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In this paper we investigate how the residuals in bundle adjustmentcan be split into a composition of simple functions. According to thechain rule, the Jacobian (linearisation) of the residual can be formedas a product of the Jacobians of the individual steps. Whenimplemented, this enables a modularisation of the computation of thebundle adjustment residuals and Jacobians where each component haslimited responsibility. This enables simple replacement of componentsto e.g. implement different projection or rotation models byexchanging a module. The technique has previously been used toimplement bundle adjustment in the open-source package DBAT (Borlinand Grussenmeyer, ¨ 2013) based on the Photogrammetric and ComputerVision interpretations of Brown (1971) lens distortion model. In thispaper, we applied the technique to investigate how affine distortionscan be used to model the projection of a tilt-shift lens. Two extendeddistortion models were implemented to test the hypothesis that theordering of the affine and lens distortion steps can be changed toreduce the size of the residuals of a tilt-shift lens calibration.Results on synthetic data confirm that the ordering of the affine andlens distortion steps matter and is detectable by DBAT. However, whenapplied to a real camera calibration data set of a tilt-shift lens, nodifference between the extended models was seen. This suggests thatthe tested hypothesis is false and that other effects need to bemodelled to better explain the projection. The relatively lowimplementation effort that was needed to generate the models suggestthat the technique can be used to investigate other novel projectionmodels in photogrammetry, including modelling changes in the 3Dgeometry to better understand the tilt-shift lens.