Ideally, one would like the signal measured in an astronomical observation to result from the target object only. However, there are various other sources that contribute to that signal, implying a less precise knowledge of the signal resulting from the astronomical object under study.
For a detection process that counts photons, as the one used at near
infrared wavelengths, in particular by CGS4, even if there was no
instrumental noise, there would still be an associated
uncertainty in the number of photons counted. This uncertainty is
intrinsic to the counting process, results from Poisson Statistics, and
can never be eliminated. If the rate of photons ariving at the detector
array from the target object is n then N=n t is the number of
photons arriving in a time interval t. If these photons induce
counts (with 
) then the standard deviation in
the number of counts for a time interval t is therefore
. The noise is therefore proportional to the square root
of the detected number of photons. This is usually known as photon noise.
At near infrared wavelengths the background emission, resulting from the atmosphere, telescope and optics can be quite substantial. Photons resulting from these sources will be counted and will therefore contribute to the noise but not to the signal of the target object since they originate elsewhere.
Further contributions to the noise result from the detector itself. CGS4 is equipped with a photovoltaic detector and therefore the relevant noise sources are: Johnson noise, shot noise, generation noise and read-out noise. From these, read-out noise dominates.
For the observations presented here the number of counts resulting from the detection of photons is much larger than the read-out noise (by 1 to 2 orders of magnitude) and therefore the dominant noise source is photon noise. Other noise sources can be neglected.
The uncertainty in each data point (pixel) was propagated throughout the data reduction procedure for observations from the UT9410 run. The resulting error bars are plotted in the relevant spectra of Figure 3.14.
Spectra from UT9512 are presented without error bars. The error in each data point was not propagated beyond sky subtraction in the data reduction sequence. This was due to a 'bug' in the optimal extraction algorithm from FIGARO that did not compute the variance of each spectral point in the extracted spectrum and that was present at the time this step in data reduction was carried out. For the UT9512 data error propagation is not crucial though. Since the continuum next to the hydrogen lines is well defined for spectra obtained during this run, a measure of the level of noise present can be determined from the point-to-point variation in the continuum. After normalization the continuum level in a given spectrum should be unity and fluctuations about this value in the continuum regions are a measure of the noise present in that spectrum. These fluctuations are determined by computing the root mean square deviation relative to unity in the continuum regions of the spectrum.
Comparing the average size of the error bars in the spectra from the UT9410 data with the result obtained by estimating the typical error bar from point-to-point variation in the continuum regions of the same spectra one sees that there is an excelent agreement between the two. For example, the average size of the error bars on the normalized spectra, obtained from error propagation in the Pa Beta spectra of DG Tau, DL Tau and DR Tau are 0.03, 0.04 and 0.04 while the estimated size of the error bars obtained from the point-to-point variation in the same spectra are 0.03, 0.04 and 0.05. Similarly, for the Br Gamma data of these stars 0.02, 0.03 and 0.02 are obtained from the propagating the errors while 0.02, 0.03 and 0.03 are obtained from the point-to-point variation. Similar results are obtained for the spectra from the remaining stars from the UT9410 observing run.
The signal in spectra obtained in UT9512 data is contaminated by the presence of ripple due to the sampling procedure and, in the case of the Br Gamma data, also due to the interference fringes produced by the CVF. Although both these effects are corrected for, the correction procedure introduces, as always, uncertainties relative to what one would get from uncontaminated data. The final noise in the spectra resulting from the detection process and from the data reduction procedures is indicated below. Imperfect removal of atmospheric features due to mismatches in airmass and time of observation of the standard star further degrades the signal in the regions where atmospheric lines are present. The removal of these lines was quite good though.
For observations from the UT9512 run, measurements of the poin-to-point variation in the continuum regions of the final reduced spectra yield typical error bars with size of 1% - 2% of the continuum flux. Since the continuum is normalized to unity error bars have a typical size of 0.01 to 0.02.