The overall image quality, in terms of angular image size and resolution, of an astronomical observation will be given by a quadratic sum of many different terms, among which the main ones are:

- Aberrations of the optical components and alignment errors in the telescope.
- Dynamic guiding errors, such as those from the servo loops
- The seeing, cf. expression ()
- Wind dependent high frequency errors

In order to guide the design of a telescope, a general error budget tree is formulated. The organization of the error tree for a modern telescope is shown in fig. . It contains both manufacturing and operation elements. The error budget is divided into two group: on the one hand fixed errors due to manufacturing tolerances and intrinsic limitations of the optical and mechanical systems; on the other hand errors with short time frequencies which depend on the variable conditions of the atmosphere. This second group comprises natural seeing and the effects of local turbulence (local seeing and wind).

The creation of an error budget among the various sources of error is often somewhat arbitrary for a complex system. In the case of a telescope an additional difficulty is given by the fact that fixed errors and tolerances should be added to terms of inherently variable nature that depend on the environmental conditions.

**Figure:** Structure of the error budget tree for the ESO VLT

The error budgets of telescope projects are traditionally given in term of angular image size where the various contributions are added quadratically.

Diericks has criticized this approach and proposed a new criterion for the evaluation of the effects of errors on the final image quality based on a parameter that he called Central Intensity Ratio (CIR) ([Diericks]), defined as

where **S** is the Strehl ratio of the telescope due to all effects:
optical aberrations, guiding errors, seeing, etc. and is the
Strehl ratio of the equivalent perfect telescope (limited only by
diffraction) * in the same natural seeing conditions*.
Therefore the CIR covers all possible sources of errors including
local seeing effects with the
single exception of seeing of the free atmosphere. It must be noted
that the CIR is then a function of natural seeing, and it
improves for bad seeing conditions because the telescope errors become
more and more masked by the natural seeing.

One may note that the CIR criterion has been proposed essentially because of its convenience for defining without risk of over-specification the polishing tolerances of the primary mirror. In this respect the CIR is also more practical than the Strehl ratio, which for a large telescope and poor seeing becomes extremely small (cf. fig. ). We will show in chapter of this report that the CIR criterion is also a most suitable tool for the objective evaluation of the disturbing influences of atmospheric turbulence on the telescope performance.

For large ratios and as long as it is , it can be shown that the relation between the CIR, the FWHM angle due to the natural seeing and the telescope errors are:

where is respectively the local seeing FWHM and/or the rms slope error and is the rms guiding error.Assuming that the individual errors are not correlated the decrease of CIR resulting from a combination of N different errors is simply the sum of the N individual CIR losses:

Fig. shows the error budget of the ESO VLT in terms of the Central Intensity Ratio.

It is to be noted that to date there are no established methodologies to verify the performance of the wind and seeing dependent terms in a manner that reflects the actual operation of the telescope and as a consequence also the budget values for these terms are generally set rather arbitrarily. A contribution toward a solution to this problem will be given in chapter .

**Figure:** Actual
image quality budget of the ESO VLT in terms of the
Central Intensity Ratio

Lorenzo Zago, zago@elgc.epfl.ch, Sun Feb 26 22:57:31 GMT+0100 1995