{"id":1996,"date":"2026-08-26T12:00:00","date_gmt":"2026-08-26T12:00:00","guid":{"rendered":"https:\/\/lumexislaser.com\/?p=1996"},"modified":"2026-08-21T17:11:42","modified_gmt":"2026-08-21T17:11:42","slug":"laser-rangefinder-beam-divergence","status":"publish","type":"post","link":"https:\/\/lumexislaser.com\/ar\/laser-rangefinder-beam-divergence\/","title":{"rendered":"\u062a\u0628\u0627\u0639\u062f \u0634\u0639\u0627\u0639 \u062c\u0647\u0627\u0632 \u062a\u062d\u062f\u064a\u062f \u0627\u0644\u0645\u062f\u0649 \u0628\u0627\u0644\u0644\u064a\u0632\u0631: \u062f\u0644\u064a\u0644 \u0627\u062d\u062a\u0645\u0627\u0644\u064a\u0629 \u0627\u0644\u0625\u0635\u0627\u0628\u0629"},"content":{"rendered":"<p>\u0642\u064a\u0645\u0629 \u062a\u0628\u0627\u0639\u062f \u0635\u063a\u064a\u0631\u0629 \u062a\u0628\u062f\u0648 \u062c\u0630\u0627\u0628\u0629 \u0641\u064a \u0648\u0631\u0642\u0629 \u0627\u0644\u0628\u064a\u0627\u0646\u0627\u062a. \u0648\u0645\u0639 \u0630\u0644\u0643\u060c \u0639\u0644\u0649 \u0627\u0644\u0645\u062f\u0649 \u0627\u0644\u0637\u0648\u064a\u0644\u060c \u064a\u0645\u0643\u0646 \u0644\u0634\u0639\u0627\u0639 \u0636\u064a\u0642 \u0623\u0646 \u064a\u062e\u0637\u0626 \u0647\u062f\u0641\u064b\u0627 \u0636\u064a\u0642\u064b\u0627 \u0639\u0646\u062f\u0645\u0627 \u064a\u062d\u0631\u0643 \u062e\u0637\u0623 \u0627\u0644\u062a\u0648\u062c\u064a\u0647\u060c \u0623\u0648 \u062d\u0631\u0643\u0629 \u0627\u0644\u0645\u0646\u0635\u0629\u060c \u0623\u0648 \u0627\u0644\u0627\u0647\u062a\u0632\u0627\u0632\u060c \u0623\u0648 \u062d\u0631\u0643\u0629 \u0627\u0644\u0647\u062f\u0641 \u0627\u0644\u0628\u0642\u0639\u0629 \u0628\u0639\u064a\u062f\u064b\u0627 \u0639\u0646 \u0627\u0644\u0646\u0642\u0637\u0629 \u0627\u0644\u0645\u0642\u0635\u0648\u062f\u0629.<\/p>\n<p>\u062c\u0639\u0644 \u0627\u0644\u0634\u0639\u0627\u0639 \u0623\u0639\u0631\u0636 \u0644\u064a\u0633 \u062d\u0644\u0627\u064b \u0645\u062c\u0627\u0646\u064a\u064b\u0627. \u0646\u0641\u0633 \u0637\u0627\u0642\u0629 \u0627\u0644\u0646\u0628\u0636\u0629 \u062a\u0646\u062a\u0634\u0631 \u0639\u0644\u0649 \u0645\u0633\u0627\u062d\u0629 \u0623\u0643\u0628\u0631\u060c \u0644\u0630\u0627 \u064a\u0635\u0644 \u0642\u062f\u0631 \u0623\u0642\u0644 \u0625\u0644\u0649 \u0647\u062f\u0641 \u0635\u063a\u064a\u0631 \u0648\u0642\u062f \u064a\u0636\u064a\u0621 \u0627\u0644\u0645\u0632\u064a\u062f \u0645\u0646\u0647\u0627 \u0623\u0633\u0637\u062d \u0627\u0644\u0645\u0642\u062f\u0645\u0629 \u0623\u0648 \u0627\u0644\u062e\u0644\u0641\u064a\u0629.<\/p>\n<p><strong>\u062a\u0628\u0627\u0639\u062f \u0634\u0639\u0627\u0639 \u062c\u0647\u0627\u0632 \u062a\u062d\u062f\u064a\u062f \u0627\u0644\u0645\u062f\u0649 \u0628\u0627\u0644\u0644\u064a\u0632\u0631 \u064a\u062d\u062f\u062f \u0645\u062f\u0649 \u0633\u0631\u0639\u0629 \u0646\u0645\u0648 \u0627\u0644\u0628\u0642\u0639\u0629 \u0627\u0644\u0645\u0631\u0633\u0644\u0629 \u0645\u0639 \u0627\u0644\u0645\u0633\u0627\u0641\u0629. \u062a\u0628\u0627\u0639\u062f 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\u0627\u0644\u064a\u0642\u064a\u0646 \u0641\u064a \u0627\u0644\u062a\u0648\u062c\u064a\u0647\u060c \u0648\u0627\u0644\u0645\u062f\u0649\u060c \u0648\u0645\u062c\u0627\u0644 \u0631\u0624\u064a\u0629 \u0627\u0644\u0645\u0633\u062a\u0642\u0628\u0644\u060c \u0648\u0627\u062d\u062a\u0645\u0627\u0644 \u0627\u0644\u0643\u0634\u0641 \u0627\u0644\u0635\u062d\u064a\u062d \u0627\u0644\u0645\u0637\u0644\u0648\u0628.<\/strong><\/p>\n<h2>\u0645\u0627 \u0627\u0644\u0630\u064a \u064a\u062d\u062f\u062f\u0647 \u062a\u0628\u0627\u0639\u062f \u0634\u0639\u0627\u0639 \u062c\u0647\u0627\u0632 \u062a\u062d\u062f\u064a\u062f \u0627\u0644\u0645\u062f\u0649 \u0628\u0627\u0644\u0644\u064a\u0632\u0631 \u0641\u0639\u0644\u064a\u064b\u0627<\/h2>\n<p>\u062a\u0628\u0627\u0639\u062f \u0627\u0644\u0634\u0639\u0627\u0639 \u0647\u0648 \u0648\u0635\u0641 \u0632\u0627\u0648\u064a \u0644\u0646\u0645\u0648 \u0627\u0644\u0634\u0639\u0627\u0639\u060c \u064a\u064f\u0628\u0644\u063a \u0639\u0646\u0647 \u0639\u0627\u062f\u0629\u064b \u0628\u0627\u0644\u0645\u064a\u0644\u064a \u0631\u0627\u062f\u064a\u0627\u0646. \u0625\u0646\u0647 \u0644\u064a\u0633 \u0645\u062e\u0631\u0648\u0637\u064b\u0627 \u0635\u0644\u0628\u064b\u0627. \u0627\u0644\u062d\u0632\u0645 \u0627\u0644\u062d\u0642\u064a\u0642\u064a\u0629 \u0644\u0647\u0627 \u062a\u0648\u0632\u064a\u0639 \u0634\u062f\u0629\u060c \u0648\u0627\u0644\u062d\u062f \u0627\u0644\u0645\u0630\u0643\u0648\u0631 \u064a\u0639\u062a\u0645\u062f \u0639\u0644\u0649 \u0643\u064a\u0641\u064a\u0629 \u062a\u0639\u0631\u064a\u0641 \u0639\u0631\u0636 \u0627\u0644\u0634\u0639\u0627\u0639.