{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,1]],"date-time":"2026-06-01T12:22:20Z","timestamp":1780316540848,"version":"3.54.1"},"reference-count":51,"publisher":"MDPI AG","issue":"24","license":[{"start":{"date-parts":[[2020,12,20]],"date-time":"2020-12-20T00:00:00Z","timestamp":1608422400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100012335","name":"National Defense Basic Scientific Research Program of China","doi-asserted-by":"publisher","award":["JCKY2019602B010"],"award-info":[{"award-number":["JCKY2019602B010"]}],"id":[{"id":"10.13039\/501100012335","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>As a typical application of indirect-time-of-flight (ToF) technology, photonic mixer device (PMD) solid-state array Lidar has gained rapid development in recent years. With the advantages of high resolution, frame rate and accuracy, the equipment is widely used in target recognition, simultaneous localization and mapping (SLAM), industrial inspection, etc. The PMD Lidar is vulnerable to several factors such as ambient light, temperature and the target feature. To eliminate the impact of such factors, a proper calibration is needed. However, the conventional calibration methods need to change several distances in large areas, which result in low efficiency and low accuracy. To address the problems, this paper presents an improved calibration method based on electrical analog delay. The method firstly eliminates the lens distortion using a self-adaptive interpolation algorithm, meanwhile it calibrates the grayscale image using an integral time simulating based method. Then, the grayscale image is used to estimate the parameters of ambient light compensation in depth calibration. Finally, by combining four types of compensation, the method effectively improves the performance of depth calibration. Through several experiments, the proposed method is more adaptive to multiscenes with targets of different reflectivities, which significantly improves the ranging accuracy and adaptability of PMD Lidar.<\/jats:p>","DOI":"10.3390\/s20247329","type":"journal-article","created":{"date-parts":[[2020,12,21]],"date-time":"2020-12-21T01:01:08Z","timestamp":1608512468000},"page":"7329","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["An Improved Calibration Method for Photonic Mixer Device Solid-State Array Lidars Based on Electrical Analog Delay"],"prefix":"10.3390","volume":"20","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9641-5029","authenticated-orcid":false,"given":"Xuanquan","family":"Wang","sequence":"first","affiliation":[{"name":"Key Laboratory of Biomimetic Robots and Systems (Ministry of Education), Beijing Institute of Technology, Beijing 100081, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1868-6517","authenticated-orcid":false,"given":"Ping","family":"Song","sequence":"additional","affiliation":[{"name":"Key Laboratory of Biomimetic Robots and Systems (Ministry of Education), Beijing Institute of Technology, Beijing 100081, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Wuyang","family":"Zhang","sequence":"additional","affiliation":[{"name":"Key Laboratory of Biomimetic Robots and Systems (Ministry of Education), Beijing Institute of Technology, Beijing 100081, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2020,12,20]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"568","DOI":"10.3390\/s90100568","article-title":"State-of-The-Art and Applications of 3D Imaging Sensors in Industry, cultural heritage, medicine, and criminal investigation","volume":"9","author":"Sansoni","year":"2009","journal-title":"Sensors"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"647","DOI":"10.1177\/0278364911434148","article-title":"RGB-D mapping: Using kinect-style depth cameras for dense 3D modeling of indoor environments","volume":"31","author":"Henry","year":"2012","journal-title":"Int. J. Robot. Res."},{"key":"ref_3","unstructured":"Okada, K., Inaba, M., and Inoue, H. (2003, January 1). Integration of real-time binocular stereo vision and whole body information for dynamic walking navigation of humanoid robot. Proceedings of the IEEE International Conference on Multisensor Fusion and Integration for Intelligent Systems, (MFI 2003), Tokyo, Japan."