The need of atmospheric information with a higher spatial and temporal resolution drives the development of small satellites and satellite constellations to complement satellite flagship missions. Since optical systems are a main contributor to the satellite size, these are the prime candidate for their miniaturization. We present here a novel optical system where the complete spectrometer part of the optical system is compressed in one flat optical element. The element consists of an array of photonic crystals which is directly placed on a detector. The photonic crystals act as optical filters with a tunable spectral transmission response. From the integrated optical signals per filter and the atmosphere model, greenhouse gas concentrations are obtained using computational inversion. We present in this article the instrument concept, the manufacturing and measurement of the photonic crystals, methods for the filter array optimization, and discuss the predicted retrieval performance for the detection of methane and carbon dioxide.