<\/p>\n<p>\u0644\u0634\u0639\u0627\u0639 \u063a\u0627\u0648\u0633\u064a\u060c \u0646\u0635\u0641 \u0627\u0644\u0642\u0637\u0631 \u0639\u0646\u062f 1\/e\u00b2 \u0647\u0648 \u0627\u0644\u0646\u0642\u0637\u0629 \u0627\u0644\u062a\u064a \u062a\u0646\u062e\u0641\u0636 \u0641\u064a\u0647\u0627 \u0627\u0644\u0634\u062f\u0629 \u0625\u0644\u0649 \u062d\u0648\u0627\u0644\u064a 13.5\u066a \u0645\u0646 \u0642\u064a\u0645\u062a\u0647\u0627 \u0639\u0644\u0649 \u0627\u0644\u0645\u062d\u0648\u0631. \u0627\u0644\u0639\u0631\u0636 \u0627\u0644\u0643\u0627\u0645\u0644 \u0639\u0646\u062f \u0646\u0635\u0641 \u0627\u0644\u062d\u062f \u0627\u0644\u0623\u0642\u0635\u0649 (FWHM) \u064a\u0635\u0641 \u062c\u0632\u0621\u064b\u0627 \u0623\u0636\u064a\u0642 \u0645\u0646 \u0646\u0641\u0633 \u0627\u0644\u0645\u0644\u0641. \u064a\u0633\u062a\u062e\u062f\u0645 ISO 11146 \u0646\u0647\u062c \u0627\u0644\u0639\u0632\u0645 \u0627\u0644\u062b\u0627\u0646\u064a\u060c \u0623\u0648 D4\u03c3\u060c \u0644\u0642\u064a\u0627\u0633\u0627\u062a \u0639\u0631\u0636 \u0627\u0644\u0634\u0639\u0627\u0639 \u0648\u0627\u0644\u0627\u0646\u062a\u0634\u0627\u0631. \u0644\u0627 \u064a\u0646\u0628\u063a\u064a \u0645\u0642\u0627\u0631\u0646\u0629 \u0647\u0630\u0647 \u0627\u0644\u0642\u064a\u0645 \u0643\u0645\u0627 \u0644\u0648 \u0643\u0627\u0646\u062a \u0642\u0627\u0628\u0644\u0629 \u0644\u0644\u062a\u0628\u0627\u062f\u0644.<\/p>\n<p>\u0627\u0644\u0645\u0648\u0627\u0635\u0641\u0629 \u0627\u0644\u0643\u0627\u0645\u0644\u0629 \u062a\u0646\u0635 \u0639\u0644\u0649 \u0645\u0627 \u0625\u0630\u0627 \u0643\u0627\u0646 \u0627\u0644\u062a\u0628\u0627\u0639\u062f \u0632\u0627\u0648\u064a\u0629 \u0643\u0627\u0645\u0644\u0629 \u0623\u0648 \u0646\u0635\u0641 \u0632\u0627\u0648\u064a\u0629. \u0627\u0644\u0634\u0639\u0627\u0639 \u0627\u0644\u0625\u0647\u0644\u064a\u0644\u062c\u064a \u064a\u062d\u062a\u0627\u062c \u0625\u0644\u0649 \u0642\u064a\u0645 \u0623\u0641\u0642\u064a\u0629 \u0648\u0631\u0623\u0633\u064a\u0629. \u0627\u0633\u0623\u0644 \u0639\u0646 \u0645\u0627 \u062a\u0645 \u0642\u064a\u0627\u0633\u0647\u060c \u0648\u0639\u0644\u0649 \u0623\u064a \u0645\u062d\u0627\u0648\u0631\u060c \u0648\u062a\u062d\u062a \u0623\u064a \u0634\u0631\u0637\u060c \u0648\u0645\u0646 \u0623\u064a \u0645\u0633\u062a\u0648\u0649 \u0645\u0631\u062c\u0639\u064a.<\/p>\n<figure><img decoding=\"async\" src=\"https:\/\/lumexislaser.com\/wp-content\/uploads\/2026\/08\/lumexis-rangefinder-divergence-body-measurement-conventions-v01.webp\" alt=\"Diagram comparing 1\/e squared, FWHM, and D4 sigma beam-width conventions with full-angle and half-angle divergence.\" \/><\/figure>\n<p>\u062f\u0644\u064a\u0644\u0646\u0627 \u062d\u0648\u0644 <a href=\"https:\/\/lumexislaser.com\/ar\/how-does-a-laser-rangefinder-work\/\">\u0643\u064a\u0641 \u064a\u0642\u064a\u0633 \u062c\u0647\u0627\u0632 \u062a\u062d\u062f\u064a\u062f \u0627\u0644\u0645\u062f\u0649 \u0627\u0644\u0646\u0628\u0636\u064a \u0627\u0644\u0645\u0633\u0627\u0641\u0629<\/a> \u064a\u0634\u0631\u062d \u0633\u0644\u0633\u0644\u0629 \u062a\u0648\u0642\u064a\u062a \u0627\u0644\u0631\u062d\u0644\u0629 \u0630\u0647\u0627\u0628\u064b\u0627 \u0648\u0625\u064a\u0627\u0628\u064b\u0627 \u0627\u0644\u0645\u0646\u0641\u0635\u0644\u0629.