Phase steps are an important type of wavefront aberrations generated by large telescopes with segmented mirrors. In a closed-loop correction cycle these phase steps have to be measured with the highest possible precision using natural reference stars, that is with a small number of photons. In this paper the classical Fisher information of statistics is used for calculating the Cramer-Rao bound, which determines the limit to the precision with which the height of the steps can be estimated in an unbiased fashion with a given number of photons and a given measuring device. Four types of measurement devices are discussed: a Shack-Hartmann sensor with one small cylindrical lenslet covering a sub-aperture centred over a border, a modified Mach-Zehnder interferometer, a Foucault test, and a curvature sensor. The Cramer-Rao bound is calculated for all sensors under ideal conditions, that is narrowband measurements without additional noise or disturbances apart from the photon shot noise. This limit is compared with the ultimate quantum statistical limit for the estimate of such a step which is independent of the measuring device. For the Shack-Hartmann sensor, the effects on the Cramer-Rao bound of broadband measurements, finite sampling, and disturbances such as atmospheric seeing and detector readout noise are also investigated. The methods presented here can be used to compare the precision limits of various devices for measuring phase steps and for optimising the parameters of the devices. Under ideal conditions the Shack-Hartmann and the Foucault devices nearly attain the ultimate quantum statistical limits, whereas the Mach-Zehnder and the curvature devices each require approximately twenty times as many photons in order to reach the same precision.
Analytical decomposition of Zernike and hexagonal modes over an hexagonal segmented optical aperture
ONERA The French Aerospace Laboratory（法国航空航天实验室）；Aix Marseille Université, CNRS, CNES, Laboratoire d’Astrophysique de Marseille (LAM)（艾克斯马赛大学）；Université Côte d’Azur, Observatoire de la Côte d’Azur, CNRS, Laboratoire Lagrange（蔚蓝海岸大学）
Fabrication-Aware Design of a Hybrid Metasurface-Bragg Mirror for Low-Noise Precision Optics
Laboratory for Emerging Nanometrology（新兴纳米计量实验室）；Friedrich Schiller University（弗里德里希·席勒大学）；Fraunhofer Institute for Applied Optics and Precision Engineering IOF（弗劳恩霍夫应用光学和精密工程研究所IOF）；Physikalisch-Technische Bundesanstalt（德国物理技术联邦研究院）；Ernst Abbe University of Applied Sciences Jena（耶拿应用科学大学）
Scattering Loss in Precision Metrology due to Mirror Roughness
LIGO Laboratory, California Institute of Technology（加州理工学院LIGO实验室）；Centre for Gravitational Astrophysics, College of Science, The Australian National University（澳大利亚国立大学理学院引力天体物理中心）；Department of Physics and Astronomy, The University of Sheffield（谢菲尔德大学物理与天文系）；Department of Applied Physics, School of Engineering, The University of Tokyo（东京大学工学部应用物理系）
Variational treatment of the electromagnetic field in an optical cavity with a moving mirror
Università di Padova（帕多瓦大学）；Centro di Ateneo Studi e Attività Spaziali, Università di Padova（帕多瓦大学校际空间研究与活动中心）；Istituto di Fotonica e Nanotecnologie, Consiglio Nazionale delle Ricerche（国家研究委员会光子和纳米技术研究所）；Dipartimento di Fisica e Astronomia “Galileo Galilei”, Università di Padova（帕多瓦大学伽利略·伽利雷物理与天文学系）；Istituto Nazionale di Fisica Nucleare (INFN), Sezione di Padova（意大利国家核物理研究所帕多瓦分部）；Padua QTech Center, Università di Padova（帕多瓦量子技术中心）；Istituto Nazionale di Ottica (INO) del Consiglio Nazionale delle Ricerche (CNR)（国家研究委员会国家光学研究所）
