Miniaturized optical instruments have become very important in industry as smart
phones and tablet PCs increase in popularity. A chronology of spectrometer development shows that a simple numerical point of view affords important insights. A tiny spectrometer, which is smaller than a few millimeters size, cannot easily rely on the conventional Fraunhofer diffraction due to its optical criterion limit. As an alternate solution to build smaller spectrometers, a Fresnel spectrometer chip with a gradient line grating is attractive. The fabricated Fresnel spectrometers have optical path volumes of about 1 mm3 and spectral resolutions of 10 to 23 nm.