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"195","DOI":"10.1109\/CVPR.2003.1211354","article-title":"High-accuracy stereo depth maps using structured light","volume":"Volume 1","author":"Scharstein","year":"2003","journal-title":"Proceedings of the 2003 IEEE Computer Society Conference on Computer Vision and Pattern Recognition"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"12010","DOI":"10.1038\/ncomms12010","article-title":"Single-pixel three-dimensional imaging with time-based depth resolution","volume":"7","author":"Sun","year":"2016","journal-title":"Nat. Commun."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Cui, Y., Schuon, S., Chan, D., Thrun, S., and Theobalt, C. (2010, January 13\u201318). 3D shape scanning with a time-of-flight camera. Proceedings of the 2010 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, San Francisco, CA, USA.","DOI":"10.1109\/CVPR.2010.5540082"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"12495","DOI":"10.1109\/ACCESS.2019.2891693","article-title":"Recent advances in 3D Data acquisition and processing by Time-of-Flight camera","volume":"7","author":"He","year":"2019","journal-title":"IEEE Access."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"1005","DOI":"10.1007\/s00138-016-0784-4","article-title":"An overview of depth cameras and range scanners based on time-of-flight technologies","volume":"27","author":"Horaud","year":"2016","journal-title":"Mach. Vis. Appl."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"992","DOI":"10.1109\/JSTSP.2017.2737784","article-title":"Single aperture spectral+ToF compressive camera: Toward hyperspectral+depth imagery","volume":"11","author":"Rueda","year":"2017","journal-title":"IEEE J. Sel. Top. Signal Process."},{"key":"ref_10","first-page":"2346","article-title":"Snapshot compressive ToF+Spectral imaging via optimized color-coded apertures","volume":"42","author":"Florez","year":"2019","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1318","DOI":"10.1016\/j.cviu.2009.11.002","article-title":"Time-of-Flight sensor calibration for accurate range sensing","volume":"114","author":"Lindner","year":"2010","journal-title":"Comput. Vis. Image Underst."},{"key":"ref_12","first-page":"524","article-title":"Lateral and depth calibration of PMD-distance sensors. advances in visual computing","volume":"Volume 4292","author":"Lindner","year":"2006","journal-title":"Advance of Visual Computing, Proceedings of the Second International Symposium on Visual Computing, Lake Tahoe, NV, USA, 6\u20138 November 2006"},{"key":"ref_13","first-page":"67640W","article-title":"Calibration of the intensity-related distance error of the PMD TOF-camera","volume":"Volume 6764","author":"Casanent","year":"2007","journal-title":"Intelligent Robots and Computer Vision XXV: Algorithms, Techniques, and Active Vision, Proceedings of Optics East, Boston, MA, USA, 9\u201312 September 2007"},{"key":"ref_14","first-page":"344","article-title":"Sub-pixel data fusion and edge-enhanced distance refinement for 2d\/3d images","volume":"5","author":"Lindner","year":"2008","journal-title":"Int. J. Intell. Syst. Technol. Appl."},{"key":"ref_15","unstructured":"Kahlmann, T., Remondino, F., and Ingensand, H. (2006, January 25\u201327). Calibration for increased accuracy of the range imaging camera SwissRanger. Proceedings of the ISPRS Commission V Symposium \u201cImage Engineering and Vision Metrology\u201d, Dresden, Germany."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1515\/JAG.2008.001","article-title":"Calibration and development for increased accuracy of 3D range imaging cameras","volume":"2","author":"Kahlmann","year":"2008","journal-title":"J. Appl. Geodesy."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Steiger, O., Felder, J., and Weiss, S. (2008, January 12\u201315). Calibration of time-of-flight range imaging cameras. Proceedings of the 2008 15th IEEE International Conference on Image Processing, San Diego, CA, USA.","DOI":"10.1109\/ICIP.2008.4712168"},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Swadzba, A., Beuter, N., Schmidt, J., and Sagerer, G. (2008, January 23\u201328). Tracking objects in 6D for reconstructing static scenes. Proceedings of the 2008 IEEE Computer Society Conference on Computer Vision and Pattern Recognition Workshops, Anchorage, AK, USA.","DOI":"10.1109\/CVPRW.2008.4563155"},{"key":"ref_19","first-page":"297","article-title":"Calibration of a PMD-camera using a planar calibration pattern together with a multicamera setup","volume":"21","author":"Schiller","year":"2008","journal-title":"ISPRS Int. J. Geo-Inf."},{"key":"ref_20","first-page":"274","article-title":"Calibration and registration for precise surface reconstruction with time of flight cameras","volume":"5","author":"Fuchs","year":"2008","journal-title":"Int. J. Int. Syst. Technol. App."