A structured illumination imaging system, comprising: a first optical arm, comprising: a first light emitter configured to emit light; a first transmissive diffraction grating configured to split light emitted by the first light emitter configured to project a first plurality of fringes on a plane of a sample; one or more optical elements (240A, 240B, 310, 410A, 410B) configured to phase shift the first plurality of fringes and the second plurality of fringes; a second optical arm, comprising: a second light emitter configured to emit light; and a second transmissive diffraction grating configured to split light emitted by the second light emitter configured to project a second plurality of fringes on the plane of the sample, wherein the first plurality of fringes are angularly offset from the second plurality of fringes on the sample plane by about 90 degrees; and an optical element configured to combine the optical paths of the first optical arm and the second optical arm, wherein the optical element to combine an optical path of the first plurality of fringes and the second plurality of fringes comprises a mirror with holes, with the mirror arranged to reflect light diffracted by the first transmissive diffraction grating and with the holes arranged to pass through at least first orders of light diffracted by the second transmissive diffraction grating; wherein the structured illumination system is a two-arm structured illumination system and the first and second transmissive diffraction gratings (230A, 230B) are mechanically fixed oriented perpendicular to each other. a first light emitter configured to emit light; a first transmissive diffraction grating configured to split light emitted by the first light emitter configured to project a first plurality of fringes on a plane of a sample; one or more optical elements (240A, 240B, 310, 410A, 410B) configured to phase shift the first plurality of fringes and the second plurality of fringes; a second optical arm, comprising: a second light emitter configured to emit light; and a second transmissive diffraction grating configured to split light emitted by the second light emitter configured to project a second plurality of fringes on the plane of the sample, wherein the first plurality of fringes are angularly offset from the second plurality of fringes on the sample plane by about 90 degrees; and an optical element configured to combine the optical paths of the first optical arm and the second optical arm, wherein the optical element to combine an optical path of the first plurality of fringes and the second plurality of fringes comprises a mirror with holes, with the mirror arranged to reflect light diffracted by the first transmissive diffraction grating and with the holes arranged to pass through at least first orders of light diffracted by the second transmissive diffraction grating; wherein the structured illumination system is a two-arm structured illumination system and the first and second transmissive diffraction gratings (230A, 230B) are mechanically fixed oriented perpendicular to each other. a second light emitter configured to emit light; and a second transmissive diffraction grating configured to split light emitted by the second light emitter configured to project a second plurality of fringes on the plane of the sample, wherein the first plurality of fringes are angularly offset from the second plurality of fringes on the sample plane by about 90 degrees; and an optical element configured to combine the optical paths of the first optical arm and the second optical arm, wherein the optical element to combine an optical path of the first plurality of fringes and the second plurality of fringes comprises a mirror with holes, with the mirror arranged to reflect light diffracted by the first transmissive diffraction grating and with the holes arranged to pass through at least first orders of light diffracted by the second transmissive diffraction grating; wherein the structured illumination system is a two-arm structured illumination system and the first and second transmissive diffraction gratings (230A, 230B) are mechanically fixed oriented perpendicular to each other.