About the calculation of errors in eis_prep.

A new version of eis_prep, v 1.23, due to Mike Marsh, has been uploaded in ssw, which includes a corrected computation of the errors.

In the old version, it was assumed that the fractional error of the intensity measured in physical (cgs) units was equal to the fractional error of the intensity measured in DN, instead of in photon units.

That is, given d, p, and I as the intensities in DN, photons and erg/cm2/s/sr/A, eis_prep set the error to

err(I)/I = err(d)/d

err(I)/I = err(p)/p

Actually, p is proportional to d * lambda: that is p = K1*d*lambda, where K1 is a constant. Henceforth inside a given window, p is almost proportional to d: p=f(d)=K*d, where K=K1*lambda is almost constant.

Errors are computed in DN as

err(d) = sqrt(d+2.5^2)

where 2.5 DN is the value of the read out noise. It follows then that

err(p) = sqrt(p+f(2.5)^2) = sqrt(K*d+(K*2.5)^2)

where f(2.5) is the read out noise in photon units. Thus, the correct expression of the fractional error is

err(I)/I = err(p)/p = sqrt(f(d)+f(2.5)^2)/f(d)

which differs from the previous err(d)/d by about a factor 1/sqrt(K) if d is greater than 2.5 DN.

The old procedure generated incorrect error values; the new error values can be more than 50% larger than the previous ones.

Alessandro Gardini

#### Update#

The read noise error now used by eis_prep ranges from 2.24 to 2.37 DN for the four CCD quadrants. These values replace the 2.5 DN value mentioned above.

Peter Young , 19-Dec-2008

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