Effect of the instrumental profile

In the analysis of the shape of spectral lines it is often necessary, as we have seen, to use spectroscopic in- 

The instrumental function is most conveniently specified in terms of the angular frequency, Wp, of the monochromatic wave which produces a maximum intensity on a detector located at the point P. In a grating spectrograph, for example, oip would vary as the detector P was moved along the focal plane. If the instrument is now illuminated by monochromatic light of angular frequency u the instrumental profile is given as the transmission function, T(u)-iOp). 

For a grating spectrograph with a relatively wide entrance slit the instrumental profile would be a rectangular function 

When the instrument is illuminated with light whose intrinsic spectral distribution is represented by I(w), the spectrogram obtained as the detector position is changed is given by the folding integral  

The effect of this convolution is illustrated in Fig,8.8 for the case of a spectrograph with a rectangular transmission function illuminated by light having a broad symmetric spectral profile. 

---