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ISAAC Quality Control:
Detector Linearity

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LW-arm linearity frames are taken bimonthly. The stack is submitted to the isaac_img_detlin recipe. Several lamp=on and lamp=off frames taken with different DITs are fit. There are 4 products of this recipe: the A-frame, the B-frame, the C-frame and a QC frame with the stdev of the fit. The A,B and C frames contain for each pixel the coefficients a,b, c where

DIT = A * flux_meas + B * flux_meas^2 + C * flux_meas^3

where flux_meas is the measured flux. We divide this equation by A, since we want coefficients to be independent on the actual lamp flux:

DIT/A = flux_meas + B / A * flux_meas^2 + C / A * flux_meas^3

and if we assume that the array is linear for low fluxes, then the first term (flux_meas) is the linear part and A is dependent on the calibration lamp flux. The second (B / A * flux_meas^2) and the third term (C / A * flux_meas^3) are the higher orders (= non-linear terms) and describe the deviation from linearity.

The A, B, and C frames are submitted together with the imaging flat to the LW-arm zeropoint recipe. We monitor the coefficient frames for three read modes (DET.NCORRS.NAME) of the LW-array : UCHB DCLB and UCHB (e.g. UCHB = UncorrelatedHighBias).

The zeropoint recipe applies the following correction:

counts_corr = counts_meas + B/A * counts_meas^2 + C/A * counts_meas^3

The effective linearity is:

lin_eff = ( counts_corr / counts_meas ) - 1 = B/A * counts_meas + C/A * counts_meas^2

and using a reference of counts_meas = 10000 ADU:

lin_eff ( 10000 ADU ) = B/A * 10^4 + C/A * 10^8  

or using a reference of counts_meas = 5000 ADU:

lin_eff ( 5000 ADU ) = B/A * 5e3 + C/A * 5e3 * 5e3  

Occasionally the SW-arm Hawaii detector suffers from the so-acalled odd-even column effect The odd columns are 1-2% brighter than the even columns. Moreover the effect cannot be flatfielded, since the amplitude of the flux differences between odd and even columns is a function of flux and detetcor quadrant. In addition to that the non-linearity relation of the odd and pixel is a function of time. The details are described on the twilight flat QC page. Another feature are sporadic sudden changes in the amplitude by about 10 ADU also found in sky observation stacks.

The odd even column effect is monitored quantitatively

  • by the odd-even QC parameters extracted from twilight flats,
  • by the robust fixed pattern noise derived from daily darks
  • by the odd-even QC parameters extracted from linearity frames (not yet public)

The odd-even column effect can be corrected

  • The isaac_img_jitter recipe has a --oddeven command line option, that takes the fourier transform of each quadrant, replaces the line in the power-spectrum that corresponds to the odd-even column effect by zero, and transforms the power spectrum back into a pixel image.
  • The isaac_img_detlin recipe records the non-linearity for each pixel individually. The raw frames can be pre-processed using the three products of the isaac_img_delin recipe. The three products can be recognized by their PRO.CATG=DETLIN_A and DETLIN_B and DETLIN_C respectively. The correction is applied to the raw frames in the same manner as described above for the LW-arm zeropoints:

    corr_frame = raw_frame + DETLIN_B / DETLIN_A * raw_frame^2 + DETLIN_C / DETLIN_A * raw_frame^3

    The limitation of this approach are: a) the function oddeven(flux) is a function of time. b) the linearity frames taken in 2008-02 and 2008-03 span a small flux range of 600 to 5000 ADU; only the linearity frames taken from 2008-04 on cover a larger flux range up to 10000 ADU.
top non-linearity parameters

QC1 parameters

parameter QC1 database: table, name procedure
linear coefficient isaac_line, qc_detlin_meda - the median of the coefficient frame A, is very close to the lamp flux
quadratic term coefficient isaac_line, qc_detlin_medb - the median of the coefficient frame B
cubic term coefficient isaac_line, qc_detlin_medc - the median of the coefficient frame C
linear fit error isaac_line, qc_detlin_medq - the median of the fit error map Q
lamp stability isaac_line, qc_detlin_lamp - the lamp flux is derived from from two flats of the same DIT but taken at the beginning and at the end of the sequence; The QC parameter is 2 (a-b)/(a+b)
normalized non-linearity isaac_line, qc_detlin_cob - coefficient ratio: qc_detlin_medb / qc_detlin_meda
effective linearity isaac_line, qc_detlin_eff - effective non-linearity at 10 000 ADU =
B/A * 10000 + C/A * 10000 * 10000


For the Hawaii array the calibrations are taken twice a year in DoubleCorr read mode. For Aladdin array the calibrations are taken monthly for three read modes: Uncorrelated at High Bias, DoubleCorrelated at Low Bias and DoubleCorrelated at High Bias.