Photometric Calibration of Haleakala Images


Observations

There were 6 exposures taken within a time interval of approximately 35 minutes. The first 2 exposures were of a nearby SDSS field in two different optical bands, for photometric-calibration purposes. The next 2 exposures were of our BRC field in the two same optical bands. The last 2 exposures were again of the nearby SDSS field in the two optical bands, also for photometric-calibration purposes.

Obs. type FITS file Obs. date Exp. time (s) Filter RA Dec Airmass
Calibration frame d_e_20111020_23_1_1_1.fits 2011-10-21T06:13:04.196 360 SDSS-R 20:39:56.903 58:1:39.98 1.2895820
Calibration frame d_e_20111020_24_1_1_1.fits 2011-10-21T06:20:10.461 240 SDSS-I 20:39:56.896 58:1:40.02 1.2972110
BRC-data frame d_e_20111020_27_1_1_1.fits 2011-10-21T06:32:04.704 120 SDSS-R 21:33:30.003 58:4:44.88 1.2655200
BRC-data frame d_e_20111020_28_1_1_1.fits 2011-10-21T06:35:11.001 120 SDSS-I 21:33:30.004 58:4:44.89 1.2670150
Calibration frame d_e_20111020_31_1_1_1.fits 2011-10-21T06:44:57.843 120 SDSS-R 20:39:56.902 58:1:39.99 1.3305270
Calibration frame d_e_20111020_32_1_1_1.fits 2011-10-21T06:47:57.704 120 SDSS-I 20:39:56.898 58:1:40.01 1.3352990

Analysis

Our goal is to photometrically calibrate the 2 BRC exposures. To do that, we match sources extracted from the calibration exposures to photometrically calibrated SDSS sources. The resulting exposure-dependent photometric zero point, denoted by ZP(t), is the amount of magnitude that will be added to the instrumental magnitudes to yield calibrated apparent magnitudes.

Since the exposure times vary somewhat with observation, we must normalize the exposures by their exposure times. When 2.5 log10(exptime) is subtracted from the respective ZP(t), where t is the time at the start of the exposure, the results are exposure-independent photometric zero points, denoted by ZP(X), that vary only with airmass, X, as explained below.

Airmass, X, is related to the angle from zenith of the telescope boresight, and is a measure of the optical attentuation by air. At zenith, X = 1.0; the airmass increases as the telescope points farther from zenith. All 6 of our exposures have slightly different airmasses, since the Earth's rotation moves the telescope away from the observed calibration and BRC fields (in these cases, X increases with each revisit of a given field). Thus, small variations in ZP(X) are expected as a function airmass. If we assume the functional relationship is linear, then we have enough data to solve for the function ZP(X).

The photometric calibration results below, which represent our first photometric-calibration attempt, ignore the uncertainties in the measured instrumental magnitudes and the uncertainties in the SDSS calibrated magnitudes. We may modify our calibration results later if we decided that it is important to include the uncertainties in our analysis.

The instrumental magnitudes were computed by Aperture Photometry Tool (APT) with the parameters listed below. Note we made use of APT's new source-list creation tool, which is an upgrade in version 2.0.0, but this version is not yet generally available.

Parameter Value
Centroid radius 5 pixels
Aperture radius 8 pixels
Inner-sky radius 9 pixels
Outer-sky radius 15 pixels
Source algorithm Model 0
Sky algorithm Model B
Calculation step size 0.01 pixels
Source detection threshold 2.0 sigma
Source minimum size 19 pixels
Source maximum size 299 pixels

The sources extracted from the Haleakala images by APT are given in the source lists below, which are source locations in terms of pixel coordinates (not equatorial coordinates). Note that we use only the source lists associated with the calibration frames for the photometric calibration; however, for completeness, source lists for all 6 data frames were computed.

