The next generation of Extremely Large Telescopes (ELT), with diameters up to 39 meters, is planned to begin operation in the next decade and promises new challenges in the development of instruments since the instrument size increases in proportion to the telescope diameter D, and the cost as D2 or faster. The growing field of astrophotonics (the use of photonic technologies in astronomy) could solve this problem by allowing mass production of fully integrated and robust instruments combining various optical functions, with the potential to reduce the size, complexity and cost of instruments. Astrophotonics allows for a broad range of new optical functions, with applications ranging from sky background filtering, high spatial and spectral resolution imaging and spectroscopy. In this paper, we want to provide astronomers with valuable keys to understand how photonics solutions can be implemented (or not) according to the foreseen applications. The paper introduces first key concepts linked to the characteristics of photonics technologies, placed in the framework of astronomy and spectroscopy. We then describe a series of merit criteria that help us determine the potential of a given micro-spectrograph technology for astronomy applications, and then take an inventory of the recent developments in integrated micro-spectrographs with potential for astronomy. We finally compare their performance, to finally draw a map of typical science requirements and pin the identified integrated technologies on it. We finally emphasize the necessary developments that must support micro-spectrograph in the coming years.
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