<\/p>\n<h2>\u062a\u062d\u0648\u064a\u0644 \u0627\u0644\u062a\u0628\u0627\u0639\u062f \u0625\u0644\u0649 \u0628\u0642\u0639\u0629 \u0639\u0646\u062f \u0627\u0644\u0645\u062f\u0649<\/h2>\n<p>\u0644\u0642\u0637\u0631 \u0634\u0639\u0627\u0639 \u0623\u0648\u0644\u064a <code>D\u2080<\/code>, \u060c \u0645\u0633\u0627\u0641\u0629 \u0627\u0644\u0639\u0645\u0644 <code>L<\/code>, \u060c \u0648\u062a\u0628\u0627\u0639\u062f \u0627\u0644\u0632\u0627\u0648\u064a\u0629 \u0627\u0644\u0643\u0627\u0645\u0644\u0629 <code>\u0398<\/code>, \u060c \u062a\u0642\u062f\u064a\u0631 \u0647\u0646\u062f\u0633\u064a \u0628\u0633\u064a\u0637 \u0647\u0648:<\/p>\n<p><code>D(L) = D\u2080 + 2L tan(\u0398\/2)<\/code><\/p>\n<p>\u0639\u0646\u062f\u0645\u0627 \u062a\u0643\u0648\u0646 \u0627\u0644\u0632\u0627\u0648\u064a\u0629 \u0635\u063a\u064a\u0631\u0629 \u0648\u0645\u0639\u0628\u0631\u064b\u0627 \u0639\u0646\u0647\u0627 \u0628\u0627\u0644\u0631\u0627\u062f\u064a\u0627\u0646\u060c \u064a\u0635\u0628\u062d \u0647\u0630\u0627 \u062a\u0642\u0631\u064a\u0628\u064b\u0627 <code>D(L) \u2248 D\u2080 + L\u0398<\/code>. \u0644\u0630\u0644\u0643 \u064a\u0636\u064a\u0641 \u0627\u0644\u0645\u064a\u0644\u064a \u0631\u0627\u062f\u064a\u0627\u0646 \u0627\u0644\u0648\u0627\u062d\u062f \u062d\u0648\u0627\u0644\u064a \u0645\u062a\u0631 \u0648\u0627\u062d\u062f \u0645\u0646 \u0627\u0644\u0642\u0637\u0631 \u0644\u0643\u0644 \u0643\u064a\u0644\u0648\u0645\u062a\u0631\u060c \u0642\u0628\u0644 \u0627\u0644\u0646\u0638\u0631 \u0641\u064a \u0627\u0644\u0642\u0637\u0631 \u0627\u0644\u0623\u0648\u0644\u064a \u0648\u062a\u0623\u062b\u064a\u0631\u0627\u062a \u0627\u0644\u0627\u0646\u062a\u0634\u0627\u0631 \u0627\u0644\u0623\u062e\u0631\u0649.<\/p>\n<p>\u064a\u0639\u0645\u0644 \u0627\u0644\u062a\u0642\u062f\u064a\u0631 \u0641\u0642\u0637 \u0639\u0646\u062f\u0645\u0627 \u064a\u0643\u0648\u0646 \u0627\u0644\u0627\u0635\u0637\u0644\u0627\u062d \u0648\u0627\u0636\u062d\u064b\u0627. \u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0646\u0635\u0641 \u0632\u0627\u0648\u064a\u0629 \u0643\u0632\u0627\u0648\u064a\u0629 \u0643\u0627\u0645\u0644\u0629 \u064a\u062e\u0644\u0642 \u062e\u0637\u0623\u064b \u0628\u0639\u0627\u0645\u0644 \u0627\u062b\u0646\u064a\u0646 \u0641\u064a \u0645\u0635\u0637\u0644\u062d \u0627\u0644\u0646\u0645\u0648. \u0627\u062d\u0633\u0628 \u0643\u0644\u0627 \u0627\u0644\u0645\u062d\u0648\u0631\u064a\u0646 \u0644\u0634\u0639\u0627\u0639 \u0625\u0647\u0644\u064a\u0644\u062c\u064a. \u0627\u0644\u0647\u062f\u0641 \u0627\u0644\u0645\u0627\u0626\u0644 \u064a\u0631\u0649 \u0623\u064a\u0636\u064b\u0627 \u0628\u0642\u0639\u0629 \u0645\u0645\u062f\u0648\u062f\u0629.<\/p>\n<p>\u0644\u0627 \u062a\u0639\u0627\u0645\u0644 \u0627\u0644\u0642\u0637\u0631 \u0627\u0644\u0645\u062d\u0633\u0648\u0628 \u0643\u062d\u062f \u062d\u0627\u062f \u064a\u062d\u062a\u0648\u064a \u0639\u0644\u0649 \u0625\u0634\u0639\u0627\u0639 \u0645\u062a\u0633\u0627\u0648\u064d. \u0645\u0644\u0641 \u0627\u0644\u0634\u0639\u0627\u0639\u060c \u0648\u0627\u0644\u0627\u0642\u062a\u0637\u0627\u0639\u060c \u0648\u062a\u0623\u062b\u064a\u0631\u0627\u062a \u0627\u0644\u0646\u0627\u0641\u0630\u0629 \u0627\u0644\u0628\u0635\u0631\u064a\u0629\u060c \u0648\u0645\u0648\u0636\u0639 \u0627\u0644\u062a\u0631\u0643\u064a\u0632\u060c \u0648\u062c\u0648\u062f\u0629 \u0627\u0644\u0634\u0639\u0627\u0639 \u062a\u063a\u064a\u0631 \u062a\u0648\u0632\u064a\u0639 \u0627\u0644\u0637\u0627\u0642\u0629 \u062f\u0627\u062e\u0644 \u0648\u062e\u0627\u0631\u062c \u0627\u0644\u0643\u0641\u0627\u0641 \u0627\u0644\u0645\u0633\u0645\u0649. \u0627\u0644\u0640 <a href=\"https:\/\/lumexislaser.com\/ar\/laser-rangefinder-module-datasheet\/\">\u062f\u0644\u064a\u0644 \u0648\u0631\u0642\u0629 \u0628\u064a\u0627\u0646\u0627\u062a \u062c\u0647\u0627\u0632 \u0642\u064a\u0627\u0633 \u0627\u0644\u0645\u062f\u0649<\/a> \u064a\u0633\u0631\u062f \u0627\u0644\u0634\u0631\u0648\u0637 \u0627\u0644\u0644\u0627\u0632\u0645\u0629 \u0644\u062a\u0641\u0633\u064a\u0631 \u0627\u0644\u0647\u0646\u062f\u0633\u0629 \u062c\u0646\u0628\u064b\u0627 \u0625\u0644\u0649 \u062c\u0646\u0628 \u0645\u0639 \u0627\u062f\u0639\u0627\u0621\u0627\u062a \u0627\u0644\u0645\u062f\u0649.