APT.calibrator.images.23.source.list.tbl
APT.calibrator.images.24.source.list.tbl
APT.BRC.data.images.27.source.list.tbl
APT.BRC.data.images.28.source.list.tbl
APT.calibrator.images.31.source.list.tbl
APT.calibrator.images.32.source.list.tbl

The source matching radius is 1 arcsecond. There were 314 SDSS calibration stars available after suitably selecting them from reasonble ranges of SDSS-catalog properties and flags. Approximately 3 times as many APT source extractions for matching with the calibrated SDSS sources. The exposure-dependent photometric zero point for each calibration frame was computed after rejecting matches with magnitude differences outside the [-0.3, 0.3] magnitude range.

Preliminary calibration results for SDSS-R band:

Calibration FITS file Exp. time (s) Filter Airmass No. matches ZP(t) (mag) ZP(X) (mag) Color-magnitude plot
d_e_20111020_23_1_1_1.fits 360 SDSS-R 1.2895820 182 28.914 22.52324375

average = 0.000111776 mag     sigma = 0.051739896 mag
d_e_20111020_31_1_1_1.fits 120 SDSS-R 1.3305270 177 27.6913 22.49334688

average = -4.44695E-05 mag     sigma = 0.062284187 mag

Preliminary calibration results for SDSS-I band:

Calibration FITS file Exp. time (s) Filter Airmass No. matches ZP(t) (mag) ZP(X) (mag) Color-magnitude plot
d_e_20111020_24_1_1_1.fits 240 SDSS-I 1.2972110 186 28.324 22.3734719

average = -6.94525E-05 mag     sigma = 0.044836308 mag
d_e_20111020_32_1_1_1.fits 120 SDSS-I 1.3352990 182 27.56 22.36204688

average = -0.000386881 mag     sigma = 0.050488657 mag

We assume ZP(X) is a linear function given by the extinction coefficient times airmass X plus the zero point at fictitious zero airmass (X=0), denoted by ZP0.

Final calibration results:

Band Extinction coefficient ZP0
SDSS-R -0.730171283 23.46485949
SDSS-I -0.299963528 22.76258788

Formula for calibrated magnitude for BRC-data frames:

magnitude = ZP(X) - 2.5 * log10( flux / exptime ) = ZP(t) - 2.5 * log10( flux )
where ZP(X) is from the table below:

BRC-data FITS file Exp. time (s) Filter Airmass, X ZP(X) (mag) ZP(t) (mag)
d_e_20111020_27_1_1_1.fits 120 SDSS-R 1.26552 22.54081313 27.73876624
d_e_20111020_28_1_1_1.fits 120 SDSS-I 1.267015 22.38252959 27.58048271

Below are APT results for our 12 sources of interest in the BRC-data frames:

SDSS-R Band (d_e_20111020_27_1_1_1.fits)

RA_cen          Dec_cen      Src_intensity  Source_unc    Data_units    Mag      Mag_unc
323.29201       58.06220      1.17202e+02   1.1658e+02        D.N.      22.566    1.079970        
323.31062       58.06439      3.96883e+03   1.3662e+02        D.N.      18.742    0.037373        
323.36375       58.07040      4.29516e+03   1.1873e+02        D.N.      18.656    0.030011        
323.37173       58.04745      4.48606e+03   1.1888e+02        D.N.      18.609    0.028770        
323.39167       58.07182     -4.25618e+01   1.0756e+02        D.N.         NaN   -2.743677        
323.39731       58.11315      2.47244e+03   1.1777e+02        D.N.      19.256    0.051717        
323.40086       58.05671      1.26974e+03   1.2605e+02        D.N.      19.979    0.107782        
323.40603       58.09550      3.67941e+02   1.1666e+02        D.N.      21.324    0.344248        
323.41173       58.10681      1.79676e+02   1.1662e+02        D.N.      22.103    0.704659        
323.42112       58.10696      3.92205e+02   1.1673e+02        D.N.      21.255    0.323129        
323.42042       58.10873      1.00031e+01   1.2555e+02        D.N.      25.238   13.626236        
323.45929       58.05723      1.90320e+03   1.4631e+02        D.N.      19.540    0.083463        