},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Fuchs, S., and Hirzinger, G. (2008, January 23\u201328). Extrinsic and depth calibration of ToF-cameras. Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR), Anchorage, AK, USA.","DOI":"10.1109\/CVPR.2008.4587828"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"10080","DOI":"10.3390\/s91210080","article-title":"Sensors for 3D Imaging: Metric Evaluation and Calibration of a CCD\/CMOS Time-of-Flight Camera","volume":"9","author":"Chiabrando","year":"2009","journal-title":"Sensors"},{"key":"ref_23","first-page":"285","article-title":"Calibration of focal length and 3D pose based on the reflectance and depth image of a planar object","volume":"5","author":"Christian","year":"2008","journal-title":"Int. J. Intell. Syst. Technol. Appl."},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Kuhnert, K.D., and Stommel, M. (2006, January 9\u201315). Fusion of stereo-camera and PMD-camera data for real-time suited precise 3D environment reconstruction. Proceedings of the IEEE\/RSJ International Conference on Intelligent Robots and Systems, Beijing, China.","DOI":"10.1109\/IROS.2006.282349"},{"key":"ref_25","unstructured":"Schmidt, M. (2011). Analysis, Modeling and Dynamic Optimization of 3d Time-of-Flight Imaging Systems. [Ph.D. Thesis, University of Heidelberg]."},{"key":"ref_26","first-page":"022164","article-title":"All Pixels Calibration for ToF Camera","volume":"Volume 170","author":"Huang","year":"2018","journal-title":"Proceedings of the IOP Conference Series: Earth and Environmental Science"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"92","DOI":"10.3390\/s17010092","article-title":"Depth errors analysis and correction for Time-of-Flight (ToF) cameras","volume":"17","author":"Ying","year":"2017","journal-title":"Sensors"},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Radmer, J., Fuste, P.M., Schmidt, H., and Kruger, J. (2008, January 23\u201328). Incident light related distance error study and calibration of the PMD-range imaging camera. Proceedings of the 2008 IEEE Computer Society Conference on Computer Vision and Pattern Recognition Workshops, Anchorage, AK, USA.","DOI":"10.1109\/CVPRW.2008.4563168"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"013602","DOI":"10.1117\/1.3070634","article-title":"Theoretical and experimental error analysis of continuous-wave time-of-flight range cameras","volume":"48","author":"Frank","year":"2009","journal-title":"Opt. Eng."},{"key":"ref_30","first-page":"11","article-title":"Increasing realism and supporting content planning for dynamic scenes in a mixed reality system incorporating a Time-of-Flight camera","volume":"Volume 7","author":"Schiller","year":"2008","journal-title":"Proceedings of the IET 5th European Conference on Visual Media Production (CVMP 2008), London, UK, 26\u201327 November 2008"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"1917","DOI":"10.1109\/JSEN.2010.2101060","article-title":"Lock-in time-of-flight (ToF) cameras: A survey","volume":"11","author":"Foix","year":"2011","journal-title":"IEEE Sens. J."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"1069","DOI":"10.3390\/rs4041069","article-title":"SR-4000 and CamCube3.0 time of flight (ToF) cameras: Tests and comparison","volume":"4","author":"Piatti","year":"2012","journal-title":"Remote Sens."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"083203","DOI":"10.1117\/1.OE.51.8.083203","article-title":"Time-of-flight depth camera accuracy enhancement","volume":"51","author":"Lee","year":"2012","journal-title":"Opt. Eng."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"073103","DOI":"10.1117\/1.OE.52.7.073103","article-title":"Depth error compensation for camera fusion system","volume":"52","author":"Lee","year":"2013","journal-title":"Opt. Eng."},{"key":"ref_35","first-page":"27","article-title":"A Comparative error analysis of current Time-of-Flight sensors","volume":"2","author":"Placht","year":"2017","journal-title":"IEEE Trans. Comput. Imaging"},{"key":"ref_36","first-page":"945","article-title":"Integrated range camera calibration using image sequences from hand-held operation","volume":"37","author":"Karel","year":"2008","journal-title":"Int. Arch. Photogramm. Remote Sens. Spat. Inf. Sci."