地球上有許多具富麗色彩的物種；其中鳥類的羽毛富有最多樣以及美麗的色彩。羽毛的顏色對鳥類而言更是扮演許多重要的角色，包括增強羽毛硬度、保護羽毛避免細菌的侵蝕、調節體溫、隱匿、展示自我以及偽裝的功能。此外，顏色的品質也是鳥隻營養狀況的指標之一；由羽支內的結構所產生的結構色，較色素色更能在吸引配偶以及同性間的競爭方面造成影響。特別是雄鳥身上的紫外光結構色，更為雌鳥所吸引。因此，在此研究中，我們試圖去了解鳥類羽毛中，產生藍紫結構色的物理機制，並建立其對應的數學模型。
本文選擇兩種台灣特有鳥類的藍色羽毛，作為研究對象：藍腹鷴(俗稱台灣山雞)與台灣藍鵲(俗稱長尾山娘)。在雄性藍腹鷴的藍色腰羽上，有一段特殊的虹彩色：其開放式正羽的部分，被分成兩個區域(外側與內側)─隨入射光角度改變，而有不同的反射強度。光源正向入射時，外側的開放式正羽反射較強；但隨著入射光角度增加，高反射發生的位置則漸漸移往內側的開放式正羽。儘管這兩個區域的小羽支內部的黑色素柱，其排列方式具有相似的二維類光子晶體奈米結構。但本研究發現：這兩個區域反射強度的差異，來自個別的小羽支與羽支間的夾角不同；且此角度由開放式正羽的外側往內側呈連續性變化。根據小羽支內的奈米結構，本研究採用多層嚴格耦合波分析法，來研究其反射現象；不論是正向入射光，或是斜向入射光，最後模擬得到的結果，皆與量測的結果、以及肉眼看到的視覺效果互相吻合。
與具有顯著虹彩色的雄性藍腹鷴腰羽不同，台灣藍鵲身上的藍色羽毛，其虹彩色在視角低於四十度時，並不是那麼明顯；而且台灣藍鵲羽毛的藍色，來自於羽支內部的奈米生物結構─海綿狀的髓角蛋白。本研究針對羽支不同位置內，髓角蛋白的穿透式電子顯微鏡影像，進行二維傅氏分析，來解釋其特殊虹彩色變化的原因。研究結果發現：羽支內的髓角蛋白為準有序的排列方式，且此奈米結構的方位，隨羽支的位置不同而變化。本文預測的反射率變化，與量測得到的結果相當接近─越遠離羽支頂點，其羽毛的反射率越高；因此當視角越大時，所看到的羽色越藍、越亮。
本論文成功地為分別來自羽支與小羽支內部奈米結構，所產生兩種不同的虹彩色，提供兩種光學模型來闡述其光學特性。

There is a great diversity of species on the earth; among them birds have the amazing and multiple colors, especially on their plumage. The colors of feathers play several important roles for birds, such as hardness of feather enhancement, protection from the erosion of feather by bacteria, thermoregulation, concealment, advertisement, and disguise. In addition, color can serve as an indicator of nutrition condition of birds. As a result, color is also a criterion of mate choice and competition to others of the same sex, especially for structural color. Particularly, there are high associations between ultra-violet color and courtship display. Therefore, in this research, we have explained the physical mechanism of the structural blue-violet coloration in birds’ feathers and build the corresponding mathematical models.
Blue feathers of two endemic avian species in Taiwan are chosen in this study, Swinhoe’s pheasant (Lophura swinhoii), and Taiwan blue magpie (Urocissa caerulea). A range of iridescent color appearances are presented by male Swinhoe’s pheasants’ mantle feathers. Two distinct regions of the open pennaceous portion of its feathers display particularly conspicuous angle-dependent reflection. A bright blue band appears in one region at normal incidence that spatially shifts to another at higher illumination angles. The two-dimensional photonic crystal-like nanostructures, melanin rods, inside the barbules of these two regions are similar. However, this study found that the spatial variation in their color appearance results from a continuously changing orientation of barbules with respect to the alignment of their associated barb. A multi-layered rigorous coupled-wave analysis approach was used to model the reflections from the identified intra-barbule structures. Well matched simulated and measured reflectance spectra, at both normal and oblique incidence, support our elucidation of the origin of the bird’s distinctive feather color appearance.
Different to the conspicuous iridescence in Swinhoe’s pheasant’s mantle feather, the iridescence of the blue feathers of the Taiwan blue magpie is not obvious when the viewing angle is less than 40-degree. In addition, the biomaterial, medullary keratin, producing the blue color of Taiwan blue magpie exists inside the barbs rather than barbules. The spongy medullary keratin inside the feather barbs is investigated by two-dimensional Fourier analysis of transmission electron microscopic images of various positions on a barb to explain this unique characteristic. The orientation of the quasi-ordered nanostructure varies depending on its position of the feather barb. The predicted reflectance increases with the distance of the nanostructures from the vertex of the feather barb, and this results agrees closely with measurements.
This research provides two optical models to elucidate two different iridescent colorations from nanostructures in barbs and barbules of bird’s feathers successfully.

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