SDSS-I Band (d_e_20111020_28_1_1_1.fits)

RA_cen          Dec_cen      Src_intensity  Source_unc    Data_units    Mag      Mag_unc
323.29027       58.06250      1.84151e+02   1.2352e+02        D.N.      21.918    0.728264        
323.31060       58.06440      8.09260e+03   1.7978e+02        D.N.      17.810    0.024119        
323.36376       58.07040      9.69786e+03   1.4519e+02        D.N.      17.614    0.016254        
323.37172       58.04745      1.88554e+04   1.5747e+02        D.N.      16.892    0.009067        
323.39158       58.07180      1.97985e+02   1.2342e+02        D.N.      21.839    0.676811        
323.39731       58.11314      8.33426e+03   1.4077e+02        D.N.      17.778    0.018338        
323.40089       58.05674      5.45621e+03   1.4350e+02        D.N.      18.238    0.028554        
323.40537       58.09611     -1.06363e+02   1.3213e+02        D.N.         NaN   -1.348720        
323.41097       58.10773      3.05981e+01   1.3220e+02        D.N.      23.866    4.690935        
323.42012       58.10742      6.97803e+02   1.4125e+02        D.N.      20.471    0.219761        
323.42064       58.10851      8.19214e+01   1.4985e+02        D.N.      22.797    1.985936        
323.45929       58.05725      4.96676e+03   2.0511e+02        D.N.      18.340    0.044836        

Additional Notes

  1. URLs to the source lists for all 6 data frames have been added to the analysis section above. Even though a 2-sigma detection threshold was used, which yields sources with a lower signal-to-noise ratio than given by the usual 3-sigma detection threshold, the spatial matching and outlier rejection in magnitude space effectively matches sources both spatially and photometrically. Thus, the matching is fairly reliable.
  2. The "sigmas" (a.k.a. standard deviations) listed underneath the above scatter plots suggest the photometric calibration is at the level of 0.04-0.06 mag, which is fair and reasonable given the limited amount of calibration data available here.
  3. A second method of photometric calibration that included a color term (R-I) in the least-squared-error data fitting was performed. It was found that this additional degree of freedom in the data fitting did not significantly lower the chi2 of the data fits (it was slightly higher in 2 of the cases, and slightly lower in the other 2 cases). Moreover, there was neither consistency in the resulting color coefficients between the 2 SDSS-R-band calibration frames, nor between the 2 SDSS-I-band calibration frames. We surmise that there are probably an insufficient number of matches for this more sophisticated photometric-calibration model to give any benefit over the simple one-parameter (zero point) photometric-calibration model.
  4. All APT photometry-table files relevant to this work are given as follows:

Ad Hoc Analysis

Below are APT results for two 2 additional sources of interest in the BRC-data frames:

SDSS-R Band (d_e_20111020_27_1_1_1.fits)

RA_cen          Dec_cen      Src_intensity  Source_unc    Data_units    Mag      Mag_unc
323.42112       58.10696      3.92205e+02   1.1673e+02        D.N.      21.255    0.323129
323.42042       58.10873      1.00031e+01   1.2555e+02        D.N.      25.238   13.626236 

SDSS-I Band (d_e_20111020_28_1_1_1.fits)

RA_cen          Dec_cen      Src_intensity  Source_unc    Data_units    Mag      Mag_unc
323.42012       58.10742      6.97803e+02   1.4125e+02        D.N.      20.471    0.219761
323.42064       58.10851      8.19214e+01   1.4985e+02        D.N.      22.797    1.985936
The first source cannot be seen in the SDSS-R data, but it is clearly present in the SDSS-I data, though faint. The second source is apparently absent in both bands, and the aperture-photometry magnitudes are probably fainter than the theoretical limiting magnitude of the data.