For many optical systems, mainly in photography, the digital correction of distortion and lateral color aberration is a common step in the image processing pipeline. It is based on images of calibration targets and the determination of coefficients for a correction model. These coefficients are specific for the optical system which forms the aerial image for the sensor. If an exchange of the optical system is necessary, e.g. for offering optics for several applications like macro mode, wide-angle or tele-photo, the entire optical system is typically exchanged and not only parts of it. Using a technique for digital identification of the optical system, e.g. via an electronic interface, the corresponding correction coefficients can be obtained and applied. If the optical system to be exchanged is only a part of the entire optical system, the situation is more difficult. As an example, this is the case in the field of digital microscopy, where objective lenses with different numerical apertures and magnifications are available for the same microscopic body. These objective lenses are no image forming optical systems and need at least a tube lens to produce an image for capturing with a sensor. Both optical systems produce contributions to the resulting overall aberrations, e.g. distortion and lateral color aberration. For a particular pairing, coefficients for a correction model can be calibrated and applied. But in the case of an exchange of the objective, only a part of the optical system changes and a new calibration is needed. We will show how this problem can be solved using a mathematical operation and individual calibration of the distinct parts of the optical system. The advantage is, that the parts of the optical system can be arbitrarily combined and the correction-model coefficients of the combination can be computed from the corresponding coefficients of the individual parts. Hence, there’s no need to calibrate every possible combination or to manage a calibration process at the customer’s location. In addition, the manufacturing and calibration of objectives and tube lenses may take place at different locations. Furthermore, the optical design can benefit from the digital aberration correction although it is made up of interchangeable components.