Forward model M x = P I C x of an integral field spectrograph with the example of the SPHERE-IFS instrument (b). The telescope forms an image of the targeted object x (a,d) on the instrument that projects a spectrum of each of its spatial elements onto the sensor (c,g). The low-crosstalk BIGRE design of the IFU (b) proposed by Antichi et al. (2009) is based on two hexagonal lenslet arrays whose effect is first modelled as a convolution C by their pupil shape, averaging the light received by a single lenslet (d → e). An interpolation I then accounts for the sampling performed by the first array of lenslets of the IFU (red) at the lenslet positions (green dots) (e → f). Finally, their spectrum is dispersed by prisms on the sensor, corresponding to a sparse matrix P linking the different wavelengths seen by a given lenslet to the location of their projection on the detector (f → g). Photo Credit: Lucasfilm Ltd.