  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.
