Principal Component Analysis of Up-the-ramp Sampled IR Array Data

We describe the results of principal component analysis (PCA) of up-the-ramp sampled IR array data from the HST WFC3 IR, JWST NIRSpec, and prototype WFIRST WFI detectors. These systems use respectively Teledyne H1R, H2RG, and H4RG-10 near-IR detector arrays with a variety of IR array controllers. The PCA shows that the Legendre polynomials approximate the principal components of these systems (i.e. they roughly diagonalize the covariance matrix). In contrast to the monomial basis that is widely used for polynomial fitting and linearization today, the Legendre polynomials are an orthonormal basis. They provide a quantifiable, compact, and (nearly) linearly uncorrelated representation of the information content of the data. By fitting a few Legendre polynomials, nearly all of the meaningful information in representative WFC3 astronomical datacubes can be condensed from 15 up-the-ramp samples down to 6 compressible Legendre coefficients per pixel. The higher order coefficients contain time domain information that is lost when one projects up-the-ramp sampled datacubes onto 2-dimensional images by fitting a straight line, even if the data are linearized before fitting the line. Going forward, we believe that this time domain information is potentially important for disentangling the various non-linearities that can affect IR array observations, i.e. inherent pixel non-linearity, persistence, burn in, brighter-fatter effect, (potentially) non-linear inter-pixel capacitance (IPC), and perhaps others.