ae60257d169a250f3065a94c1fdb8657 appsci_a2025m9v15n18p10205.pdf 7045dca353ef4efb8541b75d246c0f0c9e5f49b8 appsci_a2025m9v15n18p10205.pdf 969362f4a9a307a342324a19f861c83dc90d22eb8116d2f541b0e51ed9a8f434 appsci_a2025m9v15n18p10205.pdf Title: IPP and PRT Depolarizing Spaces for the Study of Depolarizing Samples: A Review Subject: Depolarizing spaces can reveal and emphasize depolarization origins in samples, making them suitable tools for target detection and disease diagnosis. The Indices of Polarization Purity (IPP) space, considered a representative depolarizing space, highlights the depolarization characteristics of samples, and has demonstrated its superiority in analyzing and identifying depolarization samples, i.e., biological tissues and scattering environments. Recently, a new polarization representation, the so-called Polarizance–Reflection–Transformation (PRT) space has been proposed, which has been employed to distinguish between non-depolarization systems, as well as analyze anisotropic depolarizers. Importantly, the IPP and PRT spaces provide complementary information of samples, hence presenting more polarimetric characterizations of the samples of interest. In consideration of the high importance of the IPP and PRT spaces in this topic, in this paper, we review the methodology of these two spaces and their applications in depolarizer distinction. Keywords: depolarizing spaces; IPP space; PRT space; isotropic depolarizers; anisotropic depolarizers Author: Dekui Li, Ivan Montes-Gonzalez, Irene Estevez, Mónica Canabal-Carbia, Octavi López-Coronado, Yuxuan Mao, Albert Van Eeckhout, Ignacio Moreno, Juan Campos, Zhongyi Guo, Yi Tan and Angel Lizana Creator: LaTeX with hyperref Producer: pdfTeX-1.40.25; modified using OpenPDF 1.4.2 CreationDate: Fri Sep 19 07:21:47 2025 CEST ModDate: Fri Sep 19 07:28:19 2025 CEST Custom Metadata: yes Metadata Stream: no Tagged: no UserProperties: no Suspects: no Form: none JavaScript: no Pages: 24 Encrypted: no Page size: 595.276 x 841.89 pts (A4) Page rot: 0 File size: 2973873 bytes Optimized: no PDF version: 1.5 name type encoding emb sub uni object ID ------------------------------------ ----------------- ---------------- --- --- --- --------- TFRUJJ+VnURWPalladioL Type 1 Custom yes yes yes 144 0 CDKQEL+URWPalladioL-Bold Type 1 Custom yes yes yes 145 0 QJHNRB+URWPalladioL-Roma Type 1 Custom yes yes yes 146 0 XUGWGJ+URWPalladioL-Ital Type 1 Custom yes yes yes 147 0 HVSBKL+PazoMath Type 1 Builtin yes yes yes 189 0 GIGFZE+CMR10 Type 1 Builtin yes yes yes 244 0 QOWLGJ+CMEX10 Type 1 Builtin yes yes yes 245 0 WBNSWJ+CMSY10 Type 1 Builtin yes yes yes 272 0 FVGOTS+EURB10 Type 1 Builtin yes yes yes 288 0 CSQKEL+PazoMath-Italic Type 1 Builtin yes yes yes 289 0 DJPBKI+PalatinoLinotype TrueType WinAnsi yes yes no 268 0 ZYSYNW+EURM10 Type 1 Builtin yes yes yes 332 0 DJPBLK+PalatinoLinotype,Italic TrueType WinAnsi yes yes no 353 0 DJPBKI+PalatinoLinotype TrueType WinAnsi yes yes no 354 0 DJPBLK+PalatinoLinotype,Italic TrueType WinAnsi yes yes no 401 0 DJPBKI+PalatinoLinotype TrueType WinAnsi yes yes no 402 0 DJPBLK+PalatinoLinotype,Italic TrueType WinAnsi yes yes no 427 0 DJPBKI+PalatinoLinotype TrueType WinAnsi yes yes no 428 0 DJPBKI+PalatinoLinotype TrueType WinAnsi yes yes no 463 0 DJPCKD+CambriaMath TrueType WinAnsi yes yes no 464 0 DJPBLK+PalatinoLinotype,Italic TrueType WinAnsi yes yes no 499 0 DJPBKI+PalatinoLinotype TrueType WinAnsi yes yes no 500 0 RLYTRW+CMMI10 Type 1 Builtin yes yes yes 543 0 DJPBKI+PalatinoLinotype TrueType WinAnsi yes yes no 539 0 DJPBLK+PalatinoLinotype,Italic TrueType WinAnsi yes yes no 563 0 DJPBKI+PalatinoLinotype TrueType WinAnsi yes yes no 564 0 DJPBKG+PalatinoLinotype,Bold TrueType WinAnsi yes yes no 565 0 YLHTYT+URWPalladioL-BoldItal Type 1 Custom yes yes yes 608 0 DJPBLK+PalatinoLinotype,Italic TrueType WinAnsi yes yes no 599 0 DJPBKI+PalatinoLinotype TrueType WinAnsi yes yes no 600 0 MDIKPC+CMBSY10 Type 1 Builtin yes yes yes 627 0 Jhove (Rel. 1.28.0, 2023-05-18) Date: 2025-10-23 03:50:04 CEST RepresentationInformation: appsci_a2025m9v15n18p10205.pdf ReportingModule: PDF-hul, Rel. 1.12.4 (2023-03-16) LastModified: 2025-10-22 14:11:12 CEST Size: 2973873 Format: PDF Version: 