<\/p>\n<h2>\u0627\u062d\u062a\u0645\u0627\u0644 \u0627\u0644\u0625\u0635\u0627\u0628\u0629 \u0644\u064a\u0633 \u0646\u0641\u0633 \u0627\u062d\u062a\u0645\u0627\u0644 \u0627\u0644\u0643\u0634\u0641<\/h2>\n<p>\u201c\u0627\u062d\u062a\u0645\u0627\u0644 \u0627\u0644\u0625\u0635\u0627\u0628\u0629\u201d \u064a\u064f\u0633\u062a\u062e\u062f\u0645 \u063a\u0627\u0644\u0628\u064b\u0627 \u0628\u0634\u0643\u0644 \u0641\u0636\u0641\u0627\u0636. \u0646\u0645\u0648\u0630\u062c \u0647\u0646\u062f\u0633\u064a \u0645\u0641\u064a\u062f \u064a\u0641\u0635\u0644 \u062b\u0644\u0627\u062b\u0629 \u0623\u0633\u0626\u0644\u0629 \u0639\u0644\u0649 \u0627\u0644\u0623\u0642\u0644.<\/p>\n<ol>\n<li><strong>\u0627\u062d\u062a\u0645\u0627\u0644 \u0627\u0644\u0625\u0636\u0627\u0621\u0629:<\/strong> \u0647\u0644 \u064a\u062a\u062f\u0627\u062e\u0644 \u062c\u0632\u0621 \u0643\u0627\u0641\u064d \u0645\u0646 \u0627\u0644\u0628\u0642\u0639\u0629 \u0627\u0644\u0645\u0631\u0633\u0644\u0629 \u0645\u0639 \u0627\u0644\u0647\u062f\u0641 \u0627\u0644\u0645\u0642\u0635\u0648\u062f\u060c \u0628\u0627\u0644\u0646\u0638\u0631 \u0625\u0644\u0649 \u062e\u0637\u0623 \u0627\u0644\u062a\u0648\u062c\u064a\u0647 \u0648\u0627\u0644\u062d\u0631\u0643\u0629\u061f<\/li>\n<li><strong>\u0627\u062d\u062a\u0645\u0627\u0644 \u0627\u0644\u0643\u0634\u0641 \u0627\u0644\u0634\u0631\u0637\u064a:<\/strong> \u0639\u0646\u062f\u0645\u0627 \u064a\u0643\u0648\u0646 \u0627\u0644\u0647\u062f\u0641 \u0645\u0636\u0627\u0621\u064b\u060c \u0647\u0644 \u064a\u0639\u0628\u0631 \u0639\u0627\u0626\u062f\u0647 \u0627\u0644\u0645\u0633\u062a\u0642\u0628\u0644 \u0648\u0645\u0639\u064a\u0627\u0631 \u0627\u0644\u0645\u0639\u0627\u0644\u062c\u0629\u061f<\/li>\n<li><strong>\u0627\u062d\u062a\u0645\u0627\u0644 \u0627\u0644\u0645\u062f\u0649 \u0627\u0644\u0635\u062d\u064a\u062d:<\/strong> \u0647\u0644 \u064a\u062e\u062a\u0627\u0631 \u0627\u0644\u0646\u0638\u0627\u0645 \u0627\u0644\u0635\u062f\u0649 \u0627\u0644\u0645\u0642\u0635\u0648\u062f \u0648\u064a\u0628\u0644\u063a \u0639\u0646 \u0645\u0633\u0627\u0641\u0629 \u062f\u0627\u062e\u0644 \u0646\u0627\u0641\u0630\u0629 \u0627\u0644\u062e\u0637\u0623 \u0627\u0644\u0645\u0633\u0645\u0648\u062d \u0628\u0647\u0627\u061f<\/li>\n<\/ol>\n<p>\u0628\u0642\u0639\u0629 \u0623\u0639\u0631\u0636 \u064a\u0645\u0643\u0646 \u0623\u0646 \u062a\u062d\u0633\u0646 \u0627\u0644\u0627\u062d\u062a\u0645\u0627\u0644 \u0627\u0644\u0623\u0648\u0644 \u0639\u0646\u062f\u0645\u0627 \u064a\u0647\u064a\u0645\u0646 \u0639\u062f\u0645 \u0627\u0644\u064a\u0642\u064a\u0646 \u0641\u064a \u0627\u0644\u062a\u0648\u062c\u064a\u0647. \u0642\u062f \u062a\u0642\u0644\u0644 \u0627\u0644\u062b\u0627\u0646\u064a \u0625\u0630\u0627 \u0648\u0635\u0644 \u062c\u0632\u0621 \u0635\u063a\u064a\u0631 \u0641\u0642\u0637 \u0645\u0646 \u0627\u0644\u0646\u0628\u0636\u0629 \u0625\u0644\u0649 \u0627\u0644\u0647\u062f\u0641. \u064a\u0645\u0643\u0646 \u0623\u064a\u0636\u064b\u0627 \u0623\u0646 \u062a\u0642\u0644\u0644 \u0627\u0644\u062b\u0627\u0644\u062b \u0628\u0627\u0644\u0642\u0631\u0628 \u0645\u0646 \u0627\u0644\u062d\u0648\u0627\u0641 \u0639\u0646\u062f\u0645\u0627 \u064a\u0633\u0627\u0647\u0645 \u0633\u0637\u062d \u0622\u062e\u0631 \u0628\u0635\u062f\u0649 \u0623\u0642\u0648\u0649 \u0623\u0648 \u0623\u0628\u0643\u0631.<\/p>\n<figure><img decoding=\"async\" src=\"https:\/\/lumexislaser.com\/wp-content\/uploads\/2026\/08\/lumexis-rangefinder-divergence-body-hit-vs-detection-v01.webp\" alt=\"Conceptual comparison separating beam overlap hit probability from sufficient returned signal for laser range detection.\" \/><\/figure>\n<p>\u0644\u0627 \u062a\u0628\u0644\u063a \u0639\u0646 \u0627\u0644\u062f\u0642\u0629 \u0641\u0642\u0637 \u0644\u0644\u0642\u0631\u0627\u0621\u0627\u062a \u0627\u0644\u0646\u0627\u062c\u062d\u0629. \u064a\u0645\u0643\u0646 \u0644\u0644\u0646\u0638\u0627\u0645 \u0627\u0644\u062d\u0641\u0627\u0638 \u0639\u0644\u0649 \u062e\u0637\u0623 \u0636\u064a\u0642 \u0639\u0644\u0649 \u0627\u0644\u0625\u0634\u0627\u0631\u0627\u062a \u0627\u0644\u0645\u0642\u0628\u0648\u0644\u0629 \u0628\u064a\u0646\u0645\u0627 \u064a\u062e\u0637\u0626 \u0623\u0643\u062b\u0631. \u0633\u062c\u0644 \u0627\u0644\u0625\u0634\u0627\u0631\u0627\u062a \u0627\u0644\u062e\u0627\u0637\u0626\u0629 \u0648\u0627\u0644\u063a\u0627\u0626\u0628\u0629 \u0628\u0627\u0644\u0625\u0636\u0627\u0641\u0629 \u0625\u0644\u0649 \u062a\u0648\u0632\u064a\u0639 \u0627\u0644\u062e\u0637\u0623 \u0644\u0644\u0646\u062a\u0627\u0626\u062c \u0627\u0644\u0635\u062d\u064a\u062d\u0629.