel values inside the aperture: take into account of fractional

pixels (A is a fraction of pixel’s area inside the aperture)

2. Estimate the value of the sky emission per pixel

3. Subtract the sky emission from the total count.A=1.0

A=0.7A=0.05

When does the Aperture Photometry fails?• when star images (i.e., PSFs) seriously overlap…

• PSF fitting photometry is better in this case! fitting a PSF to each star imageand the source brightness will be the summation of“scaled” PSF pixel values.

PSF fitting versus Aperture photometry• PSF fitting ≈ infinite aperture size

PSF fitAperture

background level

How do we choose the right aperture size?

Gaussian + constant

Best aperture size?

Large Aperture• include more light larger S• more contamination• added noise from the sky lower S/N

Small Aperture• less contamination• losing source signal lower S/N

Good Aperture Size• Typical choice of apertures: 0.75 to 4 times FWHM• Best S/N about 2 times the HWHM (or 1 FWHM)

radial profile ofthe object (i.e., 1D PSF)

Python HW #3 (x2 weight)• Using one of FITS files from HW#2, create a

Python script that generates a radial profile.

Measuring Sky• Sky measurement :o Need to measure the sky level at the location of the source impossible.o So, we assume that the sky does not change with location (i.e., homogeneous

sky).

Measuring Sky• Typically measuring the sky level from a sky annuluso inner sky radius : as small as possible yet large enough away from the sourceo outer sky radius : large enough to include significant # of pixels in statistics, but

not too far from the sourceo Not the mean pixel value:

• Or from a dedicated sky regionmean median mode

Measuring Sky• What about the case like Super Nova embedded in a rapidly varying

background?

How about non-variable objects in the non-uniform sky?

How about non-variable objects in the non-uniform sky?

1. Find all sources with PSF fitting2. Remove detected sources 3. heavily smooth the residual image4. subtract the smoothed residual from the source image5. do photometry

original image source subtracted image

Bright sources are not perfectly subtracted. Why?

Signal and noise in an aperture

see textbook pp313-317 for a detailed derivation

CCD equation

log (time)

log (SNR)

bright source

sky-limited faint st

arreadout noise limited

faint star

In summary…

Important Concepts• CCD equation (consult textbook!)• Aperture photometry• PSF fitting photometry

Important Terms• photon-noise limited• sky-limited• readout noise limited

Chapter/sections covered in this lecture : 9.5