1.5 Status: Well-Formed and valid SignatureMatches: PDF-hul MIMEtype: application/pdf PDFMetadata: Objects: 761 FreeObjects: 1 IncrementalUpdates: 0 DocumentCatalog: ViewerPreferences: HideToolbar: false HideMenubar: false HideWindowUI: false FitWindow: true CenterWindow: false DisplayDocTitle: false NonFullScreenPageMode: UseNone Direction: L2R ViewArea: CropBox ViewClip: CropBox PrintArea: CropBox PageClip: CropBox PageLayout: SinglePage PageMode: UseNone Outlines: Item: Title: Introduction Item: Title: Methodology of Depolarizing Spaces Children: Item: Title: The PRT Space Item: Title: The IPP Space Item: Title: Characteristic Decomposition of MMs Item: Title: Discriminating Between Anisotropic and Isotropic Depolarization Origins by the IPP Space Children: Item: Title: Anisotropic Origin Behavior Presented by IPP Channels Item: Title: Isotropic Depolarization Behavior Presented by IPP Item: Title: Combining IPP and PRT Spaces for the Characterization of Anisotropic Depolarizers Children: Item: Title: Retarder-Based and Diattenuator-Based Depolarizer Discrimination Item: Title: Characterization of Anisotropic Depolarizers According to Their Inherent Structural Characteristics Item: Title: Physical Parameter Characterization from PRT Space Polarimetric Observables Item: Title: Experimental Validation Children: Item: Title: Experimental Results for the P3 = 1 Case Item: Title: Experimental Results for the P3 < 1 Case Item: Title: Conclusions Item: Title: References Info: Title: IPP and PRT Depolarizing Spaces for the Study of Depolarizing Samples: A Review Author: Dekui Li, Ivan Montes-Gonzalez, Irene Estevez, Mónica Canabal-Carbia, Octavi López-Coronado, Yuxuan Mao, Albert Van Eeckhout, Ignacio Moreno, Juan Campos, Zhongyi Guo, Yi Tan and Angel Lizana Subject: Depolarizing spaces can reveal and emphasize depolarization origins in samples, making them suitable tools for target detection and disease diagnosis. The Indices of Polarization Purity (IPP) space, considered a representative depolarizing space, highlights the depolarization characteristics of samples, and has demonstrated its superiority in analyzing and identifying depolarization samples, i.e., biological tissues and scattering environments. Recently, a new polarization representation, the so-called Polarizance–Reflection–Transformation (PRT) space has been proposed, which has been employed to distinguish between non-depolarization systems, as well as analyze anisotropic depolarizers. Importantly, the IPP and PRT spaces provide complementary information of samples, hence presenting more polarimetric characterizations of the samples of interest. In consideration of the high importance of the IPP and PRT spaces in this topic, in this paper, we review the methodology of these two spaces and their applications in depolarizer distinction. Keywords: depolarizing spaces; IPP space; PRT space; isotropic depolarizers; anisotropic depolarizers Creator: LaTeX with hyperref Producer: pdfTeX-1.40.25; modified using OpenPDF 1.4.2 CreationDate: Fri Sep 19 07:21:47 CEST 2025 ModDate: Fri Sep 19 07:28:19 CEST 2025 ID: 0x98b4a9b8a00dc86dcbf2847243e0cb4e, 0x073c967a7119fdd0680ed9b8da140e0b Filters: FilterPipeline: FlateDecode Fonts: Type1: Font: BaseFont: FVGOTS+EURB10 FontSubset: true FirstChar: 27 LastChar: 27 FontDescriptor: FontName: FVGOTS+EURB10 Flags: Symbolic FontBBox: -30, -247, 1178, 723 FontFile: true ToUnicode: true Font: BaseFont: YLHTYT+URWPalladioL-BoldItal FontSubset: true FirstChar: 80 LastChar: 80 FontDescriptor: FontName: YLHTYT+URWPalladioL-BoldItal Flags: Symbolic FontBBox: -170, -300, 1073, 935 FontFile: true EncodingDictionary: Differences: true ToUnicode: true Font: BaseFont: CSQKEL+PazoMath-Italic FontSubset: true FirstChar: 97 LastChar: 115 FontDescriptor: FontName: CSQKEL+PazoMath-Italic Flags: Symbolic 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Subtype: Link Rect: 462, 258, 500, 269 Annotation: Subtype: Link Rect: 506, 258, 542, 269 Checksum: c16e4f8c Type: CRC32 Checksum: ae60257d169a250f3065a94c1fdb8657 Type: MD5 Checksum: 7045dca353ef4efb8541b75d246c0f0c9e5f49b8 Type: SHA-1 Checksum: 969362f4a9a307a342324a19f861c83dc90d22eb8116d2f541b0e51ed9a8f434 Type: SHA-256