<\/p>\n<h2>\u0627\u0644\u062d\u0632\u0645 \u0627\u0644\u0623\u0636\u064a\u0642 \u0648\u0627\u0644\u0623\u0639\u0631\u0636 \u062a\u062d\u0644 \u0645\u0634\u0627\u0643\u0644 \u0645\u062e\u062a\u0644\u0641\u0629<\/h2>\n<p>\u0644\u0627 \u064a\u0648\u062c\u062f \u0627\u062a\u062c\u0627\u0647 \u0623\u0641\u0636\u0644 \u0639\u0627\u0644\u0645\u064a\u064b\u0627. \u0645\u064a\u0632\u0627\u0646\u064a\u0627\u062a \u0627\u0644\u062e\u0637\u0623 \u0648\u0627\u0644\u0625\u0634\u0627\u0631\u0629 \u0627\u0644\u0645\u0647\u064a\u0645\u0646\u0629 \u0647\u064a \u0627\u0644\u062a\u064a \u062a\u0642\u0631\u0631.<\/p>\n<table>\n<thead>\n<tr>\n<th>\u0645\u0635\u062f\u0631 \u0627\u0644\u0642\u0644\u0642 \u0627\u0644\u062a\u0635\u0645\u064a\u0645\u064a<\/th>\n<th>\u0627\u0644\u062a\u0628\u0627\u0639\u062f \u0627\u0644\u0623\u0636\u064a\u0642 \u064a\u0645\u064a\u0644 \u0625\u0644\u0649 \u0627\u0644\u0645\u0633\u0627\u0639\u062f\u0629<\/th>\n<th>\u0627\u0644\u062a\u0628\u0627\u0639\u062f \u0627\u0644\u0623\u0639\u0631\u0636 \u064a\u0645\u064a\u0644 \u0625\u0644\u0649 \u0627\u0644\u0645\u0633\u0627\u0639\u062f\u0629<\/th>\n<th>\u062a\u062d\u0642\u0642 \u0642\u0628\u0644 \u0627\u0644\u0627\u062e\u062a\u064a\u0627\u0631<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>\u0645\u062f\u0649 \u0637\u0648\u064a\u0644 \u0623\u0648 \u0639\u0627\u0626\u062f \u0645\u0646\u062e\u0641\u0636<\/td>\n<td>\u0625\u0634\u0639\u0627\u0639 \u0647\u062f\u0641 \u0623\u0639\u0644\u0649 \u0639\u0646\u062f \u0627\u0644\u0645\u062d\u0627\u0630\u0627\u0629<\/td>\n<td>\u2014<\/td>\n<td>\u0637\u0627\u0642\u0629 \u0627\u0644\u0646\u0628\u0636\u0629\u060c \u0627\u0639\u062a\u0631\u0627\u0636 \u0627\u0644\u0647\u062f\u0641\u060c \u0627\u0644\u063a\u0644\u0627\u0641 \u0627\u0644\u062c\u0648\u064a\u060c \u062d\u0633\u0627\u0633\u064a\u0629 \u0627\u0644\u0645\u0633\u062a\u0642\u0628\u0644<\/td>\n<\/tr>\n<tr>\n<td>\u0645\u064a\u0632\u0629 \u0635\u063a\u064a\u0631\u0629 \u0628\u0627\u0644\u0642\u0631\u0628 \u0645\u0646 \u0627\u0644\u062e\u0644\u0641\u064a\u0629<\/td>\n<td>\u0627\u0644\u0627\u0646\u062a\u0642\u0627\u0626\u064a\u0629 \u0627\u0644\u0645\u0643\u0627\u0646\u064a\u0629<\/td>\n<td>\u2014<\/td>\n<td>\u0627\u0633\u062a\u0642\u0631\u0627\u0631 \u0627\u0644\u062a\u0648\u062c\u064a\u0647 \u0648\u0645\u0644\u0641 \u0627\u0644\u0634\u0639\u0627\u0639<\/td>\n<\/tr>\n<tr>\n<td>\u0627\u0631\u062a\u0639\u0627\u0634 \u0627\u0644\u062a\u0648\u062c\u064a\u0647 \u0623\u0648 \u062d\u0631\u0643\u0629 \u0627\u0644\u0647\u062f\u0641<\/td>\n<td>\u2014<\/td>\n<td>\u062a\u062d\u0645\u0644 \u0627\u0644\u062a\u062f\u0627\u062e\u0644 \u0627\u0644\u0647\u0646\u062f\u0633\u064a<\/td>\n<td>\u0647\u0627\u0645\u0634 \u0627\u0644\u0639\u0627\u0626\u062f \u0639\u0628\u0631 \u0627\u0644\u0628\u0642\u0639\u0629 \u0627\u0644\u0623\u0643\u0628\u0631<\/td>\n<\/tr>\n<tr>\n<td>\u0647\u062f\u0641 \u0635\u063a\u064a\u0631 \u0628\u0645\u0648\u0642\u0639 \u063a\u064a\u0631 \u0645\u0624\u0643\u062f<\/td>\n<td>Can miss outside a tight footprint<\/td>\n<td>Can cover more position uncertainty<\/td>\n<td>Fraction of pulse actually intercepted<\/td>\n<\/tr>\n<tr>\n<td>Multiple surfaces near an edge<\/td>\n<td>Less background inclusion<\/td>\n<td>\u2014<\/td>\n<td>Echo-selection and range-resolution behavior<\/td>\n<\/tr>\n<tr>\n<td>Receiver acceptance<\/td>\n<td>Does not set receiver FOV<\/td>\n<td>Does not set receiver FOV<\/td>\n<td>Transmit\/receive boresight and angular tolerances<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>The comparison assumes other variables stay constant, which is rare across modules. Divergence can change with exit optics, aperture, beam quality, temperature, assembly tolerances, or the optical window. Review the complete transmitter and receiver design.