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LSST Exposure Calculations

LSST Exposure Calculations

The online exposure calculator is here. This page has useful formulae for normalization.

Sources

To get conversions from AB magnitude to total flux in electrons/sec, chose a point source with AB = 24.0 (this is the default). Change the exposure time from 15s to 1s. Change the "analysis method" to a 100" software aperture and set the "optimal filter" to not weighted. These are not default settings and should give 100% of the signal in the aperture.

The "Total signal per exposure" gives the flux normalization as a function of the selected band, spectral type, and redshift:

Band

Type

z

Flux24/15s

Flux24/1s

r

Elliptical

0.0

807.37

53.82

0.5

821.66

54.77

1.0

813.30

54.55

Spiral

0.0

813.35

54.22

0.5

806.89

53.79

1.0

809.30

53.95

i

Elliptical

0.0

710.93

47.39

0.5

710.62

47.37

1.0

711.29

47.41

Spiral

0.0

711.50

47.43

0.5

713.93

47.59

1.0

714.35

47.62

Since these results are fairly insensitive to type and redshift, adopt fiducial values of 810 (r) and 711 (i). The scaling with AB is 10-0.4(AB-24).

Noise

Use an unweighted aperture with diameter 2*sqrt(pi/4) = 2.25676 so that the aperture size is exactly 100 pixels, then with default parameters in i-band:

  • "Background noise" = 319.48 ADU in 100 pix which implies 319.482/100 = 1020 ADU/pix of sky. Compare with 711*10-0.4(20.2-24) = 942. Results do not agree exactly since the sky and galaxies different spectra.

  • "Dark current noise" = 1.5 ADU in 100 pix which implies 1.52/100 = 0.0225 ADU/pix of dark current in a 15s exposure = 0.0015 ADU/s/pix.

  • "Readout noise" = 50 ADU in 100 pix which implies 5 ADU/pix.

Sky

Run with different bands selected to get the mag/arcsec2 and BG noise columns below, then calculate:

  • ADU/pix = (BG noise)2/100 = sky level, use sqrt(sky/n) to get sky noise in average of n exposures

  • Flux24 = (ADU/pix) 10+0.4(mag-24)/(0.2 arcsec/pix)2, use to calculate sky level for different assumed surface brightness

  • Visit Noise = sqrt(sky/2)
  • Stack Noise = sqrt(sky/(2*nvisits))
  • Last 2 columns from LSST Book Tables 1.1 and 3.2

Band

mag/arcsec2

BG Noise /100pix

ADU/pix

Flux24

Visit Noise

Stack Noise

Visits/Stack

mag/arcsec2(nom)

u

22.30521

92.04

84.7136

444.608

6.50821

0.77788

70

21.8

g

21.71681

197.69

390.813

1192.98

13.9788

1.39788

100

22.0

r

21.20972

215.86

465.955

891.605

15.2636

1.00645

230

21.3

i

20.21425

319.48

1020.67

780.778

22.5906

1.48958

230

20.0

z

19.03285

446.95

1997.64

514.752

31.6041

2.23475

200

19.1

y

17.92805

329.74

1087.28

280.171

23.3161

1.64870

200

17.5

Signal to Noise

Since the online ETC only supports Gaussian profiles specified by the fwhm, use r(half) = sqrt(log(4))*sigma, fwhm = 2*sqrt(2*log(2))*sigma, which gives fwhm = 2*r(half) (!). Assume elliptical galaxy spectrum.

Source

i(AB)

ADU/exp

r(half)

fwhm

SN/exp

SN/stack

1

26.0

112.67

0.75"

1.5"

0.66

13.05

2

26.5

71.09

0.50"

1.0"

0.42

8.24

DES / LSST Cross Calibration

DES has measured their "zero points" using the C26202 standard star, which has spectral type G, in the science verification data (from an email from Klaus H):

Band

Zpt(e-)

Zpt(e-)/Expected

g

591

1.00

r

635

1.15

i

638

1.11

z

477

1.11

Y

206

1.33

The zeropoint is defined as the number of electrons/sec collected from an AB=20 mag source.