{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T15:55:56Z","timestamp":1790870156248,"version":"4.1.0"},"reference-count":22,"publisher":"Optica Publishing Group","issue":"29","license":[{"start":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T00:00:00Z","timestamp":1790812800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/doi.org\/10.1364\/OA_License_v2#VOR"},{"start":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T00:00:00Z","timestamp":1790812800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/opg.optica.org\/policies\/opg-tdm-policy.json"}],"content-domain":{"domain":["opg.optica.org"],"crossmark-restriction":false},"short-container-title":["Appl. Opt."],"published-print":{"date-parts":[[2026,10,10]]},"abstract":"<jats:p>\n                    This paper presents a novel, to our knowledge, defocus estimation method for star sensors, leveraging the equivalent radius\n                    <jats:italic>R<\/jats:italic>\n                    <jats:sub>80<\/jats:sub>\n                    of the 80%-energy closed contour in conjunction with pixel-phase compensation. In contrast to existing approaches, the proposed method operates on a single isolated-star-spot image and circumvents the need for complex parametric reconstruction of the point-spread function. The processing pipeline comprises background subtraction, noise suppression, centroid estimation, and pixel-phase compensation, followed by subpixel interpolation and threshold-based searching to extract the largest connected region that encloses approximately 80% of the total spot energy. The radius of an equal-area circle is then adopted as\n                    <jats:italic>R<\/jats:italic>\n                    <jats:sub>80<\/jats:sub>\n                    , and a quadratic calibration model is established to relate\n                    <jats:italic>R<\/jats:italic>\n                    <jats:sub>80<\/jats:sub>\n                    to the axial defocus. Experiments conducted over a defocus range from \u22120.46875 to 0.46875\u00a0\u00b5m confirm that\n                    <jats:italic>R<\/jats:italic>\n                    <jats:sub>80<\/jats:sub>\n                    varies quadratically with defocus. Notably, pixel-phase compensation reduces the mean standard deviation of\n                    <jats:italic>R<\/jats:italic>\n                    <jats:sub>80<\/jats:sub>\n                    from 0.0426 to 0.0214 pixels, yielding a 49.8% improvement in repeatability. On independently acquired test images, the mean absolute bias of the seven position-wise mean estimates is 0.0092\u00a0\u00b5m. Owing to its single-image requirement and avoidance of iterative PSF fitting, the method is particularly well suited for practical focal-plane alignment and on-orbit image-quality assessment in star sensor systems.\n                  <\/jats:p>","DOI":"10.1364\/ao.612689","type":"journal-article","created":{"date-parts":[[2026,9,14]],"date-time":"2026-09-14T14:00:09Z","timestamp":1789394409000},"page":"10024","update-policy":"https:\/\/doi.org\/10.1364\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Defocus estimation for star sensors based on closed energy contours"],"prefix":"10.1364","volume":"65","author":[{"given":"Hongzhe","family":"Chen","sequence":"first","affiliation":[{"name":"Chinese Academy of Sciences"},{"name":"University\u00a0of\u00a0Chinese\u00a0Academy\u00a0of\u00a0Sciences"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Wenbo","family":"Zhang","sequence":"additional","affiliation":[{"name":"Chinese Academy of Sciences"},{"name":"University\u00a0of\u00a0Chinese\u00a0Academy\u00a0of\u00a0Sciences"},{"name":"Xi\u2019an Jiaotong University"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Weiguo","family":"Lu","sequence":"additional","affiliation":[{"name":"Chinese Academy of Sciences"},{"name":"University\u00a0of\u00a0Chinese\u00a0Academy\u00a0of\u00a0Sciences"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"285","published-online":{"date-parts":[[2026,10,1]]},"reference":[{"key":"ao-65-29-10024-R1","doi-asserted-by":"publisher","first-page":"6671","DOI":"10.3390\/s24206671","type":"journal-article","volume":"24","author":"Sang","year":"2024","journal-title":"Sensors"},{"key":"ao-65-29-10024-R2","doi-asserted-by":"publisher","first-page":"5896","DOI":"10.1364\/AO.494586","type":"journal-article","volume":"62","author":"Casini","year":"2023","journal-title":"Appl. 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All rights, including for text and data mining (TDM), Artificial Intelligence (AI) training, and similar technologies, are reserved.","name":"copyright","label":"Copyright"}]}}