<\/p>\n<p>For the source-versus-system boundary, see our <a href=\"https:\/\/lumexislaser.com\/ar\/solutions\/ranging-laser-sources\/\">\u0646\u0638\u0631\u0629 \u0639\u0627\u0645\u0629 \u0639\u0644\u0649 \u0645\u0635\u062f\u0631 \u0644\u064a\u0632\u0631 \u0627\u0644\u0642\u064a\u0627\u0633<\/a>. The page helps distinguish a laser-source parameter from the performance of a complete ranging module.<\/p>\n<h2>Partial Footprints Can Produce Weak or Mixed Returns<\/h2>\n<p>When the target is larger than the footprint and centered on it, nearly all incident energy can interact with that surface. If the target intercepts only part of the footprint, the remaining energy goes elsewhere. A dark foreground object in front of a bright wall may then generate a weaker return than the background even though the beam geometrically touches it.<\/p>\n<p>If foreground and background are at different ranges, their contributions can overlap or form separate echoes depending on pulse width, range separation, receiver bandwidth, and processing. First, strongest, and last return rules can choose different surfaces. A single \u201cbeam hits target\u201d statement cannot predict the reported distance.<\/p>\n<figure><img decoding=\"async\" src=\"https:\/\/lumexislaser.com\/wp-content\/uploads\/2026\/08\/lumexis-rangefinder-divergence-body-partial-footprint-depth-v01.webp\" alt=\"Oblique diagram showing a laser footprint fully on a foreground target versus spanning the target and a farther background surface.\" \/><\/figure>\n<p>Peer-reviewed mixed-pixel studies use controlled foreground\/background geometry to characterize this effect. A product-specific airborne LiDAR specification also conditions its target-detection statement on sufficient footprint interception. Those sources support the mechanism, not a transferable Lumexis performance number.<\/p>\n<h2>Divergence and Receiver Field of View Are Different<\/h2>\n<p>Transmit divergence defines where pulse energy is sent. Receiver field of view defines the angular region accepted by the receive optics and detector. They interact through boresight and alignment, but one does not substitute for the other.<\/p>\n<p>A wide transmitter paired with a narrow or misaligned receiver can illuminate positions the receiver does not accept. Increasing receiver FOV may improve angular tolerance, but it can also admit more background and requires a complete signal-to-noise review. Aperture, filter bandwidth, detector area, focal length, and processing remain part of the result.<\/p>\n<p>\u062f\u0644\u064a\u0644 <a href=\"https:\/\/lumexislaser.com\/ar\/types-of-laser-rangefinder-modules\/\">types of laser rangefinder modules<\/a> guide provides additional architecture context without treating one optical layout as universal.<\/p>\n<h2>What to Ask for in a Datasheet<\/h2>\n<p>Request more than a single mrad value:<\/p>\n<ul>\n<li>full-angle or half-angle convention;<\/li>\n<li>1\/e\u00b2, FWHM, D4\u03c3, encircled-energy, or another width definition;<\/li>\n<li>horizontal and vertical divergence with tolerance;<\/li>\n<li>exit diameter, waist\/reference plane, and focus condition;<\/li>\n<li>operating temperature, drive condition, window, and lot\/sample basis;<\/li>\n<li>transmitter-to-receiver boresight tolerance and receiver FOV;<\/li>\n<li>target size, reflectance, range, atmosphere, and footprint-interception condition;<\/li>\n<li>detection threshold, trial count, valid-range definition, and false\/no-return treatment.<\/li>\n<\/ul>\n<p>The best specification lets you reproduce the claim. A clean nominal value without tolerance or measurement definition is difficult to carry into an OEM error budget.<\/p>\n<h2>Validate Beam Divergence in the Installed System<\/h2>\n<p>Measure the final optical configuration, including its protective window and mount. Characterize the profile at several distances, then test several target sizes at the required reflectance and range.