詩經‧國風‧齊風‧猗嗟

猗嗟昌兮，頎而長兮。
抑若颺兮，美目颺兮。
巧趨蹌兮，射則臧兮。

猗嗟名兮，美目清兮。
儀既成兮，終日射侯，
不出正兮，展我甥兮。

猗嗟孌兮，清颺婉兮。
舞則選兮，射則貫兮，
四矢反兮，以禦亂兮。

 

魯莊公清颺美目來自寬容敦厚乎！所以能放管仲，因此方有

論語‧《憲問》

子貢曰：管仲非仁者與？桓公殺公子糾，不能死，又相之。

子曰：管仲相桓公，霸諸侯，一匡天下，民到于今受其賜。微管仲 ，吾其被髮左衽矣。豈若匹夫匹婦之為諒也，自經於溝瀆，而莫之知也。

論語褒貶耶？

之前我們曾經宣說 Michael Nielsen 之《神經網絡與深度學習》 Neural Networks and Deep Learning 大作。乃今談談『辨物識人』眼睛的光學原理，也算前後完整的吧。

尚未講『眼睛』之□○︰

眼（亦稱眼睛、目、招子）是視覺的器官，可以感知光線，轉換為神經中電化學的脈衝。比較複雜的眼睛是一個光學系統，可以收集周遭環境的光線，藉由虹膜調整進入眼睛的強度，利用可調整的晶狀體來聚焦，投射到對光敏感的視網膜產生影像，將影像轉換為電的訊號，透過視神經傳遞到大腦的視覺系統及其他部份。眼睛依其辨色能力可以分為十種不同的種類，有96%的動物其眼睛都是複雜的光學系統^[1]。其中軟體動物、脊索動物及節肢動物的眼睛有成像的功能^[2]。

微生物的「眼睛」構造最簡單，只偵測環境的暗或是亮，這對於晝夜節律的牽引有關^[3]。若是更複雜的眼睛，視網膜上的感光神經節細胞沿著視網膜下視丘路徑傳送信號到視叉上核來影響影響生理調節，也送到頂蓋前核控制瞳孔光反射。

 

且先提

屈光度

屈光度，或稱焦度，英語用「Dioptre」表示，是量度透鏡或曲面鏡屈光能力的單位。

焦距f的長短標誌著折光能力的大小，焦距越短，其折光能力就越大，近視的原因就是眼睛折光能力太大，遠視的人則折光能力太弱。

焦距的倒數叫做透鏡焦度，或屈光度，用φ表示，即: φ=  ，如：焦距是15m，那麼φ= 
凸透鏡（如：遠視鏡片）的度數是正數(+)，凹透鏡（如：近視鏡片）的度數是負數(-)。

一個+3屈光度的透鏡，會把平行的光線聚焦在鏡片的1/3米外。

屈光度的單位簡寫是D，國際單位制的單位是 m^-1。

一般眼鏡常使用度數來表示屈光度，以屈光度 D 的數值乘以 100 就是度數^[1] ，例如 -1.0D 等於近視眼鏡（凹透鏡）的 100度。

Dioptre

A dioptre (uk), or diopter (us), is a unit of measurement of the optical power of a lens or curved mirror, which is equal to the reciprocal of the focal length measured in metres (that is, 1/metres). It is thus a unit of reciprocal length. For example, a 3-dioptre lens brings parallel rays of light to focus at ¹⁄₃ metre. A flat window has an optical power of zero dioptres, and does not converge or diverge light.

Dioptres are also sometimes used for other reciprocals of distance, particularly radii of curvature and the vergence of optical beams. The usage was proposed by French ophthalmologist Ferdinand Monoyer in 1872, based on earlier use of the term dioptrice by Johannes Kepler.^[1][2][3]

The main benefit of using optical power rather than focal length is that the lensmaker’s equation has the object distance, image distance, and focal length all as reciprocals. A further benefit is that when relatively thin lenses are placed close together their powers approximately add. Thus, a thin 2-dioptre lens placed close to a thin 0.5-dioptre lens yields almost the same focal length as a 2.5-dioptre lens would have.

Though the dioptre is based on the SI–metric system it has not been included in the standard so that there is no international name or abbreviation for this unit of measurement—within the international system of units, this unit for optical power would need to be specified explicitly as the inverse metre (m⁻¹). However most languages have borrowed the original name and some national standardization bodies like DIN specify a unit name (dioptrie, dioptria, etc.) and derived unit symbol “dpt”.

In vision correction

The fact that optical powers are approximately additive enables an eye care professional to prescribe corrective lenses as a simple correction to the eye’s optical power, rather than doing a detailed analysis of the entire optical system (the eye and the lens). Optical power can also be used to adjust a basic prescription for reading. Thus an eye care professional, having determined that a myopic (nearsighted) person requires a basic correction of, say, −2 dioptres to restore normal distance vision, might then make a further prescription of ‘add 1’ for reading, to make up for lack of accommodation (ability to alter focus). This is the same as saying that −1 dioptre lenses are prescribed for reading.

In humans, the total optical power of the relaxed eye is approximately 60 dioptres.^[4] The cornea accounts for approximately two-thirds of this refractive power (about 40 dioptres) and the crystalline lens contributes the remaining one-third (about 20 dioptres).^[4]) In focusing, the ciliary muscle contracts to reduce the tension or stress transferred to the lens by the suspensory ligaments. This results in increased convexity of the lens which in turn increases the optical power of the eye. As humans age, the amplitude of accommodation reduces from approximately 15 to 20 dioptres in the very young, to about 10 dioptres at age 25, to around 1 dioptre at 50 and over.

Convex lenses have positive dioptric value and are generally used to correct hyperopia (farsightedness) or to allow people with presbyopia (the limited accommodation of advancing age) to read at close range. Concave lenses have negative dioptric value and generally correct myopia (nearsightedness). Typical glasses for mild myopia will have a power of −1.00 to −3.00 dioptres, while over the counter reading glasses will be rated at +1.00 to +3.00 dioptres. Optometrists usually measure refractive error using lenses graded in steps of 0.25 dioptres.

 

這個度量單位，不只是因為實務上的使用，假使簡單考察『相距 L 之兩薄透鏡組合』

pi@raspberrypi:~ f\phi = \frac{1}{f} = \frac{1}{f_1} + \frac{1}{f_2} - \frac{L}{f_1 \cdot f_2}\phi = {\phi}_{f_1} + {\phi}_{f_2} - L \cdot {\phi}_{f_1} \cdot {\phi}_{f_2}$

或能知其原由的了！！