When dealing with nonresponse in survey sampling calibration has proved to be a useful technique for dealing with bias for estimators of population totals using auxiliary information. The setup is that we take a random sample from a finite population, but due to nonresponse we only observe study variable values in the response set, which is a subset of the sample. The auxiliary information can be known either at the sample level or the population level, or both. Linear calibration as suggested in (1) and (2) is now widely used in National Offices for Statistics throughout the world. This type of calibration is akin to GREG estimation and has proved to be efficient especially in combination with simple random sampling. The distance function (measure) to be minimized corresponding to the resulting calibration weights under full response is of a simple chi-square type. It turns out that under nonresponse a similar function generates the weights which are presented in (1). This is shown in detail in (3), where it is also pointed out that a problem with the function which we want to minimize the value of, given our observation in the response set, is that we are still comparing the calibration weights with the original design weights. The latter weights should not be used under nonresponse. However, as is also shown in (3), there is an invariance property involved for many important cases for this type of calibration. Specifically, this means here that if we e.g. multiply the design weights with a constant larger than one, to compensate for the fact that we have nonresponse, the resulting weights will be the same. Furthermore, we will get the same effect if we try to group the observations where we in each group allow for a unique multiplicative constant.