<\/p>\n<p>Apply controlled horizontal and vertical offsets that cover boresight error, vibration, motion, and assembly tolerance. Repeat enough pulses at each position to report valid, false, and absent returns. Add an edge case with a foreground target and background at a different range.<\/p>\n<table>\n<thead>\n<tr>\n<th>Test group<\/th>\n<th>Hold or record<\/th>\n<th>\u0627\u0644\u0646\u062a\u064a\u062c\u0629<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>\u0647\u0646\u062f\u0633\u0629 \u0627\u0644\u062d\u0632\u0645\u0629<\/td>\n<td>Distance, axis, width convention, temperature, window<\/td>\n<td>Diameter\/profile and centroid<\/td>\n<\/tr>\n<tr>\n<td>Target overlap<\/td>\n<td>Target size, reflectance, incidence, offset<\/td>\n<td>Illumination coverage and return strength<\/td>\n<\/tr>\n<tr>\n<td>System detection<\/td>\n<td>Receiver FOV, mode, threshold, ambient condition<\/td>\n<td>Valid, false, and no-return rates<\/td>\n<\/tr>\n<tr>\n<td>Edge behavior<\/td>\n<td>Foreground\/background ranges and reflectances<\/td>\n<td>Selected echo and distance error<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>\u062f\u0644\u064a\u0644 <a href=\"https:\/\/lumexislaser.com\/ar\/solutions\/laser-ranging\/\">\u062d\u0644 \u0642\u064a\u0627\u0633 \u0627\u0644\u0645\u062f\u0649 \u0628\u0627\u0644\u0644\u064a\u0632\u0631<\/a> shows the civil and industrial system context. Lumexis <a href=\"https:\/\/lumexislaser.com\/ar\/service\/\">\u0635\u0641\u062d\u0627\u062a \u0627\u0644\u062e\u062f\u0645\u0627\u062a \u0627\u0644\u0647\u0646\u062f\u0633\u064a\u0629<\/a> can support module selection, integration, validation, and troubleshooting when the complete target and pointing envelope is available.<\/p>\n<h2>\u0645\u0627 \u064a\u062c\u0628 \u0625\u0631\u0633\u0627\u0644\u0647 \u0625\u0644\u0649 Lumexis \u0644\u0645\u0631\u0627\u062c\u0639\u0629 \u0627\u0644\u0648\u062d\u062f\u0629<\/h2>\n<p>Share the range, target size and reflectance, required valid-detection probability, pointing-error distribution, laser rangefinder beam divergence convention and axes, receiver FOV, window, update rate, and environment.<\/p>\n<p>Our applications engineers can review a standard <a href=\"https:\/\/lumexislaser.com\/ar\/shop-laser-source-module\/\">\u0648\u062d\u062f\u0629 \u062c\u0647\u0627\u0632 \u0642\u064a\u0627\u0633 \u0627\u0644\u0645\u062f\u0649 \u0628\u0627\u0644\u0644\u064a\u0632\u0631 \u0627\u0644\u0642\u064a\u0627\u0633\u064a\u0629<\/a> starting point or a custom\/private-label requirement. Final hit probability still needs evidence from the installed optical and mechanical configuration.<\/p>\n<h2>\u0627\u0644\u0623\u0633\u0626\u0644\u0629 \u0627\u0644\u0634\u0627\u0626\u0639\u0629<\/h2>\n<h3>Is Lower Beam Divergence Always Better for a Rangefinder?<\/h3>\n<p>No. Lower divergence concentrates pulse energy and reduces the chance of including nearby surfaces, but it also tightens pointing and boresight requirements. A slightly wider beam can improve geometric overlap when motion or alignment uncertainty dominates. Choose against both target-return margin and the complete angular error budget.<\/p>\n<h3>How Large Is a 1 mrad Beam at 1 km?<\/h3>\n<p>Using a full-angle, small-angle estimate, 1 mrad adds about 1 m of beam diameter over 1 km. Add the initial beam diameter and confirm whether the supplier specifies full angle, half angle, 1\/e\u00b2, FWHM, or another definition. Real irradiance has no hard edge at the calculated diameter.<\/p>\n<h3>Should a Datasheet Quote Full-Angle or Half-Angle Divergence?<\/h3>\n<p>Either can be used if it is stated clearly. The problem is an unlabeled number. Ask for full versus half angle, width convention, both beam axes, tolerance, reference plane, and measurement condition. Convert all candidates to the same convention before comparing them.<\/p>\n<h3>Does Beam Divergence Change Distance Accuracy?<\/h3>\n<p>Divergence does not change light speed or the basic time-of-flight equation. It can change which surface contributes the accepted echo, the return amplitude, and the probability of receiving a valid result. Near edges or sloped surfaces, those effects can change the reported distance or increase invalid readings.