An integral field spectrograph following the TPF coronagraph can provide the required spectral resolving power R ∼ 70 with spatial resolution at the telescope diffraction limit, and covering the coronagraphic dark hole. This allows spectra to be obtained of all planets around the star simultaneously, spectra of disks, measurement of residual speckles for subtraction, and insensitivity to roll control and alignment. Short spectra and the many spatial elements required are most easily implemented using a microlens array at the entrance to a prism spectrograph. To minimize the size of the special photon-counting CCD detectors required, a high filling factor of detector pixel usage is desired. This can be accomplished by using a crossed cylindrical microlens array to create virtual slits at the focus of each lenslet. The lenslets must be illuminated by a highly asymmetric image scale, for which we use cylindrical mirrors to magnify the image in one direction while de-magnifying in the orthogonal direction.