},{"key":"ref_37","doi-asserted-by":"crossref","unstructured":"Gao, J., Jia, B., Zhang, X., and Hu, L. (2011, January 16\u201318). PMD camera calibration based on adaptive bilateral filter. Proceedings of the 2011 Symposium on Photonics and Optoelectronics (SOPO), Wuhan, China.","DOI":"10.1109\/SOPO.2011.5780528"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"5333","DOI":"10.3390\/s140305333","article-title":"Calibration between color camera and 3D LIDAR instruments with a polygonal planar board","volume":"14","author":"Park","year":"2014","journal-title":"Sensors"},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"1501","DOI":"10.1109\/TPAMI.2014.2363827","article-title":"Time-of-flight sensor calibration for a color and depth camera pair","volume":"37","author":"Jung","year":"2015","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"ref_40","doi-asserted-by":"crossref","unstructured":"Villena-Mart\u00ednez, V., Fuster-Guill\u00f3, A., Azor\u00edn-L\u00f3pez, J., Saval-Calvo, M., Mora-Pascual, J., Garcia-Rodriguez, J., and Garcia-Garcia, A. (2017). A quantitative comparison of calibration methods for RGB-D sensors using different technologies. Sensors, 17.","DOI":"10.3390\/s17020243"},{"key":"ref_41","doi-asserted-by":"crossref","unstructured":"Zeng, Y., Yu, H., Dai, H., Song, S., Lin, M., Sun, B., Jiang, W., and Meng, M.Q. (2018). An improved calibration method for a rotating 2D LiDAR system. Sensors, 18.","DOI":"10.3390\/s18020497"},{"key":"ref_42","doi-asserted-by":"crossref","unstructured":"Zhai, Y., Song, P., and Chen, X. (2019). A fast calibration method for photonic mixer device solid-state array lidars. Sensors, 19.","DOI":"10.3390\/s19040822"},{"key":"ref_43","doi-asserted-by":"crossref","unstructured":"Fujioka, I., Ho, Z., Gu, X., and Koyama, F. (2020, January 10\u201315). Solid State LiDAR with Sensing Distance of over 40m using a VCSEL Beam Scanner. Proceedings of the 2020 Conference on Lasers and Electro-Optics, San Jose, CA, USA.","DOI":"10.1364\/CLEO_SI.2020.SM2M.4"},{"key":"ref_44","unstructured":"Prafulla, M., Marshall, T.D., Zhu, Z., Sridhar, C., Eric, P.F., Blair, M.K., and John, W.M. (2016). VCSEL Array for a Depth Camera. (US20150229912A1), U.S. Patent."},{"key":"ref_45","first-page":"97660D","article-title":"High-efficiency VCSEL arrays for illumination and sensing in consumer applications","volume":"Volume 9766","author":"Seurin","year":"2016","journal-title":"Vertical-Cavity Surface-Emitting Lasers XX, Proceedings of the SPIE OPTO, San Francisco, CA, USA, 4 March 2016"},{"key":"ref_46","first-page":"648403","article-title":"VCSEL proliferation","volume":"Volume 6484","author":"Tatum","year":"2007","journal-title":"Vertical-Cavity Surface-Emitting Lasers XI, Proceedings of the Integrated Optoelectronic Devices 2007, San Jose, CA, USA"},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"550","DOI":"10.1109\/TCSI.2016.2619762","article-title":"A wide dynamic range CMOS laser radar receiver with a time-domain walk error compensation scheme","volume":"64","author":"Kurtti","year":"2016","journal-title":"IEEE Trans. Circuits Syst. I-Regul. Pap."},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"167","DOI":"10.1145\/2508363.2508428","article-title":"Coded time of flight cameras: Sparse deconvolution to address multipath interference and recover time profiles","volume":"32","author":"Kadambi","year":"2013","journal-title":"ACM Trans. Graph."},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"1330","DOI":"10.1109\/34.888718","article-title":"A flexible new technique for camera calibration","volume":"22","author":"Zhang","year":"2000","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"ref_50","unstructured":"EMVA (2016, December 30). European Machine Vision Association: Downloads. Available online: www.emva.org\/standards-technology\/emva-1288\/emva-standard-1288-downloads\/."},{"key":"ref_51","doi-asserted-by":"crossref","unstructured":"Pappas, T.N., Safranek, R.J., and Chen, J. (2005). Perceptual Criteria for Image Quality Evaluation. Handbook of Image and Video Processing, Elsevier. [2nd ed.].","DOI":"10.1016\/B978-012119792-6\/50118-2"}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/20\/24\/7329\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T10:47:39Z","timestamp":1760179659000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/20\/24\/7329"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,12,20]]},"references-count":51,"journal-issue":{"issue":"24","published-online":{"date-parts":[[2020,12]]}},"alternative-id":["s20247329"],"URL":"https:\/\/doi.org\/10.3390\/s20247329","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,12,20]]}}}