<\/p>\n<h3>How Do Pointing Error and Beam Divergence Interact?<\/h3>\n<p>Pointing error shifts the beam center; divergence sets the footprint scale at range. A wider footprint can overlap a target across more pointing offsets, but each offset may intercept a different fraction of pulse energy. Validate their combined distribution rather than comparing one nominal pointing number with one nominal divergence number.<\/p>\n<p>Send your target, range, pointing envelope, divergence definition, receiver FOV, window, and pass\/fail criterion through the <a href=\"https:\/\/lumexislaser.com\/ar\/contact\/\">\u0635\u0641\u062d\u0629 \u0627\u0644\u0627\u062a\u0635\u0627\u0644 \u0641\u064a Lumexis<\/a>. We can identify a standard-module starting point or define the evidence needed for a custom configuration.<\/p>\n<h2>\u0627\u0644\u0645\u0631\u0627\u062c\u0639<\/h2>\n<ol>\n<li>ISO. <a href=\"https:\/\/www.iso.org\/standard\/77769.html\" target=\"_blank\" rel=\"noopener\">ISO 11146-1:2021 \u2014 Test Methods for Beam Widths, Divergence Angles and Beam Propagation Ratios<\/a><\/li>\n<li>RP Photonics Encyclopedia. <a href=\"https:\/\/www.rp-photonics.com\/beam_radius.html\" target=\"_blank\" rel=\"noopener\">Beam Radius<\/a><\/li>\n<li>Kruapech, S. and Widjaja, J. <a href=\"https:\/\/doi.org\/10.1016\/j.optlastec.2009.11.020\" target=\"_blank\" rel=\"noopener\">Laser Range Finder Using Gaussian Beam Range Equation<\/a><\/li>\n<li>Yang, P. et al. <a href=\"https:\/\/doi.org\/10.5194\/isprs-archives-XLIII-B1-2020-157-2020\" target=\"_blank\" rel=\"noopener\">Laser Ranging Modeling Under Generalized Mixed Pixels Effect<\/a><\/li>\n<\/ol>","protected":false},"excerpt":{"rendered":"<p>\u062a\u0628\u0627\u0639\u062f \u0634\u0639\u0627\u0639 \u062c\u0647\u0627\u0632 \u0642\u064a\u0627\u0633 \u0627\u0644\u0645\u0633\u0627\u0641\u0629 \u0628\u0627\u0644\u0644\u064a\u0632\u0631 \u064a\u063a\u064a\u0651\u0631 \u062d\u062c\u0645 \u0627\u0644\u0628\u0642\u0639\u0629\u060c \u0648\u062a\u0641\u0627\u0648\u062a \u0627\u0644\u062a\u0648\u062c\u064a\u0647\u060c \u0648\u0642\u0648\u0629 \u0627\u0644\u0625\u0634\u0627\u0631\u0629 \u0627\u0644\u0645\u0631\u062a\u062c\u0639\u0629. \u062a\u0639\u0631\u0651\u0641 \u0639\u0644\u0649 \u0643\u064a\u0641\u064a\u0629 \u0645\u0642\u0627\u0631\u0646\u0629 \u0645\u0648\u0627\u0635\u0641\u0627\u062a \u0627\u0644\u0645\u064a\u0644\u064a \u0631\u0627\u062f\u064a\u0627\u0646 \u0648\u0627\u0644\u062a\u062d\u0642\u0642 \u0645\u0646 \u0625\u0635\u0627\u0628\u0629 \u0627\u0644\u0623\u0647\u062f\u0627\u0641.<\/p>","protected":false},"author":3,"featured_media":1992,"comment_status":"closed","ping_status":"","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[29],"tags":[32,46],"class_list":["post-1996","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-laser-basic-knowledge-101","tag-laser-parameters","tag-laser-ranging"],"acf":[],"_links":{"self":[{"href":"https:\/\/lumexislaser.com\/ar\/wp-json\/wp\/v2\/posts\/1996","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/lumexislaser.com\/ar\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/lumexislaser.com\/ar\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/lumexislaser.com\/ar\/wp-json\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/lumexislaser.com\/ar\/wp-json\/wp\/v2\/comments?post=1996"}],"version-history":[{"count":1,"href":"https:\/\/lumexislaser.com\/ar\/wp-json\/wp\/v2\/posts\/1996\/revisions"}],"predecessor-version":[{"id":1997,"href":"https:\/\/lumexislaser.com\/ar\/wp-json\/wp\/v2\/posts\/1996\/revisions\/1997"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/lumexislaser.com\/ar\/wp-json\/wp\/v2\/media\/1992"}],"wp:attachment":[{"href":"https:\/\/lumexislaser.com\/ar\/wp-json\/wp\/v2\/media?parent=1996"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/lumexislaser.com\/ar\/wp-json\/wp\/v2\/categories?post=1996"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/lumexislaser.com\/ar\/wp-json\/wp\/v2\/tags?post=1996"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}