Detailed Derivation of the Fundamental Formulas of Kubelka-Munk Modeling

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Title:	Detailed Derivation of the Fundamental Formulas of Kubelka-Munk Modeling
Authors:	張慎餘
Contributors:	工學院
Keywords:	K-M模式理論核心方程式電腦印刷 Kubelka-Munk modeling Fundamental formulas Computer printing
Date:	2009-06-01
Issue Date:	2012-03-21 14:03:23 (UTC+8)
Abstract:	本篇論文的目的是詳細導證K-M模式理論中的兩個核心方程式。導證過程所使用的語言是基礎微積分加上清楚易懂圖形說明。這兩個方程式都是用來計算任一材料系統的反射性質。他們之所以會被成功的發明出來，主要的原因是作者會運用光學物理和適當的數學知識提出正確的假設和寫出正確的推理。另外，這兩個方程式的實用性也有在本論文中加以證明。證明的方式是用運用K-M 模式理論內所提出的概念，加上新的知識合成，推導出用來計算電腦印刷中半色調印刷用的油墨面積公式。全部的方程式推導都從解釋特定的自然現象開始，然後解釋如何將物質系統幾何化，最後再解釋如何把適當且相關的物理和數學知識加以合成發展出目標參數的方程式。 This article aims to account for the process of inventing the two fundamental formulas in the Kubelka-Munk modeling theory. The process is enunciated using the language of basic calculus with graphical illustrations for a full intelligibility. The formulation is successful because of their correct assumptions proposed based on the optical physics and of the application of just-in-time mathematical knowledge. Both formulas are for calculating the reflectance of a material system. Moreover, the practicality of these formulas in computer printing is spelled out in how the formula for counting the ink area of a halftoned image is invented. All formulations are completed from clarifying the specific natural phenomenon, to geometrizing a system, and finally to deducing the targeted formulas by appropriate synthesis of knowledge in physics and mathematics.
Relation:	華岡工程學報 24期 p.31 -39
Appears in Collections:	[College of Engineering] Chinese Culture University Hwa Kang Journal of Engineering

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