Today:   Calculating CCD gain              Photometry                         Aperture vs. PSF Photometry                          Photometric Filters                         Effects of Atmosphere – Airmass                          Differential vs. Absolute Photometry                         Photometry of Extended Sources                         SNR and Exposure Time

                  Reading: Ch. 7 (pp. 125–132), 10

Astronomy 101                                          Lecture # 6

PhotometryDirect measure of integrated flux (counts per unit time 

per unit area ) received from a celestial target.●

●

●

    F = specific flux from a target     S = transmission function that describes

           ­ Filter passband           ­ CCD response           ­ Atmospheric transmission  

F=∫0

∞

F⋅S

d

Astronomy 101                                          Lecture # 6

Magnitudes and Fluxes

m1−m2=2.5 log10 F2

F1 ● Bolometric  Magnitude:●

●

●

●Color Magnitude: mV ,1−mV ,2=2.5 log10 FV , 2

FV ,1

Astronomy 101                                          Lecture # 6

How do we measure F?

●Main Methods:● 1. Aperture photometry●    2. Point­spread­function (PSF) ●           fitting

F=∫0

∞

F⋅S

d

Astronomy 101                                          Lecture # 6

Aperture Photometry

Main stellar     aperture

Astronomy 101                                          Lecture # 6

Background   annulus

m=C−2.5 log10 [ N star−N sky ]

PSF PhotometryStars too close together to do a simple aperture count.

Need to do PSF fitting: modeling the radial “shape” of each stellar image.

Astronomy 101                                          Lecture # 6

PSF PhotometryAiry Pattern: Ideal PSF

Astronomy 101                                          Lecture # 6

Slide Credit: Don Hoard

PSF Photometry

Real PSFs are considerably more complicated.

Astronomy 101                                          Lecture # 6

Astronomy 101                                          Lecture # 6

PSF Photometry

Real PSFs are considerably more complicated.

Example: Hubble images of quasars from Bahcall et al.

Slide Credit: Don Hoard

Astronomy 101                                          Lecture # 6

PSF Photometry

Slide Credit: Don Hoard

How do we determine S?

●Main Contributions:●      1. CCD response●      2. Filter bandpass●      3. Atmospheric Transmission

F=∫0

∞

F⋅S

d

Astronomy 101                                          Lecture # 6

CCD Quantum Efficiency

●From Apogee Instruments

Astronomy 101                                          Lecture # 6

Astronomy 101                                          Lecture # 6

Wide­Band Photometric Filters

Astronomy 101                                          Lecture # 6

Medium­Band Filters

Astronomy 101                                          Lecture # 6

Narrow­Band Filters

Atmospheric Transmission Astronomy 101                                          Lecture # 6

mobs=mstar 0 sec

Astronomy 101                                          Lecture # 6

Airmass= sec−0.0018167 sec−1−0.002875 sec−12−0.0008083 sec −13

A better approximation:  

Airmass Correction

How do we invert this equationto determine F

?

●Main Methods:● 1. Differential Photometry●    2. Absolute Photometry

F=∫0

∞

F⋅S

d

Astronomy 101                                          Lecture # 6

●Converting from instrumental magnitude to apparent   magnitude.

Astronomy 101                                          Lecture # 6

m1= I1−I 2m2

mi=calibrated magnitude of star iI i=instrumental magnitude of star i

Differential Photometry

Slide Credit: Don Hoard

Astronomy 101                                          Lecture # 6Absolute Photometry

What if there are no calibrated stars in the same CCD frame as your target?

● Make separate observations of standard stars on the same night. Examples of star catalogs include

Landolt 1992, AJ, 104, 340 Stetson http://cadcwww.hia.nrc.ca/cadcbin/wdb/astrocat/stetson/query ● Standard star observations must span a range of airmasses (typically 1–

2.5) and a range of colors the same as that of science targets. ● Obtain observations of standard stars and targets in at least 2 filters. ● Use standard star observations to derive coefficients for the

“transformation equations” which can then be utilized to calibrate instrumental magnitudes of science targets.

Slide Credit: Don Hoard

Astronomy 101                                          Lecture # 6

Transformation Equations

B – V = (b–v) Tbv + Kbv X + Zbv

 V – R = (v–r) Tvr + Kvr X + Zvr

 R – I = (r–i) Tri + Kri X + Zri

 V – I = (v–i) Tvi + Kvi X + Zvi

 R = r Tr + Kr X + Zr

 V = v Tv + Kv X + Zv

B, V, R, I = calibrated magnitudesb, v, r, i = instrumental magnitudesX = airmassT = color transformation coefficientsK = atmospheric extinction coefficientsZ = zero point corrections

Use IRAF package digiphot.photcal to solve for transformation coefficients and apply calibration to data.

Slide Credit: Don Hoard

Magnitude to Flux Conversion

FX = f

, X 10−m

X/2.5

FX=FX W X

Specific flux in the center of band X:

Total flux in band X:

Astronomy 101                                          Lecture # 6

SNR and Exposure Time

SNR=SN=

N star

N starnN skyN DN R2

Poisson Noise Limited:

Background Limited:

SN≈

N star

N star

= N star∝ F star t

SN≈

N star

n N sky

∝Fstar

Fsky

t