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In this paper, we present a pipeline for the design, optimization, and fabrication of complex, customized HOEs that enhances their imaging performance and enables new applications. In particular, we propose an optimization method for grating vector fields that accounts for the unique selectivity properties of HOEs. We further show how our pipeline can be applied to two distinct HOE fabrication methods. The first uses a pair of freeform refractive elements to manufacture HOEs with high optical quality and precision. The second uses a holographic printer with two wavefront-modulating arms, enabling rapid prototyping. We propose a unified wavefront decomposition framework suitable for both fabrication approaches. To demonstrate the versatility of these methods, we fabricate and characterize a series of specialized HOEs, including an aspheric lens, a head-up display lens, a lens array, and, for the first time, a full-color caustic projection element.<\/jats:p>","DOI":"10.1145\/3414685.3417762","type":"journal-article","created":{"date-parts":[[2020,11,27]],"date-time":"2020-11-27T21:51:05Z","timestamp":1606513865000},"page":"1-15","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":80,"title":["Design and fabrication of freeform holographic optical elements"],"prefix":"10.1145","volume":"39","author":[{"given":"Changwon","family":"Jang","sequence":"first","affiliation":[{"name":"Facebook Reality Labs Research"}]},{"given":"Olivier","family":"Mercier","sequence":"additional","affiliation":[{"name":"Facebook Reality Labs Research"}]},{"given":"Kiseung","family":"Bang","sequence":"additional","affiliation":[{"name":"Facebook Reality Labs Research"}]},{"given":"Gang","family":"Li","sequence":"additional","affiliation":[{"name":"Facebook Reality Labs Research"}]},{"given":"Yang","family":"Zhao","sequence":"additional","affiliation":[{"name":"Facebook Reality Labs Research"}]},{"given":"Douglas","family":"Lanman","sequence":"additional","affiliation":[{"name":"Facebook Reality Labs Research"}]}],"member":"320","published-online":{"date-parts":[[2020,11,27]]},"reference":[{"key":"e_1_2_2_1_1","doi-asserted-by":"publisher","DOI":"10.1145\/3130800.3130892"},{"key":"e_1_2_2_2_1","doi-asserted-by":"publisher","DOI":"10.1109\/TVCG.2019.2898781"},{"key":"e_1_2_2_3_1","doi-asserted-by":"publisher","DOI":"10.1364\/JOSAA.7.000080"},{"key":"e_1_2_2_4_1","volume-title":"Curved holographic optical elements and applications for curved see-through displays. 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