COS signal to noise capabilities

Limitation of COS S/N• No good 2-D flat available.• Fixed pattern noise dominates COS spectra.

An uncalibrated COS spectrum is affected by: • Optical response

• Smooth• Fixed in wavelength space (sort of)

• Fixed pattern noise• Due to detector irregularities• Rapidly varying with detector position• Fixed in detector space

Separating fixed pattern noise and spectrum:• Iterative approach• Direct approach

The FP-POS AlgorithmData taken at several, slightly shifted wavelengths1. Align all of the spectra in λ space and create a mean

spectrum (reduces fixed pattern noise by 1/√N).

2. Divide each spectrum by the mean and average the results in detector space for an estimate of the fixed pattern noise.

3. Divide each spectrum by the fixed pattern noise estimate.

4. GOTO 1 and iterate “until done”.

Some limitations:• Algorithm can get “confused” by busy spectra.

• COS FP-POS offsets are nearly identical, so some spatial frequencies are poorly constrained.

Works well in many cases, but error estimates are a bit sketchy.

A 1-D flat derived by the FP-POS algorithm, as implemented by Tom Ake for COS. Grid wire shadows are marked.

(Left) Net spectrum of WD0308-565 from FP-Split algorithm, binned by 3 pixels (half a RESOL). Also shown: 3 weak S II IS lines, and a quadratic fit to 1220 < λ < 1250 Å.

(Upper right) Poisson S/N in each bin. Features are spectral lines or grid wires.

(Right) Normalized S II spectrum showing how well weak lines can be identified.

The Direct ApproachTo determine limiting S/N, need good error estimates for the fixed pattern template.1. Uncalibrated standard stars typically have simple

continua, whose line free regions can be represented by polynomials.

2. Align all spectra in wavelength space and fit them with one polynomial.

3. Divide each spectrum by the fit and average the results in detector space to get the fixed pattern noise.

4. No iteration needed.

5. Template errors follow from simple propagation of errors.

Some limitations:• Only works for sources with simple continua.

Agrees well with templates from iterative approach.

Examples of polynomial fits

Examples of fits to 4 FPPOS NET spectra from program 12086. Regions containing stellar lines (other than Ly α), IS lines and grid wire shadows have been eliminated. These high S/N data show how well polynomials fit the NET spectra.

Comparison of iterative and direct flats. Ratios of the NET spectra (black) and templates (red) -- both smoothed by 64 points to highlight systematic differences. Blue curve is the average of the two ratios.

Portions of a 1-D flat showing ±1σ errors. Data are binned over 3 pixels, half a RESOL, and grid wire shadows are marked.

Histograms characterizing fixed pattern noise in each grating/detector. Plots show the dispersion about the mean of the fixed pattern templates including the grid wires (black), without grid wires (red) and expected Poisson errors (blue).

The Bottom Line for Standard Processing

RMS S/N over the regions 1300 < x < 152000 for FUVA and 1000 < x < 145000 -- corrected for Poisson noise.

G130M G160M

FUVA FUVB FUVA FUVBRMS S/N 17.9 23.8 14.9 20.4Max S/N 35.7 47.6 29.9 40.8

• G130M is better than G160M because it’s fatter.

• FUVB is better than FUVA because it is.

• To improve, a full 1-D flat is needed.

• A S/N = 50 template limits overall S/N to ≤ 100.

Effect of SNFF on exposure times