the effect of non linear dispersion on continuum shape

[Robin Leadbeater]

If a theoretical star with equal flux/Angstrom is measured with a spectrograph with perfectly flat instrument response but a non linear dispersion, the resulting raw profile will be curved instead of a horizontal line. This is because each pixel does not cover an equal number of Angstroms.

When the spectrum is wavelength calibrated and a spectrum produced with equal bin widths using interpolation, the values for each bin need to be corrected for the variation in actual bin widths in the raw spectrum to produce the expected flat spectrum profile. This is not done though in either Visual Spec or ISIS according to my tests. Does anyone know if other programs eg SpcAudace, MIDAS, IRAF make this correction?

Note, if an instrument response correction, calculated using the same software, is applied then the effect cancels out but it could give problems if a mix of software is used which behave differently.

Cheers
Robin

[Andrew Smith]

Hi Robin - I don't know the answer to your question. However, is the effect you discribe not part of the instrument response? Given in reality the IR will never be uniform so won't you always need to correct for it anyway to get an estimate of the continum?

Regards Andrew

[Christian Buil]

You're right Robin, the sampling variation along the spectrum changes the measured signal (number of angstroms per pixel sample). The typical example is that of a spectrum obtained with a prism, highly nonlinear.

But the distortion in the signal is equivalent to a gain variation along the wavelength axis. During processing, the dispersion is first linearized after spectral calibration. Then, the instrument response is calculated based on a reference source in a conventional manner. Ok, the instrumental response found is not the same if the original dispersion is linear or nonlinear. That's right. But in both cases, the spectrum is properly calibrated radiometrically. Of course, as you note, it is necessary to use the same procedure (in particular the linearisation of spectral dispersion equation) for process the reference star (for compute spectral response) and the science star (for applied response correction).

For me, the dispersion non linearity is not a very critical problem for quality radiometric work with actual software (but it is better to observer with a nearly linear spectrograph - the general situation - for a more uniform noise statistic along the spectral axis).

Christian

[Robin Leadbeater]

Thinking about it more, for a slit spectrograph the same effect is seen in the flat so if a flat is used the effect cancels out. (If an ideal flat lamp with a level spectrum is used, the flat corrected raw spectrum of my theoretical test star will be flat even though the bin sizes are not all the same width.) In this case it makes sense just to interpolate the data with no correction for width to generate the same number of equal width bins.

Cheers
Robin